@inproceedings{
 title = {Model-Based Design and Optimization of Electrochemical Processes for Sustainable Aviation Fuels},
 type = {inproceedings},
 year = {2022},
 keywords = {electrochemical synthesis,hybrid modeling,process systems engineering,system identification},
 pages = {13},
 volume = {69},
 websites = {https://www.mdpi.com/2673-4591/19/1/13},
 month = {5},
 publisher = {MDPI},
 day = {17},
 city = {Basel Switzerland},
 id = {d173a24f-b63f-39bc-8799-7c606906f122},
 created = {2022-05-17T06:10:50.790Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2022-09-04T11:04:24.477Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {Aviation accounts for around 12% of all CO2 emissions from the transport sector, necessitating the use of sustainable aviation fuels. Electrofuels, which are gained from renewable sources, are attractive options for sustainable aviation fuels. Model-based electrochemical process design and optimization could very well assist in improved design and operation methods towards better conversion, selectivity, energy conversion, and economics-at a lower cost and time than the experimental approach. Moreover, nowadays, process models are also an indispensable technology for realizing Industry 4.0 and digital twin ideas for process intensification and monitoring. Thus, to design better electrofuel manufacturing processes and create digital process representations, this paper makes use of a first-principles model for electroreduction of furfural to furfuryl alcohol and methylfuran as well as hydrogen evolution. In detail, the Volmer reaction forms adsorbed hydrogen , represented by a Frumkin type isotherm. The hydrogen evolution is described by the potential dependent Heyvrosky reaction and the potential independent Tafel reaction. We critically discuss the simulation results using reference data and show its potential application for an AI-assisted process modeling strategy, i.e., predicting an optimal potential profile using the derived first-principles model and a neural network.},
 bibtype = {inproceedings},
 author = {Francis-Xavier, Fenila and Schenkendorf, René},
 doi = {10.3390/ECP2022-12613},
 booktitle = {ECP 2022}
}

Aviation accounts for around 12% of all CO2 emissions from the transport sector, necessitating the use of sustainable aviation fuels. Electrofuels, which are gained from renewable sources, are attractive options for sustainable aviation fuels. Model-based electrochemical process design and optimization could very well assist in improved design and operation methods towards better conversion, selectivity, energy conversion, and economics-at a lower cost and time than the experimental approach. Moreover, nowadays, process models are also an indispensable technology for realizing Industry 4.0 and digital twin ideas for process intensification and monitoring. Thus, to design better electrofuel manufacturing processes and create digital process representations, this paper makes use of a first-principles model for electroreduction of furfural to furfuryl alcohol and methylfuran as well as hydrogen evolution. In detail, the Volmer reaction forms adsorbed hydrogen , represented by a Frumkin type isotherm. The hydrogen evolution is described by the potential dependent Heyvrosky reaction and the potential independent Tafel reaction. We critically discuss the simulation results using reference data and show its potential application for an AI-assisted process modeling strategy, i.e., predicting an optimal potential profile using the derived first-principles model and a neural network.

@article{
 title = {Process Model Inversion in the Data-Driven Engineering Context for Improved Parameter Sensitivities},
 type = {article},
 year = {2022},
 keywords = {boundary and distributed control,data-driven engineering,differential flatness,neural ordinary differential equations,parameter sensitivities,partial differential equations,physics-informed neural networks,process systems engineering,system identification,systems theory},
 volume = {10},
 websites = {https://doi.org/10.3390/pr10091764},
 id = {f554bbe8-3ee7-378b-9a2e-c102b3a40dde},
 created = {2022-09-04T11:07:20.836Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
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 read = {true},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
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 abstract = {Citation: Selvarajan, S.; Tappe, AA.; Heiduk, C.; Scholl, S.; Schenkendorf, R. Process Model Inversion in the Data-Driven Engineering Context for Improved Parameter Sensitivities. Processes 2022, 10, 1764. Abstract: Industry 4.0 has embraced process models in recent years, and the use of model-based digital twins has become even more critical in process systems engineering, monitoring, and control. However, the reliability of these models depends on the model parameters available. The accuracy of the estimated parameters is, in turn, determined by the amount and quality of the measurement data and the algorithm used for parameter identification. For the definition of the parameter identification problem, the ordinary least squares framework is still state-of-the-art in the literature, and better parameter estimates are only possible with additional data. In this work, we present an alternative strategy to identify model parameters by incorporating differential flatness for model inversion and neural ordinary differential equations for surrogate modeling. The novel concept results in an input-least-squares-based parameter identification problem with significant parameter sensitivity changes. To study these sensitivity effects, we use a classic one-dimensional diffusion-type problem, i.e., an omnipresent equation in process systems engineering and transport phenomena. As shown, the proposed concept ensures higher parameter sensitivities for two relevant scenarios. Based on the results derived, we also discuss general implications for data-driven engineering concepts used to identify process model parameters in the recent literature.},
 bibtype = {article},
 author = {Selvarajan, Subiksha and Tappe, Aike Aline and Heiduk, Caroline and Scholl, Stephan and Schenkendorf, René},
 doi = {10.3390/pr10091764},
 journal = {Processes},
 number = {9}
}

Citation: Selvarajan, S.; Tappe, AA.; Heiduk, C.; Scholl, S.; Schenkendorf, R. Process Model Inversion in the Data-Driven Engineering Context for Improved Parameter Sensitivities. Processes 2022, 10, 1764. Abstract: Industry 4.0 has embraced process models in recent years, and the use of model-based digital twins has become even more critical in process systems engineering, monitoring, and control. However, the reliability of these models depends on the model parameters available. The accuracy of the estimated parameters is, in turn, determined by the amount and quality of the measurement data and the algorithm used for parameter identification. For the definition of the parameter identification problem, the ordinary least squares framework is still state-of-the-art in the literature, and better parameter estimates are only possible with additional data. In this work, we present an alternative strategy to identify model parameters by incorporating differential flatness for model inversion and neural ordinary differential equations for surrogate modeling. The novel concept results in an input-least-squares-based parameter identification problem with significant parameter sensitivity changes. To study these sensitivity effects, we use a classic one-dimensional diffusion-type problem, i.e., an omnipresent equation in process systems engineering and transport phenomena. As shown, the proposed concept ensures higher parameter sensitivities for two relevant scenarios. Based on the results derived, we also discuss general implications for data-driven engineering concepts used to identify process model parameters in the recent literature.

@inproceedings{
 title = {Parameter Identification Concept for Process Models Combining Systems Theory and Deep Learning},
 type = {inproceedings},
 year = {2022},
 pages = {27},
 websites = {https://www.mdpi.com/2673-4591/19/1/27},
 month = {6},
 publisher = {MDPI},
 day = {8},
 city = {Basel Switzerland},
 id = {51d58b4e-50c8-3861-82b4-f0ecb52942b8},
 created = {2022-09-04T11:08:23.369Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
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 last_modified = {2022-09-04T11:08:23.907Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 bibtype = {inproceedings},
 author = {Selvarajan, Subiksha and Tappe, Aike Aline and Heiduk, Caroline and Scholl, Stephan and Schenkendorf, René},
 doi = {10.3390/ECP2022-12686},
 booktitle = {ECP 2022}
}

@article{
 title = {Neural ODEs and differential flatness for total least squares parameter estimation},
 type = {article},
 year = {2022},
 pages = {421-426},
 volume = {55},
 publisher = {Elsevier BV},
 id = {ff0a5771-948a-32cd-9f40-bb2d8cd7193a},
 created = {2022-10-21T21:30:38.317Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
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 last_modified = {2022-10-21T21:30:38.706Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Tappe, Aike Aline and Schulze, Moritz and Schenkendorf, René},
 doi = {10.1016/j.ifacol.2022.09.131},
 journal = {IFAC-PapersOnLine},
 number = {20}
}

@article{
 title = {Kinetic analysis of the partial synthesis of artemisinin: Photooxygenation to the intermediate hydroperoxide},
 type = {article},
 year = {2021},
 id = {122f680a-7f74-3729-a565-3f82b65e98ca},
 created = {2021-10-26T13:36:40.110Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:40.110Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {The price of the currently best available antimalarial treatment is driven in large part by the limited availability of its base drug compound artemisinin. One approach to reduce the artemisinin cost is to efficiently integrate the partial synthesis of artemisinin starting from its biological precursor dihydroartemisinic acid (DHAA) into the production process. The optimal design of such an integrated process is a complex task that is easier to solve through simulations studies and process modelling. In this article, we present a quantitative kinetic model for the photooxygenation of DHAA to an hydroperoxide, the essential initial step of the partial synthesis to artemisinin. The photooxygenation reactions were studied in a two-phase photo-flow reactor utilizing Taylor flow for enhanced mixing and fast gas-liquid mass transfer. A good agreement of the model and the experimental data was achieved for all combinations of photosensitizer concentration, photon flux, fluid velocity and both liquid and gas phase compositions. Deviations between simulated predictions and measurements for the amount of hydroperoxide formed are 7.1 % on average. Consequently, the identified and parameterized kinetic model is exploited to investigate different behaviors of the reactor under study. In a final step, the kinetic model is utilized to suggest attractive operating windows for future applications of the photooxygenation of DHAA exploiting reaction rates that are not affected by mass transfer limitations.},
 bibtype = {article},
 author = {Triemer, S. and Schulze, M. and Wriedt, B. and Schenkendorf, R. and Ziegenbalg, D. and Krewer, U. and Seidel-Morgenstern, A.},
 doi = {10.1007/s41981-021-00181-2},
 journal = {Journal of Flow Chemistry}
}

The price of the currently best available antimalarial treatment is driven in large part by the limited availability of its base drug compound artemisinin. One approach to reduce the artemisinin cost is to efficiently integrate the partial synthesis of artemisinin starting from its biological precursor dihydroartemisinic acid (DHAA) into the production process. The optimal design of such an integrated process is a complex task that is easier to solve through simulations studies and process modelling. In this article, we present a quantitative kinetic model for the photooxygenation of DHAA to an hydroperoxide, the essential initial step of the partial synthesis to artemisinin. The photooxygenation reactions were studied in a two-phase photo-flow reactor utilizing Taylor flow for enhanced mixing and fast gas-liquid mass transfer. A good agreement of the model and the experimental data was achieved for all combinations of photosensitizer concentration, photon flux, fluid velocity and both liquid and gas phase compositions. Deviations between simulated predictions and measurements for the amount of hydroperoxide formed are 7.1 % on average. Consequently, the identified and parameterized kinetic model is exploited to investigate different behaviors of the reactor under study. In a final step, the kinetic model is utilized to suggest attractive operating windows for future applications of the photooxygenation of DHAA exploiting reaction rates that are not affected by mass transfer limitations.

@article{
 title = {Hybrid process models in electrochemical syntheses under deep uncertainty},
 type = {article},
 year = {2021},
 keywords = {Deep uncertainty,Electrochemical synthesis,Global parameter sensitivities,Hybrid modeling,Imprecise probabilities,Neural ordinary differential equations,Point estimate method},
 pages = {704},
 volume = {9},
 websites = {https://www.mdpi.com/2227-9717/9/4/704},
 month = {4},
 publisher = {Multidisciplinary Digital Publishing Institute},
 day = {16},
 id = {75a5132a-f83e-3c8f-a5e9-aab0f2d2ee5a},
 created = {2021-10-26T13:42:35.237Z},
 accessed = {2021-04-27},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-12-24T21:49:51.432Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Francis-Xavier2021},
 private_publication = {false},
 abstract = {Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities.},
 bibtype = {article},
 author = {Francis-Xavier, Fenila and Kubannek, Fabian and Schenkendorf, René},
 doi = {10.3390/pr9040704},
 journal = {Processes},
 number = {4}
}

Chemical process engineering and machine learning are merging rapidly, and hybrid process models have shown promising results in process analysis and process design. However, uncertainties in first-principles process models have an adverse effect on extrapolations and inferences based on hybrid process models. Parameter sensitivities are an essential tool to understand better the underlying uncertainty propagation and hybrid system identification challenges. Still, standard parameter sensitivity concepts may fail to address comprehensive parameter uncertainty problems, i.e., deep uncertainty with aleatoric and epistemic contributions. This work shows a highly effective and reproducible sampling strategy to calculate simulation uncertainties and global parameter sensitivities for hybrid process models under deep uncertainty. We demonstrate the workflow with two electrochemical synthesis simulation studies, including the synthesis of furfuryl alcohol and 4-aminophenol. Compared with Monte Carlo reference simulations, the CPU-time was significantly reduced. The general findings of the hybrid model sensitivity studies under deep uncertainty are twofold. First, epistemic uncertainty has a significant effect on uncertainty analysis. Second, the predicted parameter sensitivities of the hybrid process models add value to the interpretation and analysis of the hybrid models themselves but are not suitable for predicting the real process/full first-principles process model’s sensitivities.

