Research On Probaility-integral Method Calculation Parameters Based On Total Least Squares Robust Algorithm

In predicting surface movement and deformation in many mining areas in China,the probability integral method is often used to be relatively mature and widely used.However,due to factors such as observers,measuring instruments and external conditions,not only observation vector errors but also coefficient matrix errors are included in the data obtained from surface monitoring stations.In order to make up for the defects of Least Squares(LS)algorithm,Total Least Squares(TLS)method is proposed to obtain more reasonable and reliable parameter estimation by considering both observation vector and coefficient matrix errors.In a large number of field measurements,the observed values not only contain random errors,but also inevitably contain certain gross errors or outliers.As TLS,like LS,has not achieved the desired effect in solving the problem of gross errors,this paper uses robust estimation to deal with gross errors.In order to solve the above two problems in the evaluation of probability integrals,this paper presents Weight Total Least Squares(WTLS)method and Robust Weight Total Least Squares method.(RWTLS).The main contents and results of the study are as follows:1.To solve the errors-in-variables(EIV)problem,the Total Least Squares method is introduced.The WTLS iterative solution based on nonliner-Lagrange,Gauss-Newton and Partial EIV(PEIV)model are derived.Matlab is used to realize the relevant algorithms.The linear fitting example is used to solve the parameter estimation,and the results show that the WTLS programming is correct,WTLS is superior to the parameters obtained by LS algorithm,and it can effectively solve the problem that the coefficient matrix in the adjustment model contains random errors.2.In this paper,robust estimation is used to deal with gross errors.This paper introduces the basic principle of robust and the commonly used equivalent weight function model,deduces the RWTLS process,selects the appropriate weight function,in the iterative algorithm to constantly modify the weight,weaken or eliminate the weight of the observation value containing gross errors,to achieve the effect of resisting gross errors.Through the analysis of plane coordinate transformation examples,it is found that the estimation of parameters obtained by LS,WTLS and RWTLS varies greatly when the gross errors is included.Among them,RWTLS has the best effect and has certain advantages in processing the data containing gross errors.3.Taking the 1613(1)working face of Guqiaonan Coal Mine as an example,LS,WTLS and RWTLS were respectively used to calculate the probability integral parameters and evaluate the fitting accuracy of the measured data of the observation station.The results show that compared with LS and WTLS,the parameters obtained by RWTLS are more consistent with the measured variation law,and the fitting effect is better and the accuracy is higher.Figure[12]Table[23]Reference[84]...