求解非线性反问题的大范围收敛梯度正则化算法  

Global convergence gradient regularization algorithm for solving nonlinear inverse problems

作　　者：崔凯[1] 李兴斯[2] 李宝元[2] 杨国伟[1] 

机构地区：[1]中国科学院力学研究所高温气体动力学重点实验室,北京100080 [2]大连理工大学工程力学系,辽宁大连116023

出　　处：《计算力学学报》2005年第4期415-419,共5页Chinese Journal of Computational Mechanics

基　　金：国家重点基础研究发展规划(G1999032805)资助项目.

摘　　要：基于同伦映射的思想,改进了求解非线性反问题的梯度正则化算法。通过路径跟踪有效地拓宽了梯度正则化算法求解的收敛范围。对于正则化参数的修正,通过引入拟Sigmoid函数,提出了一种下降速率可调的连续化参数修正方法,在保证迭代稳定的条件下,得到较好的计算效率,同时保证该算法具有很好的抵抗观测噪声能力。实际算例表明,该方法收敛范围宽,计算效率高,在存在较强观测噪声的条件下也能得到很好的反演结果。Based on idea of homotopy mapping, an improved gradient regularization algorithm was developed. By using this path-following algorithm, the convergent bound of the gradient regularization method was efficiently widened. Moreover, a Sigmoid function was adopted to adjust the regularization parameter, by using this function, the efficiency and the stability of computation procedure were highly improved, while observational noises could also be resisted effectively. Numerical examples showed that the convergence bound of this algorithm is wider than normal gradient regularization algorithm, and the average efficiency is improved about 40-90%, besides, even though observational quantities were contaminated heavily by noise, an appropriate result could also be found.

关 键 词：反演 梯度正则化 同伦方法 正则化参数 

分 类 号：O39[理学—工程力学] TB12[理学—力学]