分形粗糙表面特征长度尺度参数小波识别法

Wavelet Method Identifying the Characteristic Length Scale Parameter of Fractal Rough Surface

通过对W-M函数模拟轮廓进行db2小波分解,发现其小波分解系数呈现出明显的规律性这一重要特点,基于此,提出由小波分解来识别粗糙表面轮廓特征长度尺度参数G的一种新方法,并与功率谱密度法等4种方法对W-M函数模拟轮廓、分形布朗运动模拟轮廓以及实际机械加工表面轮廓特征长度尺度参数的计算结果进行对比,结果表明,由于所采用计算方法不同,导致计算结果表现出极大的差异性,不在同一个数量级上。对W-M函数模拟轮廓,提出的小波识别法计算结果最接近于理论值,其余方法在数量级上不同于理论值,都有随分形维数减小而误差增大的趋势。功率谱密度法计算误差最大,远超过理论值,方程组法次之,其次是结构函数法,文献[6]的公式计算误差较小。对分形布朗运动模拟轮廓,小波识别法与文献[6]的公式以及结构函数法计算结果接近。对实际轮廓的计算,小波识别法与文献[6]的公式计算结果相近。总体上,小波识别法与文献[6]的公式计算结果较为接近,说明分形粗糙表面轮廓特征长度尺度参数小波识别法是一种非常有效的方法。

db2 wavelet decomposition of simulated profiles generated by W-M function with known G is executed. From the decomposition results, it is found that the wavelet decomposition parameters have obvious regularity. Based on this, a new approach to identify the characteristic length scale parameter G of a rough surface profile is proposed. The characteristic length scale parameters of the rough surface profile generated by W-M function and fractional brownian motions as well as actual machined surface profile are calculated using the proposed approach. The results are compared with the calculation results of other four kinds of methods such as the power spectral density method. But the calculation results are not of the same order of magnitude from the different methods. For simulated profiles generated by W-M function, the results from the wavelet method presented are the closest to the theoretical value. By contrast the values of the other methods differ by orders of magnitude from the theoretical value, and the errors are shown to increase with the decrease of fractal dimensions. The power spectral density method has the largest error with the calculation exceeding the theoretical value dramatically, and the error of the equations method follows, then structure function method follows. The calculating error of the equation in the literature[6] is smaller. For the simulated profiles generated by fractional brownian motions, the wavelet method and the equation in the literature[6] and structure function method give the similar calculation results as the wavelet method in this paper. For the actual profile, the wavelet method and the equation from the literature[6] give similar results. In general, the wavelet method is similar to the equation from the literature[6] and the validity of the wavelet method is proved.