双树复小波稳健滤波在工程表面粗糙度评定中的应用

讨论了现有工程表面粗糙度评定基准滤波方法的优缺点。提出双树复小波变换(DT-CWT)具有近似的平移不变性和改进方向选择性等优点适合用于三维表面基准滤波,但其滤波过于理想化易导致滤波基准在野点处畸变。为此,进一步提出将空域双边滤波思想引入DT-CWT来增强双树复小波变换在提取基准面野点处的稳健性。通过低频重构得到基准信号,并对每层重构系数进行双边滤波,最终增强DT-CWT滤波基准的稳健性。仿真结果显示:改进的DT-CWT能很好地抑制异常值干扰引起的滤波基准在野点处产生的畸变,其得到的基准面的精度误差为0.183 2×10-10 m,重构误差为0.016 1×10-10 m,低于传统方法所得。对实测数据进行处理结果表明,双树复小波稳健滤波能很好地克服边界效应并抑制工程表面上深沟对滤波结果的影响。提出的方法为工程表面粗糙度评定提供了一种新方法。     

精密光学元件表面中频误差的提取研究

能否准确对精密光学元件表面评价势必影响着光学元件研制与生产,其中中频误差的提取逐渐显得重要。提出了利用双树复小波变换(DT-CWT)对精密光学元件表面提取信号进行多尺度分解,以定义的均方根波长确定其双树复小波分解次数,进行中频误差的提取与识别。此方法应用于精磨和镀膜的精密光学元件表面中,实验证实该方法不仅可以应用于一维信号的提取,同样也适合三维表面中频波段面形误差的提取。     

基于小波变换的三维粗糙表面分形维数计算方法

基于小波变换提出一种三维粗糙表面分形维数的计算方法。该方法采用小波变换对三维表面形貌数据进行多尺度分解,通过对不同分解尺度下小波系数平方的均值进行函数拟合,继而得到粗糙表面的三维分形维数。为验证提出的方法的正确性与准确性,采用已知参数构建三维分形表面,对不同方法下分形维数的计算结果进行对比分析。对比结果显示,相比原始盒维数法与差分盒维数法,采用提出的小波变换法计算得到的分形维数误差更小。特别是在小波变换过程中选用sym4小波基函数时,分形维数的计算误差最小,误差能够控制在2%以内。将提出的方法应用于磨削表面分形维数的计算,得到了不同粗糙度下磨削表面的分形维数,进而验证了该方法的实用性。提出的方法能够更加精确地计算三维粗糙表面的分形维数,为粗糙表面分形接触模型的构建提供了参数基础。     

改进双树复小波在阶跃特征结构表面基准提取中的应用

刻线尺寸的器件表面存在着大量的如槽、台阶等不连续特征,当提取其基准面来做质量评定时,ISO规定最小二乘拟合法来实现,但其鲁棒性远远差于滤波法。而若直接采用传统滤波法(如高斯滤波、小波滤波等)在不连续特征处会产生波动。基于此,提出一种新的滤波稳健算法,通过对双树复小波变换(Dual-tree complex wavelet transform, DT-CWT)进行全变分最小化理论(Total variation minimization, TVM)梯度处理,即对每层的小波系数运用阈值方法进行初始化,借助投影次梯度法将TVM理论与DT-CWT相结合,不断迭代,最终增强DT-CWT在提取几何结构特征基准面的鲁棒性。仿真结果表明,所提算法与传统滤波方法相比,整个表征精度(最大重构误差和均方差)具有最优性,且评定高度也最接近理想高度。对一实测标块,无论从直观三维视图还是侧面对比图,其在阶跃处能很好地抑制波动,与标块实际加工的理论高度偏差只有0.040 3 μm,保证了产品的几何特征,为实际的工程应用提供了一种有效的基准提取方法。     

一种光学元件表面中频误差提取的新方法

光学元件表面面形误差属于非平稳空间信号,为了在分离光学元件表面各频段面形误差的同时尽可能保留原始信号各频段的细节特征,结合超精密抛光的球面光学元件表面特点,提出一种基于双树复小波变换(dual tree complex wavelet transform,简称DT-CWT)的自适应分离法。利用DT-CWT的多分辨分析、方向性好和良好的时频局部化分析能力等特点,对实测的抛光光学元件表面进行DT-CWT的多尺度分解,并在重构时加入自适应影响因子,成功分离了各频段的面形误差。通过对经DT-CWT直接分离法与DT-CWT自适应分离法得到的高、中、低频面形误差进行参数表征,实验证明基于DT-CWT自适应分离法更为有效地分离光学元件各个频段的面形误差及误差特征,便于后续的识别与评定工作。     

