多测点平面度误差智能评定与不确定度分析方法研究
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摘要
大尺寸、高精度工件测量点较多，用传统形状误差评定算法计算，会出现算法不收敛或计算缓慢问题，已难以适应产品检测发展要求，因此研究高准确度、高可靠性、高效率的现代评定方法具有重要实际意义。研究工作得到教育部新世纪优秀人才支持计划项目(NCET-08-0211)、广东省高校高层次人才项目(粤教师函[2010]79号)的资助。
论文讨论平面度误差定义、多测点平面度误差评定难点、评定方法优劣的性能指标，从基于数值算法平面度误差评定方法、基于计算几何法平面度误差评定方法、基于智能算法平面度误差评定方法三个方面分析讨论平面度误差评定方法的国内外研究进展，确定论文的研究内容。论文主要工作包括：
研究多测点智能评定优化算法及测量数据仿真方法。分析指出特征测量点分布在最小包容区域平面附近，提出最小二乘残差法(Least Squre Risidual,LSR)的特征测量点提取方法，减小多测点评定过程计算量；根据测量点在x、y、z轴向的坐标极值求出包容区域的两种极端情况，从而确定最小包容区域法向量范围，并作为智能算法个体初始化依据；进一步探讨智能算法适应度函数、停机条件的设计，并在以上研究基础上提出基于遗传算法、粒子群算法、蜂群算法的平面度误差智能评定方法；通过分析平面加工过程影响因素，提出了由多项式函数、三角函数、随机误差函数组成，且符合最小包容区域判别准则的加工平面仿真模型；利用该模型验证智能评定算法的性能，实验结果表明提取阈值系数kP=0.6、初始化个体数sINIT=20时，评定时间TC≤0.0508s、评定误差δt≤0.8745×10-5mm，说明以上智能评定算法处理多测点的性能较好。
研究基于β分布统示法的智能评定不确定度评估方法。以粒子群智能评定算法为例，分析新个体的包容区域宽度分布特性，得出智能评定结果概率密度函数f (t_e)分布为有界右偏概率分布；分析指出b分布统示法在h> g>1时，与f (t_e)分布特性吻合，并采用该方法对f (t_e)进行拟合；利用评定结果的最优值、 b分布的左边界与平面度误差的关系，提出一种平面度误差区间估计方法，同时采用百分位数Qp截取法保留优秀评定样本，采用最大熵方法(MEM)求解左边界的重要参数mte、ste，提高区间估计的可靠性；仿真实验结果表明b分布统示法对智能评定结果都可取得较好拟合效果，平面度误差估计区间跨度Dt T均较小，智能评定结果样本N S=100，截取百分位数Q_p=20时，Dt_T [10~-7,10~-5]mm，且都能包容平面度误差，能够有效评估智能评定的不确定度。
研究平面度误差的支持向量机(SVM)评定方法。分析支持向量回归(SVR)和平面度误差最小包容区域的数学模型，指出SVR的寻优目标——最优超平面与最小包容区域评定原则在几何机理上完全一致，并提出基于ε-SVR的平面度评定方法；针对ε难以确定，提出基于分离式支持向量机分类(SSVC)的平面度误差评定方法，并采用SMO算法将对偶化模型分解为两个样本Langarange因子求解，提高计算效率；提出基于蒙特卡罗法的测量不确定度评估方法；仿真评定实验结果表明SSVC评定方法评定误差较低，评定时间TC≤0.0508s，说明SSVC评定方法处理多测点的性能也较好；借助映射F将最小区域中心圆、最小区域中心圆柱面转换到Hilbert空间的超平面形式，探讨支持向量机(SVM)应用于圆度误差、圆柱度误差评定机理，为SVM方法应用于其他形状误差评定提供一种思路。
开展花岗岩平板、轨道板平面度误差、轴承环圆度误差智能评定实验研究，验证平面度误差及圆度误差智能评定与不确定度评估在实际测量中的实用性、有效性。
There are many measurement points for large scale and high precision workpieces,therefore, the traditional form error evaluation method in this case does not converge orcalculates slowly, and it is difficult to meet the needs of the development of product testing,so that the research of high accuracy, high reliability, high efficiency of modern evaluationmethod has important practical significance. The reaseach work received financial supportfrom Ministry of Education Support Program for New Century ExcellentTalent(NCET-08-2011), Guangdong Province Institutes of Higher Education High-qualifiedTalent Project(Yue Jiao Shi Han[2010]79).
