改进不等时距权重的灰色残差组合修正模型及其应用  

Improved unequal time-interval weight gray model and residual combined correction and its application

作　　者：徐刚年[1] 高全亭 解俊海 王有志[1] 王来永[3] 武俊彦[3] XU Gangnian;GAO Quanting;XIE Junhai;WANG Youzhi;WANG Laiyong;WU Junyan(School of Civil Engineering,Shandong University,Jinan 250061,China;Shandong Taidong Expressway Company,Tai'an 271000,China;Resemch Institute of Highway Ministry of Transport,Beijing 100088,China)

机构地区：[1]山东大学土建与水利学院,山东济南250061 [2]山东高速泰东公路有限公司,山东泰安271000 [3]交通运输部公路科学研究院,北京100088

出　　处：《测绘通报》2019年第1期69-74,共6页Bulletin of Surveying and Mapping

基　　金：国家自然科学基金(11372165);交通运输部西部建设科技项目(2011318223940)

摘　　要：为提高传统不等时距灰色模型(TUTGM)的预测精度,提出了一种改进不等时距权重的灰色残差组合修正模型(IUTWGMRCC)。首先在传统不等时距灰色模型中引入时距权重分配系数,按照累加生成和累减还原过程的生成序列不同,构建了4种不同的预测模型,并依据相似度准则确定最优拟合序列和预测值;然后采用正弦函数和谐波变化生成的周期序列函数修正残差序列,进一步提高模型的预测精度;最后对建筑物3个观测点的沉降量进行预测。结果表明,累减还原过程引入不等时距权重的灰色模型预测精度最高,经残差组合修正后,预测结果的后验差比分别为0.04、0.11和0.05,精度等级为1级。In order to improve the prediction accuracy of the traditional unequal time-interval gray model( TUTGM),an improved unequal time-interval weight gray model and residual combined correction( IUTWGM-RCC) is proposed. Firstly, the weight distribution coefficient of time interval is introduced into TUTGM. According to the different generation sequence of cumulative and reduction process,four different forecasting models are constructed,and the optimal fitting sequence and prediction value are determined based on similarity criterion. Secondly,the periodic sequence function generated by sine function and harmonic generation is used to correct the residual sequence,which further improves the prediction accuracy of the model. Finally,the settlement of three measuring points of building is predicted. The results show that the prediction accuracy of TUTGM is the highest by introducing the weight distribution coefficient in the reduction process among four different forecasting models. After the residual combined correction,the posterior error ratios are 0.04,0.11 and 0.05 respectively,and the precision rank is grade 1.

关 键 词：沉降预测 灰色理论 非等间隔 改进权重 残差修正 相似度准则 

分 类 号：P258[天文地球—测绘科学与技术]