A general two-phase Markov chain Monte Carlo approach for constrained design optimization: Application to stochastic structural optimization

This contribution presents a general approach for solving structural design problems formulated as a class of nonlinear constrained optimization problems. A Two-Phase approach based on Bayesian model updating is considered for obtaining the optimal designs. Phase I generates samples (designs) uniformly distributed over the feasible design space, while Phase II obtains a set of designs lying in the vicinity of the optimal solution set. The equivalent model updating problem is solved by the transitional Markov chain Monte Carlo method. The proposed constraint-handling approach is direct and does not require special constraint-handling techniques. The population-based stochastic optimization algorithm generates a set of nearly optimal solutions uniformly distributed over the vicinity of the optimal solution set. The set of optimal solutions provides valuable sensitivity information. In addition, the proposed scheme is a useful tool for exploration of complex feasible design spaces. The general approach is applied to an important class of problems. Specifically, reliability-based design optimization of structural dynamical systems under stochastic excitation. Numerical examples are presented to evaluate the effectiveness of the proposed design scheme.