In this paper, the problem of incipient fault prediction is studied for the nonlinear stochastic system with non-Gaussian noises and actuator fault. The incipient fault is expressed as a nonlinear function with two unknown parameters (the occurring time of fault and the incipient fault evolution rate). Based on the generalised correntropy criterion, the fault detection filter is proposed, and then the occurring time of fault can be obtained. Once the fault is detected, the unknown fault evolution rate is estimated by designing a new generalised correntropy filter-based. According to the estimated fault occurrence time and the estimated fault evolution rate, the trend of incipient fault can be predicted. Finally, the simulation results of a single-link robotic flexible manipulator system are given to show that the proposed method is validated.

本文研究了具有非高斯噪声和执行器故障的非线性随机系统的初始故障预测问题。初始故障表示为具有两个未知参数（故障发生时间和初始故障演化速率）的非线性函数。基于广义相关熵准则，提出故障检测滤波器，进而得到故障发生的时间。一旦检测到故障，就通过设计一种新的基于广义相关熵滤波器来估计未知故障演化率。根据估计的故障发生时间和估计的故障演化速率，可以预测早期故障的趋势。最后，给出了单连杆机器人柔性机械手系统的仿真结果，表明所提出的方法是有效的。