Robust Parameter Design of Functional Responses Based on Bayesian SUR Models

As for the robust parameter design of functional responses, a Bayesian Seemingly Unrelated Regression (SUR) model is proposed to take into account the model uncertainty and response variability in this paper. First of all, the SUR model is used to build the functional relationship between the output responses and the input factors at different time points. Also, Bayesian analysis of the SUR model is performed to consider the influence of the model parameter uncertainty on the research results. Secondly, the process means and variances of the functional responses at different time points are estimated by the posterior samples of the simulated responses. Moreover, an integrated performance index (i.e. mean square error) is establish by using the above process means and variances. Then, the optimal parameter settings may be found by minimizing the MSE performance index. Finally, the advantages of the proposed method are illustrated by an example from the literature

Multiple-Change-Point Modeling and Exact Bayesian Inference of Degradation Signal for Prognostic Improvement

Prognostics play an increasingly important role in modern engineering systems for smart maintenance decision-making. In parametric regression-based approaches, the parametric models are often too rigid to model degradation signals in many applications. In this paper, we propose a Bayesian multiple-change-point (CP) modeling framework to better capture the degradation path and improve the prognostics. At the offline modeling stage, a novel stochastic process is proposed to model the joint prior of CPs and positions. All hyperparameters are estimated through an empirical two-stage process. At the online monitoring and remaining useful life (RUL) prediction stage, a recursive updating algorithm is developed to exactly calculate the posterior distribution and RUL prediction sequentially. To control the computational cost, a fixed-support-size strategy in the online model updating and a partial Monte Carlo strategy in the RUL prediction are proposed. The effectiveness and advantages of the proposed method are demonstrated through thorough simulation and real case studies