An Age- and State-Dependent Nonlinear Prognostic Model for Degrading Systems
An Age- and State-Dependent Nonlinear Prognostic Model for Degrading Systems
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DOI：
10.1109/tr.2015.2419220
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发表时间：
2015-04
影响因子：
5.9
通讯作者：
Zhengxin Zhang;Xiaosheng Si;Changhua Hu
中科院分区：
文献类型：
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作者：
Zhengxin Zhang;Xiaosheng Si;Changhua Hu
非线性和随机性是影响复杂系统退化过程的两个重要因素，因此在基于统计学的随机退化建模中必须考虑这两个因素。然而，目前的研究几乎都集中在年龄相关的随机退化模型，其中大多数是线性的，或可以转化为线性模型。在本文中，我们提出了一个一般的年龄和状态相关的非线性退化模型的性能。在所提出的模型中，年龄和状态依赖的非线性漂移和波动系数的扩散过程被用来表征的动态和非线性的退化进程。为了得到估计的剩余使用寿命分布，所考虑的扩散过程首先通过Lamperti变换转换成具有年龄或状态依赖的非线性漂移但具有恒定波动性的扩散过程。然后，基于一个著名的时空变换，我们得到了一个解析近似的剩余使用寿命分布的概念，首次通过时间。在此基础上，利用Hermite展开方法，给出了退化状态转移密度函数的近似闭合形式，并给出了模型未知参数的极大似然估计方法.一个说明性的例子来展示如何得到的结果可以应用到一个特定的年龄和状态依赖的非线性退化模型。最后，所提出的模型拟合轴承退化数据。对比结果表明，在动力学中建立与年龄和状态相关的非线性退化模型的必要性。
Nonlinearity and stochasticity are two important factors contributing to the degradation processes of complicated systems, and thus have to be taken into account in stochastic degradation modeling based prognostics. However, current studies almost always focus on age-dependent stochastic degradation models, most of which are linear, or can be transformed into linear models. In this paper, we propose a general age- and state-dependent nonlinear degradation model for prognostics. In the presented model, a diffusion process with age- and state-dependent nonlinear drift and volatility coefficients is utilized to characterize the dynamics and nonlinearity of the degradation progression. To derive the estimated remaining useful life distribution, the considered diffusion process is first converted into a diffusion process with age- or state-dependent nonlinear drift but constant volatility through Lamperti transformation. Then, based on a well-known time-space transformation, we obtain an analytical approximated remaining useful life distribution in the concept of the first passage time. Furthermore, a maximum likelihood estimation method for unknown parameters in the concerned model is presented on the basis of closed-form approximated degradation state transition density functions by the Hermite-expansion method. An illustrative example is provided to show how the obtained results can be applied to a specific age- and state-dependent nonlinear degradation model. Finally, the presented model is fitted to bearing degradation data. Comparative results suggest the necessity of age- and state-dependent nonlinear degradation modeling in prognostics.