Research On Design Of Experiments And Modeling For Multi-extrimums Process

For the process featured with multi-extremums of output quality characteristics, in which the relationship between input parameters and output quality characteristics is very complex, the controlling of process and optimization of input parameters is very difficult. Methods mentioned in previous researches usually have poor performance when applied to construct global modeling of this kind of process. It is usually hard of sampling and takes high experimentation cost for multi-extremums process, In this paper, small sampling rule is adopted in the study to avoid problems, such as redundancy of samples and waste of experimentation cost, which often appeared in methods using common design of experiments. In this paper, according to whether there is incomplete prior knowledge, multi-extremums process problems are divided into two categories, and two kinds of experimental design and modeling methods are proposed correspondingly. The main contents and innovations of this paper are as follows.(1) To multi-extremums process without prior knowledge, design of experiments and global modeling method based on small sample size is studied because of sampling difficulties. The random strategy used in genetic algorithm optimization is adopted into the sample sequential additional mechanisms to avoid detect of sequential design methods mentioned in previous researches. Be charactered by a random strategy with a certain probability, the population iterative of genetic algorithm is combined with support vector machine (SVM) regression modeling method. A randomly-oriented sequential design and modeling method is put forward.(2) To multi-extremums process with incomplete prior knowledge about factor significance, studies are constructed. Different factor significance in different regions means different fluctuations of output quality characteristics. Thus, feasible region could be reasonably divided into several sub-regions which should be researched differently. A sub-regional sampling strategy is combined with support vector regression modeling method. A sub-regional design of experiments and modeling method is put forward.(3) After theoretical analysis and introduction of algorithm steps, empirical and case studies on proposed two methods are carried out separately. Firstly, the proposed randomly-oriented sequential design and modeling method is applied to modeling leaf spring heat treatment process. Next, the proposed sub-regional design of experiments and modeling method is applied to a multi-dimensional numerical example which stands for one specific multi-extremums process with prior knowledge.In empirical and case studies, single design of experiments and modeling method is used to construct models of the given examples under the same sample size. Research results indicate that, the predictive ability and optimization ability of the model constructed by proposed randomly-oriented sequential design and modeling method are average improved by21.65%and12.39%respectively; Values of the predictive ability indexes Sep, MaxE and StdE of the model constructed by proposed sub-regional design of experiments and modeling method are average reduced by8.50%,25.50%and20.40%respectively. All of the above results indicate that models constructed by the two proposed methods in this paper have excellent global description ability and demonstrate the effective applicability and superiority of the two proposed methods in this paper.