预处理最小二乘QR分解法识别桥梁移动荷载的优化分析及试验研究  

Optimization analysis and experimental study of preconditioned least square QR-factorization for moving force identification

作　　者：陈震 王震[1] 余岭 邵文达[1] CHEN Zhen;WANG Zhen;YU Ling;SHAO Wen-da(School of Civil Engineering and Communication,North China University of Water Resources and Electric Power,Zhengzhou 450045,China;Key Laboratory of Disaster Forecast and Control in Engineering of Ministry of Education,Jinan University,Guangzhou,510632,China)

机构地区：[1]华北水利水电大学土木与交通学院,河南郑州450045 [2]暨南大学重大工程灾害与控制教育部重点实验室,广东广州510632

出　　处：《振动工程学报》2018年第4期545-552,共8页Journal of Vibration Engineering

基　　金：国家自然科学基金资助项目(51678278);河南省教育厅科学技术研究重点项目(17A560006)

摘　　要：基于时域内移动荷载识别理论,针对逆问题求解存在的典型不适定性问题,提出采用预处理最小二乘QR分解法(PLSQR)识别桥梁移动荷载。两轴时变移动荷载数值仿真结果表明:与采用奇异值分解求逆的时域法(TDM)相比,由PLSQR方法识别移动荷载在识别精度、抗噪性能和抗不适定性等方面均有明显的提高。通过结合改进的Gram-Schmidt正交化,在PLSQR方法基础上对其迭代效率进行优化,改进的PLSQR方法(i-PLSQR)在保证不降低识别精度的前提下其最优迭代次数有明显降低,3种噪声水平下8种工况平均最优迭代次数较原PLSQR方法均减小超过2/3。试验研究表明i-PLSQR识别结果与真实荷载非常接近,识别精度较传统TDM有明显提高,可应用于移动荷载的现场识别。Based on the theory of moving force identification in time domain,a preconditioned least square QR-factorization(PLSQR)algorithm is developed to overcome the typical ill-posed problem existing in inverse problems.A comprehensive numerical simulation is set up based on a beam model with biaxial time-varying forces to evaluate PLSQR by comparing this technique with the conventional counterpart SVD embedded in the time domain method(TDM).Investigations show that the PLSQR has higher precision,more noise immunity and less sensitive to perturbations with the ill-posed problems compared with TDM.By combining the improved Gram-Schmidt with iterative orthogonalization,iterative optimization analysis of PLSQR is carried out.Results indicate that the improved PLSQR(i-PLSQR)can more quickly and effectively identify the moving load on bridge without sacrificing the identification accuracy compared with the PLSQR,and the average optimal numbers of iterations reduce by at least two thirds in eight cases with three noise levels.The experimental results show that the identified force obtained from the i-PLSQR is very close to the true force and the identification accuracy is significantly higher than traditional TDM,which can be applied to the field moving force identification.The study results have important reference for the research of inverse problems identification of structural dynamics.

关 键 词：移动荷载识别 桥梁 时域法 预处理最小二乘QR分解法 优化分析 

分 类 号：TU311.3[建筑科学—结构工程] U441.2[建筑科学—桥梁与隧道工程]