巴特沃思小波在表面形貌信号分离中的应用

Application of Butterworth wavelet to surface topographic signal separation

为了快速准确地分析工程表面,提出了一种基于巴特沃思小波的滤波方法。首先,讨论了小波滤波器的低通幅度传输特性,并以此作为选择适合表面形貌分析小波滤波器的依据。然后,介绍了巴特沃思小波滤波器的构造原理,并给出了它的快速实现算法;综合其优良的传输特性和高效的实现算法,以巴特沃思小波作为表面分析的滤波器,对实际表面轮廓进行了多层分解。最后,利用巴特沃思小波建立了表面轮廓评定的基准线,并给出了确定小波分解层数的方法。实验结果表明,巴特沃思小波能够快速准确地实现表面轮廓的多尺度分析,稳定可靠地提取表面中线;在普通计算机上提取11200点数据表面中线仅耗时60ms,利用该中线计算所得R值相对误差仅比利用高斯中线所得R值相对误差大0.12%。

In order to analyze engineering surfaces fast and accurately,a new filtering approach based on Butterworth wavelet is proposed.Firstly,the transmission characteristic of a low-pass filter based on a wavelet is discussed,then it is taken as a primary reference to choose an appropriate wavelet base for surface analysis.The construction principle of the Butterworth wavelet filter is briefly introduced,and a fast algorithm for implementing this filter is illuminated.By combining the eminent transmission characteristic and efficient algorithm,the Butterworth wavelet is selected as the analyzing filter to decompose the surface profile with arbitrary orders.Finally,the Butterworth wavelet is also applied to calculating the reference line for profile evaluation and to offering a method to determine decomposed orders.The experimental results indicate that the Butterworth wavelet can achieve the multi-scale analysis of surface profile quickly and accurately and can extract its mean line reliably.The total calculation of this extraction for 11 200 data points only costs 60 ms by general PC and the relative error of Ra obtained by this extracted mean line is only 0.12% larger than the result by Gaussian filter.