Advanced mode analysis for crash simulation results

Potential scatter of simulation results caused, for example, by buckling, is still a challenging issue for predictability. Principle component analysis (PCA) and correlation clustering are well-known mathematical methods for data analysis. In order to characterize scatter, methods of these types were applied to the ensemble of simulation results resulting from a number of runs using all node positions at all time steps. For industrially relevant problems, the size of the resulting data base is larger than 100 GBytes (even if compressed by FEMzip1[7]) . As a result of applying the methods, the major components and influences dominating the differences between the simulation results are available. PCA is a mathematical method which treats data bases globally, without built-in a-priori, phys ical knowledge. 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. DPCA, however, should be combined with clustering methods, for instance, in order to preprocess the data base. Correlation clustering is an efficient method for the identification of strongly correlated components in bulky data. This method can be applied for causal analysis of large ensembles of even highly resolved crash simulation results. It groups all strongly correlated data items together, separates the model to a few such clusters and represents a structure of correlators in the model at a glance. The resulting so-called partition diagram and a series of appropriate visualizations can be used for analysis directly. Computed clusters can be used for DPCA, in addition. The paper introduces the approaches and shows first results for an industrial model.