基于NSST的镀锡基板表面形貌多尺度分析

提出了基于非下采样剪切波变换的镀锡基板表面形貌分析方法。将非下采样剪切波变换与高斯滤波、二维离散小波和二维双树复小波进行对比,验证了其优异的幅频特性和平移不变性;基于低频子带能量、低频重构表面峭度以及重构表面与原始表面的均方根误差,确定非下采样剪切波变换的分解层数,并将其与二维离散小波、二维双树复小波用于基板形貌特征的重构,结果表明：非下采样剪切波变换拥有最好的重构效果。采用分水岭算法和Wolf剪枝对不同形貌特征的基板进行特征参数计算,得到表征镀锡基板表面质量的显著参数：平均峰体积S_hv和平均谷体积S_dv。     

基于小波的零件表面微观形貌多尺度重构

采用激光测量仪对车削机加工零件表面进行测量,获得零件亚纳米级的微观形貌数据,利用小波分析分时分频精细表达以及多分辨率分析的特点,建立粗糙表面多尺度重构模型,对基于真实测量数据的微观表面进行宏微观重构,并提出在不同尺度上提取粗糙表面的微凸体以精简数据的方法,从而实现在MATLAB和Pro/E中的微观表面建模仿真。提取的低频成分为零件表面二维和三维评定提供了基准,不同尺度上微观粗糙表面的重构为在不同精密等级上分析机加工工艺对零件表面粗糙度的影响提供了方法,Pro/E中重构的表面为有限元分析零件宏微观几何形貌与摩擦、润滑和密封的关联机制提供了几何模型。     

油液磨粒超声回波信号的双树复小波去噪研究

超声回波信号反映了润滑油中磨粒的大量信息。为了提取淹没在强噪声环境下的超声回波信号,提出了一种基于双树复小波变换(DT-CWT)的油液磨粒超声散射回波信号去噪新方法。利用双树复小波变换具有近似平移不变性和有效去噪等优点,首先对超声散射回波信号进行双树复小波分解,然后对分解得到的高频系数进行阈值处理,最后进行双树复小波重构。结果表明:分解层数为6层时,去噪后信号的信噪比更高、均方误差更小、相似系数更大、幅值最大偏差更小。双树复小波变换硬阈值去噪效果比传统小波去噪效果明显好。     

小波变换在粗糙表面几何形貌表征中的应用

粗糙表面几何形貌对于表面特性如摩擦、磨损、润滑、腐蚀疲劳等具有重大的影响,表面几何形貌能否及时准确地被表征具有重要的工程意义．简要叙述小波变换的特点,重点介绍目前小波变换在表面粗糙度评定、表面形貌分离与重构以及表面形貌分形维数提取等方面的应用,提出了目前小波变换在表面几何形貌表征中存在的不足,以及今后小波技术在表面形貌中发展的新趋势．     

小波分析在水切割表面拓扑结构特征提取中的应用

为了详细地研究水切割--AWJ (abrasive water jet)表面的主要特征,研究了由传统接触式测量仪和光学测量仪获得的信号.通过对信号的小波分解和重构,提取了形态误差、波纹度以及粗糙度值等表面特征.另外,还详细地论述了小波基函数的选择以及小波分解层次确定等基本的应用问题.实验结果表明小波能够有效地应用于AWJ表面拓扑结构特征的分析和描述.     

Modelling of tolerances and manufacturing dimensions

To obtain imposed dimensional and geometrical specifications for any mechanical piece, production tolerances must be calculated. So a simulation of workpiece behavior when it is machined, has permitted calculations of deviations on machined surfaces.The method of deviation calculation is based on a comparison between imposed functional tolerance and the tolerance calculated in relation to deviations on two machined surfaces or between a machined surface and the operational datum.The one direction modelling of deviations inquires practical inputs such as the planning process, the operational datum, the deviations on rough surfaces, and deviations on surface datum for any stage of machining. The developed method allows determining the deviations on machined surfaces. Then, tolerances on production dimensions were calculated in three directions. These results have permitted to define average production dimensions, which may be used for NC machine programming and to prepare an optimal rough piece configuration.The developed method has been applied for the machining of a fixing screw.     

Influence of the atomic force microscope tip on the multifractal analysis of rough surfaces

In this paper, the influence of atomic force microscope tip on the multifractal analysis of rough surfaces is discussed. This analysis is based on two methods, i.e. on the correlation function method and the wavelet transform modulus maxima method. The principles of both methods are briefly described. Both methods are applied to simulated rough surfaces (simulation is performed by the spectral synthesis method). It is shown that the finite dimensions of the microscope tip misrepresent the values of the quantities expressing the multifractal analysis of rough surfaces within both the methods. Thus, it was concretely shown that the influence of the finite dimensions of the microscope tip changed mono-fractal properties of simulated rough surface to multifractal ones. Further, it is shown that a surface reconstruction method developed for removing the negative influence of the microscope tip does not improve the results obtained in a substantial way. The theoretical procedures concerning both the methods, i.e. the correlation function method and the wavelet transform modulus maxima method, are illustrated for the multifractal analysis of randomly rough gallium arsenide surfaces prepared by means of the thermal oxidation of smooth gallium arsenide surfaces and subsequent dissolution of the oxide films.     

