Multiple failure mode reliability modeling and analysis in failure crack propagation based on time-varying copula

The fatigue failure of crack structure is influenced by fracture failure and static strength failure in the process of its growth. And the correlation characteristics between them change with the crack growth, which brings difficulties to safety assessment. To solve this problem, we propose a reliability model of failure crack propagation (FCP) based on time-varying copula. Meanwhile, a dynamic parameter estimation is put forward to build the time-varying copula. First, a flexible mixed copula model was constructed, by means of linear weighted model, to describe the nonlinear dependence among failure modes. Then the time-varying correlation parameters of copula were obtained by maximum likelihood estimation and least square polynomial fitting. Therefore, the dynamic parameter estimation of copula was realized, and then we used the built time-varying copula model to solve the reliability of joint failure. Finally, a numerical example was provided to illustrate the feasibility and application of the built time-varying copula model.

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