@article{
 title = {Machine Learning Supports Robust Operation of Thermosiphon Reboilers},
 type = {article},
 year = {2021},
 websites = {https://onlinelibrary.wiley.com/doi/10.1002/cite.202100063},
 month = {10},
 day = {26},
 id = {72cfdfa9-7f26-3245-b7ca-33c0c4415da3},
 created = {2021-10-27T12:57:18.368Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2022-05-06T12:06:29.694Z},
 read = {true},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Appelhaus, David and Lu, Yan and Schenkendorf, René and Scholl, Stephan and Jasch, Katharina},
 doi = {10.1002/cite.202100063},
 journal = {Chemie Ingenieur Technik}
}

@inproceedings{
 title = {Kinetic model for the photocatalyzed oxidation step in the partial synthesis of an antimalarial},
 type = {inproceedings},
 year = {2021},
 id = {553bc66a-2040-3ab7-a4e8-2abf3a4e0e70},
 created = {2022-01-09T21:20:43.651Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2022-01-09T21:20:43.651Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {inproceedings},
 author = {Triemer, Susann and Schulze, Moritz and Schenkendorf, René and Krewer, Ulrike and Seidel-Morgenstern, Andreas},
 booktitle = {Annual Meeting on Reaction Engineering 2021 (Jahrestreffen Reaktionstechnik)}
}

@article{
 title = {Working within the design space: Do our static process characterization methods suffice?},
 type = {article},
 year = {2020},
 keywords = {Critical process parameters,Critical quality attribute,Dynamic design space,Dynamic modeling,Flexibility,Process analytical technology,Quality by design,Reachability},
 pages = {1-15},
 volume = {12},
 id = {fcde1fea-763c-36e6-8685-72dfe2fdb07d},
 created = {2021-10-26T13:36:40.704Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:53.766Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {VonStosch2020},
 private_publication = {false},
 abstract = {The Process Analytical Technology initiative and Quality by Design paradigm have led to changes in the guidelines and views of how to develop drug manufacturing processes. On this occasion the concept of the design space, which describes the impact of process parameters and material attributes on the attributes of the product, was introduced in the ICH Q8 guideline. The way the design space is defined and can be presented for regulatory approval seems to be left to the applicants, among who at least a consensus on how to characterize the design space seems to have evolved. The large majority of design spaces described in publications seem to follow a “static” statistical experimentation and modeling approach. Given that temporal deviations in the process parameters (i.e., moving within the design space) are of a dynamic nature, static approaches might not suffice for the consideration of the implications of variations in the values of the process parameters. In this paper, different forms of design space representations are discussed and the current consensus is challenged, which in turn, establishes the need for a dynamic representation and characterization of the design space. Subsequently, selected approaches for a dynamic representation, characterization and validation which are proposed in the literature are discussed, also showcasing the opportunity to integrate the activities of process characterization, process monitoring and process control strategy development.},
 bibtype = {article},
 author = {von Stosch, Moritz and Schenkendorf, René and Geldhof, Geoffroy and Varsakelis, Christos and Mariti, Marco and Dessoy, Sandrine and Vandercammen, Annick and Pysik, Alexander and Sanders, Matthew},
 doi = {10.3390/pharmaceutics12060562},
 journal = {Pharmaceutics},
 number = {6}
}

The Process Analytical Technology initiative and Quality by Design paradigm have led to changes in the guidelines and views of how to develop drug manufacturing processes. On this occasion the concept of the design space, which describes the impact of process parameters and material attributes on the attributes of the product, was introduced in the ICH Q8 guideline. The way the design space is defined and can be presented for regulatory approval seems to be left to the applicants, among who at least a consensus on how to characterize the design space seems to have evolved. The large majority of design spaces described in publications seem to follow a “static” statistical experimentation and modeling approach. Given that temporal deviations in the process parameters (i.e., moving within the design space) are of a dynamic nature, static approaches might not suffice for the consideration of the implications of variations in the values of the process parameters. In this paper, different forms of design space representations are discussed and the current consensus is challenged, which in turn, establishes the need for a dynamic representation and characterization of the design space. Subsequently, selected approaches for a dynamic representation, characterization and validation which are proposed in the literature are discussed, also showcasing the opportunity to integrate the activities of process characterization, process monitoring and process control strategy development.

@misc{
 title = {Global sensitivity methods for design of experiments in lithium-ion battery context},
 type = {misc},
 year = {2020},
 source = {arXiv},
 keywords = {Design of experiments,Global parameter sensitivities,Lithium-ion batteries,Parameter identification,Uncertainty quantification},
 id = {620d5ab0-c947-37d9-b797-83a28204238c},
 created = {2021-10-26T13:36:41.070Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:41.070Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {Copyright © 2020, arXiv, All rights reserved. Battery management systems may rely on mathematical models to provide higher performance than standard charging protocols. Electrochemical models allow us to capture the phenomena occurring inside a lithium-ion cell and therefore, could be the best model choice. However, to be of practical value, they require reliable model parameters. Uncertainty quantification and optimal experimental design concepts are essential tools for identifying systems and estimating parameters precisely. Approximation errors in uncertainty quantification result in sub-optimal experimental designs and consequently, less-informative data, and higher parameter unreliability. In this work, we propose a highly efficient design of experiment method based on global parameter sensitivities. This novel concept is applied to the single-particle model with electrolyte and thermal dynamics (SPMeT), a well-known electrochemical model for lithium-ion cells. The proposed method avoids the simplifying assumption of output-parameter linearization (i.e., local parameter sensitivities) used in conventional Fisher information matrix-based experimental design strategies. Thus, the optimized current input profile results in experimental data of higher information content and in turn, in more precise parameter estimates.},
 bibtype = {misc},
 author = {Pozzi, A. and Xie, X. and Raimondo, D.M. and Schenkendorf, R.}
}

Copyright © 2020, arXiv, All rights reserved. Battery management systems may rely on mathematical models to provide higher performance than standard charging protocols. Electrochemical models allow us to capture the phenomena occurring inside a lithium-ion cell and therefore, could be the best model choice. However, to be of practical value, they require reliable model parameters. Uncertainty quantification and optimal experimental design concepts are essential tools for identifying systems and estimating parameters precisely. Approximation errors in uncertainty quantification result in sub-optimal experimental designs and consequently, less-informative data, and higher parameter unreliability. In this work, we propose a highly efficient design of experiment method based on global parameter sensitivities. This novel concept is applied to the single-particle model with electrolyte and thermal dynamics (SPMeT), a well-known electrochemical model for lithium-ion cells. The proposed method avoids the simplifying assumption of output-parameter linearization (i.e., local parameter sensitivities) used in conventional Fisher information matrix-based experimental design strategies. Thus, the optimized current input profile results in experimental data of higher information content and in turn, in more precise parameter estimates.

@phdthesis{
 title = {Sensitivity Analysis and Robust Design of Pharmaceutical Manufacturing Processes},
 type = {phdthesis},
 year = {2020},
 id = {a5fd3054-6dee-3982-92fc-479bbace973a},
 created = {2021-10-26T13:36:41.340Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:54.094Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {phdthesis},
 author = {Xie, Xiangzhong}
}

@article{
 title = {Robust Model Selection: Flatness-Based Optimal Experimental Design for a Biocatalytic Reaction},
 type = {article},
 year = {2020},
 keywords = {based design of experiments,differential flatness,model,model selection,nonlinear programming,parameter uncertainty,point estimate method},
 pages = {190},
 volume = {8},
 websites = {https://www.mdpi.com/2227-9717/8/2/190},
 id = {fb3fb657-91ef-36e5-92be-d383857d7602},
 created = {2021-10-26T13:36:41.545Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:54.278Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 abstract = {<p>Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.</p>},
 bibtype = {article},
 author = {Schulze, Moritz and Schenkendorf, René},
 doi = {10.3390/pr8020190},
 journal = {Processes},
 number = {2}
}

Considering the competitive and strongly regulated pharmaceutical industry, mathematical modeling and process systems engineering might be useful tools for implementing quality by design (QbD) and quality by control (QbC) strategies for low-cost but high-quality drugs. However, a crucial task in modeling (bio)pharmaceutical manufacturing processes is the reliable identification of model candidates from a set of various model hypotheses. To identify the best experimental design suitable for a reliable model selection and system identification is challenging for nonlinear (bio)pharmaceutical process models in general. This paper is the first to exploit differential flatness for model selection problems under uncertainty, and thus translates the model selection problem to advanced concepts of systems theory and controllability aspects, respectively. Here, the optimal controls for improved model selection trajectories are expressed analytically with low computational costs. We further demonstrate the impact of parameter uncertainties on the differential flatness-based method and provide an effective robustification strategy with the point estimate method for uncertainty quantification. In a simulation study, we consider a biocatalytic reaction step simulating the carboligation of aldehydes, where we successfully derive optimal controls for improved model selection trajectories under uncertainty.

@article{
 title = {Rigorous model-based design and experimental verification of enzyme-catalyzed carboligation under enzyme inactivation},
 type = {article},
 year = {2020},
 keywords = {2-hydroxy ketones,Benzaldehyde lyase,Elementary process functions,Enzyme catalysis,Optimal design,Process intensification},
 volume = {10},
 id = {14cdde3b-be16-3836-b8c2-512e6f51294a},
 created = {2021-10-26T13:36:41.844Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:41.844Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {true},
 abstract = {© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Enzyme catalyzed reactions are complex reactions due to the interplay of the enzyme, the reactants, and the operating conditions. To handle this complexity systematically and make use of a design space without technical restrictions, we apply the model based approach of elementary process functions (EPF) for selecting the best process design for enzyme catalysis problems. As a representative case study, we consider the carboligation of propanal and benzaldehyde catalyzed by benzaldehyde lyase from Pseudomonas fluorescens (Pf BAL) to produce (R)-2-hydroxy-1-phenylbutan-1-one, because of the substrate dependent reaction rates and the challenging substrate dependent Pf BAL inactivation. The apparatus independent EPF concept optimizes the material fluxes influencing the enzyme catalyzed reaction for the given process intensification scenarios. The final product concentration is improved by 13% with the optimized feeding rates, and the optimization results are verified experimentally. In general, the rigorous model driven approach could lead to selecting the best existing reactor, designing novel reactors for enzyme catalysis, and combining protein engineering and process systems engineering concepts.},
 bibtype = {article},
 author = {Hertweck, D. and Emenike, V.N. and Spiess, A.C. and Schenkendorf, R.},
 doi = {10.3390/catal10010096},
 journal = {Catalysts},
 number = {1}
}

© 2020 by the authors. Licensee MDPI, Basel, Switzerland. Enzyme catalyzed reactions are complex reactions due to the interplay of the enzyme, the reactants, and the operating conditions. To handle this complexity systematically and make use of a design space without technical restrictions, we apply the model based approach of elementary process functions (EPF) for selecting the best process design for enzyme catalysis problems. As a representative case study, we consider the carboligation of propanal and benzaldehyde catalyzed by benzaldehyde lyase from Pseudomonas fluorescens (Pf BAL) to produce (R)-2-hydroxy-1-phenylbutan-1-one, because of the substrate dependent reaction rates and the challenging substrate dependent Pf BAL inactivation. The apparatus independent EPF concept optimizes the material fluxes influencing the enzyme catalyzed reaction for the given process intensification scenarios. The final product concentration is improved by 13% with the optimized feeding rates, and the optimization results are verified experimentally. In general, the rigorous model driven approach could lead to selecting the best existing reactor, designing novel reactors for enzyme catalysis, and combining protein engineering and process systems engineering concepts.

@misc{
 title = {Model-based tools for pharmaceutical manufacturing processes},
 type = {misc},
 year = {2020},
 source = {Processes},
 volume = {8},
 issue = {1},
 id = {01743721-39d0-3108-9d44-9596a27b6c47},
 created = {2021-10-26T13:41:15.640Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:41:15.640Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 bibtype = {misc},
 author = {Schenkendorf, René and Gerogiorgis, Dimitrios I. and Mansouri, Seyed Soheil and Gernaey, Krist V.},
 doi = {10.3390/pr8010049}
}

@article{
 title = {Model-Based Uncertainty Quantification for the Product Properties of Lithium-Ion Batteries},
 type = {article},
 year = {2020},
 keywords = {Li-ion batteries,modeling,production process,uncertainty quantification methods},
 pages = {1-15},
 volume = {8},
 id = {d7a6b705-4965-376c-84f0-77c2403c2b21},
 created = {2021-10-26T13:41:51.470Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-12-24T21:49:51.433Z},
 read = {true},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 abstract = {A model-based uncertainty quantification (UQ) approach is applied to the manufacturing process of lithium-ion batteries (LIB). Cell-to-cell deviations and the influence of sub-cell level variations in the material and electrode properties of the cell performance are investigated experimentally and via modeling. The electrochemical battery model of the Doyle–Newman type is extended to cover the effect of sub-cell deviation of product properties of the LIB. The applied model is parameterized and validated using a stacked pouch cell containing Li(Ni1/3Co1/3Mn1/3)O2 (NMC) and graphite (LixC6). It is integrated into a sampling-based UQ framework. A nested point estimate method (PEM) is applied to a large number of independent normal distributed parameters. The simulations follow two consecutive nonideal manufacturing process steps: coating and calendering. The nested PEM provides a global sensitivity analysis that shows a change in sensitivity of the investigated parameters depending on the applied C-rate. Furthermore, the sub-cell level deviation of parameters in heterogeneous electrodes provokes a nonuniform current distribution in the cell. This alters the variance of the discharge capacity distribution. Therefore, sub-cell deviation has to be considered to quantify process uncertainties. The applied method is feasible and highly efficient for this purpose.},
 bibtype = {article},
 author = {Laue, Vincent and Schmidt, Oke and Dreger, Henning and Xie, Xiangzhong and Röder, Fridolin and Schenkendorf, René and Kwade, Arno and Krewer, Ulrike},
 doi = {10.1002/ente.201900201},
 journal = {Energy Technology},
 number = {2}
}

A model-based uncertainty quantification (UQ) approach is applied to the manufacturing process of lithium-ion batteries (LIB). Cell-to-cell deviations and the influence of sub-cell level variations in the material and electrode properties of the cell performance are investigated experimentally and via modeling. The electrochemical battery model of the Doyle–Newman type is extended to cover the effect of sub-cell deviation of product properties of the LIB. The applied model is parameterized and validated using a stacked pouch cell containing Li(Ni1/3Co1/3Mn1/3)O2 (NMC) and graphite (LixC6). It is integrated into a sampling-based UQ framework. A nested point estimate method (PEM) is applied to a large number of independent normal distributed parameters. The simulations follow two consecutive nonideal manufacturing process steps: coating and calendering. The nested PEM provides a global sensitivity analysis that shows a change in sensitivity of the investigated parameters depending on the applied C-rate. Furthermore, the sub-cell level deviation of parameters in heterogeneous electrodes provokes a nonuniform current distribution in the cell. This alters the variance of the discharge capacity distribution. Therefore, sub-cell deviation has to be considered to quantify process uncertainties. The applied method is feasible and highly efficient for this purpose.

