改进蜂群算法及其在圆度误差评定中的应用

针对基本人工蜂群算法(Artificial bee colony algorithm,ABC)的缺点,提出一种改进人工蜂群算法(Improved artificial bee colony algorithm,IABC),并应用于圆度误差最小区域评定中。该改进算法利用信息熵初始化种群,增强种群的多样性,并在引领蜂和跟随蜂搜索阶段,提出一种新的搜索策略,平衡算法的探索与开发能力。详细阐述IABC算法的基本原理与实现步骤,给出圆度误差满足最小包容区域条件的优化目标函数和收益度函数。通过基准测试函数验证IABC算法的有效性和准确性;通过对由三坐标机测得的多组测量数据进行圆度误差评定试验,结果表明IABC算法的评定精度优于最小二乘法、遗传算法以及粒子群算法等其他优化算法,且在求解质量和稳定性上优于ABC算法,验证了IABC算法不仅正确,而且适用于圆度误差的评定优化。     

基于多目标优化的空间直线度误差评定

根据最小区域定义及数学规划理论，建立了空间直线度评定的非线性规划模型，指出了这模型实质上是多目标优化的问题并将该优化问题转化成单目标优化问题。由于该非线性规划模型还是凸的、二次的，因此提出了用逐次二次规划的解法（SQP法）来实施。SQP法在评定过程中保留了模型中的非线性信息，对初始参数的要求低，且稳定、可靠、效率高。几个算例的结果均满足凸规划全局最优判别准则，这就有力的验证了上述结论。     

空间直线度误差评定的新算法

针对在坐标测量机CMM上测得的空间直线度误差测点集(测点序列),为提高空间直线度误差的评定精度,运用误差理论和最小二乘原理,提出了基于测点集中心的最小二乘算法(LSABC算法),推导出了LSABC算法的数学模型。并根据其基于测点集中心的特点,在按LSABC算法对全部测点进行高低排序后,以其中两最高点的中点为基点,设计出了LSABC改进算法。最后,利用UG/GRIP语言对以上新算法编制了计算机程序,以进行数字实验验证。数字实验结果表明:新算法比传统的最小二乘算法和其他多种算法具有更高的正确度。     

An improved artificial bee colony algorithm with MaxTF heuristic rule for two-sided assembly line balancing problem

Two-sided assembly line is usually used for the assembly of large products such as cars, buses, and trucks. With the development of technical progress, the assembly line needs to be reconfigured and the cycle time of the line should be optimized to satisfy the new assembly process. Two-sided assembly line balancing with the objective of minimizing the cycle time is called TALBP-2. This paper proposes an improved artificial bee colony (IABC) algorithm with the MaxTF heuristic rule. In the heuristic initialization process, the MaxTF rule defines a new task’s priority weight. On the basis of priority weight, the assignment of tasks is reasonable and the quality of an initial solution is high. In the IABC algorithm, two neighborhood strategies are embedded to balance the exploitation and exploration abilities of the algorithm. The employed bees and onlooker bees produce neighboring solutions in different promising regions to accelerate the convergence rate. Furthermore, a well-designed random strategy of scout bees is developed to escape local optima. The experimental results demonstrate that the proposed MaxTF rule performs better than other heuristic rules, as it can find the best solution for all the 10 test cases. A comparison of the IABC algorithm and other algorithms proves the effectiveness of the proposed IABC algorithm. The results also denote that the IABC algorithm is efficient and stable in minimizing the cycle time for the TALBP-2, and it can find 20 new best solutions among 25 large-sized problem cases.

     

An improved artificial bee colony algorithm for the blocking flowshop scheduling problem

This paper presents an improved artificial bee colony (IABC) algorithm for solving the blocking flowshop problem with the objective of minimizing makespan. The proposed IABC algorithm utilizes discrete job permutations to represent solutions and applies insert and swap operators to generate new solutions for the employed and onlooker bees. The differential evolution algorithm is employed to obtain solutions for the scout bees. An initialization scheme based on the problem-specific heuristics is presented to generate an initial population with a certain level of quality and diversity. A local search based on the insert neighborhood is embedded to improve the algorithm's local exploitation ability. The IABC is compared with the existing hybrid discrete differential evolution and discrete artificial bee colony algorithms based on the well-known flowshop benchmark of Taillard. The computational results and comparison demonstrate the superiority of the proposed IABC algorithm for the blocking flowshop scheduling problems with makespan criterion.     

