Reliability analysis of stochastic structure with multi-failure modes based on mixed Copula

In view of that there exist complicated correlations among failure modes of the stochastic structure because of the same uncertain variables that are contained in different failure modes, many reliability analysis methods based on empirical probability model have been developed to calculate and assess the structural reliability. However, the empirical distributions of uncertain variables are not always available or not accurate. Thus, based on the available sample data of random variables of the stochastic structural system to be analyzed, this paper presents a new reliability analysis method in which the mixed Copula is constructed to describe the correlations among multi-failure modes. First, the Gumbel Copula and Clayton Copula, which have the upper and lower tail dependence separately, are utilized to construct a mixed Copula so as to describe the correlations among multi-failure modes. Then, the sample data of the random variables is substituted into the performance functions of failure modes to calculate the sequence values thereof, and the probability density function (PDF) and cumulative distribution function (CDF) of each performance function of the structure are estimated by using the nonparametric kernel density estimation (NKDE) technique. Subsequently, the Canonical Maximum Likelihood (CML) method is applied to estimate the correlation parameters in the mixed Copula. Finally, the main girder structure of an overhead traveling crane is investigated by using the proposed method, and the results indicate that the new reliability analysis method is effective and valid. Compared with traditional reliability analysis methods, the new method, in which the available sample data of random variables is directly used to calculate the values of performance functions so as to avoid the errors caused by empirical distributions, provides some important theories and engineering contributions for the reliability design analyses and safety assessments of actual engineering structures, especially these with complex correlations among multi-failure modes.