失效非线性相关的桥梁截面可靠性Vine-Copula数据融合
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摘要
为合理融合健康监测数据分析在役桥梁截面可靠性,首先应用桥梁截面多个监测点的极值应力数据,建立监测变量非线性相关的Vine-Copula模型,实现极值应力数据的融合分析;然后结合多个监测点的功能函数,进行桥梁截面失效模式非线性相关的Vine-Copula建模分析,并融合一次二阶矩(FOSM)方法,分析失效非线性相关的桥梁截面可靠性;最后进行了在役桥梁截面监测数据的验证分析.研究表明,考虑失效模式非线性相关性所得桥梁截面可靠性较不考虑失效模式相关性所得结果小,说明不考虑失效模式相关性所得结果偏保守.
Bridge section reliability analysis method is reasonably carried on with the fusion of structural health monitoring data. Firstly, the vine-copula models considering the nonlinear correlation of multiple monitored variables were established based on the extreme stress data at the multiple monitored points of bridge section, which make the extreme stress data fusion achieved. Secondly, the vine copula models considering the nonlinear correlation of failure modes about bridge section were built with the performance functions about the multiple monitored points, further, through combining the built vine copula models with first order second moment(FOSM) method, the bridge section reliability considering the nonlinear correlation of failure modes was analyzed. Finally, the monitored data of an existing bridge was provided to illustrate the proposed model and method. The results show that the obtained bridge section reliability with considering the nonlinear correlation of failure modes is bigger than that without considering the correlation of failure modes. It is illustrated that the obtained results without considering the correlation of failure modes are conservative.
Bridge section reliability analysis method is reasonably carried on with the fusion of structural health monitoring data. Firstly, the vine-copula models considering the nonlinear correlation of multiple monitored variables were established based on the extreme stress data at the multiple monitored points of bridge section, which make the extreme stress data fusion achieved. Secondly, the vine copula models considering the nonlinear correlation of failure modes about bridge section were built with the performance functions about the multiple monitored points, further, through combining the built vine copula models with first order second moment(FOSM) method, the bridge section reliability considering the nonlinear correlation of failure modes was analyzed. Finally, the monitored data of an existing bridge was provided to illustrate the proposed model and method. The results show that the obtained bridge section reliability with considering the nonlinear correlation of failure modes is bigger than that without considering the correlation of failure modes. It is illustrated that the obtained results without considering the correlation of failure modes are conservative.
引文
[1] NI Y Q, HUA X G, KO J M. Reliability-based assessment of bridges using long-term monitoring data [J]. Key Engineering Materials, 2006:10.4028/www.scientific.net/KEM. 321-323. 217.
[2] FRANGOPOL D M, STRAUSS A, KIM S Y. Bridge reliability assessment based on monitoring [J]. Journal of Bridge Engineering, ASCE, 2008, 13(3): 258.
[3] CATBAS F N, SUSOY M, FRANGOPOL D M. Structural health monitoring and reliability estimation: Long span truss bridge application with environmental monitoring data [J]. Engineering Structures, 2008, 30: 2347.
[4] FRANGOPOL D M, STRAUSS A, KIM S Y. Use of monitoring extreme data for the performance prediction of structures: General approach [J]. Engineering Structures, 2008, 30: 3644.
[5] STRAUSS A, FRANGOPOL D M, Kim S Y. Use of monitoring extreme data for the performance prediction of structures: Bayesian updating [J]. Engineering Structures, 2008, 30: 3654.
[6] DISSANAYAKE P B R, KARUNANANDA P A K. Reliability index for structural health monitoring of aging bridges [J]. Structural Health Monitoring-An International Journal, 2008, 7(2): 175.
[7] POURALI M, MOSLEH A. A Bayesian approach to sensor placement optimization and system reliability monitoring [J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2013, 227(3): 327.
[8] 李顺龙. 基于健康监测技术的桥梁结构状态评估和预警方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2009. LI Shunlong. Approaches of condition assessment and damage alarming of bridges based on structural health monitoring [D]. Harbin: Harbin Institute of Technology, 2009.
[9] 焦美菊, 孙利民, 李清富. 基于监测数据的桥梁结构可靠度评估[J]. 同济大学学报(自然科学版), 2011, 39(10): 1452. JIAO Meiju, SUN Limin, LI Qingfu. Bridge structural reliability assessment based on health monitoring data [J]. Journal of Tongji University (Natural Science), 2011, 39(10): 1452.
[10] 赵卓. 基于ARMA模型的伊通河桥监测数据建模与可靠度分析[D]. 哈尔滨: 哈尔滨工业大学, 2012. ZHAO Zhuo. Health monitoring data modeling and reliability analysis for Yitong river bridge based on ARMA model [D]. Harbin: Harbin Institute of Technology, 2012.
[11] 陈志为. 基于健康监测系统的大跨多荷载桥梁的疲劳可靠度评估[J]. 工程力学, 2014, 31(7): 99. CHEN Zhiwei. Fatigue reliability assessment of multi-loading suspension bridges based on SHMs [J]. Engineering Mechanics, 2014, 31(7): 99.
[12] 樊学平. 基于验证荷载和监测数据的桥梁可靠性修正与贝叶斯预测[D]. 哈尔滨: 哈尔滨工业大学, 2014. FAN Xueping. Bridge reliability updating and Bayesian prediction based on proof loads and monitored data [D]. Harbin: Harbin Institute of Technology, 2014.
