D-InSAR与最优化算法的采空区几何参数反演

Inversion of goaf geometric parameters based on D-InSAR and optimization algorithm

针对采矿后遗留的采空区会诱发严重的地质灾害问题,该文提出一种采空区几何参数的反演算法,旨在及时探明采空区的分布特征与几何形状,进而有效控制灾害的发生。该文通过合成孔径雷达差分干涉(D-InSAR)技术获取采空区上方的地表连续沉降场,通过概率积分模型建立采空区几何特征与地表沉降场之间的相互关系,引入BFGS最优化算法对采空区的几何参数进行反演。仿真实验结果表明:在加入5 mm随机误差的情况下,BFGS算法能够有效反演出全部参数,且反演精度略高于遗传算法(SA)和模拟退火(GA)算法;同时,在不同的初值条件下,BFGS算法反演结果的数值稳定性与反演精度仍明显优于其他两种算法。工程应用中,反演结果显示SA与GA算法的相对误差平均值都超过了10%,而BFGS算法的相对误差平均值只有4.73%,进一步验证了BFGS算法的可靠性。

Aiming at the serious geological disasters induced by the goaf after mining,this article proposes an inversion algorithm for the geometric parameters of the goaf,which aims to detect the distribution characteristics and geometric shapes of the goaf in time and effectively control the occurrence of disasters.In this paper,the continuous subsidence field above the goaf is obtained by using differentia Interferometric synthetic aperture radar(D-InSAR)technology.Then the probability integral method(PIM)is used to establish the relationship between the geometric features of the goaf and the surface subsidence field.Finally,the BFGS optimization algorithm is introduced to invert the geometric parameters of the goaf.The simulation experiment results show that:With the addition of 5 mm random error,the BFGS algorithm can effectively invert all parameters,and the inversion accuracy is slightly higher than the(genetic algorithm)GA and simulated annealing(SA)algorithm.At the same time,under different initial conditions,the numerical stability and inversion accuracy of the inversion results of the BFGS algorithm are still significantly better than those of the other two algorithms.In engineering applications,the inversion results show that the average relative error of SA algorithm and GA algorithm both exceed 10%,and the result of BFGS algorithm is only 4.73%,which further verifies the reliability of BFGS algorithm.