Remaining Useful Lifetime Prediction of Nonlinear System with Random Effect and Measurement Error

For the problem of remaining useful lifetime (RUL) prediction of nonlinear system, the existing methods have not systematically carried out the studies on nonlinear degradation modeling with measurement error and random effect, priori parameter estimation and the corresponding RUL prediction. In this paper, a nonlinear Wiener process is used to establish a nonlinear degradation model with the consideration of measurement error and random effect to describe the implicitness, personality difference and nonlinearity of degradation process of a class of device. The expectation maximum (EM) algorithm is used to obtain the estimates of the fixed coefficient and the priori distributions of the random coefficients in the degradation model. Using the current monitoring data of the target device, the posteriori distribution of random coefficients is iteratively updated based on Bayesian inference. Using the full-probability formula, the remaining useful lifetime distribution of device is derived based on the first hitting time (FHT) distribution. A simulation example is analyzed to verify the correctness and advantage of this method.