@article{
 title = {Model-assisted Design of Experiments as a concept for knowledge-based bioprocess development},
 type = {article},
 year = {2019},
 keywords = {Chinese hamster ovary,Feeding profile,Modeling,Response surface},
 pages = {867-882},
 volume = {42},
 websites = {http://dx.doi.org/10.1007/s00449-019-02089-7},
 publisher = {Springer Berlin Heidelberg},
 id = {67c3f762-dba1-3b1a-8f11-770f5c406a03},
 created = {2021-10-26T13:36:40.446Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:53.151Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 abstract = {Design of Experiments methods offer systematic tools for bioprocess development in Quality by Design, but their major drawback is the user-defined choice of factor boundary values. This can lead to several iterative rounds of time-consuming and costly experiments. In this study, a model-assisted Design of Experiments concept is introduced for the knowledge-based reduction of boundary values. First, the parameters of a mathematical process model are estimated. Second, the investigated factor combinations are simulated instead of experimentally derived and a constraint-based evaluation and optimization of the experimental space can be performed. The concept is discussed for the optimization of an antibody-producing Chinese hamster ovary batch and bolus fed-batch process. The same optimal process strategies were found if comparing the model-assisted Design of Experiments (4 experiments each) and traditional Design of Experiments (16 experiments for batch and 29 experiments for fed-batch). This approach significantly reduces the number of experiments needed for knowledge-based bioprocess development.},
 bibtype = {article},
 author = {Möller, Johannes and Kuchemüller, Kim B. and Steinmetz, Tobias and Koopmann, Kirsten S. and Pörtner, Ralf},
 doi = {10.1007/s00449-019-02089-7},
 journal = {Bioprocess and Biosystems Engineering},
 number = {5}
}

Design of Experiments methods offer systematic tools for bioprocess development in Quality by Design, but their major drawback is the user-defined choice of factor boundary values. This can lead to several iterative rounds of time-consuming and costly experiments. In this study, a model-assisted Design of Experiments concept is introduced for the knowledge-based reduction of boundary values. First, the parameters of a mathematical process model are estimated. Second, the investigated factor combinations are simulated instead of experimentally derived and a constraint-based evaluation and optimization of the experimental space can be performed. The concept is discussed for the optimization of an antibody-producing Chinese hamster ovary batch and bolus fed-batch process. The same optimal process strategies were found if comparing the model-assisted Design of Experiments (4 experiments each) and traditional Design of Experiments (16 experiments for batch and 29 experiments for fed-batch). This approach significantly reduces the number of experiments needed for knowledge-based bioprocess development.

@article{
 title = {Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation},
 type = {article},
 year = {2019},
 keywords = {batch,batch variation,box,drying,freeze,parametric probability,pharmaceutical manufacturing,point estimate method,robust process design,to},
 pages = {509},
 volume = {7},
 websites = {https://www.mdpi.com/2227-9717/7/8/509},
 month = {8},
 publisher = {Multidisciplinary Digital Publishing Institute},
 day = {3},
 id = {47c8e372-3025-3506-8556-7f7b45eb95e3},
 created = {2021-10-26T13:36:42.167Z},
 accessed = {2019-11-21},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:54.451Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2019},
 private_publication = {false},
 abstract = {Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Schenkendorf, René},
 doi = {10.3390/pr7080509},
 journal = {Processes},
 number = {8}
}

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.

@article{
 title = {Robust optimization of a pharmaceutical freeze-drying process under non-Gaussian parameter uncertainties},
 type = {article},
 year = {2019},
 pages = {805-819},
 volume = {207},
 websites = {https://www.sciencedirect.com/science/article/pii/S0009250919305275?via%3Dihub,https://linkinghub.elsevier.com/retrieve/pii/S0009250919305275},
 month = {11},
 publisher = {Pergamon},
 day = {22},
 id = {79457ddf-9e66-351a-9e82-d378a2cd50ac},
 created = {2021-10-26T13:36:42.378Z},
 accessed = {2019-06-26},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:54.585Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2019},
 private_publication = {false},
 abstract = {Model-based design of pharmaceutical manufacturing processes has received much interest in academia and industry. Model parameter uncertainties, however, might deteriorate the predicted process performance. Probability-based robust process design concepts as a countermeasure against uncertainties might be implemented. Here, parameter uncertainties are typically limited to Gaussian parameter distributions. However, parameter uncertainties derived with experimental data can be correlated and arbitrarily distributed. In our previous work, transformation techniques were combined with the point estimate method (PEM) to address non-Gaussian and correlated parameter distributions, but at the cost of additional nonlinearities and approximation errors. In this work, we take advantage of Gaussian mixture distributions (GMD) and decompose the parameter distribution into a finite set of Gaussian distributions using the Expectation-Maximization approach. Combining the GMD with the PEM ensures a proper and effective uncertainty quantification. The improved PEM algorithm is applied to a freeze-drying process (lyophilization) aiming for high-quality products with minimum processing time. Results obtained suggest that the novel GMD-PEM algorithm has the potential to outperform conventional robustification concepts regarding credibility and efficiency.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Schenkendorf, René},
 doi = {10.1016/j.ces.2019.06.023},
 journal = {Chemical Engineering Science}
}

Model-based design of pharmaceutical manufacturing processes has received much interest in academia and industry. Model parameter uncertainties, however, might deteriorate the predicted process performance. Probability-based robust process design concepts as a countermeasure against uncertainties might be implemented. Here, parameter uncertainties are typically limited to Gaussian parameter distributions. However, parameter uncertainties derived with experimental data can be correlated and arbitrarily distributed. In our previous work, transformation techniques were combined with the point estimate method (PEM) to address non-Gaussian and correlated parameter distributions, but at the cost of additional nonlinearities and approximation errors. In this work, we take advantage of Gaussian mixture distributions (GMD) and decompose the parameter distribution into a finite set of Gaussian distributions using the Expectation-Maximization approach. Combining the GMD with the PEM ensures a proper and effective uncertainty quantification. The improved PEM algorithm is applied to a freeze-drying process (lyophilization) aiming for high-quality products with minimum processing time. Results obtained suggest that the novel GMD-PEM algorithm has the potential to outperform conventional robustification concepts regarding credibility and efficiency.

@article{
 title = {Novel electrodynamic oscillation technique enables enhanced mass transfer and mixing for cultivation in micro-bioreactor},
 type = {article},
 year = {2019},
 keywords = {cultivation,micro-bioreactor,oscillation,oxygen transfer,small scale mixing},
 volume = {35},
 id = {072846be-f036-3901-9008-0da59cb34669},
 created = {2021-10-26T13:36:42.588Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:42.588Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {© 2019 American Institute of Chemical Engineers Micro-bioreactors (MBRs) have become an indispensable part for modern bioprocess development enabling automated experiments in parallel while reducing material cost. Novel developments aim to further intensify the advantages as dimensions are being reduced. However, one factor hindering the scale-down of cultivation systems is to provide adequate mixing and mass transfer. Here, vertical oscillation is demonstrated as an effective method for mixing of MBRs with a reaction volume of 20 μL providing adequate mass transfer. Electrodynamic exciters are used to transduce kinetic energy onto the cultivation broth avoiding additional moving parts inside the applied model MBR. The induced vertical vibration leads to oscillation of the liquid surface corresponding to the frequency and displacement. On this basis, the resonance frequency of the fluid was identified as the most decisive factor for mixing performance. Applying this vertical oscillation method outstanding mixing times below 1 s and exceptionally high oxygen transport with volumetric mass transfer coefficients (kLa) above 1,000/hr can be successfully achieved and controlled. To evaluate the applicability of this vertical oscillation mixing for low volume MBR systems, cultivations of Escherichia coli BL21 as proof-of-concept were performed. The dissolved oxygen was successfully online monitored to assure any avoidance of oxygen limitations during the cultivation. The here presented data illustrate the high potential of the vertical oscillation technique as a flexible measure to adapt mixing times and oxygen transfer according to experimental demands. Thus, the mixing technique is a promising tool for various biological and chemical micro-scale applications still enabling adequate mass transfer.},
 bibtype = {article},
 author = {Frey, L.J. and Vorländer, D. and Rasch, D. and Ostsieker, H. and Müller, B. and Schulze, M. and Schenkendorf, R. and Mayr, T. and Grosch, J.-H. and Krull, R.},
 doi = {10.1002/btpr.2827},
 journal = {Biotechnology Progress},
 number = {5}
}

© 2019 American Institute of Chemical Engineers Micro-bioreactors (MBRs) have become an indispensable part for modern bioprocess development enabling automated experiments in parallel while reducing material cost. Novel developments aim to further intensify the advantages as dimensions are being reduced. However, one factor hindering the scale-down of cultivation systems is to provide adequate mixing and mass transfer. Here, vertical oscillation is demonstrated as an effective method for mixing of MBRs with a reaction volume of 20 μL providing adequate mass transfer. Electrodynamic exciters are used to transduce kinetic energy onto the cultivation broth avoiding additional moving parts inside the applied model MBR. The induced vertical vibration leads to oscillation of the liquid surface corresponding to the frequency and displacement. On this basis, the resonance frequency of the fluid was identified as the most decisive factor for mixing performance. Applying this vertical oscillation method outstanding mixing times below 1 s and exceptionally high oxygen transport with volumetric mass transfer coefficients (kLa) above 1,000/hr can be successfully achieved and controlled. To evaluate the applicability of this vertical oscillation mixing for low volume MBR systems, cultivations of Escherichia coli BL21 as proof-of-concept were performed. The dissolved oxygen was successfully online monitored to assure any avoidance of oxygen limitations during the cultivation. The here presented data illustrate the high potential of the vertical oscillation technique as a flexible measure to adapt mixing times and oxygen transfer according to experimental demands. Thus, the mixing technique is a promising tool for various biological and chemical micro-scale applications still enabling adequate mass transfer.

@article{
 title = {A point estimate method-based back-off approach to robust optimization : application to pharmaceutical processes},
 type = {article},
 year = {2019},
 keywords = {back-off approach,enzyme catal-,ibuprofen crystallization,pharmaceutical manufacturing,robust optimization,ysis},
 pages = {1-6},
 id = {7e76ca8c-8840-3136-964b-ee43633fe38e},
 created = {2021-10-26T13:36:42.853Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:54.741Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Emenike, Victor N and Xie, Xiangzhong and Krewer, Ulrike}
}

@article{
 title = {Model-Based Uncertainty Quantification for the Product Properties of Lithium-Ion Batteries},
 type = {article},
 year = {2019},
 keywords = {Li-ion batteries,modeling,production process,uncertainty quantification methods},
 pages = {1900201},
 volume = {1900201},
 websites = {https://onlinelibrary.wiley.com/doi/abs/10.1002/ente.201900201},
 month = {4},
 day = {29},
 id = {539ba7e0-95e2-3255-8dba-b2e0d60f1f78},
 created = {2021-10-26T13:36:43.568Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:55.325Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Laue2019},
 private_publication = {false},
 abstract = {A model-based uncertainty quantification (UQ) approach is applied to the manufacturing process of lithium-ion batteries (LIB). Cell-to-cell deviations and the influence of sub-cell level variations in the material and electrode properties of the cell performance are investigated experimentally and via modeling. The electrochemical battery model of the Doyle–Newman type is extended to cover the effect of sub-cell deviation of product properties of the LIB. The applied model is parameterized and validated using a stacked pouch cell containing Li(Ni 1/3 Co 1/3 Mn 1/3 )O 2 (NMC) and graphite (Li x C 6 ). It is integrated into a sampling-based UQ framework. A nested point estimate method (PEM) is applied to a large number of independent normal distributed parameters. The simulations follow two consecutive nonideal manufacturing process steps: coating and calendering. The nested PEM provides a global sensitivity analysis that shows a change in sensitivity of the investigated parameters depending on the applied C-rate. Furthermore, the sub-cell level deviation of parameters in heterogeneous electrodes provokes a nonuniform current distribution in the cell. This alters the variance of the discharge capacity distribution. Therefore, sub-cell deviation has to be considered to quantify process uncertainties. The applied method is feasible and highly efficient for this purpose.},
 bibtype = {article},
 author = {Laue, Vincent and Schmidt, Oke and Dreger, Henning and Xie, Xiangzhong and Röder, Fridolin and Schenkendorf, René and Kwade, Arno and Krewer, Ulrike},
 doi = {10.1002/ente.201900201},
 journal = {Energy Technology}
}

A model-based uncertainty quantification (UQ) approach is applied to the manufacturing process of lithium-ion batteries (LIB). Cell-to-cell deviations and the influence of sub-cell level variations in the material and electrode properties of the cell performance are investigated experimentally and via modeling. The electrochemical battery model of the Doyle–Newman type is extended to cover the effect of sub-cell deviation of product properties of the LIB. The applied model is parameterized and validated using a stacked pouch cell containing Li(Ni 1/3 Co 1/3 Mn 1/3 )O 2 (NMC) and graphite (Li x C 6 ). It is integrated into a sampling-based UQ framework. A nested point estimate method (PEM) is applied to a large number of independent normal distributed parameters. The simulations follow two consecutive nonideal manufacturing process steps: coating and calendering. The nested PEM provides a global sensitivity analysis that shows a change in sensitivity of the investigated parameters depending on the applied C-rate. Furthermore, the sub-cell level deviation of parameters in heterogeneous electrodes provokes a nonuniform current distribution in the cell. This alters the variance of the discharge capacity distribution. Therefore, sub-cell deviation has to be considered to quantify process uncertainties. The applied method is feasible and highly efficient for this purpose.

