Static parameter identification of bridge structure based on Levenberg-Marquardt algorithm
-
摘要: 为了提高桥梁结构状态评估中结构参数识别的精度和稳定性, 克服Gauss-Newton法不能有效地处理奇异和非正定矩阵以及对初始点要求苛刻的缺点, 利用Levenberg-Marquardt法, 通过在Gauss-Newton法的迭代矩阵中添加阻尼项, 对迭代矩阵加以修正, 通过Matlab自编程序实现对实际结构参数的优化求解。对一连续梁的数值模拟计算表明, 在Gauss-Newton法迭代发散的情况下, Levenberg-Marquardt法的识别结果相对误差在10%左右, Levenberg-Marquardt法基本能实现对真实结构参数的识别, 为结构进一步的状态评估提供了结构模型最基本的量化信息。Abstract: In order to improve the precision and stability of structural parameter identification in the procedure of bridge assessment, a heuristic method of using Levenberg-Marquardt algorithm to meliorate the singular iterative matrix of Gauss-Newton was put forward to overcome the harsh terms of initial value in Gauss-Newton algorithm, the numerical simulative test of a continuous beam with three spans was carried out.Simulation results show that the relative-effective error of bridge structure parameter identification is less than 10%, the application of Levenberg-Marquardt algorithm is feasible, its quantitative message can be put forward for bridge structure condition assessment.
-
表 1 参数识别效果比较
Table 1. Comparison of parameter indentification results
/(kN·m2) 待识别参数 参数初始值 参数真值 G-N法 L-M法(μ=1×10-20) L-M法(μ=1×10-19) 迭代9次 迭代5次 迭代27次 识别结果 相对误差/% 识别结果 相对误差/% 识别结果 相对误差/% EI1 4.5×105 3.0×105 — — 3.108 0×105 3.60 2.911 9×105 -2.94 EI2 4.5×105 3.0×105 3.747 4×105 24.90 3.351 6×105 11.70 2.589 3×105 -13.70 EI3 9.0×105 6.0×105 6.004 2×105 0.07 5.938 0×105 -1.03 6.533 2×105 8.89 EI4 9.0×105 6.0×105 6.003 0×105 0.05 6.148 0×105 2.47 6.182 2×105 3.04 EI5 6.0×105 4.5×105 4.495 7×105 -0.10 4.2474×105 -5.61 4.059 0×105 -9.80 EI6 6.0×105 4.5×105 4.498 6×105 -0.03 4.656 9×105 3.49 4.880 2×105 8.45 
下载: 导出CSV
-
[1] Qin Quan. Health monitoring of bridge structure[J]. China Journal of Highway and Transport, 2000, 13(2): 38-42. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-ZGGL202102002.htm [2] 崔飞. 桥梁参数识别与承载能力评估[D]. 上海: 同济大学, 2000. [3] Xiang Tian-yu, Zhao Ren-da, Liu Hai-bo, et al. Damade detection of prestressed concrete continuous beam from static response[J]. China Civil Engineering Journal, 2003, 36(11): 79-82. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC202101001.htm [4] Sanayei M, Saletnike M J. Parameter eatimation of structure frome static train measurements Ⅰ: formulation[J]. Journal of Structural Engineering, 1996, 122(5): 253-257. https://www.cnki.com.cn/Article/CJFDTOTAL-TMGC202101001.htm [5] Li Gui-ling, Wan Jian-hua, Tao Hua-xue. Nonlinear data processing based on improved Marquardt method[J]. Journal of Institute of Surveying and Mapping, 2001, 18(3): 167-169. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJX201508001.htm [6] Zhou Xian-tong, Wang Bai-sheng, Ni Yi-qing. Structural parameter identification using neural network and optimization method[J]. Chinese Journal of Computational Mechanics, 2001, 18(2): 235-238. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-JSJX202005001.htm [7] Liu Zhi-ming, Wang Zhong-xian, Song Hong, et al. Prediction of stress concentration based on Levenberg-Marquardt algorithm[J]. Journal of Jiangsu University of Science and Technology(Natural Science Edition), 2001, 22(6): 84-87. (in Chinese) https://www.cnki.com.cn/Article/CJFDTOTAL-DOUB202101002.htm [8] 数学手册编写组. 数学手册[M]. 北京: 高等教育出版社, 1979. -
点击查看大图
图(1) / 表(1)
计量
- 文章访问数: 208
- HTML全文浏览量: 59
- PDF下载量: 231
- 被引次数: 0
