Degradation Modeling and RUL Estimation of Feedback Control Systems using Stochastic Diffusion Process

Abstract

This paper considers a deteriorating feedback control system suffering from stochastic internal damage, and investigates a methodology for modeling its system-level degradation index with predicting its remaining useful life. The design of the controller allows the system output to track the input and, at the same time, hides part of the degradation and makes it difficult to be detected. To avoid the strong control impact, we equip an extra low-intensity controller while preserving the closed-loop structure and stability of the system with the aim to reveal the effects of inner damage on system performance. Then, at each inspection date, we apply only observable input and output from newly controlled system to estimate transfer function and extract the peak value of its step response as a degradation index which is thus less subject to control action. Thereafter, a stochastic diffusion process with nonlinear drift and diffusion is used to model the evolution of this index. To calculate the probability density function of system remaining useful life, Lamperti transform and Ricciardi transform are applied to convert this model to the standard Brownian motion so that an approximation of its first hitting time with a time-varying failure threshold is used to obtain the remaining useful life of our system. A case study from an inertial platform is given to proof the feasibility of the aforementioned methods.