@article{
 title = {Design of Fuel Cell Systems for Aviation: Representative Mission Profiles and Sensitivity Analyses},
 type = {article},
 year = {2019},
 keywords = {aviation,energy,flight mission profile,fuel cell,hydrogen storage,monte carlo analysis,sensitivity analysis,stochastic model,stochastic model, fuel cell, aviation, sensitivity,system design},
 volume = {7},
 id = {e243a8e7-7086-358a-871c-7af85947532f},
 created = {2021-10-26T13:36:43.874Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:55.491Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Kadyk, Thomas and Schenkendorf, René and Hawner, Sebastian and Yildiz, Bekir and Römer, Ulrich},
 doi = {10.3389/fenrg.2019.00035},
 journal = {Frontiers in Energy Research},
 number = {x}
}

@article{
 title = {Stochastic back-off-based robust process design for continuous crystallization of ibuprofen},
 type = {article},
 year = {2019},
 keywords = {Back-off,Crystallization,Ibuprofen,Polynomial chaos expansion,Quality by design,Robust optimization,Uncertainty},
 pages = {80-92},
 volume = {124},
 websites = {https://doi.org/10.1016/j.compchemeng.2019.02.009},
 publisher = {Elsevier Ltd},
 id = {ebc5f728-74b6-359a-8277-a7727df60a39},
 created = {2021-10-26T13:36:44.191Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:55.656Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2019},
 private_publication = {false},
 abstract = {Robust model-based process design in continuous pharmaceutical manufacturing aims to implement quality by design principles under uncertainty. Notably, various studies have discussed the back-off concept to solve the underlying robust optimization problem; however, for the concept to have practical value, its efficiency and convergence must be improved. In this work, we introduce a novel, highly efficient stochastic back-off strategy. Instead of using statistical moments of limited validity, we incorporate the full statistical information of the constraints to solve the robust process design problem. To ensure manageable computational costs, we make use of polynomial chaos expansion for uncertainty quantification and propagation. The proposed concept is demonstrated with the design of a tubular crystallizer for ibuprofen crystallization. The results show that the novel stochastic back-off strategy is considerably faster compared with the standard back-off concept and provides more reliable quality by design results in general.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Schenkendorf, René},
 doi = {10.1016/j.compchemeng.2019.02.009},
 journal = {Computers and Chemical Engineering}
}

Robust model-based process design in continuous pharmaceutical manufacturing aims to implement quality by design principles under uncertainty. Notably, various studies have discussed the back-off concept to solve the underlying robust optimization problem; however, for the concept to have practical value, its efficiency and convergence must be improved. In this work, we introduce a novel, highly efficient stochastic back-off strategy. Instead of using statistical moments of limited validity, we incorporate the full statistical information of the constraints to solve the robust process design problem. To ensure manageable computational costs, we make use of polynomial chaos expansion for uncertainty quantification and propagation. The proposed concept is demonstrated with the design of a tubular crystallizer for ibuprofen crystallization. The results show that the novel stochastic back-off strategy is considerably faster compared with the standard back-off concept and provides more reliable quality by design results in general.

@article{
 title = {The Effect of Correlated Kinetic Parameters on (Bio)Chemical Reaction Networks},
 type = {article},
 year = {2019},
 keywords = {Parameter correlations,Polynomial chaos expansion,Reaction networks,Sensitivity analysis},
 volume = {91},
 id = {a9a7af00-2e6d-38f2-90ed-d044f8aa26b0},
 created = {2021-10-26T13:36:44.656Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:44.656Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 private_publication = {false},
 abstract = {© 2019 WILEY-VCH Verlag GmbH  &  Co. KGaA, Weinheim Exploiting the information provided by (bio)chemical reaction networks has proved beneficial for process analysis and design. To this end, parameter uncertainties have to be included in the analysis and design of (bio)chemical processes to ensure reliable model-based results. The goal is to investigate the impact of parameter correlations on (bio)chemical reaction networks and parameter sensitivities. An efficient sensitivity analysis concept is demonstrated with two simulation studies, and the results indicate a significant impact of the parameter correlations on the derived parameter sensitivities and the model-based results in general.},
 bibtype = {article},
 author = {Xie, X. and Schenkendorf, R. and Krewer, U.},
 doi = {10.1002/cite.201800201},
 journal = {Chemie-Ingenieur-Technik},
 number = {5}
}

© 2019 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim Exploiting the information provided by (bio)chemical reaction networks has proved beneficial for process analysis and design. To this end, parameter uncertainties have to be included in the analysis and design of (bio)chemical processes to ensure reliable model-based results. The goal is to investigate the impact of parameter correlations on (bio)chemical reaction networks and parameter sensitivities. An efficient sensitivity analysis concept is demonstrated with two simulation studies, and the results indicate a significant impact of the parameter correlations on the derived parameter sensitivities and the model-based results in general.

@article{
 title = {Analyzing uncertainties in model response using the point estimate method: Applications from railway asset management},
 type = {article},
 year = {2019},
 keywords = {asset management,point estimate,prognostics and health management,reliability,uncertainty propagation analysis},
 pages = {1748006X1982559},
 websites = {http://journals.sagepub.com/doi/10.1177/1748006X19825593},
 id = {840e029d-afad-3e45-8d74-50334507a385},
 created = {2021-10-26T13:36:44.898Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
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 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Neumann, Thorsten and Dutschk, Beate and Schenkendorf, René},
 doi = {10.1177/1748006X19825593},
 journal = {Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability}
}

@article{
 title = {Efficient sensitivity analysis and interpretation of parameter correlations in chemical engineering},
 type = {article},
 year = {2019},
 keywords = {Chemical processes,Gaussian copula,Parameter correlation,Polynomial chaos expansion,Sensitivity analysis},
 pages = {159-173},
 volume = {187},
 websites = {https://doi.org/10.1016/j.ress.2018.06.010,https://linkinghub.elsevier.com/retrieve/pii/S0951832018300541},
 month = {7},
 publisher = {Elsevier Ltd},
 id = {1079dd57-3c55-3a01-9b5d-0087dff43cae},
 created = {2021-10-26T13:36:45.418Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:56.488Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 abstract = {Parameter uncertainties affect model-based system reliability analysis and may lead to safety issues in model-based process design. Global sensitivity analysis (GSA) is a valuable tool to quantify the influence of parameter uncertainties in the variation of the model output. However, GSA has not been widely employed in the field of chemical engineering, especially for processes with correlated model parameters. Parameter correlations, in turn, are quite common when identifying model parameters with experimental data. Thus, we propose and critically compare (co)variance-based and moment-independent GSA techniques for analyzing chemical processes in the absence and presence of parameter correlations. Technically, polynomial chaos expansion is used to reduce the computational burden for GSA. The proposed methods are demonstrated for a continuous synthesis process. Here, the results show significant differences in the parameter sensitivity rankings when parameter correlations are considered or not while the moment-independent technique provides a universal and easy-to-interpret sensitivity measure.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.1016/j.ress.2018.06.010},
 journal = {Reliability Engineering & System Safety},
 number = {January}
}

Parameter uncertainties affect model-based system reliability analysis and may lead to safety issues in model-based process design. Global sensitivity analysis (GSA) is a valuable tool to quantify the influence of parameter uncertainties in the variation of the model output. However, GSA has not been widely employed in the field of chemical engineering, especially for processes with correlated model parameters. Parameter correlations, in turn, are quite common when identifying model parameters with experimental data. Thus, we propose and critically compare (co)variance-based and moment-independent GSA techniques for analyzing chemical processes in the absence and presence of parameter correlations. Technically, polynomial chaos expansion is used to reduce the computational burden for GSA. The proposed methods are demonstrated for a continuous synthesis process. Here, the results show significant differences in the parameter sensitivity rankings when parameter correlations are considered or not while the moment-independent technique provides a universal and easy-to-interpret sensitivity measure.

@article{
 title = {Robust dynamic optimization of enzyme-catalyzed carboligation: A point estimate-based back-off approach},
 type = {article},
 year = {2019},
 keywords = {Back-off strategy,Benzaldehyde lyase,Dynamic optimization,Enzyme catalysis,Optimal reactor design,Point estimate method,Robust optimization},
 pages = {232-247},
 volume = {121},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/S0098135418306689},
 month = {2},
 id = {ce68022d-3dc2-3c4c-8ce1-fc4af6fc0358},
 created = {2021-10-26T13:36:46.072Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:57.046Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 abstract = {In this paper, we present a systematic robust dynamic optimization framework applied to the benzaldehyde lyase-catalyzed carboligation of propanal and benzaldehyde to produce (R)-2-hydroxy-1-phenylbutan-1-one (BA). First, the elementary process functions approach was used to screen between different dosing concepts, and it was found that simultaneously dosing propanal and benzaldehyde leads to the highest final concentration of BA. Next, we applied global sensitivity analysis and found that 10 out of 13 kinetic parameters are relevant. Time-varying back-offs were then used to handle parametric uncertainties due to these 10 parameters. A major contribution in our work is the use of the point estimate method instead of Monte Carlo simulations to calculate the back-offs in an efficient and reproducible manner. We show that this new approach is at least 10 times faster than the conventional Monte Carlo approach while achieving low approximation errors.},
 bibtype = {article},
 author = {Emenike, Victor N. and Xie, Xiangzhong and Schenkendorf, René and Spiess, Antje C. and Krewer, Ulrike},
 doi = {10.1016/j.compchemeng.2018.10.006},
 journal = {Computers & Chemical Engineering}
}

In this paper, we present a systematic robust dynamic optimization framework applied to the benzaldehyde lyase-catalyzed carboligation of propanal and benzaldehyde to produce (R)-2-hydroxy-1-phenylbutan-1-one (BA). First, the elementary process functions approach was used to screen between different dosing concepts, and it was found that simultaneously dosing propanal and benzaldehyde leads to the highest final concentration of BA. Next, we applied global sensitivity analysis and found that 10 out of 13 kinetic parameters are relevant. Time-varying back-offs were then used to handle parametric uncertainties due to these 10 parameters. A major contribution in our work is the use of the point estimate method instead of Monte Carlo simulations to calculate the back-offs in an efficient and reproducible manner. We show that this new approach is at least 10 times faster than the conventional Monte Carlo approach while achieving low approximation errors.

@article{
 title = {An efficient polynomial chaos expansion strategy for active fault identification of chemical processes},
 type = {article},
 year = {2019},
 keywords = {irish sea ice stream},
 pages = {228-237},
 volume = {122},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/S0098135418308652},
 month = {3},
 id = {dce4463f-47e9-3ea4-9885-44ed123c41f4},
 created = {2021-10-26T13:36:46.485Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2022-06-23T21:31:55.173Z},
 read = {true},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf},
 private_publication = {false},
 bibtype = {article},
 author = {Schenkendorf, René and Xie, Xiangzhong and Krewer, Ulrike},
 doi = {10.1016/j.compchemeng.2018.08.022},
 journal = {Computers & Chemical Engineering}
}

@article{
 title = {Efficient Global Sensitivity Analysis of 3D Multiphysics Model for Li-Ion Batteries},
 type = {article},
 year = {2018},
 pages = {A1169-A1183},
 volume = {165},
 websites = {http://jes.ecsdl.org/lookup/doi/10.1149/2.1301805jes},
 id = {f6a6ae0c-7f13-399d-aaa7-454afb1ee49e},
 created = {2021-10-26T13:36:45.111Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:56.285Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Lin2018},
 private_publication = {false},
 abstract = {Parameter sensitivity analysis of mechanistic battery models has the power to quantify the individual and joint effects of parameters on the performance of lithium-ion cells. This information can be beneficial for industrial cell designs, cell testing, and battery management system (BMS) configurations. The numerical quantification of these parameter sensitivities, however, is challenging in terms of computational costs and is an active field of research. In this paper, based on a 3D multiphysics model, we conduct a global sensitivity analysis for the utilizable cell discharge capacity and the maximum cell temperature at the discharge rate of 1C. The least angle regression version of the polynomial chaos expansion (PCE) concept has been identified as an optimal trade-off between approximation power and computational complexity. As a result, the sensitivities of all parameters in the 3D multiphysics model were studied using a hierarchical design and a stepwise design. We conclude that the cell discharge capacity and the thermal behavior at 1C discharge are most sensitive to the electrode parameters and their pore structure. The results reveal different dependencies and lead to new insights for cell design and operation.},
 bibtype = {article},
 author = {Lin, Nan and Xie, Xiangzhong and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.1149/2.1301805jes},
 journal = {Journal of The Electrochemical Society},
 number = {7}
}

Parameter sensitivity analysis of mechanistic battery models has the power to quantify the individual and joint effects of parameters on the performance of lithium-ion cells. This information can be beneficial for industrial cell designs, cell testing, and battery management system (BMS) configurations. The numerical quantification of these parameter sensitivities, however, is challenging in terms of computational costs and is an active field of research. In this paper, based on a 3D multiphysics model, we conduct a global sensitivity analysis for the utilizable cell discharge capacity and the maximum cell temperature at the discharge rate of 1C. The least angle regression version of the polynomial chaos expansion (PCE) concept has been identified as an optimal trade-off between approximation power and computational complexity. As a result, the sensitivities of all parameters in the 3D multiphysics model were studied using a hierarchical design and a stepwise design. We conclude that the cell discharge capacity and the thermal behavior at 1C discharge are most sensitive to the electrode parameters and their pore structure. The results reveal different dependencies and lead to new insights for cell design and operation.

