Enriched single-loop approach for reliability-based design optimization of complex nonlinear problems

Abstract

Single-loop approach (SLA) is an efficient reliability-based design optimization (RBDO) method, where the current most probable point (MPP) is located through the gradient information of previous MPP. However, the MPP obtained by SLA may not be accurate for complex nonlinear RBDO problems, which probably causes SLA to be inefficient, converge to the wrong optimal solution or even difficulty in convergence. In this study, an enriched single-loop approach based on enhanced advanced mean value (ESLA-EAMV) is proposed to improve convergence performance of the original SLA for complex nonlinear RBDO problems. First, an enhanced advanced mean value (EAMV) method is developed to find the MPP, where the negative gradient vector of the previous MPP in AMV is replaced by a vector with adaptive step size in EAMV. Then, the proposed EAMV method is integrated into the original SLA to improve the convergence ability of the original SLA. Finally, seven benchmark nonlinear problems are presented to verify the accuracy, efficiency and robustness of the proposed ESLA-MAMV compared with other existing RBDO methods. Comparison results show that the proposed ESLA-MAMV can improve the convergence performance of the original SLA.

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Acknowledgements

The authors would like to greatly appreciate the financial support provided by the National Key R&D Program of China (Grant no. 2017YFB1301300), the National Natural Science Foundation of China (Grant no. 51905146), the Foundation for Innovative Research Groups of the National Natural Science Foundation of China (Grant no. 51621004), the Key R&D Plan Program of Hebei Province (Grant no. 19211808D) and the Natural Science Foundation of Hebei Province (Grant no. E2020202066).

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Yang, M., Zhang, D. & Han, X. Enriched single-loop approach for reliability-based design optimization of complex nonlinear problems. Engineering with Computers (2020). https://doi.org/10.1007/s00366-020-01198-2

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Keywords

  • Reliability-based design optimization
  • Enhanced advanced mean value method
  • Enriched single-loop approach
  • Adaptive step-size update strategy