Abstract
To improve the computational cost and accuracy of approximate-based multi-objective optimization problems in engineering, an adaptive RBF neural network (ARBFNN) method integrating RBF neural network model, fuzzy subtractive clustering (FSC) sequence sampling method and non-dominated sorting genetic algorithm (NSGA-II) is proposed. To solve the problem that the number of new sample points is difficult to determine, FSC sequence sampling is proposed to select the clustering center points as newly added sample points. First, the ARBFNN method is verified by the five test functions. The results show that the ARBFNN method is significantly better than static RBFNN model based on multi-objective optimization (SRBFNN) in terms of global convergence and efficiency performance, and the other two adaptive approximate optimization methods in terms of overall efficiency. Based on the above, the accuracy and efficiency of ARBFNN method are very high. Finally, the method is applied to an engineering example: the lightweight and crashworthiness design of floor rails. The cab model coupled with implicit parameterized floor rails model is built using the SFE-CONCEPT software to achieve collaborative optimization design of shape-size-material. The optimization results show that the ARBFNN method can guarantee the error of the approximate optimal solution and the finite element solution (expensive solution) within 2%, so the accuracy of highly nonlinear (finite element analysis of collision conditions) approximate optimization is improved. Hence, the proposed ARBFNN method is feasible and effective in solving complex and expensive engineering optimization problems.
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This work was supported by the National Natural Science Foundation of China [grant number 51975244] and Graduate Innovation Fund of Jilin University [grant number 101832020CX131].
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Wang, D., Xie, C. & Wang, S. An adaptive RBF neural network–based multi-objective optimization method for lightweight and crashworthiness design of cab floor rails using fuzzy subtractive clustering algorithm. Struct Multidisc Optim 63, 915–928 (2021). https://doi.org/10.1007/s00158-020-02797-9
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DOI: https://doi.org/10.1007/s00158-020-02797-9