@article{
 title = {Robustifizierung und Informationsmetriken der modellgestützten Versuchsplanung},
 type = {article},
 year = {2018},
 pages = {1234-1235},
 volume = {90},
 websites = {http://doi.wiley.com/10.1002/cite.201855227},
 id = {3e2e2ac2-fd8d-3e42-a41d-b2f632f4fb5e},
 created = {2021-10-26T13:36:45.658Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:56.652Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Schenkendorf, R. and Xie, X. and Krewer, U.},
 doi = {10.1002/cite.201855227},
 journal = {Chemie Ingenieur Technik},
 number = {9}
}

@article{
 title = {Robustes Prozessdesign in der Pharmatechnik mittels performanter Ersatzfunktionen},
 type = {article},
 year = {2018},
 pages = {1243-1244},
 volume = {90},
 websites = {http://doi.wiley.com/10.1002/cite.201855249},
 id = {e305fecc-54cf-3976-8114-c721301e1271},
 created = {2021-10-26T13:36:45.883Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:56.838Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 private_publication = {false},
 bibtype = {article},
 author = {Xie, X. and Schenkendorf, R. and Krewer, U.},
 doi = {10.1002/cite.201855249},
 journal = {Chemie Ingenieur Technik},
 number = {9}
}

@article{
 title = {Toward a Comprehensive and Efficient Robust Optimization Framework for (Bio)chemical Processes},
 type = {article},
 year = {2018},
 keywords = {equality constraints,parameter correlation,point estimation method,robust optimization,uncertainty},
 pages = {183},
 volume = {6},
 websites = {http://www.mdpi.com/2227-9717/6/10/183},
 month = {10},
 publisher = {Multidisciplinary Digital Publishing Institute},
 day = {3},
 id = {a5df7455-be13-3e64-979f-cc280670bf9d},
 created = {2021-10-26T13:36:46.286Z},
 accessed = {2018-11-02},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:57.201Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2018},
 private_publication = {false},
 abstract = {Model-based design principles have received considerable attention in biotechnology and the chemical industry over the last two decades. However, parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies have been introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computational expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints for a robust process design. We also apply a global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies: (1) designing a heating/cooling profile for the essential part of a continuous production process; and (2) optimizing the feeding profile for a fed-batch reactor of the penicillin fermentation process. According to the derived results, the proposed framework of robust process design addresses uncertainties adequately and scales well with the number of uncertain parameters. Thus, the described robustification concept should be an ideal candidate for more complex (bio)chemical problems in model-based design.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.3390/pr6100183},
 journal = {Processes},
 number = {10}
}

Model-based design principles have received considerable attention in biotechnology and the chemical industry over the last two decades. However, parameter uncertainties of first-principle models are critical in model-based design and have led to the development of robustification concepts. Various strategies have been introduced to solve the robust optimization problem. Most approaches suffer from either unreasonable computational expense or low approximation accuracy. Moreover, they are not rigorous and do not consider robust optimization problems where parameter correlation and equality constraints exist. In this work, we propose a highly efficient framework for solving robust optimization problems with the so-called point estimation method (PEM). The PEM has a fair trade-off between computational expense and approximation accuracy and can be easily extended to problems of parameter correlations. From a statistical point of view, moment-based methods are used to approximate robust inequality and equality constraints for a robust process design. We also apply a global sensitivity analysis to further simplify robust optimization problems with a large number of uncertain parameters. We demonstrate the performance of the proposed framework with two case studies: (1) designing a heating/cooling profile for the essential part of a continuous production process; and (2) optimizing the feeding profile for a fed-batch reactor of the penicillin fermentation process. According to the derived results, the proposed framework of robust process design addresses uncertainties adequately and scales well with the number of uncertain parameters. Thus, the described robustification concept should be an ideal candidate for more complex (bio)chemical problems in model-based design.

@article{
 title = {Model-based optimization of biopharmaceutical manufacturing in Pichia pastoris based on dynamic flux balance analysis},
 type = {article},
 year = {2018},
 keywords = {Bilevel optimization,Biopharmaceutical manufacturing,Complementarity constraints,Dynamic flux balance analysis,Elementary process functions,Pichia pastoris},
 pages = {1-13},
 volume = {118},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/S0098135418307403},
 month = {10},
 id = {cb0be7bd-821c-3a13-bb2d-5ed0b604e76b},
 created = {2021-10-26T13:36:46.769Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:57.586Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Emenike2018b},
 private_publication = {false},
 abstract = {Biologic drugs are promising therapeutics, and their efficient production is essential for a competitive pharma industry. Dynamic flux balance analysis (dFBA) enables the dynamic simulation of the extracellular bioreactor environment and intracellular fluxes in microorganisms, but it is rarely used for model-based optimization of biopharmaceutical manufacturing in Pichia pastoris. To bridge this gap, we present a model-based optimization approach based on dFBA to produce biologics in P. pastoris that combines ideas from bilevel optimization, penalization schemes, and direct dynamic optimization. As a case study, we consider the production of recombinant erythropoietin in P. pastoris growing on glucose, and predict a 66% improvement in the productivity of erythropoietin. We show that this improvement could be obtained by implementing an almost constant optimal feeding strategy which is different from typical exponential feeding strategies and that a high activity of most pathways in the central carbon metabolism is crucial for a high productivity.},
 bibtype = {article},
 author = {Emenike, Victor N. and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.1016/j.compchemeng.2018.07.013},
 journal = {Computers and Chemical Engineering}
}

Biologic drugs are promising therapeutics, and their efficient production is essential for a competitive pharma industry. Dynamic flux balance analysis (dFBA) enables the dynamic simulation of the extracellular bioreactor environment and intracellular fluxes in microorganisms, but it is rarely used for model-based optimization of biopharmaceutical manufacturing in Pichia pastoris. To bridge this gap, we present a model-based optimization approach based on dFBA to produce biologics in P. pastoris that combines ideas from bilevel optimization, penalization schemes, and direct dynamic optimization. As a case study, we consider the production of recombinant erythropoietin in P. pastoris growing on glucose, and predict a 66% improvement in the productivity of erythropoietin. We show that this improvement could be obtained by implementing an almost constant optimal feeding strategy which is different from typical exponential feeding strategies and that a high activity of most pathways in the central carbon metabolism is crucial for a high productivity.

@article{
 title = {Flatness-Based Design of Experiments for Model Selection},
 type = {article},
 year = {2018},
 keywords = {akaike,design of experiments,differential flatness,information criterion,model selection,optimal control},
 pages = {233-238},
 volume = {51},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/S2405896318318019},
 id = {e11e8c0f-f15c-34ff-9b0c-00409f906a05},
 created = {2021-10-26T13:36:47.010Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:57.734Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schulze2018},
 private_publication = {false},
 bibtype = {article},
 author = {Schulze, Moritz and Schenkendorf, René},
 doi = {10.1016/j.ifacol.2018.09.140},
 journal = {IFAC-PapersOnLine},
 number = {15}
}

@article{
 title = {State-of-Health identification of Lithium-ion batteries based on Nonlinear Frequency Response Analysis: First steps with machine learning},
 type = {article},
 year = {2018},
 keywords = {Battery degradation,Lithium-ion batteries,Machine learning; support vector regression,Nonlinear frequency response analysis,State-of-health},
 volume = {8},
 id = {d3dd673c-834f-3960-9251-d442008c2523},
 created = {2021-10-26T13:36:47.230Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:47.230Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Harting2018},
 private_publication = {false},
 abstract = {© 2018 by the authors. In this study, we show an effective data-driven identification of the State-of-Health of Lithium-ion batteries by Nonlinear Frequency Response Analysis. A degradation model based on support vector regression is derived from highly informative Nonlinear Frequency Response Analysis data sets. First, an ageing test of a Lithium-ion battery at 25 °C is presented and the impact of relevant ageing mechanisms on the nonlinear dynamics of the cells is analysed. A correlation measure is used to identify the most sensitive frequency range for ageing tests. Here, the mid-frequency range from 1 Hz to 100 Hz shows the strongest correlation to Lithium-ion battery degradation. The focus on the mid-frequency range leads to a dramatic reduction in measurement time of up to 92% compared to standard measurement protocols. Next, informative features are extracted and used to parametrise the support vector regression model for the State of Health degradation. The performance of the degradation model is validated with additional cells and validation data sets, respectively. We show that the degradation model accurately predicts the State of Health values. Validation data demonstrate the usefulness of the Nonlinear Frequency Response Analysis as an effective and fast State of Health identification method and as a versatile tool in the diagnosis of ageing of Lithium-ion batteries in general.},
 bibtype = {article},
 author = {Harting, N. and Schenkendorf, R. and Wolff, N. and Krewer, U.},
 doi = {10.3390/app8050821},
 journal = {Applied Sciences (Switzerland)},
 number = {5}
}

© 2018 by the authors. In this study, we show an effective data-driven identification of the State-of-Health of Lithium-ion batteries by Nonlinear Frequency Response Analysis. A degradation model based on support vector regression is derived from highly informative Nonlinear Frequency Response Analysis data sets. First, an ageing test of a Lithium-ion battery at 25 °C is presented and the impact of relevant ageing mechanisms on the nonlinear dynamics of the cells is analysed. A correlation measure is used to identify the most sensitive frequency range for ageing tests. Here, the mid-frequency range from 1 Hz to 100 Hz shows the strongest correlation to Lithium-ion battery degradation. The focus on the mid-frequency range leads to a dramatic reduction in measurement time of up to 92% compared to standard measurement protocols. Next, informative features are extracted and used to parametrise the support vector regression model for the State of Health degradation. The performance of the degradation model is validated with additional cells and validation data sets, respectively. We show that the degradation model accurately predicts the State of Health values. Validation data demonstrate the usefulness of the Nonlinear Frequency Response Analysis as an effective and fast State of Health identification method and as a versatile tool in the diagnosis of ageing of Lithium-ion batteries in general.

@article{
 title = {Robust Optimization of Dynamical Systems with Correlated Random Variables using the Point Estimate Method},
 type = {article},
 year = {2018},
 keywords = {correlated model parameters,point estimate method,robust optimization,uncertainty quantification},
 pages = {427-432},
 volume = {51},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/S2405896318300776},
 id = {f8c4b4c1-18fb-3026-ba7d-e21713bde6df},
 created = {2021-10-26T13:36:47.645Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:57.878Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2018b},
 private_publication = {false},
 abstract = {Robust optimization of dynamical systems requires the proper uncertainty quantification. Monte Carlo simulations and polynomial chaos expansion are frequently used methods for uncertainty quantification and have been applied to a number of problems in process design and optimization. Both methods, however, are either computationally prohibitive for robust optimization or inappropriate for correlated random variables. The aim of this study is to introduce the point estimate method for optimization of dynamical systems with correlated random variables. The point estimate method requires only a few deterministic evaluations of the analyzed process model and estimates the statistical moments for robust optimization. The derived sample points can be adapted to random variables of arbitrary distributions and correlations. The contribution of this paper consists of presenting the point estimate method for correlated random variables in the field of model-based robust process design. The performance of the method is demonstrated with a case study of a continuous tubular reactor.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Krewer, Ulrike and Schenkendorf, René},
 doi = {10.1016/j.ifacol.2018.03.073},
 journal = {IFAC-PapersOnLine},
 number = {2}
}

Robust optimization of dynamical systems requires the proper uncertainty quantification. Monte Carlo simulations and polynomial chaos expansion are frequently used methods for uncertainty quantification and have been applied to a number of problems in process design and optimization. Both methods, however, are either computationally prohibitive for robust optimization or inappropriate for correlated random variables. The aim of this study is to introduce the point estimate method for optimization of dynamical systems with correlated random variables. The point estimate method requires only a few deterministic evaluations of the analyzed process model and estimates the statistical moments for robust optimization. The derived sample points can be adapted to random variables of arbitrary distributions and correlations. The contribution of this paper consists of presenting the point estimate method for correlated random variables in the field of model-based robust process design. The performance of the method is demonstrated with a case study of a continuous tubular reactor.

