中文摘要：

针对传统多点灰色预测模型MGM（1,n）白化背景值构造方法不合理性导致模型往往不符合变形体实际情况的问题,该文提出了一种基于遗传算法的加权MGM（1,n）模型。引入白化背景值最佳生成权值矩阵替换传统模型背景值构造公式中的紧邻均值生成权阵,较好地顾及变形区域内多监测点变形趋势的突变性与不规则性,弥补了线性系统MGM（1,n）模型在非线性动力学系统变形预测分析应用中的不足;建立多目标优化实数编码遗传算法,实现背景值最优构造权阵的迭代搜索。基于仿真和工程实例数据的建模结果表明：改进模型较传统MGM（1,n）模型预测精度提高,抗噪声干扰能力增强。

英文摘要：

Considering the issue that traditional MGM（1, n）model is usually not consistent with the actual situation of the deformation object because of fallacious construction method of whitening back- ground value, a weighted MGM（1, n）model based on genetic algorithm was proposed. A weight matrix for optimum generation of background value was introduced to substitute adjacent mean generating weight matrix in background value construction formula of traditional model, which could fit mutation and irregu- larity of the deformation trend for multi-points in the deformation region better then the deficiency of ap- plying MGM（1, n）model based on linear system to deformation prediction which is nonlinear dynamical systems was made up. A multi-objective optimization real-coded genetic algorithm was applied to calculate the optimal weight matrix through iterative search. Simulation results showed that the forecasting accura- cy and anti-noise interference capability of improved model were better than traditional MGM（1, n）model.