A combinatorial optimization approach for evaluating minimum-zone spatial straightness errors

This paper presents a new and robust approach for the accurate evaluation of minimum-zone spatial straightness error from a set of coordinate measurement data points. The algorithm iteratively searches for the specific data points that define the minimum bound of the spatial straightness zone using combinatorial optimization. It is based on the fact that the minimum circumscribed cylinder of a point set, which is equivalent to the minimum spatial straightness zone of the measurement data, will pass through three, four, or five of the data points that constitute the convex hull vertices of the entire data set. Computed results have shown that although the presented approach may lead to increased computational time, it is robust and able to construct the exact minimum circumscribed cylinder for a given point set. The minimum-zone spatial straightness error can thus be evaluated with the best possible accuracy. The advantage of the presented algorithm is demonstrated via comparison with published computed results of existing algorithms.     

并联轴直线运动直线度的检测与误差补偿

通过采用Renishaw激光干涉仪检测混联机床并联轴直线运动的直线度误差,对直线度的干涉测量原理和方法进行深入探讨,提出一种并联轴直线运动直线度的干涉测量方法和误差补偿模型的建模方法。分析干涉仪直线度评定方法和算法,做出并联轴直线运动直线度双向平均偏差特性曲线,建立直线度误差数学模型。利用最小二乘法拟合得到直线度均值误差补偿模型。对并联轴直线运动直线度进行补偿,达到了提高混联机床几何精度的目的。     

基于最小包容区域的球度误差评定方法

针对球度误差评定方法存在原理误差或模型误差,提出了一种符合最小包容区域定义的球度误差评定方法,即将几何搜索逼近算法与基于最小包容区域法的球度误差评定的几何结构和定义结合起来的准确评定方法。对仿真数据和其他文献中的数据进行了评定。所提方法与其他方法的评定结果表明,所提方法可以准确地找到最小包容区域球的球心并给出球度误差的精确解。     

直线度误差处理系统的研制

研制了与电子水平仪配套的直线度误差专用处理系统。介绍了该系统的工作原理、结构组成以及内嵌的直线度误差最小区域算法 ,阐述了该算法的原理及其在单片机上的实现方案 ,给出了系统原理图和程序框图     

传感器调零误差对直线误差分离的影响规律及其确定方法分析

分析了多点法直线 EST中传感器初始调零误差对直线误差分离结果的影响 ,指出不同方法的影响规律不同 :时域三点法中调零误差使直线形状误差按抛物线规律呈非线性增大 ,对直线误差评定产生很大影响 ;时域二点法中调零误差使直线形状误差线性增大 ,但对评定无影响 ;频域三点法的直线误差则不受调零误差的影响。提出了通过构造软基准来确定调零误差的两种方法 :时域频域结合法和对称反转配置法 ,可以克服常规方法的局限性     

评定二次曲面轮廓度误差的角度分割逼近法

提出一种基于角度分割逼近算法和粒子群算法计算二次曲面轮廓度误差的最小区域评定方法来准确评定任意位姿的二次曲面轮廓度误差。首先,给出了能够实现角度分割逼近算法的两条前提假设;基于假设,给出了更合理的算法网格布局递推公式。根据曲面轮廓度误差的定义建立了误差评定的精确模型。然后,采用角度分割逼近法求取测点到拟合二次曲面轮廓的距离;通过粒子群算法,以所有的点与二次曲面距离中的最大值为适应度值拟合出二次曲面一般方程,并实现被测轮廓与理论轮廓位置的匹配。最后,采用上述方法对某抛物面天线进行了评定,并与参数分割法、SMX-Insight和最小二乘法进行比较。实验结果显示：该方法测得的天线轮廓度误差为0.659 8 mm,比其它方法准确。结论表明：基于角度分割算法能够更有效地评定任意位姿二次曲面轮廓度误差,计算准确、迅速,而且无需确定待分割区域。     

Evaluating the geometric characteristics of cylindrical features

This paper presents mathematical models and efficient methodologies for the evaluation of geometric characteristics that define form and function of cylindrical features; namely cylindricity and straightness of median line. These two problems have similar structures and can be solved by comparable procedures. Based on the proposed methodologies, the cylindricity error evaluation can be performed using any of the following criteria: the least squares cylinders, minimum circumscribed cylinders, maximum inscribed cylinders or minimum zone cylinders. The procedures have been tested for accuracy and efficiency. The results indicate that they provide accurate results quickly.     

