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

In this work we extend a filter-based sequential quadratic programming (SQP) algorithm to solve reliability-based design optimization (RBDO) problems with highly nonlinear constraints. This filter-based SQP uses the approach of average importance sampling (AAIS) in calculating the values and the 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 to eliminate sample outliers that have low probability of occurrence and high gradient values. To ensure convergence, this algorithm replaces the penalty function by an iteration filter to avoid the ill-conditioning problems of the penalty parameters in the acceptance of a design update. A sample-reuse mechanism is introduced to improve the efficiency of the algorithm by avoiding redundant samples. ‘Unsampled’ region, the region that is not covered by previous samples, is identified by the iteration step lengths, the trust region, and constraint reliability levels. As a result, this filter-based sampling SQP can efficiently handle highly nonlinear probabilistic constraints with multiple most probable points or functions without analytical forms. Several examples are demonstrated and compared with FORM/SORM and Monte Carlo simulation. Results show that by integrating the modified AAIS with the filter-based SQP, overall computation cost can be significantly improved in solving RBDO problems.