摘要
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.
作者
张振超
袁德宝
张军
吴子若
ZHANG Zhenchao;YUAN Debao;ZHANG Jun;WU Ziruo(College of Geoscience and Surveying Engineering, China University of Mining and Technology(Beijing),Beijing 100083, China;College of Science, Inner Mongolia Agricultural University, Hohhot 010018, China)
出处
《测绘科学技术学报》
北大核心
2020年第2期124-132,共9页
Journal of Geomatics Science and Technology
基金
国家自然科学基金项目(51474217)
内蒙古自治区自然科学基金项目(2018MS03047)
内蒙古农业大学教育教学改革研究重点项目(JGZD201815)。