GM(1,1)幂模型的改进及其在沉降预测中的应用  

Improvement of GM(1,1)Power Model and Its Application on Settlement Prediction

作　　者：陈鹏宇[1] CHEN Pengyu(School of Geography and Resources Science,Neijiang Normal University,1124 Dongtong Road,Neijiang 641100,China)

机构地区：[1]内江师范学院地理与资源科学学院,四川内江市641100

出　　处：《大地测量与地球动力学》2020年第5期464-469,共6页Journal of Geodesy and Geodynamics

基　　金：长江科学院开放基金(CKWV2016391/KY);四川省教育厅科研项目(17ZB0222);内江师范学院校级科研项目(18ZC01)。

摘　　要：GM(1,1)幂模型可用于趋于稳定或具有S型变化趋势的沉降预测,但其存在灰色建模的固有缺陷、非等间隔数据的不适用性和参数求解复杂性等不足之处。结合幂函数变换与无偏GM(1,1)模型和非等间隔无偏GM(1,1)模型,建立了无偏GM(1,1)幂模型和非等间隔无偏GM(1,1)幂模型。基于Matlab程序,以拟合结果的平均相对误差最小作为优化目标,提出参数的优化求解方法,同时提出采用Origin拟合函数SRichards2的替代方法。实例分析结果显示,两种方法拟合效果相当,均可用于沉降预测。结合两者的应用效果和建模特点,建议人工处理数据时采用Origin拟合函数SRichards2;对于有特殊优化目标的情况或自动化监测设计时,可采用无偏GM(1,1)幂模型或非等间隔无偏GM(1,1)幂模型。The GM(1,1)power model can be used for the prediction of settlement that tends to be stable or has a trend of S-type.However,the GM(1,1)power model has some shortcomings,including the inherent defects of grey modeling,no applicability for non-equal interval data,and the complexity of solving parameters.In combination with the power function transformation and the unbiased GM(1,1)model or the unequal interval unbiased GM(1,1)model,we establish the unbiased GM(1,1)power model and the unequal interval unbiased GM(1,1)power model.Based on the Matlab program,we take the minimum relative mean error of the fitting results as the optimization objective,and advance the solving method of optimization parameters.Meanwhile,we propose an alternative method of Origin fitting function SRichards2.The application results of engineering examples show that the two methods have a good fitting effect and can be used in settlement prediction.Considering the application effect and the modeling characteristics of the two methods,we recommend the Origin fitting function SRichards2 is recommended for manual data processing,and the unbiased GM(1,1)model and non-equal interval unbiased GM(1,1)model for special optimization objectives or automatic monitoring design.

关 键 词：沉降 预测 GM(1 1)幂模型 灰色预测模型 Origin拟合函数 

分 类 号：P258[天文地球—测绘科学与技术]