@InProceedings{7362788,
  author = {A. Youssef and C. Delpha and D. Diallo},
  booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)},
  title = {Analytical model of the KL divergence for gamma distributed data: Application to fault estimation},
  year = {2015},
  pages = {2266-2270},
  abstract = {Incipient fault diagnosis has become a key issue for reliability and safety of industrial processes. Data-driven methods are effective for feature extraction and feature analysis using multivariate statistical techniques. Beside fault detection, fault estimation is essential for making the appropriate decision (safe stop or fault accommodation). Therefore, in this paper, we have developed an analytical model of the Kullback-Leibler Divergence (KLD) for Gamma distributed data to be used for the fault severity estimation. In the Principal Component Analysis (PCA) framework, the proposed model of the KLD has been analysed and compared to an estimated value of the KLD using the Monte-Carlo estimator. The results show that for incipient faults (<;10%) in usual noise conditions (SNR>40dB), the analytical model is accurate enough with a relative error around 10%.},
  keywords = {fault diagnosis;feature extraction;gamma distribution;Monte Carlo methods;principal component analysis;reliability;analytical model;KL divergence;gamma distributed data;fault estimation;incipient fault diagnosis;industrial processes;reliability;safety;feature extraction;feature analysis;multivariate statistical techniques;fault detection;fault accommodation;Kullback-Leibler divergence;Gamma distributed data;principal component analysis;PCA framework;KLD;Monte-Carlo estimator;incipient faults;noise conditions;Decision support systems;Europe;Signal processing;Conferences;Fault detection;KLD model and estimation;Gamma distributed data;Incipient faults},
  doi = {10.1109/EUSIPCO.2015.7362788},
  issn = {2076-1465},
  month = {Aug},
  url = {https://www.eurasip.org/proceedings/eusipco/eusipco2015/papers/1570102733.pdf},
}

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Beside fault detection, fault estimation is essential for making the appropriate decision (safe stop or fault accommodation). Therefore, in this paper, we have developed an analytical model of the Kullback-Leibler Divergence (KLD) for Gamma distributed data to be used for the fault severity estimation. In the Principal Component Analysis (PCA) framework, the proposed model of the KLD has been analysed and compared to an estimated value of the KLD using the Monte-Carlo estimator. The results show that for incipient faults (<;10%) in usual noise conditions (SNR>40dB), the analytical model is accurate enough with a relative error around 10%.","keywords":"fault diagnosis;feature extraction;gamma distribution;Monte Carlo methods;principal component analysis;reliability;analytical model;KL divergence;gamma distributed data;fault estimation;incipient fault diagnosis;industrial processes;reliability;safety;feature extraction;feature analysis;multivariate statistical techniques;fault detection;fault accommodation;Kullback-Leibler divergence;Gamma distributed data;principal component analysis;PCA framework;KLD;Monte-Carlo estimator;incipient faults;noise conditions;Decision support systems;Europe;Signal processing;Conferences;Fault detection;KLD model and estimation;Gamma distributed data;Incipient faults","doi":"10.1109/EUSIPCO.2015.7362788","issn":"2076-1465","month":"Aug","url":"https://www.eurasip.org/proceedings/eusipco/eusipco2015/papers/1570102733.pdf","bibtex":"@InProceedings{7362788,\n author = {A. Youssef and C. Delpha and D. Diallo},\n booktitle = {2015 23rd European Signal Processing Conference (EUSIPCO)},\n title = {Analytical model of the KL divergence for gamma distributed data: Application to fault estimation},\n year = {2015},\n pages = {2266-2270},\n abstract = {Incipient fault diagnosis has become a key issue for reliability and safety of industrial processes. Data-driven methods are effective for feature extraction and feature analysis using multivariate statistical techniques. Beside fault detection, fault estimation is essential for making the appropriate decision (safe stop or fault accommodation). Therefore, in this paper, we have developed an analytical model of the Kullback-Leibler Divergence (KLD) for Gamma distributed data to be used for the fault severity estimation. In the Principal Component Analysis (PCA) framework, the proposed model of the KLD has been analysed and compared to an estimated value of the KLD using the Monte-Carlo estimator. 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