基于岩石声发射信号的指数衰减型小波基构造

通过对小波变换中原函数与小波基函数关系描述发现，通用小波基函数Morlet小波、Marr小波、DOG小波、Haar小波、Daubechies小波等在满足容许条件的基础上，光滑性和紧支撑性不能同时具备的问题。在用小波分析方法研究岩石声发射信号中，困难的是找到合适的小波基函数。根据试验所得岩石声发射信号特征，采用冲击脉冲作用于二阶弱阻尼振动单位脉冲函数作为岩石声发射信号小波分析的基础函数。为拟合岩石声发射信号，提出3个构造条件，并逐一证明、优化，最后构造出带有岩石特征参数的小波基函数。经应用验证，新构造的小波基函数在处理岩石声发射信号方面比通用小波基函数更具优势，为小波分析在岩石声发射方面应用奠定了理论基础。

Construction of exponential attenuation wavelet basis by characteristics of rock acoustic emission

Through analyzing the relationship of function in wavelet transforms and the wavelet data, and meeting the conditions of the admissibility of Morlet wavelet, Marr wavelet, DOG (difference of Gaussian) wavelet, Haar wavelet and Daubechies wavelet, it is challenging to simultaneously achieve the smoothness and compactness. Moreover, it is difficult to find a suitable wavelet basis function for acoustic emission (AE) signals of rocks by wavelet analysis. According to the characteristics of AE signals of rocks, the impulse function of the 2nd-order underdamp vibration unit pulse is used as the basic function of the wavelet analysis. In order to fit the AE signals, three tectonic conditions are proposed, and the optimization is proved by each other. Finally, the wavelet based functions with rock characteristic parameters are constructed. It is proved that the new wavelet basic function has substantial advantages in comparison with normal wavelet based functions by dealing with AE signals of rocks. This method provides a theoretical foundation for the application of wavelet analysis in the field of rock acoustic emission.