The Application Research Of Total Least Square In The Data Processing Of Mining Subsidence

The error-in-variable(EIV)model takes into account the error between the observation vector and the coefficient matrix.Hence,the theory is more rigorous.The total least squares(TLS)method can be used to obtain the model solution.The total least squares method has been widely used in many fields since its introduction,such as geodesy and engineering measurement.However,it is rarely used in the field of mine surveying as an important branch of geodetic survey.Combined with the characteristics of mine measurement data,analysis that the mining measurement data processing model is mostly EIV model,if the least square method is still used to solve the model,it is not rigorous in theory.Therefore,the purpose of this paper is to combine EIV model with the data processing model of mine measurement,and apply it to the research of subsidence monitoring data processing.The main work of the thesis is as follows:1.The algorithms of TLS basic model and the general model,as well as TLS basic model were systematically introduced.The paper focuses on the analysis of the least squares-total least squares(LS-TLS)proposed by Fang Xing based on the nonlinear Gauss-Helmet model.Meanwhile,the structure matrix was introduced on the basis of this algorithm,taking into account the miscibility and structure of the coefficient matrix so as to make the algorithm more general.2.The application of the LS-TLS algorithm for the parametric inversion with probability integral method of the nonlinear Gauss-Helmut model considering the structure of the coefficient matrix is studied.In this paper,two kinds of adjustment models for parameters inversion of the probability-integral method using curved surface fitting were introduced in detail.The specific construction process of TLS adjustment model that takes into account the coordinates of the observation station and the error of subsidence value is also introduced at length,including coefficient matrix further linearized the specific form of the structure matrix etc.In addition,aiming at the ill-conditioned problems in the inversion process,this paper combines the ridge estimation algorithm to obtain the ridge parameters by the L-curve method,which solves the ill-posed problem of parameter inversion effectively.Meanwhile,the whole process of the parameter inversion was achieved on the Matlab software platform by programmatically implements.The results indicate that the TLS algorithm has no obvious advantage in inverting the probabilistic integration parameters for surface fitting,which is basically consistent with inversion results using traditional linear least-squares method.3.The robust algorithm of TLS and its application are studied.Based on the mixed TLS algorithm of the Gauss-Helmut model after the introduction of the structure matrix,the weight factor function is defined separately for the coefficient matrix and the observed vector elements according to IGG III weight function.The TLS robust algorithm is deduced.Meanwhile,the established robust TLS algorithm is applied to the parameters inversion of mining probability integral model and GPS elevation fitting experiment in mining area.The experimental results show that the TLS robust algorithm can effectively deal with the probability integral model observation vector when there is a gross error at the same time as the coefficient matrix.Meanwhile,the model parameters of the probability integration method are affected by the number of gross errors and the location of the gross error.Whatever is linear polynomial or quadratic polynomial fitting,the TLS robust algorithm can effectively resist the influence of gross errors in the GPS elevation fitting experiment.The results of the TLS robust algorithm are basically consistent with the results of the LS robust algorithm.In addition,the experiment results also show that the quadratic polynomial fitting model has higher accuracy than the linear polynomial fitting model.4.The application effect of mixed multivariate TLS in non-equal-time and multivariate grey model for data fitting and prediction of mining subsidence data is studied.The modeling mechanism of non-equal and multiple-variable gray model is studied.The mixed multi-component TLS method is introduced into solving section of the gray model parameter.Meanwhile,the model gray parameters are optimized.Finally,experiment based on the subsidence data of the Wu yun Expressway above the old mining area,The analysis results show that the multivariate grey model MGM(1,N)has a better fitting and forecasting accuracy than GM(1,1).Meanwhile,the result that the TLS adjustment method optimizes the MGM(1,N)gray parameters is also significant.However,the optimization effect of the GM(1,1)gray parameters is not obvious.