Research on microphone phase array design based on surrogate model
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摘要: 气动声学风洞试验过程中，针对目标声源特性进行麦克风相位阵列改进时，为保证风洞试验效率，必须在较短的时间内完成阵列优化设计工作。为满足这一试验需求，最大限度提升麦克风相位阵列设计效率，引入了基于Kriging代理模型的优化设计方法。采用基于点扩散函数的计算程序进行阵列性能分析，获取阵列最大旁瓣水平和分辨率。通过对样本点响应值进行计算，建立Kriging代理模型，进而以计算速度极高的Kriging代理模型作为阵列性能分析方法开展优化搜索，避免了大量调用阵列性能计算程序导致计算耗时过高的问题，显著提升了麦克风相位阵列设计效率。该阵列设计方法能够有效改善麦克风阵列的测量性能，满足声学风洞试验的特殊应用需求。Abstract: In aero-acoustic wind tunnel tests, the improvement of the microphone phase array according to the noise source features must be conducted as fast as possible to ensure the required efficiency of the tests. An optimization method based on the Kriging surrogate model is proposed in this study. The maximum sidelobe level and the resolution of the microphone phase array are obtained by analyzing the results computed from the point spread function. A Kringing surrogate model is constructed based on the response values computed on sample points. Then the surrogate model was utilized to fast assess the maximum sidelobe level and the resolution of the microphone phase array, which avoided the high computational cost caused by computing the point spread function. This method can improve the performance of the microphone phase array effectively for aero-acoustic wind tunnel tests.
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Key words:
- microphone phase array /
- optimization /
- surrogate model /
- resolution /
- maximum sidelobe level
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图 2 初始阵列与分辨率优化多臂螺旋阵列示意图
Figure 2. Schematic of initial array and resolution optimized multi-arm spiral microphone array
图 3 初始阵列与分辨率优化阵列响应图
Figure 3. Responses of initial array and resolution optimized microphone array
图 6 初始阵列与最大旁瓣水平优化矩形麦克风阵列对比
Figure 6. Comparison of initial array and MSL optimized rectangular microphone array
图 7 初始阵列与最大旁瓣水平优化矩形麦克风阵列响应图
Figure 7. Responses of initial array and MSL optimized rectangular microphone array responses
表 1 Kriging模型预测误差
Table 1. Prediction error of Kriging model
最大旁瓣水平/dB 分辨率/m 阵列性能分析结果 -14.696 0.1467 代理模型预测结果 -14.680 0.1460 相对误差 0.07% 0.45% 
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表 2 分辨率优化阵列设计变量
Table 2. Design variables of resolution optimized array
设计变量 n k a q 变量范围 8~10 0.60~1.40 0.050~0.200 0.600~1.400 初始阵列变量值 9 1.00 0.150 1.000 优化阵列变量值 9 0.89 0.147 0.716
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表 3 初始阵列与分辨率优化麦克风阵列性能
Table 3. Performance of initial array and resolution optimized microphone array
初始阵列 优化阵列 频率/
kHz最大旁瓣水平/dB 分辨率
/m最大旁瓣水平/dB 分辨率
/m1 -17.412 0.388 -14.237 0.341 2 -16.882 0.187 -14.330 0.164 3 -15.535 0.123 -11.868 0.108 4 -15.252 0.089 -11.934 0.080 5 -14.771 0.070 -11.992 0.061 6 -14.188 0.057 -10.235 0.048
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表 4 初始阵列与最大旁瓣水平优化麦克风阵列性能
Table 4. Performance of initial array and MSL optimized microphone array
初始阵列 优化阵列 频率
/kHz最大旁瓣水平/dB 分辨率
/m最大旁瓣水平/dB 分辨率
/m1 -17.412 0.388 -20.537 0.412 2 -16.882 0.187 -21.922 0.198 3 -15.535 0.123 -19.346 0.129 4 -15.252 0.089 -16.105 0.094 5 -14.771 0.070 -15.698 0.074 6 -14.188 0.057 -14.009 0.061
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表 5 初始阵列与优化矩形麦克风阵列性能
Table 5. Performance of initial array and optimized rectangular microphone array
初始阵列 优化阵列 频率
/kHz最大旁瓣水平/dB 分辨率
/m最大旁瓣水平/dB 分辨率
/m1 -12.545 0.302 -16.101 0.320 2 -11.786 0.146 -16.012 0.155 3 -11.798 0.094 -15.450 0.101 4 -11.800 0.068 -15.252 0.073 5 -11.806 0.053 -15.147 0.056 6 -6.523 0.042 -11.271 0.046
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