提取脉冲响应函数的小波变换法及时域法分析

针对有关文献提出的利用小波变换来求取结构系统脉冲响应函数的方法,指出利用小波变换的方法与传统的基于Duharmal积分的时域法具有一致性,并且时域法具有更高的效率。文中简要地介绍了这两种方法的原理,并且在小波分解层数的意义上从多层分解到一层分解以及到时域法,详细分析了利用小波分解的实质,指出时域法是小波分解方法在层数上的延伸,因此是效率最高的。用矩阵广义逆的方法克服了时域法在对输入信号采样时存在的问题。用四自由度的弹簧-质量-阻尼系统进行了仿真,并且在悬臂梁上进行了实验,结果都表明本文得出的结论是正确的。

Analysis of wavelet transform method and time-domain method for extracting the impulse response function of structural systems

The wavelet transform method is used for extracting the impulse response function of a structural system in literatures. This paper points out that the wavelet transform method is consistent with the traditional time-domain method that is based on Duharmal integral, and furthermore, the time-domain method is more efficient than the wavelet transform method. Theories of these two methods are briefly presented in this paper. Relationship of the two methods are analyzed from multi-layer wavelet decomposition to single layer wavelet decomposition and to the time-domain method, and the conclusion is that the time-domain method is the extension of the wavelet transform method in layer number, so it is the most efficient method. The generalized inversion is employed to resolve the problem of the time-domain method in sampling the input signals. Numerical simulation of 4-DOF spring-mass-damper system and experiment carried out on a cantilever beam verify that the conclusions in this paper are correct.