基于遗传算法的圆度误差评估

将遗传算法应用于圆度误差的评定.首先简介了误差评定背景和遗传算法及其特点.然后根据尺寸和公差的数学定义^[1]给出满足最小区域条件的圆度公差评定的数学模型和适应度函数.接着,以最小二乘解作为初始值,对圆度误差的遗传优化过程进行了详细的论述.最后用实例对算法进行验证.优化过程和实验结果显示了遗传算法在解决形状公差的评定这类非线性问题的优越性,通过并行搜索能最大限度地保证解的全局最优,计算精度高、效率高,且易于理解和实现.     

基于实数编码遗传算法的平面度评定

将基于实数编码的遗传算法应用于平面度的评定.根据尺寸和公差的数学定义,建立完全符合最小区域条件的平面度评定的数学模型,并在此基础上给出遗传算法的适应度函数.随后详细地介绍了算法的实现步骤,在基于实数编码的基础上,遗传选择操作采用一种正比选择策略--转轮法,遗传交叉操作采用简单算术交叉法,而遗传变异操作是随机均匀实数变异操作.最后对文献[5]的实验数据进行了评定,仿真结果表明该算法不仅合理,而且效率高、精度高,优于其它算法.     

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.     

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。     

基于遗传算法的圆度公差评定法与采用最小二乘法评定的比较

根据提出的计算模型,对基于遗传算法的圆度误差评定和传统上采用最小二乘法的评定算法进行了比较分析,根据方法本身的特点和计算结果,分析了二者的不同点以及在工程应用中的适用场合.所构造的模型包括边界控制点和区域随机点,其中边界控制点模拟了由圆度误差最小区域条件所定义的最大内切圆和最小外切圆,而区域随机点模拟了实际情况下测试点的随机性和不确定性.计算结果表明基于遗传算法的圆度评定法精度较高,优于基于最小二乘法的评定算法.     

粒子群优化算法及其在圆柱度误差评定中的应用

提出了将粒子群优化算法用于圆柱度误差评定的设想。对算法的基本原理和实现步骤做了具体阐述,给出了圆柱度误差评定的基本问题,及其优化目标函数及算法的适应度函数和编码方式,对算法进行了可行性和准确性验算。计算结果表明,该方法对于圆柱度误差评定这类具有复杂目标函数和较多参数的非线性优化问题有很好的计算性能,优于最小二乘法;与遗传算法和其它满足最小区域条件计算方法相比,计算精度略优于前者或者与前者相当,能够获得精度较高的结果,而突出优点是简单,易于实现而且计算效率较高。     

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。     

评定平面度误差的几何搜索逼近算法

为了快速准确地评定机械零件的平面度误差,提出了基于几何搜索逼近的平面度误差最小区域评定算法.阐述了利用几何优化搜索算法求解平面度误差的过程和步骤,给出了数学计算公式.首先选择被测平面的3个边缘点为参考点构造辅助点、参考平面和辅助平面,然后以参考平面和辅助平面为假定理想平面,计算测量点至这些理想平面的距离极差;通过比较判断及改变参考点,构造新的辅助点、参考平面和辅助平面,最终实现平面度误差的最小区域评定.用提出的方法对一组测量数据进行了处理.结果表明,在终止搜索的条件为0.000 01 mm时,几何搜索逼近评定算法的结果分别比凸包法、计算几何法、最小二乘法、遗传算法和进化策略计算的结果减小了17.1、7.3、18.03、6.13和0.3μm.得到的数据显示该算法不仅能准确地得到最小区域解,而且计算结果有良好的稳定性,适合在平面度误差测量仪器和三坐标测量机上使用.     

基于计算几何的平面度误差评定方法

本文针对平面度误差评定的特点,提出了一种基于计算几何凸包理论的评定方法.阐述了如何利用凸包的几何特征找出对应最小区域以完成误差评价,并详细介绍了三维凸包的构造方法.该方法不存在模型误差,具有对"最小区域"的几何直观性描述,不仅提供了在理论上严格符合公差定义中关于"最小区域"定义的精确解,而且不存在传统优化算法的局部收敛性问题.用VC编程实现算法并经过大量实例数据进行仿真,证明了该方法的可靠性和高效性.     

对称度误差的快速精确评定

以面对面对称度误差为例,介绍了定位最小包容区域法评定对称度误差的数学模型和实现方法.为了提高评定效率,采用测点筛选法对测点进行筛选,剔除与评定无关的测点,从而减少测点搜索次数,提高程序评定速度.同时给出了算例来验证算法的正确性与可行性.     

最小区域球度误差评价的弦线截交方法

最小区域球度误差评价是精密测量技术中的一个非常重要并且复杂问题。针对笛卡儿坐标系下球体形状误差评价,介绍一种利用弦线截交关系求解最小区域球度误差评价方法。通过构建笛卡儿坐标系下球度误差测量模型,提出基于一般二次曲面理论的最小二乘球心计算方法。根据最小区域球度误差模型分类,利用弦线截交关系建立起最小区域球度误差评价的2+3和3+2模型,最后通过截交几何模式产生了虚拟中心,从而准确确定球度误差评价模型的最大弦线与最大截面,达到快速精确构建模型的目的。测试数据和实例应用表明,基于弦线截交关系的最小区域球度误差评价方法具有更高的计算效率,且测量空间不受测量坐标系和零件几何形状误差的影响,并显著提高了整体评价的精度与准确性。     

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.     

