Application of several computing techniques for minimum zone straightness

This research deals with the application of several algorithms to calculate the minimum zone straightness. Generally, in the evaluation of the minimum zone value of form errors such as straightness, flatness, roundness, and cylindricity, nonlinear optimization techniques are usually applied. The problem with the nonlinear technique that depends on computing algorithm is that the computing time may be prolonged. Therefore, some linear search techniques that are relatively easy to program are applied for straightness in this article. Furthermore, the problem can also be linearized by considering the characteristics of the measured profile for straightness; thus, the reduction of computing time will be achieved. Then, the problems caused by the above consideration are clarified. Consequently, the convergence criteria and comparison of results by means of several computing methods are investigated. The relationship between flatness and straightness values in some machining conditions and the comparison with the least-squares values are studied.     

A new minimum zone method for evaluating flatness errors

A new minimum zone method for flatnes error analyis is proposed in this article. Based on the criteria for the minimum zone solution and strict rules for data exchange, a simple and rapid algorithm, called the control plane rotation scheme, is developed for the flatness analysis of a flat surface. Experimental work was performed, and some examples are given in terms of the minimum zone and least-squares solutions.     

Geometry of the minimum zone flatness functional: planar and spatial case

The zone straightness and flatness functional is constructed from the definition of the measure. The geometry of the straightness functional is illustrated in the plane, and in three dimensions, a novel means to visually represent flatness is described using the zone separation body. The zone separation body is a new construction that is uniquely associated with every measurement dataset and can be used to represent the flatness functional visually.     

A new minimum zone method for evaluating straightness errors

A new minimum zone method for straightness error analysis is proposed in this article. Based on the criteria for the minimum zone solution and strict rules for data exchange, a simple and rapid algorithm, called the control line rotation scheme, is developed for the straightness analysis of planar lines. Extended works on the error analysis of spatial lines by the least parallelepiped enclosures are also described. Some examples are given in terms of the minimum zone and least-squares. Finally, this easy-to-use method is illustrated by an example that demonstrates that, for a planar line, the minimum zone solution can even be found without the use of a computer.     

Evaluation method for spatial straightness errors based on minimum zone condition

A nonlinear mathematical model for spatial straightness error evaluation based on the minimum zone condition is established in this paper. According to the error analysis, it is proved that the mathematical model for spatial straightness error evaluation cannot be linearized. A criterion for verification of the existence and uniqueness of the minimum zone solution is proposed. A new computational method is also proposed, and practical examples are given. Finally, the correctness of this method is demonstrated using a geometrical solution. This new method is convenient for computation of uniqueness and exactness of the minimum zone solution.     

Evaluation of minimum zone flatness by means of nonlinear optimization techniques and its verification

This article deals with the application of some nonlinear optimization techniques for minimum zone flatness. The convergence criteria of the techniques, namely the downhill simplex method and the repetitive bracketing method, are considered. The least-squares method is also applied, and subsequently the three methods are compared from the viewpoint of computational accuracy. A surface profile measuring system and a noncontact sensor are used to obtain three-dimensional data. The measured data are expressed by means of perspective mapping. Subsequently, the relationship among the above three methods is clarified according to accuracy and efficiency of the computation. Furthermore, some examples of the relationship between the manufacturing method and the flatness value, and the technique of a skilled hand are described.     

Straightness and flatness tolerance evaluation: an optimization approach

This paper presents an optimization approach that could be used to calculate exact values of straightness and flatness errors as defined by the ANSI Y14.5M standards on geometric dimensioning and tolerancing. The straightness and flatness error evaluation problems are formulated as nonlinear optimization problems with linear objective function and nonlinear constraints. Because of the special structure of the problem, a linear search method is developed that reduces the nonlinear problem to a linear programming problem with only two constraints. Examples are presented to compare the optimization approach with the least-squares method and some exact methods. The results show that the optimization procedures presented in this paper provide exact values of straightness and flatness errors and are superior to the existing methods in terms of computation time.     

