基于广义逆理论的河网糙率反演研究

引入广义逆和Backus-Gilbert反演理论，构造了牛顿-广义逆方法和自然逆方法计算优化算法的搜索方向，进行 河网糙率反演，并推导了两种算法反演解估计的分辨率矩阵和单位协方差矩阵.理论分析表明,牛顿-广义逆优化算法具有 二阶收敛速度.在反演过程中结合Wiggins方法控制观测数据中的噪声，能够有效调节河道糙率反演结果的分辨率和方差. 数值仿真表明这两种算法与Wiggins方法相结合，选取适当的控制参数，既能达到较高的精度，又能有效地抑制噪声，提 高数值计算的稳定性.

Inverse analysis of channel friction based on generalized inverse theory

According to generalized inverse theory and Backus-Gilbert inverse theory,singular value decomposition(SVD) and Newton-generalized inverse matrix were used to analyze the optimization orientation.The resolution matrix and covariance matrix was deduced,which could describe inversion results reliability.Theoretical analysis showed that the degree of convergence of Newton-generalized inverse optimal algorithm was second-order.During the computation procedure, Wiggins method was integrated into the optimization algorithm.Numerical simulation showed that noise can be suppressed effectively and inversion result approach genuine solution,when proper control parameter is used,and the method can improve numerical stability.