Beginning with discussion of flatness definition, difficulties for many measurementpoints evaluation, evaluation performance indexes, this research progress at home and abroadof the flatness evaluation based on numerical algorithm, computational geometry, andintelligent algorithm were reviewed generally to determine the research content of this paper.The main research work in this paper is as follows:
Many measurement points intelligent evaluation optimization algorithm and thesimulation method for measurement points were researched. It was analyzed thatcharacteristic measurement points are distributed nearby the minimum zone planes, acharacteristic measurement points extraction method Least Square Residual-LSR wasproposed to reduce computational complexity in the evaluation. Two extreme cases ofminimum zone were calculated according to coordinate extremums of measurement points inx、y、z–axis, then minimum zone normal vector range was determined, which intelligentalgorithm individuals initialization was depending on. Fitness function and terminationcondition were researched. Based on the above, several bionic intelligent flatness evaluationmethods based on genetic algorithm, particle swarm optimization, and artificial bee colonywere proposed. According to analyze the affecting factors in the planar process, the planeprocessing simulation model was constructed, which consisted of a polynomial function,trigonometric function, random error function and satisfied minimum zone criterion. Themodel was used to verify intelligent evaluation methods, and the results showed that whenextracting threshold factor kP=0.6, initial individuals amount sINIT=20, evaluation timeTC≤0.0508s, evaluation error δt≤0.8745×10~-5mm, which proved that the intelligent evaluationmethods were effective for many points evaluation.
The assessment method for intelligent evaluation uncertainty based on β distributionuniform expression method was researched. Taking particle swarm optimization (PSO) evaluation method as an example, through analyzing enveloping zone distribution feature ofthe new particle, it was obtained that the probability density function of intelligent evaluationresults f (t_e)is bounded and right skewed. It was pointed that β distribution, if h> g>1,coincides with f (t_e)’s distribution feature, therefore β distribution was used for fitting f (t e)probability distribution. The best evaluation value and the left margin of β distribution werechosen for flatness error interval estimation, while percentile Qpintercept method wasproposed to reserve better evaluation samples, the maximum entropy method(MEM) wasused to calculate the important parameters of the left marginmte,steto improve thereliability of the interval estimation. The simulation experiments results showed that βdistribution uniform expression method has a good fitting for intelligent evaluation results,while the length of flatness estimate sectionDt Thas a short span. As the number ofintelligent evaluation samplesN S=100, intercept percentile Q p=20,Dt T [10~-7,10~-5]mm,whileDt Tincluded flatness error value. This method could effectively present intelligentevaluation uncertainty.
Flatness error evaluation method based support vector machine (SVM) was researched.Through analyzing the mathematic models of support vector machine regression (SVR) andflatness error minimum zone, it was pointed that SVR optimization goals-optimal hyper planeand the minimum zone criterion results in exactly the same geometric mechanism.Consequently, the evaluation method based on ε-SVR was proposed. Aiming at ε was hard tofix, the evaluation method based on seperated support vector machine classification (SSVC)was also proposed, which uses SMO algorithm to decomposite the even model intocalculating two samples’ Langarange factors to improve computational efficiency.Measurement uncertainty assessment methods using Monte Carlo Method was proposed. Alsosimulation measurement data evaluation experiments were performed. The simulationexperiments results showed that SSVC evaluation error was lower, and evaluation timeTC≤0.0508s, which proved that SSVC was also effective for many points evaluation. Throughmapping F, minimum zone center circle and center cylindrical surface are transformed intohyper plane in Hilbert space, SVM could be used in roundness error and cylinderity errorevaluation, which provided a new idea for other form error evaluation.
