Crashworthiness Design Optimization Using Surrogate Models
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Despite the advances in computer technology, the enormous computational cost associated with the large-scale and complex nonlinear crashworthiness simulations renders it to be impractical to rely exclusively on computer simulations for crashworthiness design optimization. A preferable strategy is to employ the computational efficient surrogate model in lieu of the expensive simulations to facilitate the optimization process and design concept exploration. An added advantage of the surrogate models is that they tends to eliminate the high-frequency numerical noise which may hinder the performance of the direct gradient-based optimization technique by constructing smooth crash responses in the crashworthiness analysis. Even thought the Design of Experiments with Response Surface Methodology technique has shown to be a promising way for crashworthiness design optimization over the years, it is still hampered by large number of function evaluations for large number of design variables or low numerical accuracy for small sample sizes. In this dissertation, we propose and develop an effective methodology based upon the sequential regularized multiquadric with output space mapping to reduce the computational cost. The proposed method overcomes the ill-conditioning of the coefficient matrix in the generalized multiquadric function for duplicate data when approaching to the optimal design. Unlike the traditional DOE/RSM methodology, the sampling point is added sequentially and thus becomes more manageable to deal with problems involving large number of design variables. Several numerical examples are employed to demonstrate the effectiveness and robustness of the methodology, including a large-scale full vehicle frontal impact problem and a helicopter skid landing gear hard landing problem. It is shown that the proposed SRMQ/OSM method reduces the computational cost by 50~70% as compared to the traditional DOE/RSM based methodology or direct gradient-based optimization technique. In addition, this dissertation investigates and implements the Implicit Space Mapping optimization algorithm for solving the nonlinear crashworthiness design optimization problems.