武汉理工大学硕士学位论文基于蒙特卡罗仿真和遗传算法的公差设计姓名：吴方才申请学位级别：硕士专业：控制理论与控制工程指导教师：曾春年20050501武汉理工大学硬上学位论文摘要本文的主要目标是提出一个公差设计的框架。我们考虑非线性约束的公差分配问题。公差按照加工成本（公差成本）和风险（满足几何需求和装配需求的概率)之间的最优平衡来分配。为了解决这个问题，本文采用了蒙特卡罗仿真和遗传算法。在工业设计中，优化问题是非常复杂，往往传统的优化算法很难或者不可能求解这类问题，所以这个优化问题采用用遗传算法。遗传算法通常包括三个主要的步骤：初始化种群，计算他们的适应值，和通过一些遗传算子产生一个新的种群，迭代这个过程直至收敛。郭淘交叉算子被采用以提高算法的优化效率，同时根据蒙特卡罗仿真的特点适应值函数被改进用以减少蒙特卡罗仿真的计算量。产品的合格率的估算是通过蒙特卡罗仿真来实现的。蒙特卡罗仿真是一种流行的公差分析的工具，它具有实现简单通用性好，同时可以工具需要调整精度，在精度上没有限制。最后一个工业设计实例用来验证整个框架的有效性，这个例子包括了公差设计的所有方面。并且这个例子中的公差转换函数是非线性的。关键字：公差分析，公差综合，蒙特卡罗仿真，遗传算法武汉理工大学硕上学位论文ABSTRACTThe main objective of this paper is to present a frame of tolerances allocation.Weconsider the nonlinearly constrained tolerance allocation problems.Indeed,tolerancesare allocated to achieve optimal ratio between the sum of the manufacturing costs(tolerances costs)and the risk (probability of the respect of geometrical requirementsand assembly requirements).The techniques of Monte Carlo simulation and geneticalgorithm are adopted to solve these problems.In the industrial cases,the optimization problem is so complex that for traditionaloptimization algorithms it may be difficult or impossible to solve it.Therefore,thisoptimization is realized by genetic algorithm.A genetic algorithm includes 3 steps:the initialization of the first population,the evaluation of the fitness of each individualof the population P and the definition of a new population by genetic operators.Wepropose Guo's Crossover operator which is improved in the design of fitness functionaccording to the characters of the Monte Carlo Simulation for reducing computationalexpense.The probability estimation is realized by statistical tolerance analysis.MonteCarlo technique is easily the most popular tool used in tolerancing problems.Indeed,the appeal of Monte Carlo lies in its applicability under very general settings and theunlimited precision that can be achieved.An illustrative example (hyperstatic mechanism -two dimensional tolerancestransfers)is given to demonstrate the efficiency of the proposed approach.Indeed,thisexample includes all problems:The tolerances transfers function is not linear becausethe gaps in the joints of mechanisms are considered and are not modelized by randomvariables.The cost function could be continue or discrete.KEYWORDS:Tolerance Analysis,Tolerance Synthesis,Monte CarloSimulation,Genetic Algorithms.2