Analytical Model of the KL Divergence for Gamma Distributed Data: Application to Fault Estimation
Résumé
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%.
Mots clés
reliability
analytical model
KL divergence
fault estimation
incipient fault diagnosis
industrial processes
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