传统的矩阵公差模型依据特征顶点建立约束条件，不同位置和数量的顶点会导致计算精度和效率的不同。同时，传统算法难以应对存在大量非线性约束条件的优化问题。为此将一般性特征变动约束方程引入到矩阵公差模型中，通过蒙特卡洛仿真方法将符合约束条件的随机数代入目标函数进行优化计算，提高了模型的计算效率和可靠性，降低了优化难度。对比分析一个简单的装配案例，说明其有效性和实用性。
The constraints of traditional matrix tolerance model are constructed by virtue of vertexes of features. Differences of locations and numbers of these vertexes may result in different computational accuracy and efficiency. Meanwhile, traditional algorithm of optimization is incapable of dealing with the situations where a large number of nonlinear inequalities exist. Therefore, the general variations and constraints of features are brought into the matrix model. Monte Carlo simulation is used to take these random numbers satisfying the constraints into computation process. This approach enhances the reliability and efficiency of the matrix model, and reduces its difficulty of the optimization. Comparative results of a simple assemble show the practicability and effectiveness of this approach.
[1] SHEN Z，AMETA G，SHAH J J，et al. A comparative study of tolerance analysis method[J]. ASME Journal of Computing and Information Science in Engineering，2005，5：247-256.
[2] AMETA G，SERGE S，GIORDANO M. Comparison of spatial math models for tolerance analysis：Tolerance-maps，deviation，domain，and TTRS[J]. ASME Journal of Computing and Information Science in Engineering，2011，11：012004-1-8.
[3] CHEN H，JIN S，LI Z，et al. A comprehensive study of three dimensional tolerance analysis methods[J]. Computer-Aided Design，2014，53：1-13.
[4] GAO J，CHASE K W，MAGLEBY S P. General 3-D tolerance analysis of mechanical assemblies with small kinematic adjustments[J]. IIE Transactions，1998，30：367-377.
[5] DAVIDSON J K，MUJEZINOVIC′ A，SHAH J J. A new mathematical model for geometric tolerances as applied to round faces[J]. ASME Journal of Mechanical Design，2002，124：609-622.
[6] DESROCHERS A，GHIE W，LAPERRIèRE L. Application of a unified Jacobian-Torsor model for tolerance analysis[J]. ASME Journal of Computing and Information Science in Engineering，2003，3：1-13.
[7] DESROCHERS A，RIVIèRE A. A matrix approach to the representation of tolerance zones and clearances[J]. International Journal of Advanced Manufacturing Technology，1997，13：630-636.
[8] CLéMENT A，RIVIèRE A，SERRé P，et al. The TTRSs：13 constraints for dimensioning and tolerancing[J]. Geometric Design Tolerancing：Theories，Standards and Applications，1998，122-131.
[9] PRISCO U，GIORLEO G. Overview of current CAT systems[J]. Integrated Computer-Aided Engineering，2002，9：373-387.
[10] WHITNEY D E，GILBERT O L，JASTRZEBSKI M. Representation of geometric variations using matrix transforms for statistical tolerance analysis in assemblies[J]. Research in Engineering Design，1994，6(4)：191-210.
[11] SALOMONS O W. Computer support in the design of mechanical products[D]. University of Twente，The Netherlands，1995.
[12] ROY U，LI B. Representation and interpretation of geometric tolerances for polyhedral objects. II. Size，orientation and position tolerances[J]. Computer-Aided Design，1999，31(4)：273-285.
[13] 蔡敏. 基于数学定义的圆柱要素公差数学建模与分析技术的研究[D]. 杭州：浙江大学，2002.CAI Ming. Study on mathematical modeling and analysis of cylindrical feature[D]. Hangzhou：Zhejiang University，2002.
[14] 王正林，龚纯，何倩. 精通MATLAB科学计算[M]. 北京：电子工业出版社，2007. WANG Zhenglin，GONG Chun，HE Qian. Proficiency of scientific calculation with MATLAB[M]. Beijing：Publishing House of Electronics Industry，2007.
[15] 杜比. 蒙特卡洛方法在系统工程中的应用[M]. 西安：西安交通大学出版社，2007. DU Bi. Monte Carlo applications in systems engineering[M]. Xi’an：Xi’an Jiaotong University Press，2007.
[16] NIGAM S D，TURNER J U. Review of statistical approaches to tolerance analysis[J]. Computer-Aided Design，1995，27(1)：6-15.
