基于Copula的失效相关系统可靠性建模理论与优化方法研究

项目名称： 基于Copula的失效相关系统可靠性建模理论与优化方法研究

项目编号： No.50805070

项目类型： 青年科学基金项目

立项/批准年度： 2009

项目学科： 金属学与金属工艺

项目作者： 周金宇

作者单位： 江苏理工学院

项目金额： 20万元

中文摘要： 对于多数工程结构系统，各单元失效之间普遍存在统计相关性，使系统可靠性建模复杂化。针对这一问题，本项目引入多元统计工具Copula，探索失效相关结构系统可靠性建模与优化设计的新途径。具体研究内容包括：以单元安全裕度、服役寿命为变量，以系统层应力-强度-寿命异量纲动态干涉理论分析为依据，构造Copula 映射系统的失效相关机制及动态演化过程，实现系统可靠性建模；根据Copula 可靠性模型导出可靠性优化目标函数，分别按线性相关、非线性相关假设，实现对称、非对称结构系统原始设计变量的快速寻优。Copula 可靠性模型的优点是：以简洁、灵活的函数形式避开传统分析方法繁冗的多重联合积分；由秩相关、尾相关系数更客观地刻画复杂结构系统失效相关的时变非线性特征。在试验验证环节，采用多缺口棒状及多孔板状试件模拟串联结构系统，试验数据反映结构系统失效模式相关现象，并易于Copula描述。将新模型用于桁架结构、核电站应急发电机组风险预测等工程实例，分析结果贴近实际。本项目研究体现了概率分析中唯象失效数据与内在耦合机理的有机统一，为失效相关的复杂机电装备系统可靠性评估、仿真及优化提供了新思路、新方法。

中文关键词： 系统可靠性；失效相关；应力-强度-寿命动态干涉；Copula

英文摘要： For most engineering structure systems, reliability modelling becomes complicated because of the common existence of the element statistical dependence. Aiming at this problem, our project explores new ways to reliability modelling and reliability optimization design of failure dependence systems by introducing the Copula function, an important tool in multivariate statistical analysis. The main studies are as follows: copula-based reliability modelling and copula-based reliability optimization. It is based on the dynamic stress-strength-life interference theory in copula-reliability modelling in which element safety margins and service lives are taken as key variables. The new model can reflect basic mechanisms and dynamic evolution process of the failure dependence. According to the copula-based reliability model, the objective function used for reliability optimization is derived, and the fast optimizing are completed for symmetric and asymmetric structure systems respectively under linear dependence and nonlinear dependence assumptions. The advantages of copula-based reliability model are that it can avoid multifarious multiple integral due to simple and flexible functions, and it can depict time-varying and nonlinear characteristics of failure dependence in complex systems more objectively by rank correlation or tail correlation coefficients. As a experiment verification work, the specimens with multiple notches and multiple holes are loaded to simulate a series system and corresponding experimental data can reflect the failure dependence mechanism which is easy to be described by Copulas. The proposed model and method are used for predicting risk probabilities of truss structures and the emergency generating set of the nuclear power station, the results are close to reality precisely. Our studies embody the organic unity of phenomenological failure data and inherent coupling mechanism in probability analysis and give a new path for reliability assessment, simulation and optimization of complex electromechanical equipment systems with failure dependence.

英文关键词： System reliability; Failure dependence; Dynamic stress-strength-life interference; Copula