变窗宽核加权估计下的变形趋势拟合方法

摘要

There are many methods of deformation monitoring data processing. Some methods have specific requirements for the amount of data and the data collection ways, others have complex calculation. Based on these shortages, a method of deformation trend fitting based on variable bandwidth kernel weighted estimation was proposed. First, the overall trend of deformation was fitted by kernel weighted estimation by using larger bandwidth. Then, the residual deformation was fitted by kernel weighted estimation by using smaller bandwidth. Based on the new method, a new bandwidth calculation method was proposed, namely the time series interval standard deviation bandwidth. The 32 elevation data deformation fitting of a certain monitoring point of a certain dam was taken as an example to compare the effect of using kernel weighted estimation based on different bandwidth and the effect of using kernel weighted estimation based on the experienced bandwidth. The result showed that the fitting precision of using kernel weighted estimation based on the time series interval standard deviation bandwidth was higher than the experienced bandwidth. What's more, the fitting precision of using kernel weighted estimation based on the variable bandwidth was higher than the time series interval standard deviation bandwidth and the experienced bandwidth.%变形监测数据处理的方法有很多,但这些方法对数据量及数据的采集方式有特定的要求,或者计算过程复杂.针对这些问题,提出了基于变窗宽核加权估计的变形趋势拟合方法,即先用较大窗宽的核加权估计去拟合变形的整体趋势,再用较小窗宽的核加权估计去拟合残余变形量——局部趋势.并针对这一新方法,提出了一种新的窗宽计算方法,即时序间隔标准差窗宽.以某大坝某一监测点32期的高程变形拟合为例,比较了不同的窗宽以及不同变窗宽组合的核加权拟合效果.结果表明,采用时序间隔标准差窗宽的核加权拟合比经验窗宽的拟合精度高；而基于变窗宽的核加权拟合比前两者精度更高.