【作者】 周晓剑；

【导师】 马义中；

【作者基本信息】 南京理工大学 ， 管理科学与工程， 2012， 博士

【摘要】 为了应对日益激烈的全球竞争,制造业如何以高质量、低成本、短周期获得竞争优势,已成为工业界和学术界极为关注的问题。从现代质量工程的观点来看,质量是设计和制造出来的,产生质量问题的根本原因是波动。质量设计作为减少波动的有效途径,被广泛地应用于产品/过程的设计阶段。经典的试验设计是质量设计的一个重要手段,但其在工业生产领域的应用过程中存在一些不足,如,试验成本高,研制周期长,实现难度大等。针对以上不足,国际上一些学者提出了计算机试验设计,其标志性文献为1989年Sacks等发表的两篇文章,它奠定了计算机试验设计的基础,对计算机试验设计的发展产生了深远影响。本文在已有的各种元模型构建技术的基础上,以基于元模型的稳健参数设计为研究对象,综合运用系统建模、仿真试验与实证研究等方法,系统地研究了基于非半正定核的支持向量回归机(supprot vector regression, SVR)的构建技术、基于梯度信息的SVR的构建技术、组合元模型的构建技术以及基于单个元模型特别是组合元模型的稳健参数设计。本文的主要研究内容归纳总结如下：首先,研究了单个元模型的构建技术。本部分重点研究了基于非半正定核的SVR构建技术和基于梯度信息的SVR的构建技术。一方面,针对现有的求解大型SVR的最小最优化(sequential minimal optimization, SMO)算法无法解决核函数为非半正定这一问题,将SVR的原始规划问题进行展开并求解其KKT(Karush-Kuhn-Tucker)条件,减少了需要考虑的Lagrange乘子数目,避免了大量繁琐的判别条件,简化了算法的实现。通过经典的测试函数及鲍鱼数据验证了基于非半正定核SVR算法的有效性。另一方面,针对小样本情形下SVR回归效果不理想这一问题,通过修改目标函数及约束条件,将梯度信息引入到传统的SVR的构建中,重新构造了决策函数。采用了三个基准函数对元模型进行了验证,提出的元模型比传统的SVR在回归精度上有明显的改进。其次,研究了组合元模型的构建技术。根据样本集来选择单个元模型会加大选用一个并不合适的元模型的概率,针对此问题,综合运用了简单算术平均的方法及递归的思想,以预测均方误差为算法的停机准则,逐步将单个元模型的算术平均模型去替代备选元模型中最差的元模型,以达到在弱化不理想的单个元模型的权重的同时加强理想的单个元模型的权重的目的。分别采用二维、三维、六维及八维的数据对元模型进行了验证,提出的组合方法有效地屏蔽了不理想的单个元模型的负面影响,并且不随样本集变化而变化明显,具有较高的稳健性。再次,研究了单个元模型特别是组合元模型在稳健参数设计中的应用。针对基于双响应曲面模型的稳健参数设计中所采用的多项式模型对样本数据(特别是方差数据)拟合精度低这一问题,提出了将SVR模型、径向基函数模型、Kriging模型特别是组合元模型应用于双响应曲面的策略。先将SVR模型、径向基函数模型、Kriging模型以及组合元模型去近似均值响应及方差响应,然后再求解基于元模型的随机优化问题,最后得到最优因子搭配水平。以打印墨水为例进行了验证分析,所得的结果与已有的采用多项式模型进行优化的结果相近,说明本文方法的有效性,同时,提出的方法得到更小的均方误差,说明本文方法的优越性。本文通过研究单个元模型的构建技术、组合元模型的构建技术以及基于单个元模型特别是组合元模型的稳健参数设计方法,进一步丰富了稳健参数设计的研究内涵。最后,本文指出了可进一步研究的问题。更多还原

