A sequential optimization framework for simultaneous design variables optimization and probability uncertainty allocatio
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RESEARCH PAPER
A sequential optimization framework for simultaneous design variables optimization and probability uncertainty allocation Hai Fang 1 & Chunlin Gong 1
&
Chunna Li 1 & Yunwei Zhang 1 & Andrea Da Ronch 2
Received: 11 May 2020 / Revised: 16 August 2020 / Accepted: 5 October 2020 # Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In engineering design, the performance of the system and the budget of design uncertainty should be balanced, which means that it is best to optimize design variables and allocate the manufacturing uncertainty simultaneously. This work formulates this problem as an uncertainty optimization problem, where the input uncertainty is modeled by the probability method and both the design variables and the uncertainty magnitude are included in the optimization variables. A sequence optimization framework is proposed to solve the optimization problem. The Taylor-based first-order method is used to translate the probability constraint into a deterministic constraint. A correction coefficient is calculated by the dimensional adaptive polynomial chaos expansion method to improve the accuracy of the uncertainty analysis. The constraint translation and the correction coefficient calculation are executed sequentially. The accuracy and effectiveness of the proposed framework are validated by three benchmark problems, including a mathematical problem, a cantilever I-beam, and a ten-bar truss case. Keywords Uncertainty allocation . Sequence optimization framework . Taylor-based uncertainty analysis . Polynomial chaos expansion . Dimensional adaptive sparse grid
1 Introduction In engineering design, it is essential to understand and predict the range of acceptable disturbance variations in design parameters. There are many sources of uncertainty in design parameters, such as material properties, operation environment, and manufacturing tolerances. In the case of a large disturbance, even small changes in the design parameters may have severe consequences on the required objective function value and the engineering system even may fail to operate. During the design process, the engineer should allocate the acceptable uncertainty amplitude of the design variables to the manufacturer to select the manufacturing method. In general, reducing manufacturing uncertainty will improve Responsible Editor: Nestor V Queipo * Chunlin Gong [email protected] 1
Shaanxi Aerospace Flight Vehicle Design Key Laboratory, School of Astronautics, Northwestern Polytechnical University, Xi’an 710072, China
2
University of Southampton, Southampton, England SO17 1BJ, UK
reliability and budget. Thus, it is better to optimize the design variable and allocate the size of manufacturing uncertainty simultaneously to reduce the budget and maintain reliability. In recent years, the method of considering uncertainty in optimization design has drawn lots of interest, coined uncertainty optimization. Compared to deterministic optimization, uncertainty optimization requires uncertainty analysis in the op
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