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.

一般路径模型和随机过程模型是两种广泛应用的概率退化模型。前者将退化数据的随机性解释为均值为零的正态分布误差。后者描述了随机过程的退化，例如维纳过程、伽马过程和逆高斯过程。对于一般路径模型，限制是正态分布误差的假设。对于随机过程模型，应考虑相对于可用随机过程的模型不确定性，但广泛应用的考虑模型不确定性的模型选择方法无法在所有候选模型拟合数据不佳时发出警告。因此，提出了一种基于小波密度估计的综合退化建模框架，它可以校准一般路径模型的误差分布，处理随机过程模型的模型不确定性。如果某些随机过程很好地拟合退化数据，则所提出的框架可以选择最佳随机过程。否则，可以校准所有候选随机过程，这克服了模型选择方法的缺点。通过案例研究和数值例子说明了所提出框架的有效性和可行性。