Department of Mathematical Information Technology, University of Jyväskylä, P.O. Box 35, FIN-40014 Jyväskylä, Finland.
J Acoust Soc Am. 2011 Sep;130(3):1359-69. doi: 10.1121/1.3621119.
This paper considers the combined use of a hybrid numerical method for the modeling of acoustic mufflers and a genetic algorithm for multiobjective optimization. The hybrid numerical method provides accurate modeling of sound propagation in uniform waveguides with non-uniform obstructions. It is based on coupling a wave based modal solution in the uniform sections of the waveguide to a finite element solution in the non-uniform component. Finite element method provides flexible modeling of complicated geometries, varying material parameters, and boundary conditions, while the wave based solution leads to accurate treatment of non-reflecting boundaries and straightforward computation of the transmission loss (TL) of the muffler. The goal of optimization is to maximize TL at multiple frequency ranges simultaneously by adjusting chosen shape parameters of the muffler. This task is formulated as a multiobjective optimization problem with the objectives depending on the solution of the simulation model. NSGA-II genetic algorithm is used for solving the multiobjective optimization problem. Genetic algorithms can be easily combined with different simulation methods, and they are not sensitive to the smoothness properties of the objective functions. Numerical experiments demonstrate the accuracy and feasibility of the model-based optimization method in muffler design.
本文考虑了混合数值方法在声学消声器建模中的综合应用和遗传算法在多目标优化中的应用。混合数值方法提供了在具有不均匀障碍物的均匀波导中声传播的精确建模。它基于将波导均匀部分中的基于波的模态解与非均匀分量中的有限元解进行耦合。有限元方法提供了复杂几何形状、变化的材料参数和边界条件的灵活建模，而基于波的解则导致了非反射边界的精确处理和消声器传输损耗 (TL) 的直接计算。优化的目标是通过调整消声器的选定形状参数，同时在多个频率范围内最大化 TL。该任务被表述为一个多目标优化问题，目标取决于模拟模型的解。NSGA-II 遗传算法用于解决多目标优化问题。遗传算法可以很容易地与不同的模拟方法相结合，并且它们对目标函数的光滑性属性不敏感。数值实验证明了基于模型的优化方法在消声器设计中的准确性和可行性。
