An approximate model can be used to replace the real model to reduce the computing time and guarantee the feasibility of optimization. However, the approximate model must meet the required accuracy. The higher the accuracy of the approximate model, the higher the reliability of optimization results. In this study, a finite element model for the 40% offset impact of minibus was established, with the thickness of 10 plates in the front of the car body as the design variable and peak acceleration of B pillar lower end, the total mass, and the intrusion volume of dashboard beam, steering column hole, and clutch pedal as the response values. We obtained 70 sample points by the Latin hypercube experimental design method and built approximate models of design variables and the response. Then, we compared the relative error scatter, mean relative error, and decision coefficient of the response surface approximate model, radial basis function network approximate model, kriging approximate model, and orthogonal polynomial approximate model. Results show that the prediction accuracy of the response surface approximate model and radial basis function network approximate model in the peak acceleration of B pillar lower end and the intrusion volume of the steering column hole and clutch pedal does not meet the requirement. The orthogonal polynomial approximate model has a high prediction accuracy in total mass, but its prediction accuracy in other responses does not meet the requirement. In addition, all three approximate models are obviously influenced by the linear relationship between the response and the variables. The kriging approximate model meets the required prediction accuracy of the four responses and is less affected by the linear relationship. Thus, the kriging approximate model is suitable to replace the original model. Then, particle swarm optimization can be performed to optimize the kriging approximate model. This study shows that the kriging approximate model has high fitting precision, and the optimization results reach the expected aim.

The collision of a vehicle is often a process of strong nonlinearity and large deformation, and the finite element method is time-consuming. For this reason, a method of collision inversion research is proposed. Through the definition of the forward and inverse problems, the forward problem is inversely solved from the perspective of the inverse problem, and the collision process can be predicted quickly while the accuracy is ensured. In this paper, the idea of inversion is introduced into the collision test of the front bumper of the vehicle. First, a finite element model is established based on the geometric model of the bumper. The accuracy of the finite element model is verified by comparing the results of the drop weight test with the simulation results of the finite element model. Then, using the built simulation model, spring mass model and drop weight test, the inversion research of vehicle collision and the front bumper of a vehicle is carried out. The inversion research of the bumper first inverts the collision course in the inversion algorithm derived from the vehicle collision, and then compares the collision course derived from the inversion algorithm formula with the simulation test results. The research results show that the change trends of the time-velocity curve and the time-deformation curve obtained by the collision inversion algorithm are basically consistent with the simulation test results, indicating that the collision inversion algorithm can realize the rapid prediction of the collision course and improve derivation efficiency significantly, and it provides a new idea. Finally, under the constant energy condition of the drop weight test E = mgh, through the relationship between energy and deformation, it is concluded that the depth deformation of low-speed collision of the front bumper is greater than that of high-speed collision.