A novel performance measure approach for reliability-based design optimization with adaptive Barzilai-Borwein steps

Traditional mean value methods of the performance measure approach (PMA) for the reliability-based design optimization (RBDO) problem may experience nonconvergence or require too many iterations to evaluate the performance measure in the face of highly nonlinear problems. This paper presents a new mean value method of PMA to address these challenges. First, an innovative descent direction of the performance function, tangent to the sphere of the target reliability index, is established to narrow down the search range of the minimum performance target point (MPTP) in iterations. Second, by taking the gradients in the previous and current iteration into account, the Barzilai-Borwein approach is employed to determine the optimal step size in iterations searching for the MPTP at a faster speed. Third, the nonmonotone line search technique is applied to ensure global convergence. Compared with some other existing mean value methods, the performance of the proposed algorithm is evaluated through six illustrative examples. Results indicate that the proposed algorithm improves the robustness and accuracy of mean value methods in addressing the performance function with multiple local optima and performs more efficiently for practical RBDO problems involving finite element analysis and dynamic analysis.