B样条滤波器建立表面轮廓中线的方法

根据离散B样条函数的Z域表达式，B样条空间中对信号的拟合和分解可以表示成FIR滤波器和IIR滤波器的滤波过程，再结合变分原则，构建了表面粗糙度测量中用于确定中线的B样条滤波器。将零相移滤波技术应用到B样条滤波器的实现中，得到了相应的差分方程。对一实际工件表面轮廓进行了实验，验证了该方法的可行性，该滤波器同样具有零相移的特性，与其它方法相比，其具有计算效率高的优点。     

广义B样条滤波器在表面形貌测量中的应用

摘 要：为了提取工件表面轮廓中线,给出一种基于三阶广义B样条函数的数字光滑滤波器。首先由线性方程微分方程推导出广义B样条函数。接着,利用广义B样条函数和变分公式结合推导出数字平滑滤波器,该数字平滑滤波器由一IIR滤波器和间接广义B样条变换组成。然后,给出了数字平滑滤波器的具体的递归算法,并且证明了该滤波器的通用特性。最后提取了一实际工件表面中线。实验结果表明：该滤波器具有比高斯滤波器更好的截止特性,该算法利用普通计算机提取11200点数据表面中线仅耗时0.002秒。该滤波器具有可调平滑性,零相移特性,克服了传统三阶样条插值的曲率低和振荡的缺陷,其递归滤波器的具体算法,算法简洁,效率高。     

样条滤波器算法的实现

在表面粗糙度测量中,样条滤波器比之前的2RC滤波器和高斯滤波器有更好的滤波效果,但是样条滤波器的截止波长λ,没有确定的定义,这使得样条滤波器的应用受到了限制.本文通过大量的计算,进行数据拟和得到了样条滤波器截止波长的拟合公式,通过该公式可以直接计算出p参数,它使得滤波器在截止波长处的传输特性为50%,而且其相关系数达到了1,非常接近实际的计算值.     

表面粗糙度测量中的稳健样条滤波算法

研究了表面异常信号对国际标准样条滤波器的影响.引入稳健统计学思想对样条滤波器进行了稳健处理,增强样条滤波的稳健性.利用该算法对实际表面进行测量,其结果表明:能够可靠地获得评定中线,实现表面信息的无失真提取和分析,与原有国际标准样条滤波器相比,稳健性更强.     

一般样条滤波器及其在表面计量中的应用

提出了样条滤波器的一般化表达式,由该表达式可以构造线性样条滤波器、稳健样条滤波和一般样条滤波器。一般样条滤波器保留了部分线性样条滤波器的特性,又具有稳健性。采用Tucky估计,分别采用一般样条滤波器、线性样条滤波器与稳健样条滤波器在表面计量中进行了对比实验,实验结果表明:当表面存在明显的深谷和尖峰时,采用稳健样条滤波器更为合适;当表面近似服从正态分布时,三种滤波器得到的表面粗糙度参数比较接近。     

三角窗逼近法实现高斯滤波器

在中心极限定理和逼近理论的基础上,提出了一种用三角滤波器的级联来实现高斯滤波器的新方法.根据三角窗函数的对称性和三角滤波器的递归性,给出了高斯滤波器的实用逼近算法.实验表明,与传统的高斯滤波方法相比,新方法算法简单,计算效率高,且易于实现.     

一种新型稳健样条轮廓滤波器

在表面计量学中,通常利用轮廓滤波器提取轮廓中线作为表面评定的基准线。由于传统轮廓滤波器极易受到划痕和深谷等奇异信号影响而产生失真甚至错误的中线,为了增强其稳健性并保证评定精度,国际标准中给出了两种替代滤波器,即稳健型样条滤波器和高斯回归滤波器。然而,这两种滤波器的构造原理和实现算法迥异,其滤波特性差异较大,从而导致对同一表面具有不同的评定结果。为解决这一问题,提出将M估计权函数与样条滤波器相结合构造了一种新型稳健样条滤波器。该滤波器不但具有更强的抗差能力,其计算效率也远高于国际标准推荐的稳健滤波器。更重要的是,大量实验表明,其滤波特性与高斯回归滤波器接近,该滤波器的应用有助于表面评定标准的传递和测量结果比对。     

