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

•We develop a fault detection, isolation and estimation method for a data-driven approach.•We derive an analytical model and estimate the fault severity for Gamma distributed noisy data.•The accuracy of the theoretical model is studied in noisy environmental conditions.•The proposal is experimentall...

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Bibliographic Details
Published in:Mechanical systems and signal processing 2017-09, Vol.93 (C), p.118-135
Main Authors: Delpha, Claude, Diallo, Demba, Youssef, Abdulrahman
Format: Article
Language:English
Subjects:
Background noise
Bearings
Computer simulation
Divergence
Engineering Sciences
Environmental monitoring
Fault detection
Fault detection and diagnosis
Faults
Feature extraction
Gamma distributed data
Gamma rays
Incipient fault estimation
Kullback-Leibler Divergence
Monte Carlo simulation
Noise levels
Principal Component Analysis
Principal components analysis
Probability density functions
Signal and Image processing
Signal monitoring
Vibration
Vibration monitoring
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Summary:•We develop a fault detection, isolation and estimation method for a data-driven approach.•We derive an analytical model and estimate the fault severity for Gamma distributed noisy data.•The accuracy of the theoretical model is studied in noisy environmental conditions.•The proposal is experimentally checked with vibration signals from monitoring bearings in drives. 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 (40dB), 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.
ISSN:0888-3270
1096-1216
DOI:10.1016/j.ymssp.2017.01.045