Granite surface plates, track plates flatness error, bearing ring roundness errorintelligent evaluation experiments were performed; the results verified that the flatness errorand roundness error intelligent evaluation and uncertainty assessment in this paper is of practicality and effectiveness in practical measurement.
论文讨论平面度误差定义、多测点平面度误差评定难点、评定方法优劣的性能指标，从基于数值算法平面度误差评定方法、基于计算几何法平面度误差评定方法、基于智能算法平面度误差评定方法三个方面分析讨论平面度误差评定方法的国内外研究进展，确定论文的研究内容。论文主要工作包括：
研究多测点智能评定优化算法及测量数据仿真方法。分析指出特征测量点分布在最小包容区域平面附近，提出最小二乘残差法(Least Squre Risidual,LSR)的特征测量点提取方法，减小多测点评定过程计算量；根据测量点在x、y、z轴向的坐标极值求出包容区域的两种极端情况，从而确定最小包容区域法向量范围，并作为智能算法个体初始化依据；进一步探讨智能算法适应度函数、停机条件的设计，并在以上研究基础上提出基于遗传算法、粒子群算法、蜂群算法的平面度误差智能评定方法；通过分析平面加工过程影响因素，提出了由多项式函数、三角函数、随机误差函数组成，且符合最小包容区域判别准则的加工平面仿真模型；利用该模型验证智能评定算法的性能，实验结果表明提取阈值系数kP=0.6、初始化个体数sINIT=20时，评定时间TC≤0.0508s、评定误差δt≤0.8745×10-5mm，说明以上智能评定算法处理多测点的性能较好。
研究基于β分布统示法的智能评定不确定度评估方法。以粒子群智能评定算法为例，分析新个体的包容区域宽度分布特性，得出智能评定结果概率密度函数f (t_e)分布为有界右偏概率分布；分析指出b分布统示法在h> g>1时，与f (t_e)分布特性吻合，并采用该方法对f (t_e)进行拟合；利用评定结果的最优值、 b分布的左边界与平面度误差的关系，提出一种平面度误差区间估计方法，同时采用百分位数Qp截取法保留优秀评定样本，采用最大熵方法(MEM)求解左边界的重要参数mte、ste，提高区间估计的可靠性；仿真实验结果表明b分布统示法对智能评定结果都可取得较好拟合效果，平面度误差估计区间跨度Dt T均较小，智能评定结果样本N S=100，截取百分位数Q_p=20时，Dt_T [10~-7,10~-5]mm，且都能包容平面度误差，能够有效评估智能评定的不确定度。
研究平面度误差的支持向量机(SVM)评定方法。分析支持向量回归(SVR)和平面度误差最小包容区域的数学模型，指出SVR的寻优目标——最优超平面与最小包容区域评定原则在几何机理上完全一致，并提出基于ε-SVR的平面度评定方法；针对ε难以确定，提出基于分离式支持向量机分类(SSVC)的平面度误差评定方法，并采用SMO算法将对偶化模型分解为两个样本Langarange因子求解，提高计算效率；提出基于蒙特卡罗法的测量不确定度评估方法；仿真评定实验结果表明SSVC评定方法评定误差较低，评定时间TC≤0.0508s，说明SSVC评定方法处理多测点的性能也较好；借助映射F将最小区域中心圆、最小区域中心圆柱面转换到Hilbert空间的超平面形式，探讨支持向量机(SVM)应用于圆度误差、圆柱度误差评定机理，为SVM方法应用于其他形状误差评定提供一种思路。
开展花岗岩平板、轨道板平面度误差、轴承环圆度误差智能评定实验研究，验证平面度误差及圆度误差智能评定与不确定度评估在实际测量中的实用性、有效性。
There are many measurement points for large scale and high precision workpieces,therefore, the traditional form error evaluation method in this case does not converge orcalculates slowly, and it is difficult to meet the needs of the development of product testing,so that the research of high accuracy, high reliability, high efficiency of modern evaluationmethod has important practical significance. The reaseach work received financial supportfrom Ministry of Education Support Program for New Century ExcellentTalent(NCET-08-2011), Guangdong Province Institutes of Higher Education High-qualifiedTalent Project(Yue Jiao Shi Han[2010]79).
