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

**Juhui Wei 1, Zhangming He 1,2,\*, Jiongqi Wang 1, Dayi Wang <sup>2</sup> and Xuanying Zhou <sup>1</sup>**


**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 *T*<sup>2</sup> 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 *T*<sup>2</sup> statistics and the cross entropy method, respectively. For unknown faults, *T*2statistics 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.

**Keywords:** fault detection; optimal bandwidth; kernel density estimation; JS divergence; bearing
