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.     

对金刚石刀具刀尖圆弧波纹度评价的滤波分析

为准确评价超精密金刚石刀具刀尖圆弧波纹度,对金刚石刀具刀尖圆弧波纹度的评价进行了滤波分析。介绍了刀尖圆弧波纹度的评价方法,针对关键的滤波环节,分析了高斯滤波、高斯回归滤波、样条滤波和小波滤波的原理,根据实际采样数据设计模拟实验对比了上述4种滤波器的滤波特性。结果表明,对于不同轮廓中线但高频分量完全相同的轮廓,样条滤波器的滤波效果优于高斯滤波器,并通过实际应用对比了高斯滤波器和样条滤波器。实验结果表明:对具有不同轮廓中线但高频分量完全相同的模拟轮廓,分别采用高斯滤波器和样条滤波器,当截止波长分别取0.25mm和0.8mm时,高斯滤波器滤波结果的标准差分别为0.4366nm和9.6544nm,样条滤波器滤波结果的标准差分别为0.0271nm和1.1844nm,说明样条滤波器更适合于超精密金刚石刀具刀尖圆弧波纹度的评价。     

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。     

高斯滤波技术提取表面粗糙度信息

在传统高斯滤波理论的基础上,提出稳健高斯滤波算法,引入M估计中的权函数对高斯滤波进行稳健处理,并结合高斯滤波逼近理论,在高斯滤波稳健算法基础上,构建高斯滤波的算法模型和零件表面形貌特征模型。利用MALTAB软件编程和仿真模拟系统,模拟出零件表面原始轮廓信号,并采用simulink系统仿真设计出FIR型数字高斯滤波器。将原始轮廓信号通过高斯滤波器,通过一次有效滤波分离提取出零件表面的粗糙度信号和滤波中线,实现高斯滤波的过程,提取粗糙度信息来评定零件表面质量。     

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。     

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。     

巴特沃思小波在表面形貌信号分离中的应用

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%。     

表面测量中高斯滤波器的B样条函数实现方法

提出一种新的高斯滤波器B样条函数实现方法。在B样条函数理论基础上,通过对变分原则引入约束条件的方法,并结合小尺度高斯滤波器级联的特性,得出了高斯滤波器的逼近滤波器。其与高斯滤波器的最大幅度偏差小于1%,并且也具有零相移的特性。在相应的滤波算法中,包括了一级零相移滤波和一级加权滤波,只进行二次循环,算法结构简单,计算效率高。对实际表面测量数据进行应用试验,能够满足高斯滤波器实现方法高精度、高效率的要求。     

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。     

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.     

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.     

The filtering method to calculate the transmission characteristics of the low-pass filters using actual measurement data

The Gaussian filter and spline filter are low-pass filters used in surface roughness estimation methods, and their transmission characteristics are well known. However, the transmission characteristics of the Gaussian filter and spline filter used at actual sites may not be in agreement with their theoretical characteristics. Generally, the spline filter is used with an open profile. Although the transmission characteristics of the periodic spline filter are well known, these transmission characteristics are not those of a nonperiodic spline filter used with an open profile. In the case of a Gaussian filter, the filter width of the theoretical transmission characteristics is ∞. However, a Gaussian filter of filter width λ_c is used at actual sites. This fact is a major problem. To solve this problem, it is necessary that the transmission characteristics of a low-pass filter are obtained from actual measurement data and the filter output. However, it is not possible to calculate the transmission characteristics from actual measurement data owing to the end effect and the discontinuity at each end of the data, etc. In this paper, we propose a new method for exactly calculating the transmission characteristics of a low-pass filter. This method involves the process in which the open profile is considered as a closed profile by repeating it periodically. The transmission characteristics of a nonperiodic spline filter and a Gaussian filter (filter width λ_c) used at actual sites were confirmed by the proposed method. The transmission characteristics of the Gaussian filter of filter width λ_c were almost the same as the theoretical characteristics. However, the transmission characteristics of the nonperiodic spline filter were considerably different from those of a periodic spline filter with well-known characteristics. Moreover, the transmission characteristics of the nonperiodic spline filter were found not to be unique.     

表面粗糙度的稳健提取方法研究

在讨论现有表面粗糙度高斯滤波方法的优缺点的基础上，推导了高斯回归滤波及高斯稳健滤波的卷积算法和快速傅里叶算法过程，编写了算法的C语言代码。对实测数据进行处理的结果表明，稳健滤波能很好地克服边界效应并抑制表面上深谷对滤波结果的影响。     

An in-line digital filtering algorithm for surface roughness profiles

The authors develop a fast algorithm for low- and high-pass Gaussian digital filters, executed while one discrete datum of a traced profile is sampled. In this report, the 8-step, modified running–box-function filter is presented. The transmission characteristics of this new filter are very close to those of the Gaussian digital filter given in ISO 468-1982. In addition, the conditions for using this filter are given for practical use.     

随动磨削曲轴表面异常轮廓误差去除方法

在高精度随动曲轴磨床中,为控制曲轴加工轮廓误差常采用预补偿的方法,如果测量时工件上有磨屑、毛刺等干扰将在测量结果中引入明显的异常轮廓,采用传统的高斯滤波器对数据进行处理将极大地影响轮廓误差的补偿精度,甚至导致废品出现。针对这一问题,给出了适用于闭轮廓的高斯滤波器、Rk滤波器和鲁棒高斯回归滤波器的理论模型。分别应用3种滤波器,对比分析结果可知,鲁棒高斯回归滤波器去除异常轮廓误差效果最理想,并通过人为改变异常轮廓的尺度,进一步验证鲁棒高斯回归滤波器的适应性和可靠性。该滤波方法集成到随动曲轴磨床软件中,实现异常轮廓的自动去除,提高了补偿效率,有效保证了曲轴磨削轮廓的误差精度。     

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。     

Periodic Gaussian filter according to ISO 16610-21 for closed profiles

It is well known that the Gaussian filter according to ISO 16610, part 21 has nice metrological properties but also has some restrictions. The evaluable measuring length of open profiles is shortened by so-called filter running-in and running-out lengths which are a factor of the width of the Gaussian weighting function. ISO 16610-21 suggests a simplistic transfer of filtering of open profiles to filtering of closed profiles (e.g. roundness measurements). And this leads, due to the running-in and running-out lengths, to an unnecessary restriction. Because in case of a closed profile, it has to be taken into consideration that the profile can be extended infinitely and thus any measuring length of an equivalent open profile can be reproduced. Hence, as this paper shows, the measuring length for closed profiles can be arbitrary for any given width of the Gaussian weighting function.     

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。