Bridge weighing-in-motion algorithm theory based on Bayesian posterior estimation and tests

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Journal of Vibration and Shock ›› 2024, Vol. 43 ›› Issue (1) : 20-27.

ZHANG Longwei1,2, YUAN Luqi1, CHEN Ning1, YUAN Shuaihua1, ZHANG Long1

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Abstract

The bridge weigh-in-motion (BWIM) can find axle weights from the measured response of the bridge acting by passing vehicles. However, since the measured response contains measurement errors, the accuracy of the traditional BWIM algorithm is reduced to a certain extent. To solve this problem, this paper proposes a novel BWIM algorithm based on Bayesian posterior estimation. The proposed algorithm considers the negative influence of measurement error on axle weight identification. Firstly, assume measurement error and axle weights both follow Gaussian distribution; Then, use the standard deviation of measurement error and axle weight standard deviation to obtain constraint factor which can restrain measurement error; Finally, the new solution equation of BWIM can be derived. In this paper, Bayesian algorithm is validated by numerical vehicle-bridge interaction model and in-situ test. The accuracy of Bayesian algorithm is compared to the results by the traditional BWIM algorithm. Results show that Bayesian algorithm can effectively suppress the effect of measurement error and improve the axle weight identification accuracy significantly.

Key words

bridge weigh-in-motion / Bayesian posterior estimation / least squares / measurement error / field test

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ZHANG Longwei1,2, YUAN Luqi1, CHEN Ning1, YUAN Shuaihua1, ZHANG Long1. Bridge weighing-in-motion algorithm theory based on Bayesian posterior estimation and tests[J]. Journal of Vibration and Shock, 2024, 43(1): 20-27

