基于填充函数与DCD的全局优化算法及其反演

A global optimization method based on filled function and DCD and its application in inverse analysis

岩土工程中以监测位移为已知信息的反演问题可通过带未知变量约束空间的优化模型去求解。该模型中的优化函数常具有非线性、非凸性等特点,使得反演结果容易陷入局部最优的困境。为了应对在运用优化算法反演此类问题时存在的困境,并提高其算法效率,依据填充函数优化思想与DCD(Dynamic Canonical Descent)思想在反演时的优良全局搜索能力及其算法优化特点,提出了基于填充函数和DCD思想的联合反演全局优化算法,并给出了其反演迭代形式。数值计算和工程应用结果均表明:对于随机给定的任何一组初始反演值,本算法都能稳定且快速地收敛到反演真值。该联合算法具有数值计算稳定性好、全局优化能力强、收敛速度快等优点,将其应用于岩土工程中的非线性反演求解中具有较好的前景。

In geotechnical engineering, it is appreciated to translate an inverse analysis problem with monitored displacements to solve unknown mechanical parameters in constraint space, into an optimization problem. Unfortunately, the objective function in translated optimization is often non-linear and non-convex for multi-extreme-points in given constraint space. Considering the optimization difficulties of multimodal objective functions in back analysis, a joint optimization method based on filled function and DCD(Dynamic Canonical Descent) is presented and an iteration scheme for nonlinear global optimization is also proposed. Finally, the joint iteration optimization scheme is applied to several known numerical tests and an elastic non-linear inverse analysis, the results show that the joint algorithm can quickly converge to the global best point and give the right parameters of inverse analysis with good stability and global optimization capability.