Statistics and Non-Linear Sensitivity Analysis with LS-OPT and D-SPEX

For stochastic simulations usually many simulations are performed, therefore much information is available for the simulation engineer. In order to evaluate this information and to assess the results of stochastic investigations software tools such as LS-OPT and D-SPEX are available. Good and clearly arranged presentation of the results is important, so that the engineer really benefit from the data mining. D-SPEX is intended to provide features that are not currently implemented in the LS-OPT viewer. Therefore, it is a complement to the visualization capabilities of LS-OPT. Its primary focus is on the visualization of meta-models although it also provides features to visualize stochastic results. D-SPEX is also thought of as a testing platform for new features that might evolve in LS-OPT. By opening the command file of LS-OPT, D-SPEX reads all data of the optimization or robustness project. The current version of D-SPEX is fully compatible with LS-OPT version 3.3. For more information on the features of D-SPEX, see [12]. Opitmization (1) 10 International LS-DYNA Users Conference 4-2 Introduction In combination with LS-OPT, D-SPEX supports CAE engineers in post-processing of stochastic analysis results. In the field of stochastic analysis D-SPEX is a valuable and easy to use tool. Tasks in stochastic analysis that can be solved with LS-OPT and D-SPEX can be arranged in the following groups: Uncertainty propagation within a stochastic analysis of a mechanical model the randomness of structural parameters (input parameters) is propagated through the computational model. Randomly distributed responses (model output) are obtained as result, see Figure 1. Together with the obtained results statistical methods allow now, e. g., the computation of the mean value and variance and the determination of distribution types of the considered random responses. Sensitivity analysis determines the significance/contribution of the structural parameters onto to considered responses. The identification of non-relevant and relevant structural parameters for model reduction purposes is one of the major tasks. The sensitivity analysis may also improve the understanding of the model behavior and may clarify interactions among input parameters. Structural reliability analysis with respect to constraints (failure, damage, requirements ...). Visualization of response variations by fringing statistical results on the FE-Model. This is possible by utilizing the DYNAstats capabilities in LS-OPT. This paper focuses in particular on the statistical analysis / post-processing of random results and the provided sensitivity analysis facilities. The sensitivity analysis is considered in view of the nonlinearity of the underling computational model (FE model). Figure 1 Uncertainty propagation in probabilistic mechanics 10 International LS-DYNA Users Conference Opitmization (1) 4-3 Statistical post-processing in D-SPEX Several statistical techniques summarize and describe an obtained data collection. These techniques are notional aggregated to the descriptive statistics techniques. They form the basis of virtually every quantitative analysis of data. The most frequently used and probably most beneficial statistical measures are introduced briefly and can be evaluated with D-SPEX. They are presented to the user in a clear and visually attractive from. Mean Value, Standard Deviation / Variance, Anthill Plots Mean value and standard deviation are basic features of the data set. They give a felling what can be expected and with which spreading. The variance is determined by (1) where denotes the expected value of the random variable . The standard deviation is defined as square root of the variance