【Abstract】 In order to deal with the increasing global competition, industrial and academic circles focus on how to have an advantage over their competitors by high quality, low cost, and short development cycle. On the view of modern quality engineering, quality originates from designing and manufacturing. Variation is the basic factor influencing the quality of products. Quality design, which is an useful tool to reduce variation, is widely employed in the design phase of product/process. Classic design of experiment is an important mean for quality design. Nevertheless, there are some shortcomings, such as, high experimental cost, time-consuming, being difficult to implement, and so on, in its application in industrial areas. Considering these inefficiencies above, some foreign scholars proposed the design of computer experiment, the typical literature of which are those two papers published by Sacks. These two papers laid the foundation for design of computer experiment, and have deep influence on it.Based on several metamodeling techniques, regarding the robust parameter design based on metamodel as its research object, and using systematic modeling, simulation techniques, and empirical research, this paper systematically studied support vector regression (SVR) based on non-positive semi-definite (non-PSD) kernels, SVR based on gradient information, ensemble of surrogates, and the robust parameter design (RPD) based on metamodeling.Firstly, the stand-alone surrogates are studied. SVR based on non-PSD kernels and SVR based on gradient information are studied in this part of the paper. On the one hand, considering the traditional sequential minimal optimization (SMO) algorithms, which is often used to solve the optimization problem in SVR, can not deal with the SVR metamodel with non-PSD, the original quadratic programming is spreaded and the Karush-Kuhn-Tucker (KKT) condition is solved in this part. After employing this strategy, the number of the Lagrange multipliers which is needed to consider is diminished, and the tedious judgments are avoided, therefore, the implementation of solving the optimization problem is simplified. The classic test functions and the abalone data are used to test the efficiency of this algorithm. On the other hand, considering the bad performance of the traditional SVR with small samples, the gradient information around the samples are added into the construction of the SVR metamodel after changing the objective function and constrained functions, then the decision function is reconstructed. Three benchmark functions are employed to test the improved SVR metamodel, and the results of the experiment show that the proposed method has better prediction accuracy than the traditional ones.Secondly, the ensemble of surrogates is studied. Considering the choice of metamodel is highly depended on the set of the samples which is used to construct the metamodels, the simple arithmetic average method and the philosophy of recursion are employed, and the root mean square error (RMSE) of prediction is adopted as the stop criterion of the algorithm. After continually replacing the worst candidate stand-alone metamodel with the arithmetic average model, the weight of the best stand-alone metamodel is raised while that of the worst one is reduced.2-dim,3-dim, and 6-dim test functions, and 8-dim abalone data are used to verify the performance of ensemble technique. The results show that the ensemble of surrogates efficiently kicks out the negative effects of the improper stand-alone metamodels, and the performance of the ensemble of surrogates does not vary apparently with samples. Therefore, ensemble of surrogates to a certain extent is a robust model.Thirdly, the RPD based on the stand-alone metamodel and the ensemble of surrogates is studied. Considering the dual response surface model in RPD are highly depended on the metamodeling, the SVR metamodel, Kriging metamodel, and radius basis function(RBF) metamodel, and especially the ensemble of surrogates made from these three metamodels are applied into the dual response surface in RPD. Above all, the SVR metamodel, Kriging metamodel, and RBF metamodel are constructed respectively, and then the ensemble of surrogates is also constructed using the above-mentioned metamodels. The next, the mean response and the variation response are built using these stand-alone metamodels and the ensemble of surrogates respectively. In addition, the random optimization process is taken, and the best recommended setting is obtained. The printing ink experiment is employed to test the performances of these stand-alone metamodels and the ensemble of surrogates. These metamodels proposed in this paper have similar recommended settings to the previous polynomial models, which indicates the effectiveness of these metamodels, and the mean square errors (MSEs) with SVR and ensemble of surrogates are lower than the traditional polynomial models, which indicates the superiority of our proposed metamodels.The stand-alone metamodels, the ensemble of surrogates, and the RPD based on the metamodels are studied systematically, which extends the scientific connotation of RPD. Finally, this paper points out the topics for further study.更多还原