Degradation modeling of turbofan engines based on a flexible nonlinear wiener process with random drift diffusion

Degradation modeling using condition monitoring (CM) data is fundamental for prognostics and health management (PHM). However, due to the variations in manufacturing materials and operating environments, degradation heterogeneity makes life prediction difficult. Motivated by this problem, a flexible nonlinear Wiener process with random drift diffusion is proposed for degradation modeling. Different from traditional methods, this approach regards both drift and diffusion coefficients as random parameters to describe the heterogeneity of the degradation rate and volatility simultaneously. In addition, the model supports the selection of appropriate distribution types for the random parameters according to the statistical characteristics of the actual data to improve fitting performance. To effectively overcome the parameter estimation difficulties caused by model assumptions, we propose a two-stage maximum likelihood estimation (MLE) algorithm embedded with a distribution selection strategy to estimate the model parameters. Specifically, the method is first used to estimate the drift and diffusion coefficients of each unit. Then, the estimated coefficients are used to select the distribution types and perform MLE for parameters in the selected distributions. The effectiveness of the proposed parameter estimation algorithm is demonstrated with both simulated datasets and real turbofan engine datasets. A comparison of results show that compared to simplified versions and traditional methods, the proposed degradation model improves the fitting performance and life prediction accuracy.