基于阻尼粒子群优化的地磁场测量误差补偿

针对三轴磁力仪在磁场测量过程中的磁干扰问题,提出了基于阻尼粒子群优化算法的磁测误差补偿方法。建立了磁力仪误差和载体磁干扰的一体化误差补偿模型,分别采用阻尼粒子群算法和Two-step方法对非线性观测模型进行参数估计。以质子磁力仪数据作为真值,借助无磁转台充分连续采样,实验结果显示,阻尼粒子群算法对于磁场测量误差具有良好的抑制作用。补偿后,由阻尼粒子群算法和Two-step方法得到的均方根误差分别由1 025.7降至60.304 4、581 n T。结果表明,阻尼粒子群算法取得了更好的补偿效果,补偿精度提高了至少一个数量级,为磁场测量误差提供了一种非常有效的补偿方法。     

平面内直线度误差最小区域法的完备性研究

针对国家标准GB/T 11336-2004中用于平面内直线度误差最小包容区域评定的极点计算法对有些数据的处理结果不符合最小包容区域的高-低-高或低-高-低原则,即存在不完备性,因此提出定向极点搜索与迭代的评定方法。理论分析和平面内直线度误差数据的处理实例证明本方法完全符合平面内直线度误差评定的最小包容区域的高-低-高或低-高-低原则。数据处理的结果还进一步显示新方法完备性好,评定结果精准、可靠,计算过程绝对收敛、速度也更快,可以克服国家标准GB/T 11336-2004中平面内直线度误差评估的极点计算法存在的缺陷。     

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.     

基于光学扫描法的导轨直线度测量方法

基于多测头光学扫描法对导轨直线度的在位测量方法,提出一种新的倾角补偿的三测头扫描方法。介绍了测量原理,推导了基于最小二乘法的直线度形状重构方法,重构出的形状可精确反映直线度误差的高频成分,且对测量噪声有良好抑制能力。对算法进行了仿真验证,并由实验验证了提出方法的有效性。实验结果表明,该方法可以精确地还原出台阶状的直线度形状,测量标准偏差在10μm以内。     

Evaluation of angular error between two lines

The error caused by the fitting of a set of data points to two lines having a specified angle is defined as the angular error. The evaluation of angular error needs to find two pairs of parallel lines that follow the angular constraint and bound the data points under the minimum zone criterion. The evaluation of angular error is difficult in mathematics, so it is usually simplified by treating one line as the datum and the form error of the other line calculated from the datum as the solution. The datum is assumed to be perfect that doesn’t tell the real properties of the actual line but gives incorrect solutions in general. To give an exact solution to the angular error problem based on the minimum zone criterion, a new mathematical model is proposed in this paper. The basic idea of this model is to rotate the data points of one line to the same direction as that of the other line so that the evaluation of angular error is simplified as solving a straightness problem. The angular error obtained from the proposed model is proved to be minimum. The proposed model offers a simple approach to solve the tough angular error problem, and it also provides a feasible tool to explore more complicated problems, like 3D angular error and polygon error.     

平面直线度误差数值分析判定

建立直线度误差的相对坐标,基于最小二乘对坐标内的离散点进行曲线拟合,而后对其进行相似坐标变换,利用数值分析方法得到坐标变换的一系列旋转因子(旋转参数)与满足最小条件的包容区域,最后通过比较法实现对直线度误差的数值判定.文中给出一实例,验证了该方法的可行性与有效性.     

Effect of working position on vertical motion straightness of open hydrostatic guideways in grinding machine

Hydrostatic guideways have various applications in precision machine tools due to their high motion accuracy. The analysis of motion straightness in hydrostatic guideways is generally ignoring the external load on the slider. A variation force also exists, caused by the different working positions, together with the dead load of the slider and that of other auxiliary devices. The effect of working position on vertical motion straightness is investigated based on the equivalent static model, considering the error averaging effort of pressured oil film in open hydrostatic guideways. Open hydrostatic guideways in LGF1000 are analyzed with this approach. The theoretical results show that the slider has maximum vertical motion straightness when the working position is closer the guiderail of Y axis. The vertical motion straightness reaches a minimum value as the working position is located at the center of the two guiderails on the Y axis. The difference between the maximum and minimum vertical motion straightness is 34.7%. The smaller vertical motion straightness is attributed to the smaller spacing of the two pads centers, along the Y direction. The experimental results show that the vertical motion straightness is 4.15 μm/1200 mm, when the working position is located in the middle of the X beam, and 5.08 μm/1200 mm, when the working position is approaching the Y guiderails, denoting an increase of 18.3%. The changing trends of the measured results validate the correctness of the theoretical model. The research work can be used to reveal the variation law of accuracy of the open hydrostatic guideways, under different working positions, to predict the machining precision, and provides the basis for an error compensation strategy for gantry type grinding machines.     

基于LabVIEW直线度误差测量数据处理方法研究

针对传统的直线度误差测量与评定中存在的若干问题,设计了基于LabVIEW的测量与评定软件。由软件控制采集卡获得被测数据、实现数字滤波、生成误差曲线、自动计算直线度误差值。实验结果表明,软件具有良好的人机界面、计算准确、稳定可靠,满足了工业测试的需要。