基于权重反分析方法的加权距离判别法及应用  

Weighted distance discriminant method based on weight back analysis method and its application

作　　者：邱道宏[1] 张乐文[1] 李术才[1] 肖云华[2] 孙怀凤[1] 

机构地区：[1]山东大学岩土与结构工程研究中心,济南250061 [2]长江三峡勘测研究院有限公司(武汉),武汉430074

出　　处：《岩土力学》2010年第10期3243-3247,3253,共6页Rock and Soil Mechanics

基　　金：教育部科学技术研究重点项目(No108158);中国博士后科学基金(No20090461203);山东省自然开学基金面上项目(NoY2007F53)

摘　　要：距离判别分析法在应用过程中常将各评价指标的重要性视为一致,实际上各指标重要性是不同的,故需对各指标进行加权处理。权重的合理取值对最终的评判结果有着很大的影响,目前尽管确定权重的方法有很多,但都有其不足之处。鉴于此,在马氏距离的基础上,推导了加权马氏距离的求解公式,并采用一对多的分类方法建立了多总体加权马氏距离判别准则。在确定各指标权重时采用了基于优化理论权重反分析的新思路,把直接给权重问题转化为通过实际工程样本反求各影响因素权重问题,该方法不需先知经验,求解过程完全由实际样本驱动,具有很强的可操作性。将改进后的加权距离判别分析方法应用于实际工程中的围岩分类问题,结果表明,该方法的判别结果是可靠的。距离加权的方法完善了距离判别分析法理论,权重反分析方法是一种通用方法,可用于任何求解权重的问题,为权重的求解提供了一种新思路。The importances of evaluation indices are considered to be the same in the application process of distance discriminant analysis method commonly.But the importance of each factor is different in fact,so that weighting to each factor is necessary.It has a great influence to the final evaluation results for the reasonable weight values of the evaluation indices.Although there are a lot of methods to determine weights of influencing factors recently,these methods have some deficiencies.To solve these problems,weighted Mahalanobis distance formula is derived based on the conception of Mahalanobis distance;and the corresponding evaluation criterion of many collectivities is obtained according to the method of one to many.Based on optimization theory weight back analysis method is used to determine weights;it changes the directly given weights methods to back analyzing influence factors weights according to engineering samples.The method is fully derived by engineering samples,no experience is necessary,and it is very useful especially in the absence of expertise.The result by using this method in surrounding rock classification shows that this method is reliable.Weighted distance method improves the theory of distance discriminant analysis method.Weight back analysis method is universal,it shows a new idea and can be used in any weights problems.

关 键 词：距离判别分析 权重 反分析 可拓学 围岩分类 

分 类 号：TB114[理学—概率论与数理统计]