主梁变形预报的改进非等间隔权重灰色修正模型

Main Girder Deformation Prediction Model with Improved Unequal Interval Weight Gray Correction

针对斜拉体系加固张拉施工阶段主梁变形难以预报,传统非等间隔灰色模型在其应用中存在精度低的问题,提出了一种马尔科夫链残差修正的改进非等间隔权重灰色主梁变形预测模型。首先,该模型将主梁变形量和索力差分别看作传统非等间隔灰色模型中的原始数据列和时间差,考虑在累加生成和累减还原过程中是否引入权重分配系数,构建了4种不同的非等间隔权重灰色预测模型,并依据相似度准则确定相应的最优权重分配系数和最佳计算模型,提高预测精度;然后,采用马尔可夫链法反映出主梁变形残差序列的随机波动特征,从而对改进非等间隔权重灰色模型的预测值进行修正,较好地弥补了单一预测模型预测精度偏低的不足,进一步提高模型的预测精度;最后,通过该模型对斜拉体系加固主梁变形进行预测。研究表明,相对传统非等间隔灰色模型,在模型累减过程中引入权重分配系数后的模型相对误差平均值降低0.47%;采用马尔可夫链法对预测结果进行修正后,相对误差平均值降低10.32%,能显著提高预测模型的精度;与马尔科夫链修正后的传统模型相比,经累减还原优化后的修正模型相对误差平均值降低3.50%,预测精度更高,能够较好地反映出了斜拉体系加固主梁变形的发展趋势;该模型的核心理论是灰色系统理论,对实测数据并无特殊要求和限制,同样适应于其他工程领域的变形预测问题。

It is difficult to predict the deformation of main girder enhanced by stay cable system in the tensioning stage,and the traditional unequal interval gray model(TUIGM)has the problems of low accuracy in its application.In order to solve these problems,an improved unequal interval weight gray prediction model of main girder deformation modified by Markov chains residual was proposed.First,the girder deformation and cable force difference were taken as the original data sequence and time difference of the TUIGM respectively.Considering whether the weight distribution coefficient was introduced during the accumulation and regression process,four different gray prediction models with unequal interval weight were constructed,and the most optimal weight distribution coefficient and the prediction value of girder deformation were determined based on the similarity criterion,thus elevating the prediction accuracy.Second,the Markov chains method was adopted to reflect the random fluctuation feature of the residual sequence,made corrections to modify the prediction values of the improved unequal interval weight gray model(IUIWGM),which overcome the low accuracy of the single model,and further improved the accuracy.Finally,this model was applied to predict the deformation of main girder enhanced by stay cable system.The results showed that compared with the TUIGM,the average relative error of the model decreases by 0.47%after the weight distribution coefficient is introduced into the accumulation process.After modifying the prediction results by Markov chains method,the average relative error of the prediction model is reduced by 10.32%,which can greatly improve its prediction accuracy.Compared with the TUIGM modified by Markov chains,the average relative error of the modified model which has been optimized by the regression process decreases by 3.50%,this model has higher prediction accuracy and can reflect the development trend of the deformation of the main girder enhanced by stay cable system.The main theory of this model is grey theory and it is suitable for deformation prediction without any special requirement or limitation on the measured data.