Full parameters inversion model for mining subsidence prediction using simulated annealing based on single line of sight D-InSAR

Due to the inability of the single line of sight D-InSAR to monitor the three-dimensional deformation of the surface, the conventional methods are unable to obtain the prediction parameters (probability integral parameters) of surface subsidence in coal mining. In this paper, a calculation method of simulated annealing (SA) for probability integral parameters based on single line of sight D-InSAR is proposed. Firstly, the method predicts the subsidence, the horizontal movement in the north–south direction and the horizontal movement in the east–west direction of the target pixel by using the probability integral method. Based on the projection relationship between the three-dimensional deformation and the LOS deformation, the predicted movement and deformation of the target pixel in LOS direction (riLOS′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{{i{\text{LOS}}}}^{'}$$\end{document}) are calculated. Using the measured movement and deformation of the target pixel in LOS direction (riLOS\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$r_{{i{\text{LOS}}}}$$\end{document}), the residuals of the target pixel are calculated (vi=riLOS-riLOS′\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$v_{i} = r_{{i{\text{LOS}}}} - r_{{i{\text{LOS}}}}^{'}$$\end{document}) and the error function of the parameter is constructed (ε(B)=∑|vi|\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon (B) = \sum {|v_{i} |}$$\end{document}). Then based on the criteria (ε(B)=min\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varepsilon (B) = \hbox{min}$$\end{document}), all the probability integral parameters are obtained accurately by the SA method. The accuracy and robustness of the proposed method are verified by simulation experiments. At last, the predicted parameters of mining subsidence in 9310 working face of Nantun Coal Mine are calculated by this method, and the characteristics of probability integral parameters are analyzed.