Microstructural topology optimization for minimizing the sound pressure level of structural-acoustic systems with multi-scale bounded hybrid uncertain parameters

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Abstract This paper mainly provides a robust microstructural topology optimization method for minimizing the sound pressure level (SPL) of the structural-acoustic system with multi-scale bounded hybrid uncertainties. During the microstructural topology optimization process, both the uncertainty at macro-scale that comes from the physical parameters of the structural-acoustic system and the uncertainty existed in the constituent material properties of the microstructure are taken into account and handled by the bounded hybrid uncertain model, in which the uncertain parameters are treated as either bounded random variables or interval variables. The homogenization-based Gegenbauer polynomial expansion method (HGPEM) is introduced to calculate the sound pressure of the bounded hybrid uncertain structural-acoustic system. On the basis of the HGPEM, the microstructural topology optimization is conducted through the enhanced genetic algorithm (GA) with adaptive crossover and mutation probability. Two numerical examples are used to demonstrate the capabilities and efficiency of the presented robust microstructural topology optimization method. The results indicate that the robust optimum design considering multi-scale bounded hybrid uncertainties can achieve better performance than the deterministic optimum design.