BFGS method based inversion of parameters in probability integral model

Probability integral model is an important mathematical model to describe the surface deformation law caused by coal mining. Usually the traditional optimization algorithm and intelligent optimization algorithm are used to invert the unknown parameters in the probability integral model to determine the explicit surface defor-mation characteristics. In this paper,the authors propose to adopt the optimization methods to perform the inversion of the parameters. Specifically, the BFGS method is used as an example of a widely used unconstrained op-timization method. Based on the BFGS meth- od,the authors can utilize the displacement between two adjacent iteration points to generate the search direction by Newton equation. On this basis,the iterative process is completed through inexact line search to obtain the optimal pa- rameters. In the experimental part,the authors employ the pattern search method and genetic algorithm as the representa- tives of the traditional optimization algorithm and intelligent optimization algorithm. The simulation results show that the BFGS method can effectively invert all parameters,and the parameter inversion accuracy of BFGS method is significantly higher than the pattern search method and genetic algorithm under different error levels. In addition,the parameter inver- sion accuracy of BFGS algorithm is still better than the other two algorithms under different gross error levels and data missing conditions,which,to some extent,illustrates the feasibility and superiority of introducing BFGS method for pa- rameter inversion in probability integral model. In the engineering case,the fitting curves of the inversion results and the sinking values further verify the reliability and accuracy of the new algorithm. However,the unit weight error in the case is significantly larger than that in the simulation experiment. Taking the actual factors of the case into consideration,the main reason for the large difference of the unit weight error is the large surface fluctuations in the mining area,which causes the larger model error of the probability integral method. Therefore,for the specific engineering case,in addition to the effective parameter inversion method,it is necessary to determine a reasonable inversion scheme according to the ac- tual situation,in order to achieve better parameter inversion effect.