因子间存在高阶交互作用和约束条件的复杂过程

响应曲面法是质量改进与优化的主要工具。当影响因素与质量特性之间的关系较为复杂时,参数RSM只能在很小区域内近似的描述实际工业过程,不能拟合真实的曲面;而非参数RSM需要较大的样本量,在有限样本的情况下泛化性差,并且模型难以优化。本研究将目前关于小样本统计学习和预测的最佳机器学习理论——支持向量回归机(SVR)引入到了RSM,目的在于针对多极值、因子间存在高阶交互作用和约束条件的复杂过程,发展一种包括模型拟合、过程优化、实验设计阶段在内的RSM实现方法。方法具有泛化能力强、所需样本量小等特点。研究的主要内容及创新点包括:1.在机器学习的框架之内描述了RSM的模型拟合,将其归结为一类有限制条件、可主动获取样本点的小样本学习问题;提出一种实用性的SVR核函数及参数选择方法,在不增加样本的情况上优化了SVR的参数;提出了基于SVR的复杂过程RSM拟合方法;2.提出一种基于支持向量聚类的序列二次规划法(SQP)用于RSM的过程优化,即首先对SVR拟合所得的支持向量进行聚类,然后再以各聚类中心为起点,采用SQP并行寻优;3.提出两种基于SVR的复杂过程RSM的实验设计方法。方法一以等间距空间网格设计为基础,将可行域划分为若干子区域,根据先验知识确定各子区域内的平坦性权值并调整实验点数目;方法二基于序贯性设计思想,以大间距空间网格设计为基础,通过寻优确定极值点的大致区域,然后再拟合二阶模型获得对极值点更精确的估计;4.给出了基于SVR的复杂过程RSM的总体步骤和流程图,并进行了应用研究。对于降低吡啶二乙基硼烷合成反应综合成本的实验,给出了三种优化方案;对于减小叶片弹簧自由高度波动的实验,提出了基于SVR的双响应曲面法(DRSM),并提出了两种估计均方误差MSE的策略;理论与应用研究表明,基于SVR的RSM方法的泛化性能、对响应曲面的重现能力等均优于现有RSM,而且所需样本量最少,寻优则可以发现多个过程极值。同时,采用所提的核函数及参数选择方法得到的SVR拟合模型,其泛化误差与理论最小泛化误差的平均偏离率在20%以内;对支持向量的聚类分析,有效地降低了寻优的迭代次数;与等间距空间网格设计和经典RSM相比,所提实验设计方法的实验次数降低了约20%。说明了基于SVR的复杂过程RSM的有效性与优越性。
逆变焊机
Response Surface Methodology (RSM) is one of the main approaches for quality improvement and optimization. When the relationship between influential input factors and output quality characteristics of a process is complex, both parametric RSM and nonparametric RSM have their limitations. For parametric RSM, it can only roughly describe the real industrial process within a very narrow region, and thereby fails to fit the real surface. For nonparametric RSM, it needs relatively larger sample size, which means that the generalization performance is poor for small samples, and it leads to difficulties in process optimization as well.This dissertation introduces Support Vector Regression (SVR)--currently the best machine learning theory about small sample statistical learning and forecast-- into RSM. The purpose of the dissertation is to develop a complex process oriented, SVR-based RSM approach which includes the phases of model fitting, process optimization, and design of experiment. Here the complex process is defined as an industrial process which includes several extrema as well as high order interactions and constraints within the influential factors. The proposed approach needs relatively small sample size and have strong generalization performance as well. The main contents and contributions of the dissertation include:1. First, the model fitting phase of RSM is described as a sort of constrained small-sample learning problem which is able to actively gain sample points. Therefore further research could be carried on under the field of machine learning theory. After that, a practically selecting method for SVR kernel functions and parameters is proposed, through which the SVR parameters is optimized without additional samples. Then a method for the model fitting phase of SVR-based RSM is proposed.2. A support vector clustering based Sequential Quadratic Programming (SQP) method is proposed for the process optimization phase of SVR-based RSM. First, the support vectors which are derived from SVR fitting equation are clustered, and then several SQP courses are started concurrently from these cluster centers to achieve process optimization.3. Two methods for the experiment design phase of SVR-based RSM are proposed. Methods I runs an equal interval space filling design to gain the original experiment points at first. Then it divides the feasible region into several sub-regions. After that, the weights of flatness of each sub-region are determined according to prior knowledge about the complex process, and then, the original experiment points are adjusted according to the weights of flatness. Method II, which is based on the sequential mode, runs a large interval space filling design at first. Then it determines the rough regions of each extremum through process optimization, and then fits the second order models in the regions to gain the precise estimations of the extrema.4. The general procedures and flow charts of SVR based RSM are proposed, and then two application studies are conducted. In the study of reducing the comprehensive cost of synthesis of pyridyl diethyl borane, three optimization plans are provided. In the study of decreasing the free height variation of leaf spring, a SVR-based Dual RSM is proposed and two strategies for estimating mean squared error (MSE) are provided as well.Both theoretical analysis and applied studies indicate that the proposed SVR-based RSM approach is better than the existing RSM approaches in generalization performance and recurrence capability of response surface. Moreover, the proposed approach requires relatively smaller sample size, and is able to discover several process extrema. In addition, by using a practical selecting method for SVR kernel function and parameters, the average deviation ratio of SVR generalized error from the theoretically minimum is controlled within 20%; the number of iteration is effectively decreased by cluster analysis of support vectors, and the average experiment times of the approach decrease about 20% compared with equal interval space filling design and the classic RSM. All these demonstrate the adaptability and superiority of the approach proposed in the dissertation.