Design for crashworthiness optimization using the meta-modeling technique with extended-HCA framework 2020-01-0627
In most engineering design problems, it is either difficult or impossible to directly couple the analyzing tool (e.g., finite element analysis) with the optimization algorithms. For instance, in the design optimization for crashworthiness, the implicit relationship between the design parameters and the crash indicators are not generally available. Moreover, the computational cost associated with repeated explicit finite element analysis of a crash simulation is substantial. Therefore, surrogate modeling or meta-model-based analysis have been widely used to solve such optimization problems. Among the different techniques, Kriging meta-model has shown good accuracy for highly non-linear problems. In this study, the extended Hybrid Cellular Automaton (xHCA) framework is employed to design for targeting desired crash indicators (maximum intrusion and maximum deceleration). To this end, the volume fraction and the design time are used as the main meta-parameters to create a purposive design of the experiment. The proposed method is implemented into the numerical example of B-pillar under a side rigid wall impact. The set of 24 experiments are used as training points to generate surrogate models. Therefore, the meta-models can predict the design parameters (volume fraction and design time) corresponding to the desired crash indicators. The best regression and correlation functions are determined using cross-validation of Kriging models. Also, reduced design of the experiment with four function evaluation is utilized to target a locally optimal point. The minimum Euclidean distance between the target and the interpolation lines of crash indicators are calculated, and the corresponding design parameters are predicted using the meta-models. The training points are iteratively updated, and the interpolation lines are modified based on a linear or polynomial approach. The accuracy of the different methods and their computation cost are compared.
Sajjad Raeisi, Andres Tovar, Chandan Mozumder, Simon Xu
Purdue University-West Lafayette, Indiana University-Purdue University Indianapolis, General Motors LLC