Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（GPS） requires the measurement uncertainty characterizing the reliability of the resul...Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（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.展开更多
Measurement uncertainty plays an important role in laser tracking measurement analyses. In the present work, the guides to the expression of uncertainty in measurement(GUM) uncertainty framework(GUF) and its supplemen...Measurement uncertainty plays an important role in laser tracking measurement analyses. In the present work, the guides to the expression of uncertainty in measurement(GUM) uncertainty framework(GUF) and its supplement, the Monte Carlo method, were used to estimate the uncertainty of task-specific laser tracker measurements. First, the sources of error in laser tracker measurement were analyzed in detail, including instruments, measuring network fusion, measurement strategies, measurement process factors(such as the operator), measurement environment, and task-specific data processing. Second, the GUM and Monte Carlo methods and their application to laser tracker measurement were presented. Finally, a case study involving the uncertainty estimation of a cylindricity measurement process using the GUF and Monte Carlo methods was illustrated. The expanded uncertainty results(at 95% confidence levels) obtained with the Monte Carlo method are 0.069 mm(least-squares criterion) and 0.062 mm(minimum zone criterion), respectively, while with the GUM uncertainty framework, none but the result of least-squares criterion can be got, which is 0.071 mm. Thus, the GUM uncertainty framework slightly underestimates the overall uncertainty by 10%. The results demonstrate that the two methods have different characteristics in task-specific uncertainty evaluations of laser tracker measurements. The results indicate that the Monte Carlo method is a practical tool for applying the principle of propagation of distributions and does not depend on the assumptions and limitations required by the law of propagation of uncertainties(GUF). These features of the Monte Carlo method reduce the risk of an unreliable measurement of uncertainty estimation, particularly in cases of complicated measurement models, without the need to evaluate partial derivatives. In addition, the impact of sampling strategy and evaluation method on the uncertainty of the measurement results can also be taken into account with Monte Carlo method, which plays a guiding role in measurement planning.展开更多
The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performanc...The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification（GPS）, the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm（IlEA） is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement（GUM） method to evaluate measurement uncertainty. Adaptive Monte Carlo method（AMCM） is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine（CMM）. The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error（MZCE） rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.展开更多
The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not...The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method(GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method(AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.展开更多
We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,...We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.展开更多
The vehicle system studied in this paper is a type of complex repairable system in which the subsystems follow various failure distributions and conform to arbitrary failure and repair distributions.The failure data o...The vehicle system studied in this paper is a type of complex repairable system in which the subsystems follow various failure distributions and conform to arbitrary failure and repair distributions.The failure data of subsystems are sometimes lacking,and the reliability test sample sizes tend to be small.Monte-Carlo technique combined with Bayes method is used to evaluate its dependability(reliability and maintainability).Following the "first-in,first-out" queuing rule,the logic relation of dependability is established by means of repairing priority and event lists.Simulation outputs the entire history of a mission,statistics of reliability and maintainability parameters and provides the basic data for system reliability design and maintainability management.展开更多
在定义计划评审技术(program evaluation and review technique,PERT)网络局部关键活动、关键活动、关键路线和活动关键度的基础上,提出了关键活动、关键路线的分析方法;根据活动不确定性对项目计划工期影响的大小,即活动敏感性指标的大...在定义计划评审技术(program evaluation and review technique,PERT)网络局部关键活动、关键活动、关键路线和活动关键度的基础上,提出了关键活动、关键路线的分析方法;根据活动不确定性对项目计划工期影响的大小,即活动敏感性指标的大小,确定活动在项目进度控制中的重要程度;在定义活动相对敏感性、活动敏感性的基础上,利用全概率公式,得到活动敏感性指标计算公式,进而提出了最关键活动分析方法。算例表明,利用本研究提出的方法可便捷地找出PERT网络的关键路线和最关键活动。展开更多
基金supported by National Natural Science Foundation of China (Grant No. 51075198)Jiangsu Provincial Natural Science Foundation of China (Grant No. BK2010479)+2 种基金Innovation Research of Nanjing Institute of Technology, China (Grant No. CKJ20100008)Jiangsu Provincial Foundation of 333 Talents Engineering of ChinaJiangsu Provincial Foundation of Six Talented Peak of China
文摘Straightness error is an important parameter in measuring high-precision shafts. New generation geometrical product speeifieation（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.
基金Project(51318010402)supported by General Armament Department Pre-Research Program of China
文摘Measurement uncertainty plays an important role in laser tracking measurement analyses. In the present work, the guides to the expression of uncertainty in measurement(GUM) uncertainty framework(GUF) and its supplement, the Monte Carlo method, were used to estimate the uncertainty of task-specific laser tracker measurements. First, the sources of error in laser tracker measurement were analyzed in detail, including instruments, measuring network fusion, measurement strategies, measurement process factors(such as the operator), measurement environment, and task-specific data processing. Second, the GUM and Monte Carlo methods and their application to laser tracker measurement were presented. Finally, a case study involving the uncertainty estimation of a cylindricity measurement process using the GUF and Monte Carlo methods was illustrated. The expanded uncertainty results(at 95% confidence levels) obtained with the Monte Carlo method are 0.069 mm(least-squares criterion) and 0.062 mm(minimum zone criterion), respectively, while with the GUM uncertainty framework, none but the result of least-squares criterion can be got, which is 0.071 mm. Thus, the GUM uncertainty framework slightly underestimates the overall uncertainty by 10%. The results demonstrate that the two methods have different characteristics in task-specific uncertainty evaluations of laser tracker measurements. The results indicate that the Monte Carlo method is a practical tool for applying the principle of propagation of distributions and does not depend on the assumptions and limitations required by the law of propagation of uncertainties(GUF). These features of the Monte Carlo method reduce the risk of an unreliable measurement of uncertainty estimation, particularly in cases of complicated measurement models, without the need to evaluate partial derivatives. In addition, the impact of sampling strategy and evaluation method on the uncertainty of the measurement results can also be taken into account with Monte Carlo method, which plays a guiding role in measurement planning.