表面形貌评定的B样条小波基准线的实现

随着科学技术的发展,对工件的表面精度提出了更高的要求。表面形貌特征在很大程度上影响了工件的技术性能和使用功能。近年来,国内外对表面形貌特征进行了大量的研究,制定了相关的标准。但是仍然存在一些不确定性和模糊性。文中针对高斯滤波器存在边界效应和对缺陷表面产生形变的不足,提出了一种B样条小波获取表面形貌功能评定基准线的方法。首先建立表面形貌的数学模型,采用小波分析的分解与重构原理,实现了表面形貌的数学模型的小波构建。最后根据小波变换的定义,用B样条函数构造出B样条小波函数,并将其应用于表面形貌的分析,从而实现了表面轮廓与基准线的分离。通过实例对比分析,该方法要优于高斯滤波获取基准线的方法。B样条小波分离法不仅消除了边界效应,而且消除了表面异常值高斯基准线的变形。     

基于MATLAB GUI的表面粗糙度评定算法的实现

表面粗糙度评定算法及系统的实现是表面形貌测量方法应用的关键.针对这一问题,首先对比分析了表面粗糙度评定中高斯滤波和B样条小波分解两种算法.在此基础上基于MATLAB GUI(Graphical User Interfaces,GUI)研究并实现了表面粗糙度评定系统;实验和分析表明,实现的两种滤波方法均能满足表面形貌分析的精度要求,所实现的系统直观易用、结果可靠.     

减小表面粗糙度测量高斯滤波幅度偏差

提出了一种减小表面粗糙度测量用的高斯滤波器幅度传输特性偏差的新方法。根据中心极限定理,可以构造出不同的高斯逼近滤波器。用多级一阶巴特沃思滤波器和多级移动平均滤波器分别去逼近高斯滤波器时,两者的幅度偏差方向相反、极值位置相近,所以这两种方法的线性组合可以大大减小偏差。用这两种不同逼近滤波器的并联方法构成的一个简单的线性组合滤波器,去逼近高斯滤波器的幅度传输特性,其幅度传输特性的最大偏差只有0．11％。这种新的逼近方法,算法简单、精度高,实现了表面测量高斯滤波处理的高精度和高效率的高度统一。     

3D Profile Filter Algorithm Based on Parallel Generalized B-spline Approximating Gaussian

Currently, the approximation methods of the Gaussian filter by some other spline filters have been developed. However, these methods are only suitable for the study of one-dimensional filtering, when these methods are used for three-dimensional filtering, it is found that a rounding error and quantization error would be passed to the next in every part. In this paper, a new and high-precision implementation approach for Gaussian filter is described, which is suitable for three-dimensional reference filtering. Based on the theory of generalized B-spline function and the variational principle, the transmission characteristics of a digital filter can be changed through the sensitivity of the parameters(t1, t2), and which can also reduce the rounding error and quantization error by the filter in a parallel form instead of the cascade form. Finally, the approximation filter of Gaussian filter is obtained. In order to verify the feasibility of the new algorithm, the reference extraction of the conventional methods are also used and compared. The experiments are conducted on the measured optical surface, and the results show that the total calculation by the new algorithm only requires 0.07 s for 480′480 data points; the amplitude deviation between the reference of the parallel form filter and the Gaussian filter is smaller; the new method is closer to the characteristic of the Gaussian filter through the analysis of three-dimensional roughness parameters, comparing with the cascade generalized B-spline approximating Gaussian. So the new algorithm is also efficient and accurate for the implementation of Gaussian filter in the application of surface roughness measurement.     

A fast algorithm for determining the Gaussian filtered mean line in surface metrology

A fast recursive algorithm for determining the Gaussian filtered mean line was deduced using the central limit theorem and an approximation method. This recursive algorithm uses a small number of multiplications per loop and otherwise such simple computer operations as addition and subtraction, and therefore, can achieve a very high computational speed. Special cases are also presented in which the relatively inefficient multiplication operation in the computer can be replaced by the efficient digit shifting operation, and the filtering computational efficiency is enhanced further. High-order algorithms are proposed for practical use to improve filtering accuracy. The “forward filtering” and “backward filtering” implementation of the recursive algorithm results in zero phase distortion of the filtered mean line. A new relationship between the Gaussian filtering method and the classical 2RC filtering method is also established using this algorithm.     

Filter with variable transmission characteristics for determination of three-dimensional roughness

In this study, we propose a low-pass filter whose transmission characteristics are determined to be more than 99.99% identical to the designed transmission characteristics at wavelengths greater than the cut-off wavelength. This low-pass filter is realized using a frequency-domain method which uses down-sampling, a frequency filter, and a cubic B-spline. When the frequency characteristics of a Gaussian filter (GF) were used as the designed transmission characteristics, this low-pass filter perfectly replaced the GF. In addition, no end effects and directional characteristics developed, and high-speed computation was possible. Furthermore, we can easily realize a low-pass filter having transmission characteristics that rise sharply at a right angle like a step edge.     

