扩展GM(1,M)模型混沌优化及其在边坡监测中的应用

Chaos Optimization of Extended Grey Model(1,M) and its application in slope monitoring

基于GM(1,1)与常规GM(1,M)模型缺陷的分析,给出了扩展GM(1,M)模型(E-GM)及其响应递推式,进而指出了背景值生成因子的双重约束特性。扩展模型采用最新历史数据作为响应值初始条件,并提出以模型精度与法矩阵病态程度为准则引入混沌优化方法搜索最佳生成因子。工程实例计算表明,扩展模型预测精度及可靠性优于GM(1,1)及常规GM(1,M)模型。

The inherent defect of the GM(1,1) and the normal GM(1,M) is explicitly illuminated in this paper,then the extended GM(1,M) and its recursive algorithm is proposed in detail.In the modeling process,the latest historical data is used as the initial terms of responding value,and the best generating factor for background value is searched using Chaos optimizing method based on the precision and the standardized condition number of normal matrix.Finally,the computation results show that the E-GM(1,M) is more re...