基金Supported by National Natural Science Foundation of China(Grant No.51075198)Jiangsu Provincial Natural Science Foundation of China(Grant No.BK2010479)+1 种基金Jiangsu Provincial Project of Six Talented Peaks of ChinaJiangsu Provincial Project of 333 Talents Engineering of China(Grant No.3-45)
文摘The cone is widely used in mechanical design for rotation, centering and fixing. Whether the conicity error can be measured and evaluated accurately will directly influence its assembly accuracy and working performance. According to the new generation geometrical product specification（GPS）, the error and its measurement uncertainty should be evaluated together. The mathematical model of the minimum zone conicity error is established and an improved immune evolutionary algorithm（IlEA） is proposed to search for the conicity error. In the IIEA, initial antibodies are firstly generated by using quasi-random sequences and two kinds of affinities are calculated. Then, each antibody clone is generated and they are self-adaptively mutated so as to maintain diversity. Similar antibody is suppressed and new random antibody is generated. Because the mathematical model of conicity error is strongly nonlinear and the input quantities are not independent, it is difficult to use Guide to the expression of uncertainty in the measurement（GUM） method to evaluate measurement uncertainty. Adaptive Monte Carlo method（AMCM） is proposed to estimate measurement uncertainty in which the number of Monte Carlo trials is selected adaptively and the quality of the numerical results is directly controlled. The cone parts was machined on lathe CK6140 and measured on Miracle NC 454 Coordinate Measuring Machine（CMM）. The experiment results confirm that the proposed method not only can search for the approximate solution of the minimum zone conicity error（MZCE） rapidly and precisely, but also can evaluate measurement uncertainty and give control variables with an expected numerical tolerance. The conicity errors computed by the proposed method are 20%-40% less than those computed by NC454 CMM software and the evaluation accuracy improves significantly.
基金Supported by National Natural Science Foundation of China(Grant No.51675378)National Science and Technology Major Project of China(Grant No.2014ZX04014-031)
文摘The current researches mainly adopt "Guide to the expression of uncertainty in measurement(GUM)" to calculate the profile error. However, GUM can only be applied in the linear models. The standard GUM is not appropriate to calculate the uncertainty of profile error because the mathematical model of profile error is strongly non-linear. An improved second-order GUM method(GUMM) is proposed to calculate the uncertainty. At the same time, the uncertainties in different coordinate axes directions are calculated as the measuring points uncertainties. In addition, the correlations between variables could not be ignored while calculating the uncertainty. A k-factor conversion method is proposed to calculate the converge factor due to the unknown and asymmetrical distribution of the output quantity. Subsequently, the adaptive Monte Carlo method(AMCM) is used to evaluate whether the second-order GUMM is better. Two practical examples are listed and the conclusion is drawn by comparing and discussing the second-order GUMM and AMCM. The results show that the difference between the improved second-order GUM and the AMCM is smaller than the difference between the standard GUM and the AMCM. The improved second-order GUMM is more precise in consideration of the nonlinear mathematical model of profile error.
基金partially supported by the Hong Kong Ph D Fellowship Schemesupported by the Hong Kong RGC General Research Funds(Projects 27300616,17300817,and 17300318)+2 种基金National Natural Science Foundation of China(Project 11601457)Seed Funding Programme for Basic Research(HKU)Basic Research Programme(JCYJ20180307151603959)of the Science,Technology and Innovation Commission of Shenzhen Municipality。
文摘We propose a multiscale multilevel Monte Carlo(MsMLMC)method to solve multiscale elliptic PDEs with random coefficients in the multi-query setting.Our method consists of offline and online stages.In the offline stage,we construct a small number of reduced basis functions within each coarse grid block,which can then be used to approximate the multiscale finite element basis functions.In the online stage,we can obtain the multiscale finite element basis very efficiently on a coarse grid by using the pre-computed multiscale basis.The MsMLMC method can be applied to multiscale RPDE starting with a relatively coarse grid,without requiring the coarsest grid to resolve the smallestscale of the solution.We have performed complexity analysis and shown that the MsMLMC offers considerable savings in solving multiscale elliptic PDEs with random coefficients.Moreover,we provide convergence analysis of the proposed method.Numerical results are presented to demonstrate the accuracy and efficiency of the proposed method for several multiscale stochastic problems without scale separation.
基金Sponsored by National Post Doctor Science Foundation of China (2003033180)
文摘The vehicle system studied in this paper is a type of complex repairable system in which the subsystems follow various failure distributions and conform to arbitrary failure and repair distributions.The failure data of subsystems are sometimes lacking,and the reliability test sample sizes tend to be small.Monte-Carlo technique combined with Bayes method is used to evaluate its dependability(reliability and maintainability).Following the "first-in,first-out" queuing rule,the logic relation of dependability is established by means of repairing priority and event lists.Simulation outputs the entire history of a mission,statistics of reliability and maintainability parameters and provides the basic data for system reliability design and maintainability management.
文摘在定义计划评审技术(program evaluation and review technique,PERT)网络局部关键活动、关键活动、关键路线和活动关键度的基础上,提出了关键活动、关键路线的分析方法;根据活动不确定性对项目计划工期影响的大小,即活动敏感性指标的大小,确定活动在项目进度控制中的重要程度;在定义活动相对敏感性、活动敏感性的基础上,利用全概率公式,得到活动敏感性指标计算公式,进而提出了最关键活动分析方法。算例表明,利用本研究提出的方法可便捷地找出PERT网络的关键路线和最关键活动。