评定直线度误差的最小二乘法与最小包容区域法精度之比较

介绍了直线度误差评定的最小二乘法和最小包容区域法的算法模型与实现方法。在三坐标测量机上对八种不同被测直线进行了采样点坐标数据提取,分别用最小二乘法和最小包容区域法的基于搜索逼近-逐次旋转逼近法进行了给定平面内直线度误差的评定。结果表明:最小二乘法的评定结果与最小包容区域法的基于搜索逼近-逐次旋转逼近法的评定结果完全一致,即直线度误差的最小二乘法评定结果符合最小条件。     

基于区间牛顿法的点到参数曲线最小距离的计算方法

求解点到参数曲线的最小距离常常用一般的搜索算法。针对搜索算法的稳定性和有效性通常不高的问题,基于参数曲线的几何特性,将求最小距离转化为方程求解问题,应用了区间牛顿法来求解方程。研究结果表明,区间牛顿法是一个全局收敛的方程求根算法,具有较高的稳定性。     

An exact minimum zone solution for three-dimensional straightness evaluation problems

A mathematical model giving the exact solution for three-dimensional (3-D) straightness evaluation based on the minimum zone criterion is presented in this paper. This model builds upon the convex hull of the measured point set to show that the 3-D straightness is determined simply by some measured points on the vertices of the convex hull. The axis of the critical cylinder giving the minimum objective value is proved to be parallel to one of the edges of the convex hull. This model is effective and easy for implementation.     

Monte carlo method for the uncertainty evaluation of spatial straightness error based on new generation geometrical product specification

Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product specification(GPS) requires the measurement uncertainty characterizing the reliability of the results should be given together when the measurement result is given. Nowadays most researches on straightness focus on error calculation and only several research projects evaluate the measurement uncertainty based on "The Guide to the Expression of Uncertainty in Measurement(GUM)". In order to compute spatial straightness error(SSE) accurately and rapidly and overcome the limitations of GUM, a quasi particle swarm optimization(QPSO) is proposed to solve the minimum zone SSE and Monte Carlo Method(MCM) is developed to estimate the measurement uncertainty. The mathematical model of minimum zone SSE is formulated. In QPSO quasi-random sequences are applied to the generation of the initial position and velocity of particles and their velocities are modified by the constriction factor approach. The flow of measurement uncertainty evaluation based on MCM is proposed, where the heart is repeatedly sampling from the probability density function(PDF) for every input quantity and evaluating the model in each case. The minimum zone SSE of a shaft measured on a Coordinate Measuring Machine(CMM) is calculated by QPSO and the measurement uncertainty is evaluated by MCM on the basis of analyzing the uncertainty contributors. The results show that the uncertainty directly influences the product judgment result. Therefore it is scientific and reasonable to consider the influence of the uncertainty in judging whether the parts are accepted or rejected, especially for those located in the uncertainty zone. The proposed method is especially suitable when the PDF of the measurand cannot adequately be approximated by a Gaussian distribution or a scaled and shifted t-distribution and the measurement model is non-linear.     

基于正则化 AdaBound 的区间二型模糊 神经网络软测量建模

针对复杂化工过程中存在强非线性、多变量耦合、参数时变及大时滞等因素,导致监测变量软测量精度不高的问题,提 出了一种基于正则化 AdaBound 的区间二型模糊神经网络(RAIT2FNN) 软测量建模方法。 首先为了解决区间二型神经网络 (IT2FNN)结构难以确定的问题,提出了一种采用激励强度和相似度定义增长和删减指标的自组织产生规则的算法。 该算法利 用激励强度的大小决定是否产生规则,并根据相似度进行规则的删减从而确定了区间二型模糊神经网络的结构。 其次,本文提 出正则化和 AdaBound 相结合的算法对 RAIT2FNN 模型相关参数进行修正,使得不同参数具有有界的自适应学习速率。 最后将 RAIT2FNN 作为软测量模型应用于环己烷无催化氧化过程尾氧浓度预测问题中。 实验结果为测试时间为 0. 008 2,训练 RMSE 为 0. 018 2,测试 RMSE 为 0. 009 6,表明 RAIT2FNN 作为软测量模型具有预测及时且预测精度较高的优点。     

改进蜂群算法在平面度误差评定中的应用

为了准确快速评定平面度误差,提出将改进人工蜂群( MABC)算法用于平面度误差最小区域的评定.介绍了评定平面度误差的最小包容区域法及判别准则,并给出符合最小区域条件的平面度误差评定数学模型.叙述了MABC算法,该算法在基本人工蜂群算法( ABC)模型的基础上引入两个牵引蜂和禁忌搜索策略.阐述了算法的实现步骤,通过分析选用两个经典测试函数验证了MABC算法的有效性.最后,应用MABC算法对平面度误差进行评定,其计算结果符合最小条件.对一组测量数据的评定显示,MABC算法经过0.436 s可找到最优平面,比ABC算法节省0.411 s,其计算结果比最小二乘法和遗传算法的评定结果分别小18.03μm和6.13 μm.对由三坐标机测得的5组实例同样显示,MABC算法的计算精度比遗传算法和粒子群算法更有优势,最大相差0.9 μm.实验结果表明,MABC算法在优化效率、求解质量和稳定性上优于ABC算法,计算精度优于最小二乘法、遗传算法和粒子群算法,适用于形位误差测量仪器及三坐标测量机.     