Beginning with discussion of flatness definition, difficulties for many measurementpoints evaluation, evaluation performance indexes, this research progress at home and abroadof the flatness evaluation based on numerical algorithm, computational geometry, andintelligent algorithm were reviewed generally to determine the research content of this paper.The main research work in this paper is as follows:
Many measurement points intelligent evaluation optimization algorithm and thesimulation method for measurement points were researched. It was analyzed thatcharacteristic measurement points are distributed nearby the minimum zone planes, acharacteristic measurement points extraction method Least Square Residual-LSR wasproposed to reduce computational complexity in the evaluation. Two extreme cases ofminimum zone were calculated according to coordinate extremums of measurement points inx、y、z–axis, then minimum zone normal vector range was determined, which intelligentalgorithm individuals initialization was depending on. Fitness function and terminationcondition were researched. Based on the above, several bionic intelligent flatness evaluationmethods based on genetic algorithm, particle swarm optimization, and artificial bee colonywere proposed. According to analyze the affecting factors in the planar process, the planeprocessing simulation model was constructed, which consisted of a polynomial function,trigonometric function, random error function and satisfied minimum zone criterion. Themodel was used to verify intelligent evaluation methods, and the results showed that whenextracting threshold factor kP=0.6, initial individuals amount sINIT=20, evaluation timeTC≤0.0508s, evaluation error δt≤0.8745×10~-5mm, which proved that the intelligent evaluationmethods were effective for many points evaluation.
The assessment method for intelligent evaluation uncertainty based on β distributionuniform expression method was researched. Taking particle swarm optimization (PSO) evaluation method as an example, through analyzing enveloping zone distribution feature ofthe new particle, it was obtained that the probability density function of intelligent evaluationresults f (t_e)is bounded and right skewed. It was pointed that β distribution, if h> g>1,coincides with f (t_e)’s distribution feature, therefore β distribution was used for fitting f (t e)probability distribution. The best evaluation value and the left margin of β distribution werechosen for flatness error interval estimation, while percentile Qpintercept method wasproposed to reserve better evaluation samples, the maximum entropy method(MEM) wasused to calculate the important parameters of the left marginmte,steto improve thereliability of the interval estimation. The simulation experiments results showed that βdistribution uniform expression method has a good fitting for intelligent evaluation results,while the length of flatness estimate sectionDt Thas a short span. As the number ofintelligent evaluation samplesN S=100, intercept percentile Q p=20,Dt T [10~-7,10~-5]mm,whileDt Tincluded flatness error value. This method could effectively present intelligentevaluation uncertainty.
Flatness error evaluation method based support vector machine (SVM) was researched.Through analyzing the mathematic models of support vector machine regression (SVR) andflatness error minimum zone, it was pointed that SVR optimization goals-optimal hyper planeand the minimum zone criterion results in exactly the same geometric mechanism.Consequently, the evaluation method based on ε-SVR was proposed. Aiming at ε was hard tofix, the evaluation method based on seperated support vector machine classification (SSVC)was also proposed, which uses SMO algorithm to decomposite the even model intocalculating two samples’ Langarange factors to improve computational efficiency.Measurement uncertainty assessment methods using Monte Carlo Method was proposed. Alsosimulation measurement data evaluation experiments were performed. The simulationexperiments results showed that SSVC evaluation error was lower, and evaluation timeTC≤0.0508s, which proved that SSVC was also effective for many points evaluation. Throughmapping F, minimum zone center circle and center cylindrical surface are transformed intohyper plane in Hilbert space, SVM could be used in roundness error and cylinderity errorevaluation, which provided a new idea for other form error evaluation.
Granite surface plates, track plates flatness error, bearing ring roundness errorintelligent evaluation experiments were performed; the results verified that the flatness errorand roundness error intelligent evaluation and uncertainty assessment in this paper is of practicality and effectiveness in practical measurement.
引文
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