@article{
 title = {The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design},
 type = {article},
 year = {2018},
 keywords = {Global parameter sensitivities,Optimal design measures,Optimal experimental design,Point estimate method,Robustification},
 pages = {27},
 volume = {6},
 id = {59cf63d0-a045-31fa-a1f9-1bc0427d5885},
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 abstract = {In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.},
 bibtype = {article},
 author = {Schenkendorf, René and Xie, Xiangzhong and Rehbein, Moritz and Scholl, Stephan and Krewer, Ulrike},
 doi = {10.3390/pr6040027},
 journal = {Processes},
 number = {4}
}

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

@article{
 title = {The Impact of Global Sensitivities and Design Measures in Model-Based Optimal Experimental Design},
 type = {article},
 year = {2018},
 keywords = {global parameter sensitivities,optimal design measures,optimal experimental design,point estimate method,robustification},
 pages = {27},
 volume = {6},
 websites = {http://www.mdpi.com/2227-9717/6/4/27},
 publisher = {Multidisciplinary Digital Publishing Institute},
 day = {21},
 id = {466bef54-beed-3ecd-b9bf-c16895d1e627},
 created = {2021-10-26T13:36:48.147Z},
 accessed = {2018-03-21},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
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 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2018},
 private_publication = {false},
 abstract = {In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.},
 bibtype = {article},
 author = {Schenkendorf, René and Xie, Xiangzhong and Rehbein, Moritz and Scholl, Stephan and Krewer, Ulrike},
 doi = {10.3390/pr6040027},
 journal = {Processes},
 number = {4}
}

In the field of chemical engineering, mathematical models have been proven to be an indispensable tool for process analysis, process design, and condition monitoring. To gain the most benefit from model-based approaches, the implemented mathematical models have to be based on sound principles, and they need to be calibrated to the process under study with suitable model parameter estimates. Often, the model parameters identified by experimental data, however, pose severe uncertainties leading to incorrect or biased inferences. This applies in particular in the field of pharmaceutical manufacturing, where usually the measurement data are limited in quantity and quality when analyzing novel active pharmaceutical ingredients. Optimally designed experiments, in turn, aim to increase the quality of the gathered data in the most efficient way. Any improvement in data quality results in more precise parameter estimates and more reliable model candidates. The applied methods for parameter sensitivity analyses and design criteria are crucial for the effectiveness of the optimal experimental design. In this work, different design measures based on global parameter sensitivities are critically compared with state-of-the-art concepts that follow simplifying linearization principles. The efficient implementation of the proposed sensitivity measures is explicitly addressed to be applicable to complex chemical engineering problems of practical relevance. As a case study, the homogeneous synthesis of 3,4-dihydro-1H-1-benzazepine-2,5-dione, a scaffold for the preparation of various protein kinase inhibitors, is analyzed followed by a more complex model of biochemical reactions. In both studies, the model-based optimal experimental design benefits from global parameter sensitivities combined with proper design measures.

@article{
 title = {Moment-Independent Sensitivity Analysis of Enzyme-Catalyzed Reactions with Correlated Model Parameters},
 type = {article},
 year = {2018},
 keywords = {3},
 pages = {753-758},
 volume = {51},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/S2405896318301320},
 id = {72218666-33e2-3ab1-a877-75efec66cd06},
 created = {2021-10-26T13:36:48.358Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
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 last_modified = {2021-10-26T13:36:58.196Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2018c},
 private_publication = {false},
 abstract = {The dynamic models used for biological and chemical process analysis and design usually include a significant number of uncertain model parameters. Sensitivity analysis is frequently applied to provide quantitative information regarding the influence of the parameters, as well as their uncertainties, on the model output. Various techniques are available in the literature to calculate parameter sensitivities based on local derivatives or changes in dedicated statistical moments of the model output. However, these methods may lead to an inevitable loss of information for a proper sensitivity analysis and are not directly available for problems with correlated model parameters. In this work, we demonstrate the use of a moment-independent sensitivity analysis concept in the presence and absence of parameter correlations and investigate the correlation effect in more detail. Moment-independent sensitivity analysis calculates parameter sensitivities based on changes in the entire probability density distribution of the model output and is formulated independently of whether the parameters are correlated or not. Technically, a single-loop Monte Carlo simulation method in combination with polynomial chaos expansion is implemented to reduce the computational cost significantly. A sampling procedure derived from Gaussian copula formalism is used to generate sample points for arbitrarily correlated uncertain parameters. The proposed concept is demonstrated with a case study of an enzyme-catalyzed reaction network. We observe evident differences in the parameter sensitivities for cases with independent and correlated model parameters.},
 bibtype = {article},
 author = {Xie, Xiangzhong and Ohs, Rüdiger and Spieß, Antje and Krewer, Ulrike and Schenkendorf, René},
 doi = {10.1016/j.ifacol.2018.04.004},
 journal = {IFAC-PapersOnLine},
 number = {2}
}

The dynamic models used for biological and chemical process analysis and design usually include a significant number of uncertain model parameters. Sensitivity analysis is frequently applied to provide quantitative information regarding the influence of the parameters, as well as their uncertainties, on the model output. Various techniques are available in the literature to calculate parameter sensitivities based on local derivatives or changes in dedicated statistical moments of the model output. However, these methods may lead to an inevitable loss of information for a proper sensitivity analysis and are not directly available for problems with correlated model parameters. In this work, we demonstrate the use of a moment-independent sensitivity analysis concept in the presence and absence of parameter correlations and investigate the correlation effect in more detail. Moment-independent sensitivity analysis calculates parameter sensitivities based on changes in the entire probability density distribution of the model output and is formulated independently of whether the parameters are correlated or not. Technically, a single-loop Monte Carlo simulation method in combination with polynomial chaos expansion is implemented to reduce the computational cost significantly. A sampling procedure derived from Gaussian copula formalism is used to generate sample points for arbitrarily correlated uncertain parameters. The proposed concept is demonstrated with a case study of an enzyme-catalyzed reaction network. We observe evident differences in the parameter sensitivities for cases with independent and correlated model parameters.

@article{
 title = {Model-based optimization of biopharmaceutical manufacturing in Pichia pastoris based on dynamic flux balance analysis},
 type = {article},
 year = {2018},
 keywords = {Bilevel optimization,Biopharmaceutical manufacturing,Complementarity constraints,Dynamic flux balance analysis,Elementary process functions,Pichia pastoris},
 pages = {1-13},
 volume = {118},
 id = {33c22b54-1774-3d75-a4c3-20c657c4d1e5},
 created = {2021-10-26T13:36:49.404Z},
 file_attached = {true},
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 last_modified = {2021-10-26T13:36:58.530Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Emenike2018},
 private_publication = {false},
 abstract = {Biologic drugs are promising therapeutics, and their efficient production is essential for a competitive pharma industry. Dynamic flux balance analysis (dFBA) enables the dynamic simulation of the extracellular bioreactor environment and intracellular fluxes in microorganisms, but it is rarely used for model-based optimization of biopharmaceutical manufacturing in Pichia pastoris. To bridge this gap, we present a model-based optimization approach based on dFBA to produce biologics in P. pastoris that combines ideas from bilevel optimization, penalization schemes, and direct dynamic optimization. As a case study, we consider the production of recombinant erythropoietin in P. pastoris growing on glucose, and predict a 66% improvement in the productivity of erythropoietin. We show that this improvement could be obtained by implementing an almost constant optimal feeding strategy which is different from typical exponential feeding strategies and that a high activity of most pathways in the central carbon metabolism is crucial for a high productivity.},
 bibtype = {article},
 author = {Emenike, Victor N. and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.1016/j.compchemeng.2018.07.013},
 journal = {Computers and Chemical Engineering},
 number = {October}
}

Biologic drugs are promising therapeutics, and their efficient production is essential for a competitive pharma industry. Dynamic flux balance analysis (dFBA) enables the dynamic simulation of the extracellular bioreactor environment and intracellular fluxes in microorganisms, but it is rarely used for model-based optimization of biopharmaceutical manufacturing in Pichia pastoris. To bridge this gap, we present a model-based optimization approach based on dFBA to produce biologics in P. pastoris that combines ideas from bilevel optimization, penalization schemes, and direct dynamic optimization. As a case study, we consider the production of recombinant erythropoietin in P. pastoris growing on glucose, and predict a 66% improvement in the productivity of erythropoietin. We show that this improvement could be obtained by implementing an almost constant optimal feeding strategy which is different from typical exponential feeding strategies and that a high activity of most pathways in the central carbon metabolism is crucial for a high productivity.

@article{
 title = {A systematic reactor design approach for the synthesis of active pharmaceutical ingredients},
 type = {article},
 year = {2018},
 keywords = {Active pharmaceutical ingredients,Continuous pharmaceutical manufacturing,Elementary process functions,Intensified reactors,Nucleophilic aromatic substitution,Optimization},
 pages = {75-88},
 volume = {126},
 websites = {http://linkinghub.elsevier.com/retrieve/pii/S093964111630916X,https://linkinghub.elsevier.com/retrieve/pii/S093964111630916X},
 month = {5},
 id = {8b60607f-aaf6-313d-8303-ce46fd25bfc6},
 created = {2021-10-26T13:36:49.625Z},
 file_attached = {true},
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 last_modified = {2021-10-26T13:36:58.721Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Emenike2018a},
 private_publication = {false},
 abstract = {Today's highly competitive pharmaceutical industry is in dire need of an accelerated transition from the drug development phase to the drug production phase. At the heart of this transition are chemical reactors that facilitate the synthesis of active pharmaceutical ingredients (APIs) and whose design can affect subsequent processing steps. Inspired by this challenge, we present a model-based approach for systematic reactor design. The proposed concept is based on the elementary process functions (EPF) methodology to select an optimal reactor configuration from existing state-of-the-art reactor types or can possibly lead to the design of novel reactors. As a conceptual study, this work summarizes the essential steps in adapting the EPF approach to optimal reactor design problems in the field of API syntheses. Practically, the nucleophilic aromatic substitution of 2,4-difluoronitrobenzene was analyzed as a case study of pharmaceutical relevance. Here, a small-scale tubular coil reactor with controlled heating was identified as the optimal set-up reducing the residence time by 33% in comparison to literature values.},
 bibtype = {article},
 author = {Emenike, Victor N. and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.1016/j.ejpb.2017.05.007},
 journal = {European Journal of Pharmaceutics and Biopharmaceutics}
}

Today's highly competitive pharmaceutical industry is in dire need of an accelerated transition from the drug development phase to the drug production phase. At the heart of this transition are chemical reactors that facilitate the synthesis of active pharmaceutical ingredients (APIs) and whose design can affect subsequent processing steps. Inspired by this challenge, we present a model-based approach for systematic reactor design. The proposed concept is based on the elementary process functions (EPF) methodology to select an optimal reactor configuration from existing state-of-the-art reactor types or can possibly lead to the design of novel reactors. As a conceptual study, this work summarizes the essential steps in adapting the EPF approach to optimal reactor design problems in the field of API syntheses. Practically, the nucleophilic aromatic substitution of 2,4-difluoronitrobenzene was analyzed as a case study of pharmaceutical relevance. Here, a small-scale tubular coil reactor with controlled heating was identified as the optimal set-up reducing the residence time by 33% in comparison to literature values.

@inbook{
 type = {inbook},
 year = {2017},
 keywords = {Active Fault Detection and Isolation,Dynamic Optimization,Least Angle Regression,Polynomial Chaos Expansion},
 pages = {1675-1680},
 volume = {40},
 websites = {https://linkinghub.elsevier.com/retrieve/pii/B9780444639653502816},
 publisher = {Elsevier},
 city = {Amsterdam},
 id = {61c33cf1-5813-3179-9323-9ac52210dc9d},
 created = {2021-10-26T13:36:48.604Z},
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 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2017},
 private_publication = {false},
 abstract = {© 2017 Elsevier B.V. To gain profit from complex chemical processes, it is essential to ensure its proper operation, i.e. to avoid costly unexpected downtimes of underlying processing units. This paper explores a highly efficient active fault detection and isolation (FDI) framework, which facilitates the discriminability of a set of analysed model candidates including the reference model (nominal behaviour) as well as pre-defined failure models (faulty behaviour). Practically, an auxiliary, model-discriminating input is derived by solving a dynamic optimization problem. While using a model-based approach, the active FDI implementation has to be robustified against the inherent model parameter uncertainties. To this end, a non-intrusive polynomial chaos expansion (PCE) is used to address these uncertainties. To guarantee a computationally feasible performance, the original PCE setting has been considerably improved. Here, the basic idea is to render the design variables (auxiliary inputs) into random variables as well. Thus, the derived PCE results are not only sensitive to the model parameters but also to the design variables. To lower the computational burden further, a least angle regression strategy is applied utilizing the sparsity property of the PCE approach. The overall effectiveness of this One-Short Sparse Polynomial Chaos Expansion (OS 2 -PCE) concept for FDI is illustrated conceptually by analysing a tubular plug flow reactor.},
 bibtype = {inbook},
 author = {Schenkendorf, René and Xie, Xiangzhong and Krewer, Ulrike},
 doi = {10.1016/B978-0-444-63965-3.50281-6},
 chapter = {An Efficient Polynomial Chaos Expansion Strategy for Active Fault Identification of Chemical Processes},
 title = {Computer Aided Chemical Engineering}
}

© 2017 Elsevier B.V. To gain profit from complex chemical processes, it is essential to ensure its proper operation, i.e. to avoid costly unexpected downtimes of underlying processing units. This paper explores a highly efficient active fault detection and isolation (FDI) framework, which facilitates the discriminability of a set of analysed model candidates including the reference model (nominal behaviour) as well as pre-defined failure models (faulty behaviour). Practically, an auxiliary, model-discriminating input is derived by solving a dynamic optimization problem. While using a model-based approach, the active FDI implementation has to be robustified against the inherent model parameter uncertainties. To this end, a non-intrusive polynomial chaos expansion (PCE) is used to address these uncertainties. To guarantee a computationally feasible performance, the original PCE setting has been considerably improved. Here, the basic idea is to render the design variables (auxiliary inputs) into random variables as well. Thus, the derived PCE results are not only sensitive to the model parameters but also to the design variables. To lower the computational burden further, a least angle regression strategy is applied utilizing the sparsity property of the PCE approach. The overall effectiveness of this One-Short Sparse Polynomial Chaos Expansion (OS 2 -PCE) concept for FDI is illustrated conceptually by analysing a tubular plug flow reactor.

