Estimation of High Structural Reliability Involving Nonlinear Dependencies Based on Linear Correlations

Stochastic nonlinear dependencies have been reported extensively between different uncertain parameters or in their time or spatial variance. However, the description of dependency is commonly not provided except a linear correlation. The structural reliability incorporating nonlinear dependencies thus needs to be addressed based on the linear correlations. This paper first demonstrates the capture of nonlinear dependency by fitting various bivariate non-Gaussian copulas to limited data samples of structural material properties. The vine copula model is used to enable a flexible modeling of multiple nonlinear dependencies by mapping the linear correlations into the non-Gaussian copula parameters. A sequential search strategy is applied to achieve the estimate of numerous copula parameters, and a simplified algorithm is further designed for reliability involving stationary stochastic processes. The subset simulation is then adopted to efficiently generate random variables from the corresponding distribution for high reliability evaluation. Two examples including a frame structure with different stochastic material properties and a cantilever beam with spatially variable stochastic modulus are investigated to discuss the possible effects of nonlinear dependency on structural reliability. Since the dependency can be determined qualitatively from limited data, the proposed method provides a feasible way for reliability evaluation with prescriptions on correlated stochastic parameters.