The Research Of Multivariate Experimental Design And Optimization Analysis System Based On Small Sample Data

With the development of society, the multivariate test of small sample has drawn more and more attention. However, until now, the research on such test is not much, and the whole system scheme into practice of analyzing it is much more less. Based on the source of subject, this paper proposes an effective system overall solution which can design, analysis and optimize such test, and develops the multivariate experimental design and optimization analysis system for the multivariate test of small sample. The system overall solution combines experimental design, improved multiple regression analysis algorithms and global optimization analysis, and improves the representation and information content of small samples of test data. In addition, it can obtain the regression function relationship between the experimental factors and test indicators and global optimization information. And it solves some problems that are not easy to do, such as:the existence of multicollinearity and regression analysis while analysis and optimize the small sample test data.This article compares the development situation of our country and the foreign countries about experimental design and data analysis. Through comparative analysis, it is preliminary to select the type of experimental design and the algorithms for regression analysis and global optimization, and to prepare to improve them. In the experimental design, the basic principle of uniform design and its indicators are introduced, and give the implementation process. Against regression analysis for multivariate tests of the small sample, this paper puts forward a new algorithm that is self-selection partial least squares regression algorithm based on the quadratic polynomial model, and provides some necessary testing methods for it. In side of test global optimization, using the method of adding the weight coefficients, this paper transforms multiple regression relationship into single-objective multi-function. After that, it can get global optimal point of the single-objective multi-function based on particle swarm optimization algorithm and obtain the best test plan binding the research background. In short, this paper proposes a system solution which can effectively design analysis and optimize the multivariate test of small sample, and proves that improved algorithms have better performance than that of the traditional method through experimental analysis and example verification. The experimental results show that the effectiveness of the system solution is not only more than the existing general analysis method about such test, and more flexible. In addition, Based on the system solution, this paper develop a software product that is described as multivariate experimental design and optimization analysis system for multivariate test of small sample, achieve the theoretical to the actual conversion.After a summary of the work in this article, the main innovation is summarized as follows:1) According to the multivariate test of small sample, gave a new experimental analysis program on the basis of combining experimental design, multiple regression analysis and global optimization analysis organically.2) Generate the uniform design table based on the improved integer coded genetic algorithm, to improve the uniformity and usability of the uniform design table.3) Based on partial least squares method, propose a new regression analysis algorithm, it can effectively excavate and extract the information of small-sample test data and overcome the lack of small sample data.