@book{
 title = {Robust Design of Chemical Processes Based on a One-Shot Sparse Polynomial Chaos Expansion Concept},
 type = {book},
 year = {2017},
 source = {Computer Aided Chemical Engineering},
 keywords = {chemical processes,least angle regression,optimization,polynomial chaos expansion,robust design,uncertainty},
 pages = {613-618},
 volume = {40},
 publisher = {Elsevier},
 city = {Amsterdam},
 id = {76e31659-3bd9-3bfb-ab53-c845faf9b044},
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 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Xie2017b},
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 abstract = {The application of robust model-based design concepts for complex chemical processes is limited due to the repeated cpu-intensive uncertainty quantification step for any new tested process design configuration. Therefore, an efficient One-Shot Sparse Polynomial Chaos Expansion (OS2-PCE) based process design framework is introduced in this work. The key idea is to define the process design variables as uncertain quantities as well and, in consequence, they become an integral part of the robust optimization routine. Moreover, by utilizing the sparsity feature of the PCE approach, the implementation of a least angle regression (LAR) concept leads to a significant reduction in computational costs. The overall performance of the novel OS2-PCE approach is illustrated by a robust process design study of a jacketed tubular reactor. In comparison to state-of-the-art concepts, the proposed framework shows promising results in terms of efficiency and robustness.},
 bibtype = {book},
 author = {Xie, Xiangzhong and Schenkendorf, René and Krewer, Ulrike},
 doi = {10.1016/B978-0-444-63965-3.50104-5}
}

The application of robust model-based design concepts for complex chemical processes is limited due to the repeated cpu-intensive uncertainty quantification step for any new tested process design configuration. Therefore, an efficient One-Shot Sparse Polynomial Chaos Expansion (OS2-PCE) based process design framework is introduced in this work. The key idea is to define the process design variables as uncertain quantities as well and, in consequence, they become an integral part of the robust optimization routine. Moreover, by utilizing the sparsity feature of the PCE approach, the implementation of a least angle regression (LAR) concept leads to a significant reduction in computational costs. The overall performance of the novel OS2-PCE approach is illustrated by a robust process design study of a jacketed tubular reactor. In comparison to state-of-the-art concepts, the proposed framework shows promising results in terms of efficiency and robustness.

@article{
 title = {Flatness-Based Model Selection of Benzaldehyde Lyase Catalysed Biochemical Reaction Network},
 type = {article},
 year = {2017},
 id = {b638b68d-2606-3713-9a25-d5eaedcf4f40},
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@inproceedings{
 title = {Parameter Sensitivity Study of a 3D Multiphysics Model of Large-format Li-ion Batteries},
 type = {inproceedings},
 year = {2017},
 pages = {82},
 websites = {https://www.modval14.kit.edu/downloads/Updated_BookOfAbstracts.pdf},
 id = {37091086-ef32-37a4-a5ed-f41a531150a3},
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 bibtype = {inproceedings},
 author = {Lin, Nan and Xie, Xiangzhong and Schenkendorf, René and Krewer, Ulrike},
 booktitle = {14th Symposium on Fuel Cell and Battery Modelling and Experimental Validation}
}

@inproceedings{
 title = {Supporting the shift towards continuous pharmaceutical manufacturing by condition monitoring},
 type = {inproceedings},
 year = {2016},
 pages = {593-598},
 volume = {2016-Novem},
 month = {9},
 publisher = {IEEE},
 id = {3b1a3718-4e9e-3dc0-b40d-d00dbcdeae0a},
 created = {2021-10-26T13:36:50.762Z},
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 read = {true},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2016c},
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 abstract = {© 2016 IEEE.Over the last decade there has been an increased interest in the pharmaceutical industry to shift the manufacturing process of drugs from batch to continuous operation. The continuous manufacturing of pharmaceuticals provides significant benefits, e.g. savings in cost, time and materials - to name but a few. The implementation of a continuous manufacturing strategy, however, is challenging. To gain profit from a continuous process one has to ensure its proper operation, i.e. a long time-span until the next prospective unscheduled downtime. Thus, the installed operation units have to be: 1) robust against disturbances by engineering design principles and by advanced fault tolerant control schemes, respectively; and 2) the condition of the operation units has to be monitored reliably to trigger, in case of need, appropriate intervention strategies in a timely manner. In this paper, the focus is on the monitoring aspect. Here, a model-based fault detection and identification framework is implemented, which selects the most data-supported model candidate from a set of predefined model hypotheses including the reference model (normal behavior) as well as failure models. In addition, to enable an improved diagnosis the system under study can be steered deliberately based on the proposed concept resulting into an active fault diagnosis framework. Preliminary results are demonstrated by an academic three-tank system.},
 bibtype = {inproceedings},
 author = {Schenkendorf, Rene},
 doi = {10.1109/SYSTOL.2016.7739813},
 booktitle = {2016 3rd Conference on Control and Fault-Tolerant Systems (SysTol)}
}

© 2016 IEEE.Over the last decade there has been an increased interest in the pharmaceutical industry to shift the manufacturing process of drugs from batch to continuous operation. The continuous manufacturing of pharmaceuticals provides significant benefits, e.g. savings in cost, time and materials - to name but a few. The implementation of a continuous manufacturing strategy, however, is challenging. To gain profit from a continuous process one has to ensure its proper operation, i.e. a long time-span until the next prospective unscheduled downtime. Thus, the installed operation units have to be: 1) robust against disturbances by engineering design principles and by advanced fault tolerant control schemes, respectively; and 2) the condition of the operation units has to be monitored reliably to trigger, in case of need, appropriate intervention strategies in a timely manner. In this paper, the focus is on the monitoring aspect. Here, a model-based fault detection and identification framework is implemented, which selects the most data-supported model candidate from a set of predefined model hypotheses including the reference model (normal behavior) as well as failure models. In addition, to enable an improved diagnosis the system under study can be steered deliberately based on the proposed concept resulting into an active fault diagnosis framework. Preliminary results are demonstrated by an academic three-tank system.

@article{
 title = {Aspekte einer datengetriebenen, zustandsabhängigen Instandhaltung ­},
 type = {article},
 year = {2015},
 pages = {21-25},
 id = {4810c235-74af-3ccd-a89a-a9fb21b4c3c8},
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 citation_key = {Merkmalsextraktion2015},
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 author = {Merkmalsextraktion, Informative},
 number = {Teil 1}
}

@article{
 title = {Global Sensitivity Analysis applied to Model Inversion Problems: A Contribution to Rail Condition Monitoring},
 type = {article},
 year = {2015},
 volume = {6},
 id = {3bd4fd48-5b52-3a5e-8a84-eebe27382b8f},
 created = {2021-10-26T13:36:43.309Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:55.175Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2015c},
 private_publication = {false},
 abstract = {© 2015, Prognostics and Health Management Society. All rights reserved.Rising demands on railroad infrastructure operator by means of profitability and punctuality call for advanced concepts of Prognostics and Health Management. Condition based preventive maintenance aims at strengthening the rail mode of transport through an optimized scheduling of maintenance actions based on the actual and prognosticated infrastructure condition, respectively. When applying model-based algorithms within the framework of Prognostics and Health Management unknown model parameters have to be identified first. Which of these parameters should be known as precisely as possible can be figured out systematically by a sensitivity analysis. A comprehensive global sensitivity analysis, however, might be prohibitive by means of computation load when standard algorithms are implemented. In this study, it is shown how global parameter sensitivities can be calculated efficiently by combining Polynomial Chaos Expansion and Point Estimate Method principles. The proposed framework is demonstrated by a model inversion problem which aims to recalculate the track quality by measurements of the vehicle acceleration, i.e. analyzing the dynamic railway track-vehicle interaction.},
 bibtype = {article},
 author = {Schenkendorf, René and Groos, J.C. Jörn},
 journal = {IJPHM}
}

© 2015, Prognostics and Health Management Society. All rights reserved.Rising demands on railroad infrastructure operator by means of profitability and punctuality call for advanced concepts of Prognostics and Health Management. Condition based preventive maintenance aims at strengthening the rail mode of transport through an optimized scheduling of maintenance actions based on the actual and prognosticated infrastructure condition, respectively. When applying model-based algorithms within the framework of Prognostics and Health Management unknown model parameters have to be identified first. Which of these parameters should be known as precisely as possible can be figured out systematically by a sensitivity analysis. A comprehensive global sensitivity analysis, however, might be prohibitive by means of computation load when standard algorithms are implemented. In this study, it is shown how global parameter sensitivities can be calculated efficiently by combining Polynomial Chaos Expansion and Point Estimate Method principles. The proposed framework is demonstrated by a model inversion problem which aims to recalculate the track quality by measurements of the vehicle acceleration, i.e. analyzing the dynamic railway track-vehicle interaction.

@article{
 title = {Strengthening the rail mode of transport by condition based preventive maintenance},
 type = {article},
 year = {2015},
 keywords = {Georeferencing,Localization,Maintenance engineering,Multisensor integration,Prognostics and health management,Rail track,Sensitivity analysis},
 pages = {964-969},
 volume = {28},
 id = {2054bb47-4440-3d8a-b85b-6c4561619ecb},
 created = {2021-10-26T13:36:50.191Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:50.191Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2015b},
 private_publication = {false},
 abstract = {In recent years, the demands on railroad infrastructure operators have been rising by means of profitability, availability, safety, and punctuality. Here, the condition based preventive maintenance aims at strengthening the rail mode of transport through an optimized scheduling of maintenance actions taking account of the actual infrastructure condition and its expected further degradation. Two crucial aspects of such a predictive maintenance strategy are 1) the reliable precise localization of faults within a widespread, distributed infrastructure system, and 2) the consideration of parameter uncertainties by the prediction of the degradation trend for the near future of the infrastructure under study. Both aspects are addressed in this contribution, the challenges are highlighted and some illustrative, preliminary results are shown.},
 bibtype = {article},
 author = {Schenkendorf, R. and Groos, J. C. and Johannes, L.},
 doi = {10.1016/j.ifacol.2015.09.651},
 journal = {IFAC-PapersOnLine},
 number = {21}
}

In recent years, the demands on railroad infrastructure operators have been rising by means of profitability, availability, safety, and punctuality. Here, the condition based preventive maintenance aims at strengthening the rail mode of transport through an optimized scheduling of maintenance actions taking account of the actual infrastructure condition and its expected further degradation. Two crucial aspects of such a predictive maintenance strategy are 1) the reliable precise localization of faults within a widespread, distributed infrastructure system, and 2) the consideration of parameter uncertainties by the prediction of the degradation trend for the near future of the infrastructure under study. Both aspects are addressed in this contribution, the challenges are highlighted and some illustrative, preliminary results are shown.

@phdthesis{
 title = {Optimal Experimental Design for Parameter Identification and Model Selection},
 type = {phdthesis},
 year = {2014},
 keywords = {Chemical Engineering,Control Theory,Flatness,Kalman Filter,Model Selection,OED,Optimal Experimental Design,Parameter Identification,Systems Biology},
 pages = {180},
 institution = {Otto-von-Guericke-University Magdeburg},
 id = {853161b0-24d1-3a56-8499-fd1ac71f6632},
 created = {2021-10-26T13:36:51.134Z},
 accessed = {2014-07-24},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:59.182Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2014c},
 user_context = {Dissertation},
 private_publication = {false},
 bibtype = {phdthesis},
 author = {Schenkendorf, René}
}

@inproceedings{
 title = {A General Framework for Uncertainty Propagation Based on Point Estimate Methods},
 type = {inproceedings},
 year = {2014},
 id = {ecef6d87-175d-3673-8b0c-58c2c0fdfb09},
 created = {2021-10-26T13:36:51.398Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:59.353Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2014},
 private_publication = {false},
 bibtype = {inproceedings},
 author = {Schenkendorf, René},
 booktitle = {Phme14}
}

@article{
 title = {Parameter identification for ordinary and delay differential equations by using flat inputs},
 type = {article},
 year = {2014},
 keywords = {delay,differential equations,flat inputs,flatness,parameter estimation,parameter identification,sensitivity,uncertainty},
 pages = {594-607},
 volume = {48},
 websites = {http://link.springer.com/10.1134/S0040579514050224},
 day = {12},
 id = {e7277ee0-0f6b-3405-80da-3fa6eb918388},
 created = {2021-10-26T13:36:51.671Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:59.512Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2014b},
 private_publication = {false},
 abstract = {The concept of differential flatness has been widely used for nonlinear controller design. In this contribution, it is shown that flatness may also be a very useful property for parameter identification. An identification method based on flat inputs is introduced. The treatment of noisy measurements and the extension of the method to delay differential equations are discussed. The method is illustrated by two case studies: the well-known FitzHugh-Nagumo equations and a virus replication model with delays.},
 bibtype = {article},
 author = {Schenkendorf, René and Mangold, Michael},
 doi = {10.1134/S0040579514050224},
 journal = {Theoretical Foundations of Chemical Engineering},
 number = {5}
}

The concept of differential flatness has been widely used for nonlinear controller design. In this contribution, it is shown that flatness may also be a very useful property for parameter identification. An identification method based on flat inputs is introduced. The treatment of noisy measurements and the extension of the method to delay differential equations are discussed. The method is illustrated by two case studies: the well-known FitzHugh-Nagumo equations and a virus replication model with delays.

