基于参数方程的小波基自适应选择

研究了小波基的参数表达问题，得到包含不同参数的小波基的两个参数方程，提出通过对参数方程中参数的搜索来实现信号的自适应小波基分解。从不同应用角度定义了评价小波基分解效果的两个适应度函数，针对适应度与参数的非线性关系，提出了一种改进的遗传算法对小波基参数方程中的参数进行搜索，同时利用适应度函数对搜索到的小波的分析效果进行评价，当适应度达到最大值时就可得到最佳小波基。利用这一算法实现了一个铣削力信号的自适应小波基分解，并与Daubechies小波的分解结果进行了对比，结果表明自适应小波基能够更充分地分离出信号中的有用信息。

ADAPTIVE SELECTION OF WAVELET BASED ON PARAMETRIC EQUATION

The parametric representation for wavelet base is researched and wavelet base's two parametric equations including different parameters are obtained. It's pointed out that signal's adaptive wavelet decomposition can be realized through parameters being searched in parametric equation. Two fitness functions are defined to appraise wavelet bases' decomposing effect for different applying purpose. The non-linear relationship between the fitness and parameters being taken into account, an improved genetic algorithm is proposed to search parameters in wavelet parametric equation and at the same time the fitness function is. used to appraise the analyzing effect of the searched wavelet base. When the fitness gets the maximum value then the optimal wavelet base can be searched. A milling force signal's adaptive wavelet decomposition is brought into effect by virtue of this algorithm and is compared with Daubechies wavelet's decomposing results. The comparing results show that adaptive wavelet can extract much more useful information from signal than Daubechies wavelet.