In vehicular crash reconstruction, software packages such as PC-Crash, SMAC (Simulation Model of Automobile Collisions), WinSmash and HVE (Human Vehicle Environment) use physical evidences such as tire marks along with measurements of the deformed vehicles and photographs of the accident scene to determine the crash energy, impact velocity, and Principal Direction Of Force (PDOF). However, accurate determination of these parameters requires more sophisticated numerical methods, such as Finite Element (FE) modeling. At present, multiple runs of FE models need to be performed on a trial-and-error basis before the model predicted results are consistent with the actual ones. An optimization method to quickly and accurately determine key sensitive parameters in vehicular accident reconstruction is desired. We propose the use of Kriging model and sequential quadratic programming in conjunction with Latin Hypercube Sampling (LHS) to minimize the time needed for reconstruction and minimize the disparity between the actual and FE model predicted vehicular deformations. A selected number of modeling parameters, namely the velocity of impact, PDOF and initial impact position, are varied using this optimization approach until the deformation of six points measured on the impacted vehicle closely matches those measured in real world case. The optimization is performed in two stages. In the first stage, an approximated model was created by simplifying detailed FE models of the vehicles involved to reduce the simulation time without sacrificing accuracy. In the second stage, an assessment index ‘E’, the objective function, is maximized. To improve computational efficiency, the Kriging model is employed. The sampling points are distributed uniformly over the entire design space using the LHS. For evaluating the approximated model’s performance, the regression parameter is used as the error indicator. The objective functions based on approximated models are optimized using a sequential quadratic programming which has a higher efficiency and better convergence. Results show that through the application of this method, the deformations of the key points are in accord to the measured deformation within a small window of variability. The average difference between the deformation measured from the actual crash and that calculated from FE simulation using the optimum parameters as inputs is around 31 mm. The difference in the assessment index calculated from FE simulation with optimal assessment parameters and that from the Kriging model is only 1%. The proposed optimization methodology is a good tool to promptly reveal key parameters in a crash while simultaneously providing scientific basis for crash reconstruction.
Parameter Analysis and Optimization of Annular Jet Pump Based on Kriging Model
