改进的边坡变形非线性时变系统的不确定性分析

摘要

Geodesy data usually contains many uncertainties with unknown statistical information,possibly causing morbid theory model and affecting the accuracy and reliability of parameter estimation.This paper researches the mechanical principle of the nonlinear time series evolution system of slope displacements,and improves the original model by using polynomial fitting.In the process of parameters calculation,the negative influences of results caused by uncertainties of measurement data are considered.The accuracy ofparameters calculation is improved by restricting uncertainty and using the min-max criterion.Comparing the forecasting results with displacement observational data shows that the results of the least-squares with uncertainty (ULS) approach are closer to measurement data,as compared with least-square (LS) and total least-square(TLS).It is also indicated that the effectiveness of predicting displacements by improved nonlinear time series evolution system of slope displacements.%大地测量数据往往包含许多不确定性,可能导致所建立的函数模型产生病态,影响参数估计的准确性和可靠性.通过研究边坡变形非线性时变系统的力学原理,利用多项式拟合方法改进原模型,在参数解算过程中,考虑到测量数据的不确定性给解算结果带来消极影响,通过限制不确定度,利用min-max准则,提高参数解算的准确性,并将预测变形结果与实测边坡位移数据对比.结果表明,带不确定性的平差算法(least-square with uncertainty,ULS)与最小二乘平差(least-squares,LS)和整体最小二乘平差(total least-square,TLS)相比,其预测结果更接近实际测量数据,证明了改进的边坡变形非线性时变系统预测变形的有效性.