Abstract： Engineering surfaces always have fractal characteristics and now a composite evaluation method is proposed in which the dual tree complex wavelet combined with fractal theory. By using the dual-tree complex wavelets approximate translation invariance and good directions, signal is decomposed into a more delicate low and high frequency signals. Meanwhile, according to the invariance of the signals fractal dimension under multi - scale, the fractal dimension of signals is obtained by the use of the autocorrelation image gray value, and the dual tree complex wavelets decomposition scale is verified by calculating the different fractal dimensions between the high and low frequency signals (the fractal dimension distance). The simulation results show that the datum can be well extracted by the use of the composite evaluation method, and the accuracy of decomposition level which is confirmed by the fractal dimension distance is verified by the use of the root mean square value. Two examples illustrate that reference and waviness of the nano-scale three-dimensional rough surfaces which have fractal characteristic can be well extracted by the use of the composite evaluation method, which provides a reliable theoretical basis for the assessment of the actual engineering surface.
[1] Fisher J，Dowson D, Hamdzah H, et al. The effect of sliding velocity on the friction and wear of UHMWPE for use in total artificial joints [ J]. Wear, 1994, 175 ：219 -225.
[2] Hall R M, Unsworth A, Siney P, et al. The surface-topography of retrieved femoral heads [ J ]. Journal of Materials Science-Materials in Medicine, 1996, 7：739 -744.
[3] 杨大勇，刘莹，李小兵.小波分析及其在摩擦表面研究 中的应用[J ].江西科学，2006，24 (4) : 238 - 241.
[4] 孙延奎.小波分析及其应用[M].北京:机械工业出版 社，2005:31 -58.
[5] 陈武凡.小波分析及其图像处理中的应用[M].北京: 科学出版社，2002:27 -30.
[6] 李水根，吴纪桃.分形与小波[M].北京:科学出版 社，2002:1 -7.
[7] Grzesik W, Brol S. Wavelet and fractal approach to surface roughness characterization after finish turning of different workpiece materials [ J ]. Journal of materials processing technology, 2009, 209(6) ：2522 -2531.
[8] Podsiadlo P W, Stachowiak G W. Fractal-wavelet based classification of tribological surfaces [ J ]. Wear, 2003 , 254(11) ：1189 -1198.
[9] Nick Kingsbury. The dual-tree complex wavelet transform： A new efficient tool for image restoration and enhancement [ G ] //In Proceedings of European Signal Processing Conference, Rhodes, 1998, 319 -322.
[10] Jiang X Q, Blunt L. Third generation wavelet for the extraction of morphological features from micro and nano scalar surfaces [ J ]. Wear, 2004 , 257 (12) ： 1235 -1240.
2014, Vol. 35 
