Threshold Selection for the Extreme Value Estimation of Bridge Strain Under Vehicle Load

YANG Xia; ZHANG Jing; REN Wei-xin; YUAN Ping-ping.

doi:10.21656/1000-0887.370395

Volume 38 Issue 5

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(5): 503-512

YANG Xia, ZHANG Jing, REN Wei-xin, YUAN Ping-ping.. Threshold Selection for the Extreme Value Estimation of Bridge Strain Under Vehicle Load[J]. Applied Mathematics and Mechanics, 2017, 38(5): 503-512. doi: 10.21656/1000-0887.370395

Citation:

PDF( 2161 KB)

Threshold Selection for the Extreme Value Estimation of Bridge Strain Under Vehicle Load

doi: 10.21656/1000-0887.370395

¹School of Civil Engineering, Hefei University of Technology, Hefei 230009, P.R.China;²School of Civil Engineering, Central South University, Changsha 410075, P.R.China

Funds: China Postdoctoral Science Foundation（2015M581982）

Received Date: 2016-12-26
Rev Recd Date: 2017-03-24
Publish Date: 2017-05-15

Abstract

Abstract

The selection of a reasonable threshold is critical to estimate the extreme strain under vehicle load on bridges with the peak-over-threshold method. Little information can be used if the threshold is too high, while the bias of parameters of the general Pareto distribution will be large if the threshold is too low. Common threshold selection methods are not suitable to be applied in estimation of the extreme strain under vehicle load. Based on 1-year strain data of the Taiping Lake Bridge, 3 types of mixed distributions for the strain peaks induced by vehicle load were chosen to generate a large number of samples with the Monte-Carlo method. The estimated extreme values of the samples based on the generalized Pareto distributions with different thresholds were compared and analyzed. Then, an empirical threshold selection method was proposed for the strain data induced by vehicle load. Finally, the Taiping Lake Bridge was chosen as the case verification. It is demonstrated that the estimated weekly extreme strain based on the threshold selected with the proposed method is more close to the measured results than those with the common methods.
- bridge health monitoring,
- threshold selection method,
- extreme strain,
- generalized Pareto distribution

FullText(HTML)

References(16)

References

[1]	公路桥涵设计通用规范: JTG/D 60—2015[S].（General code for design of highway bridges and culverts: JTG/D 60—2015[S].（in Chinese））
[2]	孙守旺, 孙利民. 基于实测的公路桥梁车辆荷载统计模型[J]. 同济大学学报(自然科学版), 2012,40(2): 198-204.(SUN Shou-wang, SUN Li-min. Statistic of vehicle loads for highway bridges[J]. Journal of Tongji University (Natural Science),2012,40(2): 198-204.（in Chinese））
[3]	Mei G, Qin Q, Lin D J. Bimodal renewal processed models of highway vehicle loads[J].Reliability Engineering & System Safety,2004,83(3): 333-339.
[4]	王涛. 高速公路桥梁交通荷载调查分析及仿真模拟[D]. 博士学位论文. 西安：长安大学, 2010.（WANG Tao. Investigation statistics and simulation of random traffic loading of expressway bridge[D]. PhD Thesis. Xi’an: Chang’an University, 2010.（in Chinese））
[5]	史道济. 实用极值统计方法[M]. 天津：天津科学技术出版社, 2006： 28-32.（SHI Dao-ji. Practical Extremum Statistical Method [M]. Tianjin: Tianjin Science and Technology Press, 2006： 28-32.（in Chinese））
[6]	李植淮, 李春前, 孙健康, 等. 基于GPD模型的车辆荷载效应极值估计[J]. 工程力学, 2012,〖STHZ〗 29(S1): 166-171.（LI Zhi-huai, LI Chun-qian, SUN Jian-kang, et al. Estimation of extreme vehicle load effect based on GPD model[J]. Engineering Mechanics,2012,29(S1): 166-171.（in Chinese））
[7]	史道济, 张春英. 尾部指标估计中的阈值选择[J]. 天津理工大学学报, 2006,〖STHZ〗 22(6): 78-82.（SHI Dao-ji, ZHANG Chun-ying. Threshold selection in tail index estimation[J]. Journal of Tianjin University of Technology,2006,22(6): 78-82.（in Chinese））
[8]	Thompson P, Cai Y Z, Reeve D, et al. Automated threshold selection methods for extreme wave analysis[J]. Coastal Engineering,2009,56(10): 1013-1021.
[9]	李强. 基于Copula理论和GPD模型的金融市场风险测试研究[D]. 博士学位论文. 重庆: 重庆大学, 2012.（LI Qiang. The study of financial market risk measurement based on Copula theory and GPD model[D]. PhD Thesis. Chongqing: Chongqing University, 2012.（in Chinese））
[10]	赵旭. 广义Pareto分布的统计推断[D]. 博士学位论文. 北京: 北京理工大学, 2012.（ZHAO Xu. Statistical inference of the generalized Pareto distribution[D]. PhD Thesis. Beijing: Beijing University of Technology, 2012.(in Chinese））
[11]	段忠东, 欧进萍, 周道成. 极值风速的最优概率模型[J]. 土木工程学报, 2002,35(5): 11-16.（DUAN Zhong-dong, OU Jin-ping, ZHOU Dao-cheng. The optimal probabilistic distribution for extreme wind speed[J]. China Civil Engineering Journal,2002,35(5): 11-16.(in Chinese））
[12]	Mcneil A J, Frey R. Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach[J]. Journal of Empirical Finance,2000,7(3/4): 271-300.
[13]	花拥军, 张宗益. 基于峰度法的POT模型对沪深股市极端风险的度量[J]. 系统工程理论与实践, 2010,30(5): 786-796.（HUA Yong-jun, ZHANG Zong-yi. POT model based on kurtosis and its empirical study on extreme risk of Chinese stock markets[J]. Systems Engineering—Theory & Practice,2010,30(5): 786-796.(in Chinese)）
[14]	Caers J, Berilant J, Maes M A. Statistics for modeling heavy tailed distribution in geology—partⅠ: methodology[J]. Mathematical Geology,1999,4(31): 391-410.
[15]	Caers J, Maes M A. Identifying tails, bounds and end-points of random variables[J].Structure Safety,1998,20(1): 1-23.
[16]	段忠东, 周道成. 极值概率分布参数估计方法的比较研究[J]. 哈尔滨工业大学学报, 2004,36(12): 1605-1609.（DUAN Zhong-dong, ZHOU Dao-cheng. A comparative study on parameter estimation method for extremal value distribution[J]. Journal of Harbin Institution of Technology,2004,36(12): 1605-1609.（in Chinese））