Abstract
Uncertainty-based multidisciplinary design optimization (UMDO) is a practical methodology to cope with uncertainties in the design of sophisticated systems. To alleviate the computing burden, the time-consuming computer simulation models are often replaced by metamodels. Nonetheless, inconsistency between metamodel and simulation model, or metamodel uncertainty, could be introduced into the multidisciplinary design optimization process due to lack of data. The optimal solution may deviate from the true result or even become infeasible if the metamodel uncertainty is neglected. In this research, a new UMDO approach based on polynomial chaos expansion (PCE) for feedback-coupled systems is proposed aiming at improving the accuracy and efficiency of UMDO process under metamodel uncertainty. In this approach, PCE is utilized for the Kriging metamodel uncertainty propagation. The decoupled formulation is used to solve the UMDO. PCE is integrated into the decoupled UMDO framework naturally since the PCE coefficients could be regarded as design variables, which can assure the satisfaction of disciplinary consistency by matching the distribution mean and variance functions of coupling variables under stochastic uncertainty. Then, a modified particle swarm optimization algorithm is proposed to implement the UMDO efficiently. The effectiveness of the proposed approach is verified by a mathematical problem and a fire-detection satellite design problem.
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The authors would like to acknowledge the support from Key National Natural Science Foundation of China (Grant No. U1864211), Natural Science Foundation of Shanghai (Grant No. 21ZR1431500).
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Replication of results
Detailed flowcharts of the proposed methods have been presented in Sects. 3.2 And 3.3, one can follow them and reproduce the results. The Kriging metamodels are built by the toolbox SURROGATES, which can be learned about through the website (http://sites.google.com/site/felipeacviana/surrogatestoolbox). The PCE models are constructed by the toolbox UQLab, which can be learned through the website (https://www.uqlab.com).
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Liu, Z., Song, Z. & Zhu, P. A novel polynomial chaos expansion-based method for feedback-coupled multidisciplinary design optimization under metamodel uncertainty. Struct Multidisc Optim 65, 117 (2022). https://doi.org/10.1007/s00158-022-03207-y
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DOI: https://doi.org/10.1007/s00158-022-03207-y