多目標基因演算法於揚聲器腔體最佳化之研究

Using Multi-Objective Genetic Algorithm for Loudspeaker Enclosure Optimization

蔣多惟(Do-Wei Chiang)

指導教授 ： 王昭男

國立臺灣大學/工學院/工程科學及海洋工程學研究所/碩士(2012年)

https://doi.org/10.6342/NTU.2012.01187

摘要

本研究主要為利用等效電路法模擬出揚聲器系統的頻率響應曲線，並利用多目標基因演算法，以響應曲線為最佳化目標，對包括前、後腔體組成的揚聲器系統進行輸出效能的最佳化，進而找到最佳的揚聲器系統設計參數；此種設計方法與傳統之試錯法相比，將有利於提升揚聲器系統設計之效率與準確度。
本研究共分為兩部分。首先，利用等效電路法，把揚聲器系統簡化為電機聲等效電路，再利用此三個等效電路導出三組方程式，聯立求解並進而模擬出揚聲器系統的響應曲線。其次，在指定揚聲器單體的情形下，利用Matlab軟體的最佳化工具箱，以多目標基因演算法對揚聲器系統的前腔體與後腔體容積進行最佳化分析，求出響應曲線表現最佳之腔體設計。第二個部分，將挑選三種揚聲器系統設計，製作出實體之揚聲器系統樣本，並利用這些實體樣本在無響室中實際量測出各別的響應曲線。之後，把模擬與量測之曲線做比較，以觀察等效電路法與最佳化方法之可靠性。
研究結果顯示，在固定揚聲器單體及前腔體，並設定後腔體容積為在限制範圍內變動之變數的狀況下，經過最佳化後，揚聲器系統之響應曲線達到廠商標準以上之比例為80%左右。而更進一步只固定揚聲器單體，前腔體及後腔體皆為變數的狀況下，經過最佳化後更可以使達到廠商標準以上的比例為100%。

關鍵字

揚聲器系統 ； 機電聲等效電路法 ； 基因演算法 ； 多目標基因演算法

並列摘要

This thesis is mainly about using multi-objective genetic algorithm to optimize loudspeaker system’s performance by changing the volume of loudspeaker system’s enclosure. The optimization method used in this thesis is more efficient and accurate than the trial-and-error.
This thesis consists of two parts. First, the loudspeaker system was simplified to electro-mechano-acoustic analogous circuits; then, the frequency response of the loudspeaker system can be plotted by calculating the volume velocity in the acoustic analogous circuit. After that, under the circumstances of specified loudspeaker and front enclosure, the best decisions of the volume of the rear enclosure will be chosen by the Non-dominated Sorting Genetic Algorithm-II.
The second part of the thesis is about using real models to find out whether the simulation and the optimization are reliable. To begin, three sample models which follow the design in simulation are made, and each ones’ frequency response are measured in the anechoic room. After that, the measured frequency response and simulated one are compared in order to see whether these two curves match perfectly.
According to the result, under the circumstances of specified loudspeaker and front enclosure, the frequency response of the loudspeaker system can reach to the limitation that the company required by 80% at best after the optimization. Further, if the dimensions of both front and rear enclosures are variable, the frequency response of the loudspeaker system can reach to the limitation by 100% at best.

並列關鍵字

loudspeaker system ； EMA analogous circuits ； genetic algorithm ； NSGA-II

參考文獻

[21] 林豐澤, "演化式計算下篇：基因演算法以及三種應用實例," 智慧科技與應用統計學報, 第三卷，第一期, 2005.

[5] R. H. Small, "Direct-Radiator Loudspeaker System Analysis," Journal of Audio Engineering Society, vol. 20, 1972.

[6] R. H. Small, "Closed-Box Loudspeaker Systems," Journal of Audio Engineering Society, vol. 20, 21, 1972.

[7] R. H. Small, "Vented-Box Loudspeaker Systems," Journal of Audio Engineering Society, vol. 21, 1973.

[8] H. F. Olson, Elements of Acoustical Engineering. New York: D. Van Nostrand Company, Inc., 1948.