The Disturbed Fault Diagnosis for Discrete-Time Euler–Lagrange System With Multi-Sensors Based on χ 2 $$ {\chi}^2 $$ -Detection

Abstract

This article investigates the sensor fault diagnosis problem of the discrete-time Euler–Lagrange (EL) system with multi-sensors. Firstly, the discrete-time EL system is converted into a second-order non-linear discrete-time system using the famous Dragon Gekuta method. Secondly, the proposed strategy leverages the multi-sensors data fusion framework, employing multiple local unscented Kalman filters for state estimation. Moreover, the convergence of the local estimation is analyzed such that the local estimation errors are stable in faults-free case. Thirdly, considering the sensor fault in the presence of process and measurement noises, the residual signal based on the local estimation error is designed to detect and isolate faults. The fault detection and isolation logic is conducted using ${\chi }^2$ detection, where the threshold is determined through the cumulative distribution function of ${\chi }^2$ distribution. Finally, a single-link robot is used to illustrate the effectiveness of the proposed fault diagnosis based on the multi-sensors data fusion.