基于改进共轭梯度算法的桥梁移动载荷识别

Bridge moving load identification based on improved conjugate gradient method

针对时域法对噪声敏感问题以及传统共轭梯度法数值表现较差的问题,提出一种基于改进共轭梯度法的桥梁移动载荷识别方法。针对系统矩阵条件数较大导致的病态问题,采用预处理技术将原问题转化为条件数较小的等价问题。将等价问题转化为无约束优化问题,并使用修正的Hestenes-Stiefel共轭梯度法求解。通过数值模拟仿真以验证所提方法有效性,并将其结果与3种共轭梯度法识别结果进行对比分析。结果表明,在各种传感器配置下,所提出预处理修正的Hestenes-Stiefel共轭梯度法(PMHSCG)可准确识别桥梁移动载荷;较传统预处理Fletcher-Reeves共轭梯度法(PFRCG)和预处理Polak-Ribiére-Polyak共轭梯度法(PPRPCG),PMHSCG法识别精度提升约51%;较预处理Hestenes-Stiefel共轭梯度法(PHSCG),PMHSCG法识别精度提升约28%。

For the question of that the time-domain method is sensitivity to noise and the inadequate numerical performance of the traditional conjugate gradient method,a bridge moving load identification method based on the improved conjugate gradient method was proposed.In order to solve the ill-conditioned problem caused by the large condition number of the system matrix,the preconditioned technology was utilized to transform the original problem into the equivalent problem with smaller condition number.The equivalent problem was transformed into an unconstrained optimization problem and solved by the modified Hestenes-Stiefel conjugate gradient method.Numerical simulation was carried out to verify the effectiveness of the proposed method,and the results were compared with those of 3 conjugate gradient methods.The results show that the proposed preconditioned modified Hestenes-Stiefel conjugate gradient method(PMHSCG)can accurately identify the moving load of the bridge under various sensor configurations.Compared with the conventional preconditioned Fletcher Reeves conjugate gradient method(PFRCG)and preconditioned Polak Ribiere Polyak conjugate gradient method(PPRPCG),the identification accuracy of PMHSCG is improved by about 51%.Compared to the preconditioned Hestenes-Stiefel conjugate gradient method(PHSCG),the identification accuracy of PMHSCG is improved by about 28%.