基于多方向连续小波构造的粗糙表面建模
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摘要
参数可控的表面形貌建模方法依赖于高效的数学建模工具,而传统的表面建模方法由于参数的非稀疏性和冗余性,难以将平稳纹理过程与非平稳随机分形过程相互有机结合。本文通过引入多方向小波建模并与多重分形建模方法相结合,构造了具有多尺度、多方向、多重分形性质的基于多方向小波的表面形貌建模方法。通过人工设定不同表面形貌参数,计算机可以对铣加工表面形貌的特征进行建模仿真,并生成对应的功率谱进行对比与分析。实验表明,通过多方向小波构造的粗糙表面相较于传统的各向异性分形表面建模或纹理建模,具有更优秀的纹理控制能力与多尺度建模能力,可以在任意方向与尺度上按需求建立准确的表面纹理形貌与多重分形特征,有效实现所需的表面形貌。
Modeling method of parametricrough surface morphological depends on efficient mathematical modeling tools. The traditional rough surface modeling methods are difficult to control stationary texture or combine processes with nonstationary stochastic fractal processes due to the non-sparseness and redundancy of the control parameters. In this paper,combining multi-directional wavelet modeling with multi-fractal modeling method,an improved rough surface modeling method based on the multi-directional wavelet,with multi-scale,multi-directional and multi-fractal properties is constructed.By manually setting different surface morphological parameters,the program can model and analyze surface shape or corresponding power spectrum of milling surface. The results show that the rough surface constructed by multi-directional wavelet is more suitable than the traditional anisotropic fractal surface modeling or texture modeling. Method of multi-directional wavelet modeling has better texture control ability and multi-scale modeling ability,can satisfy the required surface morphology in any directional and scale.
Modeling method of parametricrough surface morphological depends on efficient mathematical modeling tools. The traditional rough surface modeling methods are difficult to control stationary texture or combine processes with nonstationary stochastic fractal processes due to the non-sparseness and redundancy of the control parameters. In this paper,combining multi-directional wavelet modeling with multi-fractal modeling method,an improved rough surface modeling method based on the multi-directional wavelet,with multi-scale,multi-directional and multi-fractal properties is constructed.By manually setting different surface morphological parameters,the program can model and analyze surface shape or corresponding power spectrum of milling surface. The results show that the rough surface constructed by multi-directional wavelet is more suitable than the traditional anisotropic fractal surface modeling or texture modeling. Method of multi-directional wavelet modeling has better texture control ability and multi-scale modeling ability,can satisfy the required surface morphology in any directional and scale.
引文
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[18]Easley G,Labate D,Lim W Q.Sparse directional image representations using the discrete shearlettransform[J].Applied and Computational Harmonic Analysis,2008,25(1):25-46.
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[20]Mandelbrot B B,Passoja D E,Paullay A J.Fractal character of fracture surfaces of metals[J].Nature,1984,308(5961):721-722.
[21]数学辞海编委会.数学辞海(第5卷)[M].北京:中国科学技术出版社,2002.
[2]Mishra P C,Rahnejat H,King P D.Tribology of the ringbore conjunction subject to a mixed regime of lubrication[J].Proceedings of the Institution of Mechanical Engineers,Part C:Journal of Mechanical Engineering Science,2009,223(4):987-998.
[3]Vallet C,Lasseux D,Sainsot P,et al.Real versus synthesized fractal surfaces:contact mechanics and transport properties[J].Tribology International,2014,42(2):250-259.
[4]吴振森,谢东辉,谢品华,等.粗糙表面激光散射统计建模的遗传算法[J].光学学报,2002,22(8):897-901.
[5]易成,张亮,陈忠辉,等.一种新的描述粗糙表面形貌尺度分维参数Rd的研究[J].中国矿业大学学报,2007,36(1):75-80.
[6]潘家华,赵晓明,赵国伟,等.正交车铣表面形貌的计算机仿真[J].上海交通大学学报,2005,39(7):1182-1186.
[7]裘辿,刘振宇,周思杭,等.基于多尺度高度场修正的零件表面形貌建模及应用[J].计算机辅助设计与图形学学报,2012,24(12):1631-1639.
[8]赵厚伟,张松,赵斌,等.球头铣刀加工表面形貌仿真预测[J].计算机集成制造系统,2014,20(4):880-889.
[9]Lu H,Zhang L,Serikawa S.Maximum local energy:An effective approach for multisensor image fusion in beyond wavelet transform domain[J].Computers&Mathematics with Applications,2012,64(5):996-1003.
[10]Mallat S G.A theory for multiresolution signal decomposition:the wavelet representation[J].IEEE transactions on pattern analysis and machine intelligence,1989,11(7):674-693.
[11]闫敬文,屈小波.超小波分析及应用[M].北京:国防工业出版社,2008.
[12]任志英,高诚辉,林建兴,等.基于双树复小波变换的三维粗糙表面评定方法研究[J].中国机械工程,2014,25(13):1795-1799.
[13]周超,黄健萌,高诚辉.各向异性分形表面建模研究[J].中国机械工程,2015,26(8):1019-1023,1061.
[14]张德丰.MATLAB小波分析(MATLAB工程应用书库)[M].北京:机械工业出版社,2009.
[15]Do M N,Vetterli M.The finite ridgelet transform for image representation[J].IEEE Transactions on Image Processing,2003,12(1):16-28.
[16]Starck J L,Candès E J,Donoho D L.The curvelet transform for image denoising[J].IEEE Transactions on Image Processing,2002,11(6):670-684.
[17]Do M N,Vetterli M.The contourlet transform:an efficient directional multiresolution image representation[J].IEEE Transactions on image processing,2005,14(12):2091-2106.
[18]Easley G,Labate D,Lim W Q.Sparse directional image representations using the discrete shearlettransform[J].Applied and Computational Harmonic Analysis,2008,25(1):25-46.
[19]Yi S,Labate D,Easley G R,et al.A shearlet approach to edge analysis and detection[J].IEEE Transactions on Image Processing,2009,18(5):929-941.
[20]Mandelbrot B B,Passoja D E,Paullay A J.Fractal character of fracture surfaces of metals[J].Nature,1984,308(5961):721-722.
[21]数学辞海编委会.数学辞海(第5卷)[M].北京:中国科学技术出版社,2002.