Abstract The paper shows how to use a genetic algorithm to design quasi one-dimensional structures with given properties. The superlattices were surrounded by water and made of epoxy resin and glass, with a layer thicknesses selected in such a way that a phononic bandgap occurs in the frequency range of acoustic waves. Multilayer transmission was calculated using the Transfer Matrix Method algorithm. In order to determine the optimal objective function for the genetic algorithm, the entire space of the possibility of the layers’ distribution for a six-layer structure was analyzed. The spread of the transmission integral values even for the 6-layer structure was significant and ranged from 11.9% to 81.5%. Minimizing the value of the transmission integral as an objective function could lead to a large number of high transmission peaks with a small half width. It allowed the determining of the optimal objective functions for minimizing transmission in a given frequency range, and another allowing for its maximization. The phase diagram of the solution space for the transmission integral from the integral of the absolute value of the transmission functions derivative was determined. Transmission of the most and the least optimal six-layer structures was shown depending on the assumed objective function. Then, the analysis of fifteen and thirty-layer structures was carried out. From the dependence of the objective function values for the best individuals for each generation, it was determined that despite carrying out a thousand iterations, the stable state was determined before reaching 250 iterations of the algorithm, and thus the optimal structure was determined. The transmissions ratio of analyzed structures in the studied frequency range (up to 20 kHz) to full transmission (without structures) in this acoustic frequency range for the analyzed optimal 6, 15 and 30-layer structures were 16.78%, 9.6% and 4.41%, respectively.

中文翻译：

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基于遗传算法的准一维声滤波器结构优化

摘要 本文展示了如何使用遗传算法设计具有给定特性的准一维结构。超晶格被水包围，由环氧树脂和玻璃制成，层厚的选择方式使得声子带隙出现在声波的频率范围内。使用传输矩阵方法算法计算多层传输。为了确定遗传算法的最优目标函数，对六层结构的层分布可能性的整个空间进行了分析。即使对于 6 层结构，透射积分值的分布也很显着，范围从 11.9% 到 81.5%。最小化作为目标函数的透射积分值可能会导致大量具有小半宽的高透射峰。它允许确定在给定频率范围内最小化传输的最佳目标函数，另一个允许其最大化。由传递函数导数的绝对值的积分确定传递积分的解空间的相图。根据假定的目标函数，显示了最佳和最差六层结构的传输。然后，进行了十五层和三十层结构的分析。根据每一代最佳个体的目标函数值的依赖性，可以确定，尽管进行了一千次迭代，在算法迭代250次之前就确定了稳定状态，从而确定了最优结构。对于所分析的最佳 6、15 和 30 层结构，在研究频率范围内（高达 20 kHz）的分析结构与在该声频范围内的全传输（无结构）的传输比分别为 16.78%、9.6% 和 4.41% ， 分别。