An active learning method combining Kriging and accelerated chaotic single loop approach (AK-ACSLA) for reliability-based design optimization

Abstract

To achieve an optimal design of complicated structures with stochastic parameters, the reliability-based design optimization (RBDO) usually needs to handle the nested double optimization loops, which results in unbearable computational cost. In this paper, a new active learning method for RBDO combining with Kriging metamodel and accelerated chaotic single loop approach (AK-ACSLA) is developed, in which the most probable learning function (MPLF) is proposed to search the most probable point instead of the limit state function in entire design space with an active learning behavior. To ensure the high efficiency, the system’s most probable learning function (SMPLF) is further constructed to solve the RBDO problem of series system with multiple probabilistic constraints, and then the ACSLA is proposed by taking full advantage of chaos feedback control methodology for guaranteeing the validity of AK-ACSLA. Nonlinear mathematical examples and complex RBDO engineering examples illustrate the high efficiency and accuracy of AK-ACSLA through comparison with both existing gradient-based methods and active learning methods.