Resampling method for reliability-based design optimization based on thermodynamic integration and parallel tempering

In this paper, a fully decoupled simulation method is proposed for reliability-based design optimization (RBDO) based on thermodynamic integration and parallel tempering (TIPT). We show that the failure probability function and its gradient can be obtained simultaneously with once generalized reliability analysis, and thus the RBDO problem is converted to the traditional optimization problem efficiently. Firstly, the design parameters are deemed as uniformly distributed random variables, and an auxiliary probability density function (PDF) of random design variables is constructed to cover its whole parameter space. Then, based on thermodynamic integration, the estimation of failure probability is converted to a series of simple integration problems with smooth integrand, and they are estimated by running multiple Markov chains using the so-called parallel tempering method. Finally, importance sampling (IS) is used to estimate the failure probability function and its gradient, and the IS samples are obtained by resampling from the existing Markov chains without extra computation. The proposed method is tested with severa benchmarks, and the results show that it provides robust solution for problems with various nonlinear constraints compared to other popular methods, include double-loop Monte Carlo simulation (MCS), Quantile MCS, sequential optimization and reliability assessment, performance measure approach and reliability index approach.