A Study On SVR-based Response Surface Methodology For Complex Processes

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.