结合坐标变换的GM(1,1)模型及其变形预测应用  

GM(1,1) model improved by coordinate transformation and its application in deformation prediction

作　　者：邱利军[1,2] 张波 周占学[1,2] 张京奎 QIU Lijun;ZHANG Bo;ZHOU Zhanxue;ZHANG Jingkui(Hebei University of Architecture,Zhangjiakou 075000,China;Hebei Key Laboratory of Diagnosis,Reconstruction and Anti-disaster of Civil Engineering,Zhangjiakou 075000,China;54th Research Institute of CETC,Shijiazhuang 050081,China)

机构地区：[1]河北建筑工程学院,河北张家口075000 [2]河北省土木工程诊断、改造与抗灾重点实验室,河北张家口075000 [3]中国电子科技集团公司第54研究所,河北石家庄0500813

出　　处：《人民长江》2021年第4期209-213,共5页Yangtze River

基　　金：国家自然科学基金项目(91638203);河北省高校百名优秀创新人才支持计划资助项目(SL-RC2017033);河北省教育厅2020年度河北省高等学校科学研究项目(Z2020222);张家口市科技计划项目(2021028D)。

摘　　要：传统GM(1,1)模型以指数函数预测,而其一次累加序列的拟合函数曲线与实测序列的一次累加序列曲线并不重合,存在相近、相交或相离的趋势,导致后期预测的一次累加值存在误差。基于此,提出以序列下标(时间)为横轴,以序列值为纵轴建立平面直角坐标系,在坐标系内对一次累加序列拟合预测值进行先平移后旋转的坐标变换。变换后的点形成新的折线,则将原横坐标在新的折线或折线延长线上对应的纵坐标值作为一次累加最终预测值,累减还原后即可得到建模序列后期预测值。以两个工程实例对变形预测数据进行了验证,证实该方法可有效提高预测精度,对实际工程具有参考价值。The traditional GM(1,1)model uses exponential function for prediction, and the fitting function curve of the first accumulation data does not coincide with the first accumulation curve of the measured data, having a trend of closeness, intersection or separation between them, and it will lead to the error of first accumulated value of later prediction.Therefore, it was proposed to set up a plane coordinate system with sequence index(time)as the horizontal axis and sequence value as the vertical axis.In this coordinate system, the coordinate transformation of first translation and then rotation was carried out for the fitting prediction value of a cumulative sequence.After the transformation, the transformed points formed a new broken line, and then the ordinate value corresponding to the original abscissa on the new broken line or the broken line extension line was used as a cumulative final prediction value.After cumulative reduction, the late prediction value of the modeling sequence was obtained.The measured deformation data of two cases were used to verify this method, which was proved that it can effectively improve the prediction accuracy, has much reference value for practical engineering.

关 键 词：沉降变形 变形预测 GM(1 1)模型 坐标变换 

分 类 号：TV698[水利工程—水利水电工程]