摘要目前商用桥梁动态称重系统（weigh-in-motion systems，BWIM）大多基于Moses算法，虽然能高效快速地识别行驶于桥梁的车辆轴重，但轴重识别精度偏低。为解决这一问题，本文提出基于迭代加权最小二乘的桥梁动态称重算法（iteratively reweighted least squares，IRLS）。与Moses算法不同，IRLS算法考虑了荷载响应中存在的多种不确定性因素，为每个荷载响应值提供一个合适的权重系数，区分不同荷载响应对轴重识别的贡献度。首先，将迭代加权最小二乘引入桥梁动态称重，推导出相应的轴重识别计算公式；然后，通过车桥数值仿真模型，分别用IRLS算法和Moses算法识别轴重，对比分析两种算法的精度及影响因素；最后，基于怀化舞水五桥引桥的车桥动力试验，进一步验证IRLS算法用于桥梁动态称重的有效性和准确性。结果表明，IRLS算法能较合理地分配不同荷载响应对轴重识别的贡献度，在一定程度上提高车辆轴重识别的精度。
Abstract：At present, the commercial bridge weigh-in-motion systems (BWIM) are generally based on the Moses algorithm. Although they can efficiently and quickly identify the axle weights of vehicles driving by bridges, the accuracy is low. To solve this problem, this paper presents a novel algorithm that finds axle weights using the bridge response subjected to the drive-by vehicles. Unlike Moses’ algorithm assuming all the bridge response have the same uncertainties, the proposed algorithm based on iteratively reweighted least squares (IRLS) considers the unequal uncertainties and can assign each observed response data its proper amount of influence over the axle weights estimates. Firstly, derive the formula of axle weights identification using IRLS; then, Numerical simulations are conducted to verify the IRLS algorithm using a simply supported beam-vehicle interaction model; finally, based on the field test of Wushui Fifth Bridge approach bridge, compares and analyses the axle weight identification of Moses algorithm and IRLS algorithm. Results show that IRLS algorithm reasonably allocates the contribution of different load responses to axle load identification and it can get more accurate axle weights than Moses’ algorithm.
张龙威，尹诗定，陈宁，汪建群，原璐琪. 基于迭代加权最小二乘的桥梁动态称重理论与试验研究[J]. 振动与冲击, 2023, 42(12): 187-193.
ZHANG Longwei,YIN Shiding,CHEN Ning,WANG Jianqun,YUAN Luqi. A bridge weigh-in-motion system based on iteratively reweighted least squares. JOURNAL OF VIBRATION AND SHOCK, 2023, 42(12): 187-193.
[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] 王宁波.桥梁动态称重技术适用范围与测试精度研究[J].桥梁建设,2015,45(05):36-41.
Wang ningbo. Research on application scope and test accuracy of dynamic weighing technology for bridge [J]. Bridge Construction,2015,45(05):36-41.
[3] Moses F. Weigh-in-motion system using instrumented bridges[J]. Transportation Engineer-ing Journal of ASCE, 1979, 105(3): 233-249.
[4] 王宁波,任伟新,万华平.基于动应变的桥梁动态称重及其优化算法[J].振动与冲击,2013,32(04):116-120.
Wang Ningbo, Ren Weixin, Wan Huaping. Dynamic weighing of Bridges based on dynamic strain and its optimization algorithm [J]. Journal of vibration and shock,2013,32(04):116-120.
[5] Yu Y, Cai C S, Deng L. Nothing-on-road bridge weigh-in-motion considering the transverse position of the vehicle[J]. Structure and Infrastructure Engineering, 2018, 14(8): 1108-1122.
[6] 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.
[7] OBrien E J, Quilligan M J, Karoumi R. Calculating an influence line from direct measurements[J].Bridge Engineering, 2006, 159(1): 31-34.
[8] Zheng X, Yang D H, Yi T H, et al. Development of bridge influence line identification methods based on direct measurement data: A comprehensive review and comparison[J]. Engineering Structures, 2019, 198: 109539.
[9] 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.
[10] Lansdell A, Song W, Dixon B. Development and testing of a bridge weigh-in-motion method considering nonconstant vehicle speed[J]. Engineering Structures, 2017, 152: 709-726.
[11] Žnidarič A, Kalin J, Kreslin M. Improved accuracy and robustness of bridge weigh-in-motion systems[J]. Structure and Infrastructure Engineer-ing, 2018, 14(4): 412-424.
[12] 张豪,陈尚新,余敏,等.基于温度效应的桥梁动态称重识别研究[J].浙江工业大学学报,2017,45(06):682-687+693.
Zhang Hao, Chen Shangxin, Yu Min, et al. Identification of bridge dynamic weighing based on temperature effect [J]. Journal of Zhejiang Un-iversity of Technology,2017,45(06):682-687+693.
[13] 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.
[14] Rowley C, Gonzalez A, OBrien E, et al. Comparison of conventional and regularized bridge weigh-in-motion algorithms[C]. Proceed-ings of the International Conference on Heavy Vehicles. 2008: 19-22.
[15] 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.
[16] Quillugan, M. Bridge Weigh-in-Motion: Development of a 2-D multi-vehicle algorithm[J]. Trita-BKN. Bulletin, 2003.
[17] Cantero D, González A, O'Brien E J. Comparison of bridge dynamic amplification due to articulated 5-axle trucks and large cranes[J]. Baltic Journal of Road and Bridge Engineering, 2011, 6(1): 39-47.
[18] International Organization for Standardization.Mechanical vibration-Road surface profiles-Reporting of measured data. International Organization for Standardization (ISO) Geneva.
[19] González A, Rowley C, OBrien E J. A general solution to the identification of moving vehicle forces on a bridge[J]. International Journal for Numerical Methods in Engineering, 2008, 75(3): 335-354.
[20] 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.
