M. De Munck, Efficient optimisation approaches for interval and fuzzy Finite Element Analysis, 2009

Abstract

Today, detailed numerical models of new designs and their environments and advanced simulation techniques allow designers to accurately predict the behaviour of these designs in their environments. These virtual prototypes can not only be used in the design validation stage, as physical prototypes, but also in earlier stages of the design.Unfortunately, numerical models and numerical simulation inevitably introduce uncertainties. Although some uncertainties can be reduced by using more accurate models and more advanced simulation techniques, other uncertainties, especially these caused by a lack of knowledge of a lack of information in the design stage and these caused by variability in the production stage, are inherent to the design process and the design itself. Therefore, non-deterministic numerical analysis is gaining more and more attention. But despite numerous research efforts, the high computational cost associated with these non-deterministic techniques is still a bottleneck to their widespread use.This dissertation focuses on efficient implementations of non-deterministic numerical analysis methods that use non-probabilistic parameter descriptions (intervals and fuzzy numbers). Two novel methods, both combining the global optimisation based approach for interval and fuzzy analysis with the response surface methodology, are proposed. The first method is an adaptive optimisation algorithm based on linear regression based response surfaces and the second method is an adaptive optimisation algorithm based on Kriging response surfaces.The applicability, efficiency and accuracy of these methods is illustrated on a number of transient and steady state structural dynamic analyses on models ranging from simple academic models to industrially sized models.

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Order Code

Code: 09D03