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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。
Aiming at the problem that the traditional multi-point gray predictive model MGM (1, n) construction method is not reasonable, the model often does not meet the actual situation of the deformable body. This paper presents a weighted MGM (1, n) model. By introducing the optimal generating weight matrix of albino background value instead of the generating matrix of proximate mean value in the formula of background value of traditional model, the mutation and irregularity of deformation trend of multiple monitoring points in deformation area are better taken into account, which makes up for the linear system MGM (1, n) model in the nonlinear dynamic system deformation prediction and analysis of the application of deficiencies; the establishment of multi-objective optimization of real-coded genetic algorithm to achieve the background value of the optimal construction of the Iterative search matrix iterative search. The simulation results based on simulation and engineering example data show that the improved model has higher prediction accuracy and better anti-noise ability than the traditional MGM (1, n) model.