Adaptive Monte Carlo and GUM methods for the evaluation of measurement uncertainty of cylindricity error

Measurement uncertainty is one of the most important concepts in geometrical product specification (GPS). The “Guide to the expression of uncertainty in measurement (GUM)” is the internationally accepted master document for the evaluation of uncertainty. The GUM method (GUMM) requires the use of a first-order Taylor series expansion for propagating uncertainties. However, when the mathematical model of measurand is strongly non-linear the use of this linear approximation may be inadequate. Supplement 1 to GUM (GUM S1) has recently been proposed based on the basis of probability density functions (PDFs) using the Monte Carlo method (MCM). In order to solve the problem that the number of Monte Carlo trials needs to be selected priori, adaptive Monte Carlo method (AMCM) described in GUM S1 is recommended to control over the quality of the numerical results provided by MCM.The measurement and evaluation of cylindricity errors are essential to ensure proper assembly and good performance. In this paper, the mathematical model of cylindricity error based on the minimum zone condition is established and a quasi particle swarm optimization algorithm (QPSO) is proposed for searching the cylindricity error. Because the model is non-linear, it is necessary to verify whether GUMM is valid for the evaluation of measurement uncertainty of cylindricity error. Then, AMCM and GUMM are developed to estimate the uncertainty. The procedure of AMCM scheme and the validation of GUMM using AMCM are given in detail. Practical example is illustrated and the result shows that GUMM is not completely valid for high-precision evaluation of the measurement uncertainty of cylindricity error if only the first-order terms in the Taylor series approximation are taken into account. Compared with conventional methods, not only the proposed QPSO method can search the minimum zone cylindricity error precisely and rapidly, but also the Monte Carlo simulation is adaptive and AMCM can provide control variables (i.e. expected value, standard uncertainty and lower and higher coverage interval endpoints) with an expected numerical tolerance. The methods can be extended to the evaluation of measurement uncertainty of other form errors such as roundness and sphericity errors.     

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。     

基于误差转换的汽车曲轴圆度及圆柱度误差评价数学模型构建研究

针对国内汽车曲轴轴颈圆度误差、圆柱度误差检测普遍存在的效率低、精度低等问题,建立基于误差转换的平面曲线和空间曲线误差数学模型,结合圆和圆柱的数学表达建立满足最小包容条件的圆度和圆柱度误差评定数学模型,并采用遗传优化算法计算出符合最小评定要求的曲轴轴颈形位误差,解决了理想包容要素位姿参数不精确的问题。同时,建立基于图像域的汽车曲轴轴颈形状误差检测试验台,针对测量过程中连杆轴颈沿主轴颈公转运动,从而导致连杆轴颈图像域检测数据存在坐标不归一问题,以曲轴法兰端特征孔为基准,通过模板匹配特征与孔边缘提取实现了连杆轴颈圆度和圆柱度测量数据空间坐标归一化处理。以某型号发动机曲轴为例进行大样本误差检测试验,并与三坐标测量机测得的结果进行对比,数据分析表明提出的曲轴轴颈形状误差检测方法的精度为1μm,且重复检测误差在0.1μm以内,证明了其理论上的正确性及实践操作的可行性。     

Conicity error evaluation using sequential quadratic programming algorithm

Form error evaluation plays an important role in processing quality evaluation. Conicity error is evaluated as a typical example in this paper based on sequential quadratic programming (SQP) algorithm. The evaluation is carried out in three stages. Signed distance function from the measured points to conical surface is defined and the cone is located roughly by the method of traditional least-squares (LS) firstly; the fitted cone and the measured point coordinates are transformed to simplify the optimal mathematical model of conicity error evaluation secondly; and then optimization problem on conicity error evaluation satisfying the minimum zone criterion is solved by means of SQP algorithm and kinematic geometry, where approximate linear differential movement model of signed distance function is deduced in order to reduce the computational complexity. Experimental results show that the conicity error evaluation algorithm is more accurate, and has good robustness and high efficiency. The obtained conicity error is effective.     

RESEARCH ON THE MINIMUM ZONE CYLINDRICITY EVALUATION BASED ON GENETIC ALGORITHMS

A genetic algorithm (GA)-based method is proposed to solve the nonlinear optimization problem of minimum zone cylindricity evaluation. First, the background of the problem is introduced. Then the mathematical model and the fitness function are derived from the mathematical definition of dimensioning and tolerancing principles. Thirdly with the least squares solution as the initial values, the whole implementation process of the algorithm is realized in which some key techniques, for example, variables representing, population initializing and such basic operations as selection, crossover and mutation, are discussed in detail. Finally, examples are quoted to verify the proposed algorithm. The computation results indicate that the GA-based optimization method performs well on cylindricity evaluation. The outstanding advantages conclude high accuracy, high efficiency and capabilities of solving complicated nonlinear and large space problems.