Probability Integral Method Parameter Determination by SBAS‐InSAR Technology and GWO Algorithm

Abstract

This paper proposed a method based on the SBAS‐InSAR and gray wolf optimization algorithm aiming at the time‐consuming and laborious defects of the traditional method used to obtain the expected parameters of the probability integral method and the shortcomings of the InSAR technology in the field of large gradient deformation detection in the mining area. The fitness function of the algorithm was established based on the geometric relationship between the radar side imaging and the three‐dimensional model of the probability integral method. The stable sinking point of the settlement boundary obtained by SBAS‐InSAR was used as the input value for the calculation of the predicted parameters of the probability integral method. Firstly, the simulation experiment was employed for the simulation of the direction of the InSAR line of sight combined with the geological mining conditions of the assumed working face, thereby obtaining the probability integral prediction parameters of the working face. Consequently, the maximum relative error of q, b, tanβ, and θ0 does not exceed 8%, and that of S1, S2, S3, and S4 does not exceed 35.5% (low parameter sensitivity). The error of the LOS‐direction deformation fitting is 0.076 m, which meets the tolerance requirements, and the result is trustworthy. At last, the parameter finding method is applied to the engineering example, that is, the 112201 working face of Xiaobaodang Coal Mine in the northern Shaanxi mining area. The settlement value of the stable boundary point is obtained based on the SBAS‐InSAR results, which is substituted into the fitness function. And the GWO optimization algorithm is used for optimization and parameter finding; the probability integral expected parameters of the working face are calculated as q = 0.63, b = 0.37, tanβ = 2.76, θ0 = 83.94, S1 = −36.34 m, S2 = 26.69 m, S3 = −45.64 m, and S4 = 39.62 m. Substitute the obtained parameters into the probability integral model for the prediction of the vertical and horizontal displacements of the working face, and verify its accuracy with the GPS measured data. The results showed that the maximum absolute error of vertical displacement reached 116 mm, the median error was 63 mm, and the maximum absolute error of north‐south horizontal movement reached 56 mm; meanwhile, the median error was 23 mm, the maximum absolute error of east‐west horizontal movement reached 61 mm, and the median error was 29 mm; all the above parameters are within the tolerance range, indicating that the method for the calculation of probability integral parameters proposed in this paper is applicable in actual engineering.