Fault Detection Based on Multi-Dimensional KDE and Jensen–Shannon Divergence

Abstract

Weak fault signals, high coupling data, and unknown faults commonly exist in fault diagnosis systems, causing low detection and identification performance of fault diagnosis methods based on T2 statistics or cross entropy. This paper proposes a new fault diagnosis method based on optimal bandwidth kernel density estimation (KDE) and Jensen–Shannon (JS) divergence distribution for improved fault detection performance. KDE addresses weak signal and coupling fault detection, and JS divergence addresses unknown fault detection. Firstly, the formula and algorithm of the optimal bandwidth of multidimensional KDE are presented, and the convergence of the algorithm is proved. Secondly, the difference in JS divergence between the data is obtained based on the optimal KDE and used for fault detection. Finally, the fault diagnosis experiment based on the bearing data from Case Western Reserve University Bearing Data Center is conducted. The results show that for known faults, the proposed method has 10% and 2% higher detection rate than T2 statistics and the cross entropy method, respectively. For unknown faults, T2statistics cannot effectively detect faults, and the proposed method has approximately 15% higher detection rate than the cross entropy method. Thus, the proposed method can effectively improve the fault detection rate.

Testing Hypotheses for Geological Controls on Hydraulic-Fracturing-Induced Seismicity in the Montney Formation, Canada

“…After computing crosscorrelation coefficients, the level of similarity between observed and simulated catalogs is further investigated using Kullback-Leibler divergence and Jensen-Shannon divergence tests along with two-sample Kolmogorov-Smirnov statistics [41]. The Kullback-Leibler (KL) divergence (relative entropy) and Jensen-Shannon both provide a quantitative measure of proximity between two probability distributions and are used in a wide range of applications [46][47][48][49]. Tests can be used jointly to provide a more complete view of similarity between compared distributions [50], although studies suggest a higher efficiency and flexibility of the Jensen-Shannon test [51,52].…”

Information Theory and Its Application in Machine Condition Monitoring

“…Targeting the challenges regarding weak fault signal, coupling among different dimensions of the collected signal, and scarcity of fault datasets, Wei et al proposed a novel fault detection based on multi-dimensional KDE and Jensen–Shannon divergence [ 5 ]. Addressing the limitations of the conventional KDE method regarding information loss for multidimensional problems, in this research, it was extended to a multidimensional version for tackling the weak fault signal and coupling problem of the collected signal.…”