优化反演方法及数值反演试验初步研究

PRIMARY STUDY ON LOCAL OPTIMIZATION METHODS AND NUMERICAL INVERSION TEST

基于典型力学模型 ,以研究区域的岩性参数和研究块体的边界力作为反演参数进行数值模拟 ,研究了单纯形法、模式搜索法、鲍威尔法、变量轮换法、混合罚函数法、复合形法等 6种最优化反演方法的反演效果和可靠性。结果显示 6种方法都有较好的表现。在恰当的条件下 ,6种方法反演所得参数都达到或接近参数的理论值 ,迭代收敛图、位移拟合曲线和残差统计分布图直观地反映出 6种方法的效果和可靠性 ,但对单纯形法和复合形法应给予较高的迭代收敛精度。

On the basis of the representative mechanical model, the numerical inversion test is made with the rock parameters of studied region and the driving forces acting on the boundaries of studied blocks as the inversion parameters, and the inversion effect and reliability of six different local optimization methods such as Covering Simple method, Pattern Search method, Powell method, Variable Cyclical method, Sequential Unconstrained Minimization technique and Covering Complex method are studied as well. The good results show that the inversed parameters obtained by the six methods are all reach or close to the theoretical values of those parameters only higher iteration precision should be given for the Covering Simple method and Covering Complex method. The effect and reliability of the six methods can also be directly seen from the iteration curve of inversion, the fitting curves of displacements and the statistical histogram for fitting difference of the displacements. Thus all these methods are simple, efficient and feasible inversion methods for geodesy inversion.