References

[1] 李小年, 陈艾荣, 马如进. 桥梁动态称重研究综述 [J]. 土木工程学报, 2013, 46(03): 79-85. Li Xiaonian, Chen Airong, Ma Rujin. Review on dynamic weighing of Bridges [J]. China Civil Engineering Journal,2013,46(03):79-85. [2] 任伟新, 左小晗, 王宁波, 等. 非路面式桥梁动态称重研究综述 [J]. 中国公路学报, 2014, 27(07): 45-53. Ren Weixin, Zuo Xiaohua, Wang Ningbo.Review of Non-pavement Bridge Weigh-in-motion [J]. China Journal of Highway and Transport, 2014, 27(07): 45-53. [3] 邓露, 李树征, 淡丹辉, 等. 桥梁动态称重技术在中小跨径混凝土梁桥上的适用性研究 [J]. 湖南大学学报(自然科学版), 2020, 47(03): 89-96. DENG Lu, LI Shuzheng, DAN Danhui, et al.Study on Applicability of Bridge Weigh-in-Motion Technology in Short- to Medium-span Concrete Girder Bridges [J]. Journal of Hunan Uni-versity (Natural Science), 2020, 47(03): 89-96. [4] MOSES F. Weigh-in-motion system using instrumented bridges [J]. Transportation Engineering Journal of ASCE, 1979, 105(3): 233-249. [5] OBRIEN E J Q M J, KAROUMI R. Calculating an influence line from direct measurements [J]. Proceedings of the Institution of Civil Engineers-Bridge Engineering, 2006: 31-34. [6] 王宁波, 任伟新, 何立翔. 基于桥梁动力响应的应变影响线提取 [J]. 中南大学学报(自然科学版), 2014, 45(12): 4362-4369. WANG Ningbo, REN Weixin, HE Lixiang. Extraction of strain influence line of bridge from dynamic responses [J]. Journal of Central South University of Technology (Natural Science), 2014, 45(12): 4362-4369. [7] ZHENG X, YANG D-H, YI T-H, et al. Bridge Influence Line Identification Based on Regularized Least-Squares QR Decomposition Method [J]. Journal of Bridge Engineering, 2019, 24(8): 06019004. [8] 张龙威, 汪建群, 陈宁, 等. 桥梁动态称重迭代算法的理论与试验研究 [J]. 振动与冲击, 2021, 40(06): 171-176. Zhang Longwei, Wang Jianqun, Chen Ning, et al. Theoretical and Experimental Research on Iterative Algorithm for Dynamic Weighing of Bridges [J]. Journal of Vibration and Shock, 201,40(06):171-176. [9] HEITNER B, SCHOEFS F, OBRIEN E J, et al. Using the unit influence line of a bridge to track changes in its condition [J]. Journal of Civil Structural Health Monitoring, 2020, 10(4): 667-78. [10] 宫亚峰, 宋加祥, 谭国金, 等. 多车桥梁动态称重算法 [J]. 吉林大学学报(工学版), 2021, 51(02): 583-596. GONG Ya-feng, SONG Jia-xiang, TAN Guo-jin, et al. Multi⁃vehicle bridge weigh⁃in⁃motion algorithm. [J]. Journal of Jilin University(Engineering and Technology Edition), 2021, 51(02): 583-596. [11] 谭承君, 赵华, 张斌, 等. 适用于随机车流的二维桥梁动态称重应用 [J]. 湖南大学学报(自然科学版), 2022, 49(05): 111-119. TAN Chengjun, ZHAO Hua, ZHANG Bin, et al.A 2-Dimension Bridge Weigh-in-Motion System under Random Traffic [J]. Journal of Hunan Uni-versity (Natural Science), 2022, 49(05): 111-119. [12] ZHAO H, TAN C, OBRIEN E J, et al. Developing Digital Twins to Characterize Bridge Behavior Using Measurements Taken under Random Traffic [J]. Journal of Bridge Engineering, 2022, 27(1): 04021101. [13] 邓露, 罗鑫, 凌天洋, 等. 基于卷积神经网络的多车桥梁动态称重算法 [J]. 湖南大学学报:自然科学版, 2022, 49(01): 33-41. DENG Lu, LUO Xin, LING Tianyang, et al.Bridge Weigh-in-motion Algorithm Considering Multi-vehicle Based on Convolutional Neural Network [J]. Journal of Hunan Uni-versity (Natural Science), 2022, 49(01): 33-41. [14] 邓露, 施海, 何维, 等. 基于虚拟简支梁法的桥梁动态称重研究 [J]. 振动与冲击, 2018, 37(15): 209-215. Deng Lu, Shi Hai, He Wei, et al.. Dynamic weighing of Bridges based on virtual simply supported beam method [J]. Journal of Vibration and Shock,2018,37(15):209-215. [15] ROWLEY C, GONZALEZ A, O’BRIEN E, et al. Comparison of conventional and regularized bridge weigh-in-motion algorithms [J]. Proceedings of the international conference on heavy vehicles, 2008: 19-22. [16] OBRIEN E J, ZHANG L, ZHAO H, et al. Probabilistic bridge weigh-in-motion [J]. Canadian Journal of Civil Engineering, 2018, 45(8): 667-675. [17] 陈适之, 冯德成, 杨干, 等. 基于宏应变曲率的桥梁式动态称重方法研究 [J]. 工程力学, 2021, 38(10): 229-237. CHEN Shi-zhi，FENG De-cheng, YANG Gan, et al. Study on bridge weigh-in-motion method using macro strain curvature [J]. Engineering Mechanics,2021, 38(10): 229-237. [18] CHEN S-Z, WU G, FENG D-C. Development of a bridge weigh-in-motion method considering the presence of multiple vehicles [J]. Engineering Structures, 2019, 191: 724-739. [19] QUILLIGAN M, KAROUMI R, OBRIEN E. Development and Testing of a 2-Dimensional Multi-Vehicle Bridge-WIM Algorithm [M]. 2002. [20] 茆诗松编著. 贝叶斯统计 [M]. 北京：中国统计出版社, 1999. Mao Shisong. Bayesstatistics [M].Bei jing:China Statistics Press, 1999. [21] PARK Y, REICHEL L, RODRIGUEZ G, et al. Parameter determination for Tikhonov regularization problems in general form [J]. Journal of Computational and Applied Mathematics, 2018, 343: 12-25. [22] 龙波. 移动车辆轴重识别MOSES算法在宽桥中的应用研究 [D]; 湖南大学, 2014. Long Bo. The application of Moses algorithm on the identification of axle weigts of moving vehicles on wide bridge [D]; Hunan University, 2014. [23] 赵华, 谭承君, 张龙威, 等. 基于小波变换的桥梁动态称重系统车轴高精度识别研究 [J]. 湖南大学学报：自然科学版, 2016, 43(07): 111-119. Zhao Hua, Tan Chengjun, Zhang Longwei, et al. Research on axle high-precision identification of bridge dynamic weighing system based on wavelet transform [J]. Journal of Hunan Uni-versity (Natural Science),2016,43(07):111-119.