分层构权灰色主成分评价模型及其应用

Multi-layer weighted grey principal component evaluation model and its application

针对评价实践中客观存在的"原始变量不多"与"样本量不多",构建分层构权灰色主成分评价模型.首先,在科学设置评价子系统及下属指标项的前提下,分层赋予相应归一化重要性权;其次,生成评价所需的加权规格化矩阵,据此计算灰色相似关联度矩阵,替代相关系数矩阵求解评价样本各子系统的主成分综合得分;然后,将所得分值按各子系统重要性权进一步合成得出最终评价依据;最后,结合火电机组性能综合评价实例,对不同评价方法得出的评价实际效果进行对比分析.理论研究与案例分析论证表明,对于评价实践中存在的少变量、小样本以及评价指标间不一定满足线性相关关系的情形,分层构权灰色主成分评价模型具备科学性、有效性和较优的适用性.

Considering the lack of primitive variables and samples,which exists objectively in the evaluation practice,the multi-layer weighted grey principal component evaluation model is constructed.Firstly,the normalized importance weights are assigned to the subsystem of the evaluation system and the corresponding indices respectively under the premise that all of them are established scientifically.On that basis,the weighted normalized matrix for evaluation is generated to calculate the grey similitude correlation degree matrix,and the principal component scores of each evaluation subsystem are calculated based on it instead of the traditional correlation matrix.Then,the final evaluation basis is obtained through weighting the scores of each evaluation subsystem by their importance weights.Finally,performances of thermal power generation units are analyzed comparatively by using different evaluation models including the proposed model.Theoretical research and case analysis demonstrate that the proposed model is scientific,effective and more suitable in these situations where there are insufficient evaluation variables,or the sample size is small,as well as there may be a non-linear correlation between evaluation indicators.