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斐波那契网格传声器阵列多目标结构优化研究

Multi-objective Structural Optimization Of Fibonacci Grid Microphone Array

  • 摘要: 针对不同关注频率下声源定位对传声器阵列性能需求的差异,提出一种基于改进第二代非支配排序遗传算法(non-dominated sorting genetic algorithm II,NSGA-II)的斐波那契网格传声器阵列多目标结构优化方法。以最大旁瓣级和主瓣宽度为目标函数,将控制阵元启停状态作为决策变量,通过多目标进化获得由多个高性能阵列结构组成的解集,并利用个体选择函数获得关注频率下性能更优的改进阵列。最后通过蒙特卡洛仿真评估阵元位置误差下该方法的鲁棒性,并探讨了向大规模阵列推广的可能性。研究结果表明,在2000 Hz 条件下,改进阵列在最大旁瓣级约为−10.42 dB的条件下,将主瓣宽度从54°降低至44°,降幅约为18.5%,该方法仅通过控制阵元启停,实现了针对特定频率的阵列结构优化。

     

    Abstract: To address the differing performance requirements of microphone arrays for sound source localization at various frequencies of interest, a multi-objective structural optimization method for Fibonacci-grid microphone arrays—based on an improved Non-dominated Sorting Genetic Algorithm II (NSGA-II)—is proposed. Taking the maximum sidelobe level and mainlobe width as objective functions and the on/off states of array elements as decision variables, the method yields a Pareto-optimal solution set comprising multiple high-performance array configurations via a multi-objective evolutionary process. An individual selection function is then applied to identify an optimized array configuration that exhibits superior performance at the target frequency. Monte Carlo simulations are further conducted to evaluate the robustness of the proposed method against array element position errors, and the feasibility of scaling it up to larger arrays is discussed. Numerical results show that, at 2000 Hz, the optimized array reduces the mainlobe width from 54° to 44° (a reduction of approximately 18.5%) while maintaining the maximum sidelobe level at approximately −10.42 dB—demonstrating that the proposed method enables frequency-specific structural optimization of the array through binary element activation (i.e., switching elements on or off) alone.

     

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