【作者】 李文；

【导师】 肖攸安；

【作者基本信息】 武汉理工大学 ， 通信与信息系统， 2012， 硕士

【摘要】 随着社会的不断发展,小样本多元试验也越来越受到人们的关注,但目前关于此类试验的研究并不多,将整体方案付诸于实践则更加少。基于课题来源,本文提出了一套能有效地设计和分析此类试验的系统方案,并开发了小样本多元试验设计与优化分析系统。该系统方案将试验方案设计、多元回归分析以及全局优化分析三者融为一体,提高了小样本试验数据代表性和信息含量,能够获取试验因素和试验指标之间的回归函数关系式及全局优化信息,解决了小样本试验数据分析与优化中存在的数据之间相关性大,存在多重共线性,不易做回归分析等难题。本文介绍了国内外试验设计与数据分析的发展现状,通过对比分析,选取了适合小样本多元试验的试验设计、回归分析算法及全局优化算法,并加以改进。在试验设计方面,主要介绍了均匀设计的基本原理及衡量指标,给出了均匀设计的改进方法和实现过程。针对小样本多元试验的回归分析,则提出了基于二次多项式模型的自选择偏最小二乘回归算法,并给出了必要的检验方法。在试验全局优化方面,采用添加权系数的方法,将多个多元回归关系式转化为单目标多元函数,然后基于粒子群优化算法对单目标多元函数进行全局优化,最后结合试验背景得到最优的试验方案。总之,本文提出了一套针对小样本多元试验的试验设计与优化分析的方案,并对改进的算法进行实验分析和实例验证。实验分析表明,改进算法的性能超过了现有的此类算法,且算法的应用方式更加灵活。实例验证表明,系统的试验设计与优化分析方案能够达到实际应用的精度,具有可行性和有效性。通过软件开发对整体方案进行了实现,形成了小样本多元试验设计与优化分析系统,实现了理论向实际的转化。经过对本文工作的总结,主要的创新工作归纳如下：1)针对小样本多元试验,提出了一种新的试验分析方案,该方案将试验方案设计、多元回归分析与全局优化分析有机地结合在一起。2)采用基于整数编码的改进遗传算法来生成均匀设计表,提高了均匀设计表的均匀性和易用性。3)基于偏最小二乘法,提出了改进的多元回归分析算法,新的算法能有效地挖掘和提取小样本试验数据信息,克服了小样本数据带来的不足。更多还原

【Abstract】 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.更多还原