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

• Published in: Computer methods in applied mechanics and engineering Vol. 357; p. 112570
• Main Authors: Meng, Zeng, Zhang, Zhuohui, Zhang, Dequan, Yang, Dixiong
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.12.2019; Elsevier BV
• Subjects: Active learning; AK-ACSLA; Complicated structures; Design optimization; Design parameters; Feedback control; Kriging; Kriging metamodel; Learning; Metamodels; Most probable learning function; Reliability-based design optimization; Teaching methods; Uncertainty optimization; Complicated structures; Reliability-based design optimization; Uncertainty optimization; Most probable learning function; Kriging metamodel; AK-ACSLA
• ISSN: 0045-7825; 1879-2138
• DOI: 10.1016/j.cma.2019.112570

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. •AK-ACSLA is proposed for reliability-based design optimization of complicated structures.•A novel most probable learning function (MPLF) is proposed to perform reliability analysis.•A new chaotic single loop approach is developed based on chaos feedback control theory.•The system’s most probable learning function (SMPLF) is further constructed.•Benchmark and engineering examples illustrate the superiority of the proposed method.