共轭梯度最小二乘迭代正则化算法在冲击载荷识别中的应用

Application of conjugate gradient least squares iteration regularization algorithm in impact load identification

结构动载荷识别反问题是典型的病态问题,需要应用正则方法克服其病态特性而获得稳定的解。与直接正则化算法Tikhonov方法相比,共轭梯度最小二乘(Conjugate Gradient Least Squares,CGLS)迭代算法在载荷识别反问题的正则化过程有无须对传递矩阵求逆、无须明确正则化参数的优点。提出共轭梯度最小二乘迭代正则化算法和启发式迭代收敛终止准则,用于三自由度仿真模型和壳结构试验模型的冲击载荷识别,并与经典的Landweber迭代正则化算法和直接正则化算法Tikhonov方法比较。仿真和实验结果表明:CGLS迭代正则化算法在识别精度、收敛速度、计算效率和抗噪性方面有明显优势。

Regularization methods should be developed to overcome the ill-posedness of inverse problem of structural dynamic load identification for getting a stable solution.The conjugate gradient least squares （CGLS）iterative regularization algorithm has several advantages over direct regularization methods such as the Tikhonov method on solving inverse problems：the inversion of matrix is not required,and no explicit regularization parameter is required.A CGLS iteration regularization algorithm with the heuristic stopping rule was proposed and as examples was applied to reconstruct the impact load acting on a three-degree-of-freedom system and a shell structure.The results were compared with those by the classical Landweber iteration regularization algorithm and Tikhonov regularization method.Simulations and experiments demonstrate that the CGLS algorithm for impact load identification works better in the aspects of accuracy,convergence rate,cost time and anti-noise.