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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。
Based on the description of the relationship between primitive function and wavelet basis function in wavelet transform, it is found that the general wavelet basis function Morlet wavelet, Marr wavelet, DOG wavelet, Haar wavelet and Daubechies wavelet can not meet the requirements of smoothness and tight support The problem. In the wavelet analysis of rock acoustic emission signal, the difficulty is to find a suitable wavelet basis function. According to the acoustic emission characteristics of the rock, the impulse function is applied to the pulse function of the second-order weakly damped vibration unit as the basic function of the rock acoustic emission signal wavelet analysis. In order to fit the rock acoustic emission signal, three structural conditions are proposed, and each one is proved and optimized one by one. Finally, a wavelet basis function with rock characteristic parameters is constructed. The new constructed wavelet basis function has more advantages than general wavelet basis function in processing acoustic emission signals of rock, and has laid a theoretical foundation for the application of wavelet analysis in rock acoustic emission.