Singularity distribution entropy analysis of impulsive acoustic signals
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摘要: 为了对低信噪比复杂环境下脉冲信号的奇异性差异进行有效的分析和标定，提出了一种基于模极大值理论的奇异性分布熵特征分析模型。首先对脉冲信号进行归一化并进行小波变换，计算各尺度下模极大值及其特定分布，可以体现具有奇异性差异的模极大值曲线族。为定量描述这种差异性，用熵值表达构成模极大值曲线族的模极大值点分布，并构建能有效分析脉冲信号奇异性差异的奇异性分布熵特征模型。该模型能对低噪比下信号的奇异性差异进行刻画。实验结果表明，在信噪比为−6 dB的环境下对典型的直升机脉冲信号（桨/涡干扰信号和高速脉冲信号）进行分析，能够得到89.25%和87.63%的正确率。Abstract: In order to effectively analyze and calibrate the singularity difference of impulsive acoustic signals in complex environment with low signal-to-noise ratio, a singularity distribution entropy features analysis model based on the mode maximum theory is proposed. Firstly, the impulsive signal is normalized and wavelet transform is carried out to calculate the mode maximum and its specific distribution at each scale, which can reflect the family of mode maximum curves with singular differences. In order to describe the difference quantitatively, entropy is used to describe the distribution of the maximum points which constitute the family of modal maximum curves, and a singular distribution entropy feature model which can effectively analyze the singularity difference of impulsive signals is constructed. The model can describe the singularity difference of signals at low signal-to-noise ratio. Experiments show that the accuracy of 89.25% and 87.63% of typical helicopter impulsive signals (blade-vortex interaction signals and high-speed impulsive signals) can be obtained when the signal to noise ratio is −6dB.
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图 1 BVI和HSI信号的时域模拟信号、模极大值曲线及其衰减曲线图
Figure 1. Time domain analog signal of BVI and HSI signal, mode maximum curve and its attenuation curve
图 2 一阶高斯小波基函数$\varphi (t)$和其原函数$\theta (t)$的时域图
Figure 2. Time domain diagram of the first order Gaussian wavelet basis function $\varphi (t)$ and its antiderivative function $\theta (t)$
图 5 小波基函数为一阶高斯小波时BVI和HSI信号的模极大值线及其衰减曲线
Figure 5. The modal extremum line and attenuation curve of BVI and HSI signal when the wavelet basis function is first order Gaussian wavelet
图 6 BVI/HSI信号低信噪比下的时域信号及其对应的模极大值衰减曲线
Figure 6. Time domain signal diagram and attenuation curve of corresponding mode maximum line under low SNR of BVI and HSI signals
图 7 二阶高斯小波基函数时域图
Figure 7. Time domain diagram of second order Gaussian wavelet basis function
图 8 Gaus1和Gaus2小波基函数下BVI/HSI信号的模极值曲线衰减图
Figure 8. Attenuation diagram of maximum modulus curve of BVI/HSI signal under Gaus1 and Gaus2 wavelet basis functions
图 9 不同参数下的实测BVI和HSI信号
Figure 9. Measured BVI and HSI signals with different parameters
图 10 BVI和HSI信号在不同信噪比下的Lipschitz指数值
Figure 10. Lipschitz index values of BVI and HSI signals at different signal-to-noise ratios
图 11 BVI和HSI信号的奇异性分布熵值
Figure 11. Singularity distribution entropy of BVI and HSI signal
表 1 BVI/HSI信号在Gaus1和Gaus2小波基函数时奇异性分布熵大小关系
Table 1. Singularity distribution entropy of BVI/HSI signals in Gaus1 and Gaus2 wavelet base functions
奇异性分布熵 小波基函数 ：Gaus1 小波基函数 ：Gaus2 BVI信号 大 小 HSI信号 小 大 
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