二维经验模态分解在工程表面形貌误差评定中的应用

针对目前表面微观形貌面形误差分离方法中存在边界畸变及自适应差等缺点,提出了将具有自适应时频分辨能力的二维经验模态分解算法(bidimensional empirical mode decomposition,BEMD)应用于三维工程表面面型误差分离中,同时用Riesz变换构造单演信号,计算信号整体的频率特征,完成对二维经验模态分解算法的终止准则的改进,使其能严格按照ISO4287所规定的截止波长分离三维表面各频段形貌误差。仿真结果表明,本文新方法相比于国标ISO中高斯滤波以及常用小波滤波,在分离三维工程粗糙表面各面型误差时,所得分离图形效果远优于传统方法所得,且各频段误差对应的三维评定参数误差均小于5%。最后对光学镀膜元件实例进行分析,结果表明该算法能够很好地分离各形貌误差的的空间信息,所得参数评定基准面相对传统方法不存在边界畸变等问题,因此该方法在实际工程表面评定应用中具有可行性。     

A New Method for Rough Surface Profile Simulation Based on Peak–Valley Mapping

Starting from random process theory and taking peaks and valleys as reconstruction carriers to replace surface height distribution and autocorrelation function (ACF), a new method for rough surface simulation is proposed based on the peak–valley mapping principle. The proposed method is used to simulate rough surfaces with different correlation lengths. The simulated roughness parameters and ACF are examined. Comparisons of simulation precision and simulation efficiency between the proposed method and fast Fourier transform (FFT) are provided. Finally, the applications of the method are discussed briefly.     

Mallat算法的光学实现方法

现有的光学小波变换方法均基于连续小波变换,基于离散信号的小波变换算法（Mallat算法）的光学小波变换还没有出现,这阻碍了光学小波变换应用的发展。针对这一问题,分析利用光学4f系统实现Mallat算法的基本原理,提出Mallat算法的光学实现方法。针对空间光调制器只能实现非负的实函数,且CCD只能记录光的强度,给出一种应用于光学4f系统的光学小波滤波器的设计方法。使用该种光学小波滤波器,利用光学4f系统实现Mallat算法的小波分解部分,并通过数值计算实现Mallat算法的小波重构部分。仿真分析和光学实验结果验证了方法的正确性。     

基于价值函数的二维小波变换小波脊提取算法

条纹图存在噪声干扰时,将二维小波变换系数模的最大值作为小波脊,会产生较大误差。针对这一问题,提出了基于价值函数的二维小波变换小波脊提取算法。首先,提取二维小波变换系数模的最大值点,并将最大值90%的局部极值点提取出来,共同作为小波脊候选点;其次,在模上引入尺度因子的梯度,建立价值函数进而评估所有候选点的价值,利用对数Logistic模型进行权值调整改进,从而得到更加合理的价值估计;最后,使用动态规划思想准确找出最优的小波脊线,提取脊线处的相位即可得到包裹相位。其优势在于能准确解调信噪比较低的条纹图案,抗噪性能优于直接最大模的小波脊提取;并且只需投影一幅条纹图案即可重建物体形貌,可用于恶劣环境下的动态三维测量。计算机仿真和实验结果表明,对于含有噪声污染的条纹图,所提算法相较于最大模的小波脊提取算法,三维形貌恢复精度明显提高;而相较于全部局部极值点提取,其运算时间缩短了46.9%。同时,应用不同母小波于所提方法,仿真结果表明二维Cauchy小波具有更好的方向性和更高的精度。     

Tribological Behavior of Sheet Metal Forming Process Using Acoustic Emission Characteristics

In this study, acoustic emissions (AE) signal processing using wavelet packet transform technique was used to identify damage mechanisms during sheet metal forming simulation experiments. Current investigation was carried out based on decomposing the recorded AE signals into different wavelet levels. Following decomposition process, the energy distribution criteria were used to characterize dominant components, which are considered to be related to dominant damage mechanisms. Results revealed that the energy of AE signals was distributed dominantly on four components, which can be correlated by 3 specific damage mechanisms occurred during simulation experiments. After comparison with previous works, results were validated by surface observations in order to establish a meaningful relation between dominant wavelet components and surface damage mechanisms.     

Simulation and experiment of secondary contact stiffness of rough surface

Machined surfaces usually need to be loaded several times during assembly. The surface morphology after the simulation loading may be quite different from the physical loading, which subsequently causes differences between the contact stiffness after secondary simulation loading and secondary physical loading results. The fractal theory was used to reconstruct the measured surface morphology, followed by contact stiffness simulation and test. The results show that contact stiffness of new morphology obtained by the first simulated loading using the elastic-plastic deformation theory are smaller than the first loading test results, with an average error of −9.71 %. Contact stiffness of used morphology obtained by the first simulated loading using the pure elastic deformation theory are in good agreements with the second loading test results, with an average error of 4.71 %. However, the average contact stiffness of new morphology obtained by the second simulated loading using the elastic-plastic deformation theory, which is traditionally used for contact analysis, are 2.15 times larger than the second loading test result. These research results demonstrate a feasible finite element method (FEM) for solving the contact problem of rough surfaces that need to be assembled multiple times.