优化非等间距GM(1,1)模型及其在变形监测中的应用

Optimized Non-Equidistant GM(1,1)Model and Its Application in Deformation Monitoring

针对非等间距GM(1,1)模型的拟合和预测问题,考虑灰作用量的时变特征,系统地证明了一种优化灰作用量的非等间距GM(1,1)模型,并提出通过粒子群算法选取拟合模型最优的背景值权重参数来构造优化模型的最优背景值。以典型的变形监测数据为算例,构建了非等间距GM(1,1)模型、优化灰作用量的非等间距GM(1,1)模型和优化灰作用量与背景值的非等间距GM(1,1)模型。通过算例的分析与对比,结果表明优化灰作用量的非等间距GM(1,1)模型和优化灰作用量与背景值的非等间距GM(1,1)模型对原始数据的拟合和预测具有较高的精度,优化模型具有可行性和有效性。

For the problem of fitting and prediction of non-equidistance GM(1,1)model,considering the time-varying characteristics of grey action,a non-equidistance GM(1,1)model for optimizing grey action is systematically proved,and the optimal background value of the fitting model is constructed by selecting the optimal weight parameters of the fitting model by particle swarm optimization(PSO).Taking typical deformation monitoring data as examples,non-equidistance GM(1,1)model,non-equidistance GM(1,1)model of optimizing grey action and non-equidistance GM(1,1)model of optimizing grey action with optimal background value are constructed respectively.The analytical and comparative results indicate that non-equidistance GM(1,1)model of optimizing grey action and non-equidistance GM(1,1)model of optimizing grey action with optimal background value have high accuracy in fitting and forecasting the original data,and the model is feasible and effective.