In structural reliability, the Markovian cumulative damage approaches such as Gamma process seem promising to model a nonreversible deterioration that involves gradually over time with small time increments. However, in many degradation phenomena, its evolution depends on the level of the degradation rather than the increments of time. Further, the measured data are usually collected with random error whose dispersion depends on the current degradation level. Therefore, the deterioration model should take in consideration such dependency and uncertainty for more accurate prediction. In this paper, a new statistical, data-driven state-dependent and perturbed model is proposed to model the state dependence (hidden level-degradation) both in temporal increments and measurement uncertainty. The construction of the degradation model will be discussed within an application to the pitting corrosion and synthetic data. Numerical experiments will later be conducted to identify preliminary properties of the model in terms of statistical inferences. Algorithm and estimates are proposed to compute the parameters of the model, the hidden state, and failure probabilities.

中文翻译：

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退化建模中具有状态相关增量和测量不确定性的扰动马尔可夫过程

在结构可靠性方面，诸如 Gamma 过程之类的马尔可夫累积损伤方法似乎有望模拟不可逆的退化，该退化涉及随着时间的推移逐渐增加小时间增量。然而，在许多退化现象中，其演变取决于退化的程度而不是时间的增加。此外，测量数据的收集通常带有随机误差，其离散程度取决于当前的退化水平。因此，劣化模型应该考虑这种依赖性和不确定性，以便进行更准确的预测。在本文中，提出了一种新的统计、数据驱动的状态相关和扰动模型，以对时间增量和测量不确定性中的状态相关（隐藏级别退化）进行建模。退化模型的构建将在点蚀和合成数据的应用中讨论。稍后将进行数值实验，以确定模型在统计推断方面的初步属性。提出了算法和估计来计算模型的参数、隐藏状态和故障概率。