Hybrid adaptive moment estimation based performance measure approach for complex reliability-based design optimization

The complexity of engineering problems often poses challenges, especially in reliability-based design optimization, where the nonlinearity of the performance function is not known in advance. The substantial costs and oscillating results significantly impede the engineering application for highly nonlinear problems. To address this issue, a hybrid adaptive moment estimation (HAME) method is proposed in this work. Given that the performance measure approach is heavily influenced by the gradient of performance function, this method employs the statistical moment information of the gradient, thereby accelerating the search for the minimum performance target point. By combining gradient mean and modified chaos control as new search directions, oscillation phenomena are resolved. To filter the aggregated gradient calculations, the gradient variance and state variable are introduced to approximate the gradients for weakly nonlinear performance functions or in later iterations by the dynamic identification of the nonlinearity of the performance function. The proposed method eliminates the limitation of taking the upper bound for the chaos control factor and addresses the balance issue between efficiency and robustness. The advantages of the proposed method are demonstrated through inverse reliability analysis problems, several highly nonlinear classic RBDO examples, and engineering applications of the crank rod mechanism of an engine.