Kullback-Leibler Divergence for fault estimation and isolation : Application to Gamma distributed data

In this paper we develop a fault detection, isolation and estimation method based on data-driven approach. Data-driven methods are effective for feature extraction and feature analysis using statistical techniques. In the proposal, the Principal Component Analysis (PCA) method is used to extract the features and to reduce the data dimension. Then, the Kullback-Leibler Divergence (KLD) is used to detect the fault occurrence by comparing the Probability Density Function of the latent scores. To estimate the fault amplitude in case of Gamma distributed data, we have developed an analytical model that links the KLD to the fault severity, including the environmental noise conditions. In the Principal Component Analysis 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 > 40 dB), the fault amplitude estimation is accurate enough with a relative error less than 1%. The proposed approach is experimentally verified with vibration signals used for monitoring bearings in electrical machines.