Advanced Mode Analysis for Crash Simulation Results

Potential scatter of simulation results caused for exampleby buckling, is still a challenging issue for the predictability. Principle component analysis (PCA) is a well-known mathematical method for data analysis. In order to characterize scatter PCA analysis was applied to the simulation results from a number of runs using all node positions at all time steps. For industrials relevant problems the size of the data base is larger than 100 GBytes (even, if compressed by FEMzip[7]) . As a result the major components dominating the differences between the simulation results are available. Since PCA is a mathematically based method, the selected modes do not separate different physical effects like buckling at different parts of the model. PCA rather tries to maximize the variations by combining several physical effects into one mode. Difference PCA(DPCA) applies PCA analysis to the results for each part and time step. By analysis of the related covariance matrices, the local dimension of the scatter subspace can be identified and correlation between the scatter at different places can be analyzed. Using DPCA, different origins of scatter can be identified and physically meaningful components can be determined. The paper introduces the approach and shows results for an industrial model. Introduction In [8] and [4] scatter of the Chrysler Neon model and a model of BMW were analyzed in detail. Buckling and contact heuristics were identified as major sources for scatter. For the design and optimization of car models it is very helpful to deal with a simulation model, which generates similar results even if slight changes of the model are performed. In order to investigate reasons for scatter several optimization tools like LS-OPT [6] support the generation of variants as well as the analysis of scatter of key results (like intrusion). In addition LS-OPT also supports correlation analysis between changes model parameters and field results (like displacements at various nodal points) and various functions to visualize correlations and scatter of simulation results. In [4] a new methods using correlation between displacements of nodes were introduced, which allow to find the origin of scatter in crash simulation. All these methods work, if there is a single dominating source of scatter but fail to separate the impact of several sources. PCA Analysis for Crash Simulation Results According to [3] Principle Component Analysis (PCA) was introduced by Pearson in the context of biological phenomena [5] and by Karhunen in the context of stochastic processes [2]. 1 FEMzip is a registered trademark of Fraunhofer Gesellschaft, Munich Automotive (3) 11 International LS-DYNA Users Conference 18-16 In [1] PCA was applied to full crash simulation results. Let be the displacement of simulation run i out of n simulation runs at node p and time t. If is the mean of all simulation runs, the covariance matrix C can be defined as