An integrated degradation modeling framework considering model uncertainty and calibration

Abstract

General path models and stochastic process models are two widely applied categories of probabilistic degradation models. The former explains the randomness of degradation data as normal distributed errors with zero mean. The latter describes degradation with stochastic processes such as Wiener process, Gamma process and Inverse Gaussian process. For general path models, a limitation is the assumption of normally distributed errors. For stochastic process models, model uncertainty with respect to the available stochastic processes should be considered, but the widely-applied model selection methods in consideration of model uncertainty are unable to warn when all the candidate models fit data poorly. Therefore, an integrated degradation modeling framework based on wavelet density estimation is proposed, which can calibrate the distribution of errors for general path models and deal with model uncertainty for stochastic process models. The proposed framework can select the best stochastic process if certain stochastic processes fit the degradation data well. Otherwise, all the candidate stochastic processes can be calibrated, which overcomes the drawback of model selection methods. The effectiveness and feasibility of the proposed framework are illustrated through a case study and a numerical example.