Abstract
The actual structural systems have many failure modes. Due to the same random sources owned by the performance functions of these failure modes, there usually exist some nonlinear correlations between the various failure modes. How to handle the nonlinear correlations is one of the main scientific problems in the field of structural system reliability. In this paper, for the two-component systems and multiple-component systems with multiple failure modes, the mixed copula models for time-independent reliability analysis of series systems, parallel systems, series-parallel systems, and parallel-series systems are presented. These obtained mixed copula models, considering the nonlinear correlation between failure modes, are obtained with the chosen optimal copula functions with the Bayesian selection criteria and Monte Carlo Sampling (MCS) method. And a numerical example is provided to illustrate the feasibility and application of the built mixed models for structural system reliability.
Highlights
Today’s structural systems are becoming more complex and more sophisticated
The classic Pearson correlation coefficient is mainly used for characterizing the correlation among failure modes of structural system before; it has a few disadvantages
The mixed copula models are commonly built through different combinations of several copula functions, which respectively possess various characteristics in aspect of the dependence modeling
Summary
The evaluation of structural system reliability is becoming harder This means that the derivations based on classical assumptions are no longer satisfactory for the analysis of systems in terms of reliability. How to model the correlation among failure modes in aspect of the reliability analysis of structural systems is one of the most significant topics. The copulas, unlike the Pearson correlation coefficient only applied for describing linear correlation, offer a flexible tool for deriving nonlinear dependence, especially tail dependence among failure modes. The aim of this study is to introduce the copula function as a useful tool for modeling the dependence among failure modes of bridge system. Based on the introduced copulas, with the aid of copula Bayesian selection criteria [7, 10, 11], a flexible mixed copula model is constructed, by means of linear weighted model, to model the nonlinear dependence among failure modes. A numerical example is provided to illustrate the feasibility and application of the built mixed copula models
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