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This dissertation addresses the development of a new approach to assess the inter-relationship among dynamic responses, and their sensitivities and robustness in crash simulation applications. Given inherent uncertainties in the laboratory data and appropriate input parameters of the model, this approach has the ability to assess the sensitivity and robustness of the model more efficiently. A systematic approach using proper orthogonal decomposition (POD) is developed to correlate various dynamic responses from simulation output. POD is a mathematical procedure for decomposing high-dimensional data into low-dimensional approximate descriptions, called proper orthogonal mode (POM). In this research, POD is utilized to analyze and assess the dynamic system responses by decomposing multiple time histories into low-dimensional POMs in the space and time domain. The features of POMs are studied to interpret the physical meanings with respect to the crash events. By using POD, a method to assess the inter-relationship of multiple dynamic responses in a crash simulation is developed. POM is also utilized to propagate uncertainties of simulation models and input parameters in conjunction with the design of experiment and stochastic process in an effective and more accurate way. By projecting dynamic responses of each sample onto spatial POMs of the baseline model as a basis function, POMs are grouped and regarded as stochastic processes using the Karhunen-Loève transform. The developed methods are evaluated systematically through the analytical analysis of non-linear functions, and applications of non-linear impact dynamic structural problems. The efficiency and accuracy are verified through a comparative study by comparing the statistical outcome using the developed method with that using the traditional methods. The method developed in this research improves the efficiency and accuracy in the assessment of simulation models by providing: (1) a method to identify and assess the inter-relationship and dominance among multiple dynamic responses, and (2) a method to propagate uncertainty more effectively than the traditional method to evaluate the sensitivity and robustness of dynamic responses.

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