[13] FAN X P, LIU Y F. Time-variant reliability prediction of bridge system based on BDGCM and SHM data[J]. Structural Control and Health Monitoring, 2018, 25(1):10.1002/stc.2185.
[14] LIU Y F, FAN X P. Gaussian Copula-Bayesian dynamic linear model–based time-dependent reliability prediction of bridge structures considering nonlinear correlation between failure modes [J]. Advances in Mechanical Engineering, 2016, 8(11): 1.
[15] 刘月飞. 考虑失效模式和验证模式相关性的桥梁结构体系可靠度分析[D]. 哈尔滨: 哈尔滨工业大学, 2015. LIU Yuefei. System reliability analysis of bridge structures considering correlation of failure modes and proof modes [D]. Harbin: Harbin Institute of Technology, 2015.
[16] BEDFORD T, COOKE R M. Probability density decomposition for conditionally dependent random variables modeled by vines [J]. Annals of Mathematics & Artificial Intelligence, 2001, 32(1-4): 245.
[17] BEDFORD T, COOKE R M. Vines: A new graphical model for dependent random variables [J]. Annals of Statistics, 2002, 30(4): 1031.
[18] NELSEN R B. An Introduction to copulas[M]. New York: Springer, 2006.
[2] FRANGOPOL D M, STRAUSS A, KIM S Y. Bridge reliability assessment based on monitoring [J]. Journal of Bridge Engineering, ASCE, 2008, 13(3): 258.
[3] CATBAS F N, SUSOY M, FRANGOPOL D M. Structural health monitoring and reliability estimation: Long span truss bridge application with environmental monitoring data [J]. Engineering Structures, 2008, 30: 2347.
[4] FRANGOPOL D M, STRAUSS A, KIM S Y. Use of monitoring extreme data for the performance prediction of structures: General approach [J]. Engineering Structures, 2008, 30: 3644.
[5] STRAUSS A, FRANGOPOL D M, Kim S Y. Use of monitoring extreme data for the performance prediction of structures: Bayesian updating [J]. Engineering Structures, 2008, 30: 3654.
[6] DISSANAYAKE P B R, KARUNANANDA P A K. Reliability index for structural health monitoring of aging bridges [J]. Structural Health Monitoring-An International Journal, 2008, 7(2): 175.
[7] POURALI M, MOSLEH A. A Bayesian approach to sensor placement optimization and system reliability monitoring [J]. Proceedings of the Institution of Mechanical Engineers, Part O: Journal of Risk and Reliability, 2013, 227(3): 327.
[8] 李顺龙. 基于健康监测技术的桥梁结构状态评估和预警方法研究[D]. 哈尔滨: 哈尔滨工业大学, 2009. LI Shunlong. Approaches of condition assessment and damage alarming of bridges based on structural health monitoring [D]. Harbin: Harbin Institute of Technology, 2009.
[9] 焦美菊, 孙利民, 李清富. 基于监测数据的桥梁结构可靠度评估[J]. 同济大学学报(自然科学版), 2011, 39(10): 1452. JIAO Meiju, SUN Limin, LI Qingfu. Bridge structural reliability assessment based on health monitoring data [J]. Journal of Tongji University (Natural Science), 2011, 39(10): 1452.
[10] 赵卓. 基于ARMA模型的伊通河桥监测数据建模与可靠度分析[D]. 哈尔滨: 哈尔滨工业大学, 2012. ZHAO Zhuo. Health monitoring data modeling and reliability analysis for Yitong river bridge based on ARMA model [D]. Harbin: Harbin Institute of Technology, 2012.
[11] 陈志为. 基于健康监测系统的大跨多荷载桥梁的疲劳可靠度评估[J]. 工程力学, 2014, 31(7): 99. CHEN Zhiwei. Fatigue reliability assessment of multi-loading suspension bridges based on SHMs [J]. Engineering Mechanics, 2014, 31(7): 99.
[12] 樊学平. 基于验证荷载和监测数据的桥梁可靠性修正与贝叶斯预测[D]. 哈尔滨: 哈尔滨工业大学, 2014. FAN Xueping. Bridge reliability updating and Bayesian prediction based on proof loads and monitored data [D]. Harbin: Harbin Institute of Technology, 2014.
[13] FAN X P, LIU Y F. Time-variant reliability prediction of bridge system based on BDGCM and SHM data[J]. Structural Control and Health Monitoring, 2018, 25(1):10.1002/stc.2185.
[14] LIU Y F, FAN X P. Gaussian Copula-Bayesian dynamic linear model–based time-dependent reliability prediction of bridge structures considering nonlinear correlation between failure modes [J]. Advances in Mechanical Engineering, 2016, 8(11): 1.
[15] 刘月飞. 考虑失效模式和验证模式相关性的桥梁结构体系可靠度分析[D]. 哈尔滨: 哈尔滨工业大学, 2015. LIU Yuefei. System reliability analysis of bridge structures considering correlation of failure modes and proof modes [D]. Harbin: Harbin Institute of Technology, 2015.
[16] BEDFORD T, COOKE R M. Probability density decomposition for conditionally dependent random variables modeled by vines [J]. Annals of Mathematics & Artificial Intelligence, 2001, 32(1-4): 245.
[17] BEDFORD T, COOKE R M. Vines: A new graphical model for dependent random variables [J]. Annals of Statistics, 2002, 30(4): 1031.
[18] NELSEN R B. An Introduction to copulas[M]. New York: Springer, 2006.