基于RSM的关联多响应试验设计与稳健性优化研究
发布时间：2018-08-07 21:49
【摘要】：在实际生产中,产品经常具有多个质量特性且特性之间互有影响,本文主要对关联多响应问题的稳健性优化进行研究,目的在于在响应间具有相关性的情况下考虑到因子容差的波动对于响应的影响,最终找到问题的稳健最优解。以此为目标,本文通过响应曲面法建立影响因子与响应之间的关系模型,使用马氏距离函数法对响应之间的相关性进行了考虑,进一步对存在因子容差的条件下如何进行稳健性优化并获得稳健最优解进行了研究。具体研究内容如下:首先,本文阐述了试验设计与响应曲面法的基本理论与方法,并进一步对多响应稳健性优化的概念与几种常见的优化方法进行了介绍与总结,选取考虑了方差-协方差矩阵的马氏距离函数,将关联多响应优化问题转化为使总体马氏距离函数最小化的问题。其次,引入结合了遗传算法与模式搜索的混合智能算法对总体马氏距离函数进行极小化寻优,先使用遗传算法在可行域内进行全局性寻优,再采用模式搜索算法对返回的解进行局部精确寻优。与单一的模式搜索算法相比,混合智能算法可以更好的处理具有高度复杂性的函数的优化问题,并且比单一的智能算法更能提高最优解的精度。最后,分析因子容差对马氏距离函数的影响,针对因子容差波动的影响对马氏距离函数进行优化,并使用遗传算法与模式搜索的混合智能算法寻找稳健最优解,该方法可以得到落在稳健可行域中的稳健最优解,这样的解对因子容差的波动是不敏感的。
[Abstract]:In actual production, the product often has multiple quality characteristics and the characteristics affect each other. In this paper, the robust optimization of correlated multi-response problems is studied. The aim of this paper is to find the robust optimal solution of the problem by considering the effect of the fluctuation of factor tolerance on the response when the response is correlated. In this paper, the response surface method is used to establish the relationship model between the factors and the response, and the correlation between the responses is considered by using the Markov distance function method. Furthermore, how to optimize the robustness and obtain the robust optimal solution under the condition of factor tolerance is studied. The specific research contents are as follows: firstly, the basic theory and method of experimental design and response surface method are expounded, and the concept of multi-response robust optimization and several common optimization methods are introduced and summarized. The Markov distance function which considers the variance-covariance matrix is selected to transform the associated multi-response optimization problem into the problem of minimizing the total Markov distance function. Secondly, a hybrid intelligent algorithm combining genetic algorithm and pattern search is introduced to minimize the global Mahalanobis distance function. Then the pattern search algorithm is used to optimize the returned solution with local precision. Compared with the single pattern search algorithm, the hybrid intelligent algorithm can better deal with the optimization problem with high complexity, and can improve the accuracy of the optimal solution better than the single intelligent algorithm. Finally, the influence of factor tolerance on Markov distance function is analyzed. The Mahalanobis distance function is optimized according to the influence of factor tolerance fluctuation, and the robust optimal solution is found by using the hybrid intelligent algorithm of genetic algorithm and pattern search. This method can obtain the robust optimal solution in the robust feasible domain, which is insensitive to the fluctuation of factor tolerance.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114;TP18
本文编号：2171448
[Abstract]:In actual production, the product often has multiple quality characteristics and the characteristics affect each other. In this paper, the robust optimization of correlated multi-response problems is studied. The aim of this paper is to find the robust optimal solution of the problem by considering the effect of the fluctuation of factor tolerance on the response when the response is correlated. In this paper, the response surface method is used to establish the relationship model between the factors and the response, and the correlation between the responses is considered by using the Markov distance function method. Furthermore, how to optimize the robustness and obtain the robust optimal solution under the condition of factor tolerance is studied. The specific research contents are as follows: firstly, the basic theory and method of experimental design and response surface method are expounded, and the concept of multi-response robust optimization and several common optimization methods are introduced and summarized. The Markov distance function which considers the variance-covariance matrix is selected to transform the associated multi-response optimization problem into the problem of minimizing the total Markov distance function. Secondly, a hybrid intelligent algorithm combining genetic algorithm and pattern search is introduced to minimize the global Mahalanobis distance function. Then the pattern search algorithm is used to optimize the returned solution with local precision. Compared with the single pattern search algorithm, the hybrid intelligent algorithm can better deal with the optimization problem with high complexity, and can improve the accuracy of the optimal solution better than the single intelligent algorithm. Finally, the influence of factor tolerance on Markov distance function is analyzed. The Mahalanobis distance function is optimized according to the influence of factor tolerance fluctuation, and the robust optimal solution is found by using the hybrid intelligent algorithm of genetic algorithm and pattern search. This method can obtain the robust optimal solution in the robust feasible domain, which is insensitive to the fluctuation of factor tolerance.
【学位授予单位】：天津大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：TB114;TP18
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