Numerical design methods based on deterministic multi-objective optimization provide − for conflicting objective functions − a Pareto-optimal set including diverse trade-off solutions. Based on the visualization of the set in the objective space − the Pareto-front − the decision maker is able to choose a satisfying design. Though, the presence of uncertain input variables in the optimization task requires a new concept for the identification of the Pareto-front and the projection of uncertainty within the front. In this contribution, an approach for considering the epistemic uncertainty within the evolutionary multiobjective optimization method based on Nondominated Sorting Genetic Algorithm (NSGA-II) is presented. The description of uncertainty occurs within the framework of the Fuzzy set theory. The proposed approach is coupled to the Finite Element Analysis and response surface approximations based on artificial neural networks.
This publication presents a numerical approach for analyzing tires based on multiobjective optimization, with particular consideration of uncertainties. Within the optimization, which uses evolutionary algorithms, the evaluation of a three-dimensional, finite element tire model at steady-state rolling is performed. To obtain a reliable and high-quality design, data uncertainty caused, e.g., by variation in production conditions of the tire components, as well as incomplete information concerning loading, have to be considered. Among several design goals, this study looked at durability as an example. An improvement is achieved by the consideration of two objective functions: one focusing on reducing wear, and the other on providing resistance to fatigue. In addition, the proposed optimization measures robustness implicitly. A tire model is regarded as robust when large variations of the uncertain influencing factors mentioned, e.g., loading or material properties, lead to only minor variations in uncertain structural responses, e.g., strains, stresses, or contact pressures. To improve the numerical efficiency of the proposed design approach, a response-surface approximation, based on artificial neural networks, is applied.
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