Abstract: Aiming at the mechanical system related to multi-component failure, a reliability evaluation method of multi-component system based on time-varying Copula function was proposed. Firstly, the nonlinear Wiener process was introduced to characterize the performance degradation process, and the Copula function was used to characterize the correlation between multiple component failures. Secondly, based on the evolutionary equation of the Copula function approximation of the Fourier series, the fitting effect of the Fourier series on common time-varying forms was verified by Monte Carlo (MC) simulation. In addition, the likelihood ratio statistic was used to test the existence of time-varying correlation, indicating the necessity of time-varying correlation research. The example analysis shows that compared with the static correlation model, the log-likelihood function value of the time-varying correlation model is increased by 4.36%, and the Akaike Information Criterion (AIC) is reduced by 3.81%, and the reliability evaluation results are more accurate and have a good model application effect.

Key words: Wiener process, Time-varying Copula function, Fourier series, Likelihood ratio test, reliability assessment

摘要： 针对多部件失效相关的机械系统，提出一种基于时变Copula函数的多部件系统可靠性评估方法。首先，引入非线性Wiener过程刻画性能退化过程，并采用Copula函数刻画多部件失效间的相关性；其次，基于傅里叶级数近似Copula函数的演化方程，并通过蒙特卡洛(MC)模拟验证傅里叶级数对常见时变形式的拟合效果；此外，采用似然比统计量检验时变相关性的存在性，指明时变相关性研究的必要性。算例分析结果表明，与静态相关性模型相比，时变相关性模型对数似然函数值提高4.36%、赤池信息量准则(AIC)减小3.81%，可靠性评估结果更加准确，具有良好的模型应用效果。

关键词: Wiener过程, 时变Copula函数, 傅里叶级数, 似然比检验, 可靠性评估