基于Signature的复杂多状态系统可靠性非参数分析研究

Complex multi-state systems exist widely in various fields such as aerospace, nuclear power, civilian industry, the reliability evaluation of which is one of the important contents. The reported methods are limited to analyze and evaluate the system's reliability from the data of components, and have some problems including intractably large state dimensions, the difficulties of calculation. In this project, the reliability evaluation of the multi-state system and its components will be analyzed from the perspective of nonparametric statistics based on the theory of Signature. The study will focus on the inference and analysis of components' characteristics of reliability from the system's monitoring data of states, reduce the number of dimensions of state space, and relax the restriction of assumption for components' lifetime distribution. Firstly, the general calculation method and the optimized algorithm for the Signature of multi-state system will be investigated when the number of components is large. Secondly, the nonparametric inference methods for the complete and censoring samples and the nonparametric Bayesian inference methods for the small samples will be studied to derive the reliability characteristics of multi-state system and its components, respectively. Finally, we will establish the model of Signature for the multi-state system of which the components' lifetimes are from different underlying distributions. The nonparametric statistical methods for the reliability characteristics of components will be discussed. This project will provide some new methods and ideas for the quality and reliability management of complex multi-state system.

复杂多状态系统广泛存在于航空航天、核电、民用生产等各个领域，其可靠性评估是一项重要的研究内容。现有方法主要局限于通过部件数据对系统的可靠性进行评估建模和分析，且面临状态维数过多、难以计算的问题。本项目将基于Signature理论，从非参数统计角度研究复杂多状态系统及部件的可靠性评估，侧重于通过系统状态监测数据对部件可靠性特征进行推断和分析，降低状态空间维数，放宽寿命分布假定限制。首先，研究部件数目较大时多状态系统Signature的一般计算方法和优化算法；其次，研究全样本和截尾样本情况下多状态系统及其部件可靠性特征的非参数推断方法以及小样本情况下的非参数贝叶斯推断方法；最后，建立部件寿命服从不同分布情况下多状态系统的Signature模型，并给出部件可靠性特征的非参数统计方法。本项目将为复杂多状态系统的质量和可靠性管理提供新的方法和思路。

本项目基于Signature理论，从统计角度研究复杂多状态系统及部件的可靠性评估。经过三年的研究，已基本完成了预期的研究计划。研究主要围绕多状态复杂系统可靠度Signature计算、小样本截尾竞争失效数据的统计推断、多类型部件系统数据贝叶斯分析三方面展开。. 通过计算次序统计量所对应的最小路径数量，得到了应力强度多状态系统和动态应力强度系统Signature计算方法。该方法解决了部件数量较大系统Signature的计算问题，具有一般性且易于编程实现。. 针对小样本截尾数据，给出了多状态系统可靠度推断的贝叶斯分析方法。对于相依风险情形，通过Copula函数建立了竞争失效系统可靠度模型。贝叶斯分析方法通过融合先验信息，弥补了样本量太小和截尾数据所导致的估计偏差，为数据更新下可靠度评估提供了理论依据。. 不同类型的多状态部件会增加系统Signature建模的难度，通过对类型分类加权，得到了多状态系统的可靠度模型。给出了不同分布情形下多状态应力强度生存Signature模型和截尾数据情形下不同类型部件可靠度分析的非参数贝叶斯推断方法。通过对轴承寿命数据和电绝缘器失效数据的实际分析，验证了方法的可行性和效果。. 本项目的研究为复杂多状态系统的可靠性评估和管理提供了理论依据和方法支持。

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