@article{
 title = {Prognoseverfahren zur Gleislageabweichung bei Einzelfehlern},
 type = {article},
 year = {2014},
 id = {6b958e31-54e8-3815-83f3-5c5ed0b91042},
 created = {2021-10-26T13:36:51.892Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:51.892Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Linder2014},
 private_publication = {false},
 bibtype = {article},
 author = {Linder, C and Lackhofe, C and Schenkendorf, R},
 journal = {EI - Eisenbahningenieur},
 number = {2}
}

@article{
 title = {Online model selection approach based on Unscented Kalman Filtering},
 type = {article},
 year = {2013},
 keywords = {kalaman filtering,model discrimination,model selection,online model selection,optimal experimental design,sigam points,unscented kalman filtering},
 pages = {44-57},
 volume = {23},
 websites = {http://linkinghub.elsevier.com/retrieve/pii/S0959152412002387,https://linkinghub.elsevier.com/retrieve/pii/S0959152412002387},
 month = {1},
 id = {1de071a9-8371-3847-8843-94725925b90b},
 created = {2021-10-26T13:36:52.412Z},
 accessed = {2014-03-21},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:52.412Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2013},
 private_publication = {false},
 abstract = {Highly predictive mathematical models are of inestimable value in systems biology. Their application ranges from investigations of basic processes in living organisms up to model based drug design in the field of pharmacology. For the development of reliable models suitable model candidates and related model parameters have to be identified by minimising the difference between the model outcome and available measurement data. Due to the complexity of the analysed processes mathematical models capture only the essential features of interest. This approximate representation, which is usually combined with a vague knowledge of basic processes, leads in many cases to a variety of potential model candidates describing the real process almost equally well. To determine the most plausible model candidate is the objective of model selection or model discrimination methods. If under given operation conditions no sufficient discrimination can be achieved, Optimal Experimental Designs (OED) comes into play. OED searches for operation conditions which facilitate the overall selection process. In this work an online model selection framework is presented. Here, the Unscented Kalman Filter (UKF) provides statistical information which is used to assign probability values to every model candidate. These probability values are immediately updated as soon as new measurement data become available. In addition, during the experimental run the process is steered in a fashion which maximises the differences in these candidates. To overcome limitations caused by parameter uncertainties the most sensitive model parameters are simultaneously estimated in the course of the model selection framework. The combined application of the online framework and the joint estimation of sensitive model parameters provides a very efficient usage of measurement data reducing the overall number of experiments. The method is demonstrated for a well known motif in signalling pathways, the mitogen-activated protein (MAP) kinase.},
 bibtype = {article},
 author = {Schenkendorf, René and Mangold, Michael},
 doi = {10.1016/j.jprocont.2012.10.009},
 journal = {Journal of Process Control},
 number = {1}
}

Highly predictive mathematical models are of inestimable value in systems biology. Their application ranges from investigations of basic processes in living organisms up to model based drug design in the field of pharmacology. For the development of reliable models suitable model candidates and related model parameters have to be identified by minimising the difference between the model outcome and available measurement data. Due to the complexity of the analysed processes mathematical models capture only the essential features of interest. This approximate representation, which is usually combined with a vague knowledge of basic processes, leads in many cases to a variety of potential model candidates describing the real process almost equally well. To determine the most plausible model candidate is the objective of model selection or model discrimination methods. If under given operation conditions no sufficient discrimination can be achieved, Optimal Experimental Designs (OED) comes into play. OED searches for operation conditions which facilitate the overall selection process. In this work an online model selection framework is presented. Here, the Unscented Kalman Filter (UKF) provides statistical information which is used to assign probability values to every model candidate. These probability values are immediately updated as soon as new measurement data become available. In addition, during the experimental run the process is steered in a fashion which maximises the differences in these candidates. To overcome limitations caused by parameter uncertainties the most sensitive model parameters are simultaneously estimated in the course of the model selection framework. The combined application of the online framework and the joint estimation of sensitive model parameters provides a very efficient usage of measurement data reducing the overall number of experiments. The method is demonstrated for a well known motif in signalling pathways, the mitogen-activated protein (MAP) kinase.

@article{
 title = {Influence of non-linearity to the Optimal Experimental Design demonstrated by a biological system},
 type = {article},
 year = {2012},
 keywords = {Box Bias,Fisher Information Matrix,Kriging Interpolation,Optimal Experimental Design,Sigma Point method,mean square error,parameter estimation},
 pages = {413-426},
 volume = {18},
 month = {8},
 publisher = {Taylor & Francis},
 id = {8c8ca8e2-f8e0-31bf-8195-fce58ece25c6},
 created = {2021-10-26T13:36:52.764Z},
 accessed = {2014-03-21},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:52.764Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2012a},
 private_publication = {false},
 abstract = {A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is shown that Sigma Points can also be used to define design criteria for OED that incorporate the influence of parameter uncertainties on the simulated model states, i.e. mean square error of prediction. To reduce the computational effort of OED further, the Kriging Interpolation approach is applied leading to an easily evaluable surrogate cost function. The advantages of the Sigma Point method combined with the Kriging Interpolation in the framework of OED are demonstrated for the example of a biological two-substrate uptake model. A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is shown that Sigma Points can also be used to define design criteria for OED that incorporate the influence of parameter uncertainties on the simulated model states, i.e. mean square error of prediction. To reduce the computational effort of OED further, the Kriging Interpolation approach is applied leading to an easily evaluable surrogate cost function. The advantages of the Sigma Point method combined with the Kriging Interpolation in the framework of OED are demonstrated for the example of a biological two-substrate uptake model.},
 bibtype = {article},
 author = {Schenkendorf, René and Kremling, Andreas and Mangold, Michael},
 doi = {10.1080/13873954.2011.642385},
 journal = {Mathematical and Computer Modelling of Dynamical Systems},
 number = {4}
}

A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is shown that Sigma Points can also be used to define design criteria for OED that incorporate the influence of parameter uncertainties on the simulated model states, i.e. mean square error of prediction. To reduce the computational effort of OED further, the Kriging Interpolation approach is applied leading to an easily evaluable surrogate cost function. The advantages of the Sigma Point method combined with the Kriging Interpolation in the framework of OED are demonstrated for the example of a biological two-substrate uptake model. A precise estimation of parameters is essential to generate mathematical models with a highly predictive power. A framework that attempts to reduce parameter uncertainties caused by measurement errors is known as Optimal Experimental Design (OED). The Fisher Information Matrix (FIM), which is commonly used to define a cost function for OED, provides at the best only a lower bound of parameter uncertainties for models that are non-linear in their parameters. In this work, the Sigma Point method is used instead, because it enables a more reliable approximation of the parameter statistics accompanied by a manageable computational effort. Moreover, it is shown that Sigma Points can also be used to define design criteria for OED that incorporate the influence of parameter uncertainties on the simulated model states, i.e. mean square error of prediction. To reduce the computational effort of OED further, the Kriging Interpolation approach is applied leading to an easily evaluable surrogate cost function. The advantages of the Sigma Point method combined with the Kriging Interpolation in the framework of OED are demonstrated for the example of a biological two-substrate uptake model.

@inproceedings{
 title = {Qualitative and quantitative optimal experimental design for parameter identification of a MAP kinase model},
 type = {inproceedings},
 year = {2011},
 volume = {18},
 issue = {PART 1},
 id = {bf2270f7-83c4-3902-8bff-e830d7390e1e},
 created = {2021-10-26T13:36:50.493Z},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:50.493Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 citation_key = {Schenkendorf2011b},
 private_publication = {false},
 abstract = {Mathematical models ensuring a highly predictive power are of inestimable value in systems biology. Their application ranges from investigations of basic processes in living organisms up to model based drug design in the field of pharmacology. For this purpose simulation results have to be consistent with the real process, i.e, suitable model parameters have to be identified minimizing the difference between the model outcome and measurement data. In this work graph based methods are used to figure out if conditions of parameter identifiability are fulfilled. In combination with network centralities, the structural representation of the underlying mathematical model provides a first guess of informative output configurations. As at least the most influential parameters should be identifiable and to reduce the complexity of the parameter identification process further a parameter ranking is done by Sobol' indices. The calculation of these indices goes along with a highly computational effort, hence monomial cubature rules are used as an efficient approach of numerical integration. All methods are demonstrated for a well known motif in signaling pathways, the MAP kinase cascade. © 2011 IFAC.},
 bibtype = {inproceedings},
 author = {Schenkendorf, R. and Mangold, M.},
 doi = {10.3182/20110828-6-IT-1002.02882},
 booktitle = {IFAC Proceedings Volumes (IFAC-PapersOnline)}
}

Mathematical models ensuring a highly predictive power are of inestimable value in systems biology. Their application ranges from investigations of basic processes in living organisms up to model based drug design in the field of pharmacology. For this purpose simulation results have to be consistent with the real process, i.e, suitable model parameters have to be identified minimizing the difference between the model outcome and measurement data. In this work graph based methods are used to figure out if conditions of parameter identifiability are fulfilled. In combination with network centralities, the structural representation of the underlying mathematical model provides a first guess of informative output configurations. As at least the most influential parameters should be identifiable and to reduce the complexity of the parameter identification process further a parameter ranking is done by Sobol' indices. The calculation of these indices goes along with a highly computational effort, hence monomial cubature rules are used as an efficient approach of numerical integration. All methods are demonstrated for a well known motif in signaling pathways, the MAP kinase cascade. © 2011 IFAC.

@article{
 title = {Two state estimators for the barium sulfate precipitation in a semi-batch reactor},
 type = {article},
 year = {2009},
 keywords = {[Distributed parameter system, Observation by onli},
 volume = {64},
 id = {a43ffb5d-6dc0-3fca-99d4-c4a05dba07c6},
 created = {2021-10-26T13:36:49.918Z},
 file_attached = {true},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:58.867Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {false},
 hidden = {false},
 citation_key = {Mangold2009},
 private_publication = {false},
 abstract = {The on-line determination of particle property distributions by direct measurements is often difficult, because the measurement equations are not invertible or because the inverse problem is ill-posed. If the process is observable, one can use state estimation techniques in order to reconstruct unmeasurable internal states of the process. This is discussed here for a semi-batch precipitation reactor. A square root unscented Kalman filter and state estimation by online minimisation are studied for the case of a measurable average particle size. Both estimators use a one-dimensional population balance model. The two approaches are compared in simulations. © 2008 Elsevier Ltd. All rights reserved.},
 bibtype = {article},
 author = {Mangold, M. and Bück, A. and Schenkendorf, R. and Steyer, C. and Voigt, A. and Sundmacher, K.},
 doi = {10.1016/j.ces.2008.05.039},
 journal = {Chemical Engineering Science},
 number = {4}
}

The on-line determination of particle property distributions by direct measurements is often difficult, because the measurement equations are not invertible or because the inverse problem is ill-posed. If the process is observable, one can use state estimation techniques in order to reconstruct unmeasurable internal states of the process. This is discussed here for a semi-batch precipitation reactor. A square root unscented Kalman filter and state estimation by online minimisation are studied for the case of a measurable average particle size. Both estimators use a one-dimensional population balance model. The two approaches are compared in simulations. © 2008 Elsevier Ltd. All rights reserved.

@article{
 title = {Optimal experimental design with the sigma point method},
 type = {article},
 year = {2009},
 keywords = {Algorithms,Biological,Bioreactors,Computer Simulation,Confidence Intervals,Fisher Information Matrix,Kinetics,Models,Monte Carlo Method,Research Design,Systems Biology,Systems Biology: methods},
 pages = {10-23},
 volume = {3},
 websites = {https://digital-library.theiet.org/content/journals/10.1049/iet-syb_20080094},
 month = {1},
 day = {1},
 id = {f5eb642d-cc8f-3e5e-b697-085677c67fde},
 created = {2021-10-26T13:36:52.157Z},
 accessed = {2014-03-21},
 file_attached = {false},
 profile_id = {46206c9e-d69a-378c-9478-6dd168f65080},
 group_id = {cc302413-c146-306b-8008-abbf67f3b420},
 last_modified = {2021-10-26T13:36:52.157Z},
 read = {false},
 starred = {false},
 authored = {false},
 confirmed = {true},
 hidden = {false},
 citation_key = {Schenkendorf2009},
 private_publication = {false},
 abstract = {Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.},
 bibtype = {article},
 author = {Mangold, Michael and Schenkendorf, R and Kremling, A},
 doi = {10.1049/iet-syb:20080094},
 journal = {IET Systems Biology},
 number = {1}
}

Using mathematical models for a quantitative description of dynamical systems requires the identification of uncertain parameters by minimising the difference between simulation and measurement. Owing to the measurement noise also, the estimated parameters possess an uncertainty expressed by their variances. To obtain highly predictive models, very precise parameters are needed. The optimal experimental design (OED) as a numerical optimisation method is used to reduce the parameter uncertainty by minimising the parameter variances iteratively. A frequently applied method to define a cost function for OED is based on the inverse of the Fisher information matrix. The application of this traditional method has at least two shortcomings for models that are nonlinear in their parameters: (i) it gives only a lower bound of the parameter variances and (ii) the bias of the estimator is neglected. Here, the authors show that by applying the sigma point (SP) method a better approximation of characteristic values of the parameter statistics can be obtained, which has a direct benefit on OED. An additional advantage of the SP method is that it can also be used to investigate the influence of the parameter uncertainties on the simulation results. The SP method is demonstrated for the example of a widely used biological model.