Enhanced sequential approximate programming using second order reliability method for accurate and efficient structural reliability-based design optimization

Second-order reliability method (SORM) can provide sufficient accuracy for evaluating the probabilistic constraints in reliability-based design optimization (RBDO). However, the application of SORM in RBDO significantly increases the computational burden, as it is necessary to calculate the second-order sensitivities of the performance function. In order to achieve equal efficiency to that of the first-order reliability method-based RBDO approach, enhanced sequential approximate programming (ESAP) is proposed by implementing the SORM-based RBDO method. Based on the diagonal quadratic approximation method, the Hessian matrix is calculated without generating additional computational costs for providing the design sensitivity analysis of probabilistic constraints within the same iterations. Furthermore, ESAP is applied to the reliability-based topology optimization domain, and five numerical benchmark RBDO problems with two complex engineering examples are studied. The proposed ESAP is compared with other RBDO methods, including the reliability index approach, performance measure approach, sequential optimization and reliability assessment method, and SAP, and the results demonstrate the superiority of the proposed ESAP.