应用广义回归神经网络重建点云曲面

针对现有曲面重建神经网络算法误差大的缺点,并根据广义回归神经网络解决函数逼近问题的特点,提出了一种针对点云曲面重构的广义回归神经网络,并编制Matlab程序对点云曲面做了仿真试验；仿真结果表明：该模型逼近曲面误差精度达到网络设计要求的10~(-4)mm,网络学习速度快,重建曲面光顺．     

Verification of form tolerances part II: Cylindricity and straightness of a median line

Most inspectors measure form tolerances as the minimum zone solution, which minimizes the maximum error between the datapoints and a reference feature. Current coordinate measuring machines verification algorithms are based on the least-squares solution, which minimizes the sum of the squared errors, resulting in a possible overestimation of the form tolerance. Therefore, although coordinate measuring machines algorithms successfully reject bad parts, they may also reject some good parts. The verification algorithms developed in this set of papers compute the minimum zone solution of a set of datapoints sampled from a part. Computing the minimum zone solution is inherently a nonlinear optimization problem. This paper develops a single verification methodology that can be applied to the cylindricity and straightness of a median line problems. The final implementable formulation solves a sequence of linear programs that converge to a local optimal solution. Given adequate initial conditions, this solution will be the minimum zone solution. This methodology is also applied to the problems of computing the minimum circumscribed cylinder and the maximum inscribed cylinder. Experimental evidence that the formulations are both robust and efficient is provided.     

直线度平面度公差的快速评定测点分类法

在直线度、平面度公差判定的最小包容区域法中提出一个新的、快速的实施方法。新方法将所有测量点分成“高点”、“低点”和“鞍点”三种类型。并指出最小包容区域法中的最高点只出现在“高点”中,最低点只出现在“低点”中,最高(低)点不会出现在“鞍点”中。这样极大的减少了搜索的范围,提高了软件的效率,而且测量点越多,效果越显著。通过70个测点平面度评定的典型算例,表明此算法比传统的最小区域法要快几十倍。     

基于神经网络的摄像机标定方法研究

提出了一种新的基于神经网络的摄像机标定方法。该方法将标定物从三维降到二维,在获得网络样本时,通过Harris角点检测法和张正友二维平板标定法得到,使其能够在保证精度的基础上,降低时间复杂度。实验结果表明,该方法得到了较好的实验结果。     

Soft sensor modeling of chemical process based on self-organizing recurrent interval type-2 fuzzy neural network

This study introduces a novel self-organizing recurrent interval type-2 fuzzy neural network (SRIT2FNN) for the construction of a soft sensor model for a complex chemical process. The proposed SRIT2FNN combines interval type-2 fuzzy logic systems (IT2FLSs) and recurrent neural networks (RNNs) to improve the modeling precision. The Gaussian interval type-2 membership function is used to describe the antecedent part of the SRIT2FNN fuzzy rule, and the consequent part is of the Mamdani type with an interval random number. An adaptive optimal clustering number of fuzzy kernel clustering algorithm based on a Gaussian kernel validity index (GKVI-AOCN-FKCM) is developed to determine the structure of the SRIT2FNN and fuzzy rule antecedent parameters, and the parameter learning of SRIT2FNN used the gradient descent method. Finally, the proposed SRIT2FNN is applied to the soft sensor modeling of ethylene cracking furnace yield in a typical chemical process. Comparisons between the SRIT2FNN and conventional fuzzy neural network (FNN) and interval type-2 fuzzy neural network (IT2FNN) are made via simulation experiments. The results show that the proposed SRIT2FNN performs better than the conventional FNN and IT2FNN.     

免疫神经网络在故障诊断中的应用

利用生物免疫学的原理,将神经网络和免疫算法结合起来,形成免疫神经网络,并应用于电液伺服阀的故障诊断中.结果表明,免疫神经网络能够以较小的网络规模实现对多种故障模式的准确识别,具有高效率、容错性能好和强大的自适应能力.     

Research on calculation method of free flow discharge based on artificial neural network and regression analysis

Taking the Huaidian Sluice on the Shaying River in China as an example, this paper establishes the calculation model of the free flow based on artificial neural network and regression analysis. Four forms of discharge coefficient calculation equations were obtained by regression analysis, and three neural network models were established. The model is fully verified by using the measured data. The experimental results show that the third-order polynomial and multilayer perceptron neural network have better adaptability. The advantages and disadvantages of the different methods are analyzed and the cause of the error is identified. It provides a theoretical basis for dealing with the discharge calculation of small and medium dam.