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 θ 0 does not exceed 8%, and that of S 1 , S 2 , S 3 , and S 4 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 , tan β = 2.76 , θ 0 = 83.94 , S 1 = − 36.34 m , S 2 = 26.69 m , S 3 = − 45.64 m , and S 4 = 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.

Residue Classification-Based Robust Phase Unwrapping in High-Noise Region

“…In order to obtain the smallest error between the wrapped phase gradient and the unwrapped phase gradient, calculate k 1 and k 2 , as shown in the formulas ( 6) and (7):…”

“…When the unit-price of freight is 1, the length of the path is equal to the freight. Let ω 1 = ω 2 = 1 in formula (6), and the value of k is 0 or 1, and the formula (3) is incorporated into the formula (7); then, the formulas (8) and ( 9) are obtained:…”

“…Therefore, the requirements for early warning of natural disasters and emergency responses after disasters are more stringent. Synthetic aperture radar interferometry (InSAR) [1][2][3] is a powerful and well-established remote-sensing technique used to measure many important geophysical parameters, e.g., surface height of topography [4] or ground deformation [5][6][7][8], which plays an important role in early warning of natural disasters and emergency responses after disasters. Phase unwrapping (PU) is one of the key steps of InSAR [9].…”

Research on Mining Subsidence Prediction Parameter Inversion Based on Improved Modular Vector Method

“…For instance, Zha et al [12] successfully applied a genetic algorithm to the probability integral method for parameter inversion, demonstrating notable advantages in terms of accuracy and reliability. Subsequent investigations explored the use of the modular vector method [13][14][15], particle swarm algorithms [16][17][18][19], simulated annealing algorithms [20,21], and others [22][23][24][25][26][27] for parameter inversion within the probability integral method framework, all yielding highly satisfactory results. In a comparative analysis of parameter inversion outcomes using various intelligent algorithms, Han Mei et al [28] confirmed that, with an appropriate choice of initial exploration values, the modular vector method excels in accuracy and reliability when contrasted with other algorithms.…”