A decoupling approach for time-dependent robust optimization with application to power semiconductor devices

• Published in: Applied Mathematical Modelling 2021-11, Vol.99, p.129-146
• Main Authors: Huang, Zhiliang, Guo, Xiaohui, Yang, Tongguang, Lei, Shuwen, Zhao, Zhiguo
• Format: Article
• Language: English
• Subjects: Decoupling; Decoupling algorithm; Design optimization; Iterative methods; Mathematical analysis; Power semiconductor device; Power semiconductor devices; Quality loss function: Robust design optimization; Robustness (mathematics); Stochastic processes; Time dependence; Time-dependent problem
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.06.010

•An time-dependent robust design optimization model is formulated based on the expected interval quality loss.•A decoupling framework separates the robustness analysis from the optimization, driving them to alternate for convergence.•A semi-second-order approximation performs the robustness analysis based on the information at the previous iteration.•Two applications of power semiconductor devices involve a real context and high-fidelity finite element models. In this paper, a time-dependent robust optimization model is proposed by introducing a concept of expected interval quality loss as the robustness metric. The purpose is to provide a potential analysis tool for power semiconductor devices involving stochastic processes. Unlike conventional robustness indicators, the metric is formulated by calculating the expectation and variation of the maximal instantaneous quality loss and capturing the auto-correlation of the quality loss over the time interval. In terms of model solving, the time-dependent robust optimization involves a nested optimization, namely the outer design optimization requires to call the inner robustness analysis frequently. It will lead to extremely low computational efficiency. For reducing robustness evaluations, a decoupling framework is proposed to convert the nested optimization into a sequential iterative process of design optimization and time-dependent robustness analysis. For further improving the efficiency of each robustness analysis, a semi-second-order approximation of quality characteristics is created based on the information at the previous iteration. Two engineering applications of power semiconductor devices verify the validity and feasibility of the proposed approach. [Display omitted]