改进的卡尔曼灰色模型在隧道沉降预测中的应用

摘要

为提高地表沉降预测精度,针对灰色预测模型(GM (1,1))易受随机干扰影响致使预测精度不高的问题,建立了基于卡尔曼滤波的灰色理论预测模型.考虑到沉降量受到温度和时间因素影响较大的特点,将地表的沉降看作时间、温度的相关函数来建立卡尔曼滤波模型,并利用迭代滤波理论和LevenbergMarquardt优化滤波,构建改进的卡尔曼滤波模型.改进的卡尔曼滤波模型与灰色模型相结合,应用于地表沉降预测中,并将改进的卡尔曼滤波灰色模型预测结果与卡尔曼滤波灰色模型的预测结果进行对比.实例计算表明,使用改进的卡尔曼滤波对消除检测数据扰动误差后的数据进行灰色模型预测的精度相比于单纯灰色预测的预测精度更高.%In order to improve the prediction accuracy of surface subsidence, and solve the problem that the gray prediction model (GM (1, 1) ) is easily affected by random interference, the gray theory prediction model based on kalman filter is established.Since the subsidence can be greatly affected by temperature, precipitation and time, the subsidence of land surface is regarded as the correlation function of these factors.The improved kalman filter model is constructed by using the iterative filtering theory and levenberg-marquardt optimization filter, which is combined with the gray model and applied to the prediction of surface subsidence.The result shows that the accuracy of the improved model is higher than that of the pure gray model.