A Filter-Based Sample Average SQP for Optimization Problems With Highly Nonlinear Probabilistic Constraints

Abstract

In this work, we develop a filter-based sequential quadratic programming (SQP) algorithm for solving reliability-based design optimization (RBDO) problems with highly nonlinear constraints. The proposed filter-based SQP uses the approach of average importance sampling (AAIS) in calculating the values and gradients of probabilistic constraints. AAIS allocates samples at the limit state boundaries such that relatively few samples are required in calculating constraint probability values to achieve high accuracy and low variance. The accuracy of probabilistic constraint gradients using AAIS is improved by a sample filter that eliminates sample outliers that have low probability of occurrence and high gradient values. To ensure convergence, the algorithm uses an iteration filter in place of the penalty function to avoid the ill-conditioning problems of the penalty parameters in the acceptance of a design update. A sample reuse mechanism that improves the efficiency of the algorithm by avoiding redundant samples is introduced. The “unsampled” region, the region not covered by previous samples, is identified using iteration step lengths, the trust region, and constraint reliability levels. As a result, the filter-based sampling SQP efficiently handles highly nonlinear probabilistic constraints with multiple most probable points or functions without analytical forms. Several examples are demonstrated, and the results are compared with those from first order reliability method/second order reliability method and Monte Carlo simulations. Results show that by integrating the modified AAIS with the filter-based SQP, the overall computation cost of solving RBDO problems can be significantly reduced.