一种快速稳健高斯回归滤波算法

针对稳健高斯回归滤波器运行速度过慢的问题,利用截断高斯权函数的快速卷积提高了算法运行速度。在详细分析稳健高斯回归滤波器和卷积函数的基础上,推导了截断高斯权函数,并通过实验确定了合适的参数值。实验结果表明,截断高斯权函数能使稳健高斯回归滤波器在精度损失很小的情况下运行时间明显缩短。     

三维表面测量中的高斯滤波快速算法

基于中心极限定理提出了一个高斯滤波器逼近模型,并利用冲激响应不变法设计了数字高斯滤波器.通过级联方法,该滤波器的幅度传输特性偏差可控制在(-0.28％～+1.14％)以内,扩展为二维高斯滤波器,其三维幅度传输特性偏差可控制在(-0.42％～+1.12％)以内.该滤波器采用递归实现算法,算法简便,易于实现.在递归算法的基...     

磨损表面的稳健高斯滤波评定方法研究

磨损表面形貌的评定方法,对于磨损表面状态评定、摩擦特性的分析有着重要的作用,而表面形貌数据的滤波方法,是评定方法中的关键组成之一。采用Tukey、Hampel、IGGI和QC 4种典型稳健权函数分别与高斯滤波结合组成的稳健高斯滤波方法,对由实验得到的黏着磨损和磨料磨损盘表面采集的数据进行稳健滤波分离;通过由稳健高斯滤波与标准高斯滤波得到的三维磨损表面低频基准面的对比分析,以及从磨损表面滤波分离出的高频评定参数的影响分析,研究稳健高斯滤波的滤波稳健性和滤波效率;从滤波后的高频功率谱密度分布特性方面,进一步探讨滤波的稳健性;讨论磨损表面形貌数据中特异值与磨损特征的关系。研究表明：Tukey和Hampel稳健高斯滤波具有良好的滤波稳健性,能有效地分离磨损表面的低频评定基准和包含磨损特征的高频信息;而磨损特征主要分布在高频信息的低频段区间,其功率谱密度函数与表面磨损状态及其摩擦学特性相关。     

High-order spline filter: Design and application to surface metrology

The differences between the transmission characteristics of the standard cubic spline filter and the Gaussian filter lead to different evaluation results even for the same profile. There is indeed an adverse impact on the comparison of measurement results and the applications of the related international standards. A novel high-order spline filter is proposed to resolve this practical problem of approximating the Gaussian filtering characteristic. The design of the new filter is based on an improved variational approach by adding the high order derivative terms to the bending energy part whose structural parameters are determined by the aid of the universal Taylor series, so as to realize the convergence to the function of the Gaussian filter. In addition, a cascade algorithm in terms of the low-order filters is also developed in order to ensure stable performance of the high-order filter. Its effectiveness and application were verified by the experiments.     

Edge effect elimination in the recursive implementation of Gaussian filters

The paper discusses a general methodology to the design of recursive Gaussian filters to be used for separating the form, waviness and roughness components of the surface texture. By selecting appropriate initial values for the filter difference equations, it is possible to eliminate the so-called edge effect and evaluate the whole registered profile. Two ways of filter implementation were considered: series and parallel. The incremental difference operator is applied in place of the usual shift operator z to describe the filter transfer function. This increases the accuracy of the representation of filter parameters and decreases the number of rounding errors. The results of the analysis were illustrated using 2D and 3D roughness profiles of a ball bearing race. The data show that the mean line and the mean surface were correctly determined for the whole area of the measured profile.     

一种时间序列异常检测用参数化熵滤波器

针对机械系统中近似高斯分布的低信噪比时间序列,设计出一种用于异常检测的参数可调熵滤波器。为检测均值漂移和方差变动这两类统计特性异常,对基于滑动窗的Shannon熵滤波器的参数设置策略进行研究。引入单调因子K1,在保证滤波器工作单调性的同时,可以获取不同的平滑效果。通过引入尺度因子K2,实现对熵滤波器正常信号容限的调节,从而实现时间序列的可变尺度异常检测。以时间序列中异常信号与正常信号统计特性重合度在滤波前后之比作为滤波器性能评价指标,利用仿真信号分析两个参数在检测均值漂移和方差变动异常时的合理取值范围。对电子清纱器颜色异纤信号的检测试验结果表明,这种带参数的熵滤波器对近似高斯分布的时间序列信号具有良好的异常检测能力。