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Seismic fragility analysis of bridges by relevance vector machine based demand prediction model

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Abstract

A relevance vector machine (RVM) based demand prediction model is explored for efficient seismic fragility analysis (SFA) of a bridge structure. The proposed RVM model integrates both record-to-record variations of ground motions and uncertainties of parameters characterizing the bridge model. For efficient fragility computation, ground motion intensity is included as an added dimension to the demand prediction model. To incorporate different sources of uncertainty, random realizations of different structural parameters are generated using Latin hypercube sampling technique. Mean fragility, along with its dispersions, is estimated based on the log-normal fragility model for different critical components of a bridge. The effectiveness of the proposed RVM model-based SFA of a bridge structure is elucidated numerically by comparing it with fragility results obtained by the commonly used SFA approaches, while considering the most accurate direct Monte Carlo simulation-based fragility estimates as the benchmark. The proposed RVM model provides a more accurate estimate of fragility than conventional approaches, with significantly less computational effort. In addition, the proposed model provides a measure of uncertainty in fragility estimates by constructing confidence intervals for the fragility curves.

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References

  • Bakhshinezhad S and Mohebbi M (2021), “Multiple Failure Function Based Fragility Curves for Structures Equipped with TMD,” Earthquake Engineering and Engineering Vibration, 20(2): 471–482.

    Article  Google Scholar 

  • Bayat M, Kia M, Soltangharaei V, Ahmadi HR and Ziehl P (2020), “Bayesian Demand Model Based Seismic Vulnerability Assessment of a Concrete Girder Bridge,” Advances in Concrete Construction, 9(4): 337–343.

    Google Scholar 

  • Boore DM (2003), “Simulation of Ground Motion Using the Stochastic Method,” Pure and Applied Geophysics, 160(3–4): 635–676.

  • Box GEP and Tiao GC (1992), Bayesian Inference in Statistical Analysis, 1st Ed., John Wiley and Sons, New Jersey, United States.

    Book  Google Scholar 

  • Caltrans (2004), “Caltrans Seismic Design Criteria,” California Department of Transportation, Sacramento, CA.

  • Cheng H, Li HN, Yang YB and Wang DS (2019), “Seismic Fragility Analysis of Deteriorating RC Bridge Columns with Time-Variant Capacity Index,” Bulletin of Earthquake Engineering, 17(7): 4247–4267.

    Article  Google Scholar 

  • Cheng J and Li Q (2012), “Artificial Neural Network-Based Response Surface Methods for Reliability Analysis of Pre-Stressed Concrete Bridges,” Structure and Infrastructure Engineering, 8(2): 171–184.

    Article  Google Scholar 

  • Dueñas-Osorio L and Padgett JE (2011), “Seismic Reliability Assessment of Bridges with User-Defined System Failure Events,” Journal of Engineering Mechanics, 137(10): 680–690.

    Article  Google Scholar 

  • Gardoni P, Mosalam KM and Kiureghian AD (2003), “Probabilistic Seismic Demand Models and Fragility Estimates for RC Bridges,” Journal of Earthquake Engineering, 7(sup001): 79–106.

    Article  Google Scholar 

  • Gaxiola-Camacho JR, Haldar A, Reyes-Salazar A, Valenzuela-Beltran F, Vazquez-Becerra GE and Vazquez-Hernandez AO (2018), “Alternative Reliability-Based Methodology for Evaluation of Structures Excited by Earthquakes,” Earthquakes and Structures, 14(4): 361–377.

    Google Scholar 

  • Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A and Rubin DB (2013), Bayesian Data Analysis, Chapman and Hall/CRC.

  • Ghosh S and Chakraborty S (2017), “Seismic Performance of Reinforced Concrete Building in Guwahati City, Northeast India,” Scientia Iranica A, 24(4): 1821–1833.

    Article  Google Scholar 

  • Ghosh S and Chakraborty S (2020), “Seismic Fragility Analysis of Structures Based on Bayesian Linear Regression Demand Models,” Probabilistic Engineering Mechanics, 61: 103081.

    Article  Google Scholar 

  • Ghosh S, Ghosh S and Chakraborty S (2018), “Seismic Reliability Analysis of Reinforced Concrete Bridge Pier Using Efficient Response Surface Method-Based Simulation,” Advances in Structural Engineering, 21(15): 2326–2339.

    Article  Google Scholar 

  • Ghotbi AR (2014), “Performance-Based Seismic Assessment of Skewed Bridges with and Without Considering Soil-Foundation Interaction Effects for Various Site Classes,” Earthquake Engineering and Engineering Vibration, 13(3): 357–373.

    Article  Google Scholar 

  • Gokkaya BU, Baker JW and Deierlein G (2015), “Illustrating a Bayesian Approach to Seismic Collapse Risk Assessment,” 12th International Conference on Applications of Statistics and Probability in Civil Engineering, ICASP12.

  • IRC6 (2014), Standard Specifications and Code of Practice for Road Bridges, Section II — Loads and Stresses, Indian Road Congress, New Delhi, India.

  • IRC21 (2000), Standard Specification and Code of Practice for Road Bridges, Section III — Cement Concrete (Plain and Reinforced), Indian Road Congress, New Delhi, India.

  • IS1893 (2016), Indian Standard Criteria for Earthquake Resistant Design of Structures, Part 1 — General Provisions and Buildings, Bureau of Indian Standards, New Delhi, India.

  • Jalayer F, De Risi R and Manfredi G (2015), “Bayesian Cloud Analysis: Efficient Structural Fragility Assessment Using Linear Regression,” Bulletin of Earthquake Engineering, 13(4): 1183–1203.

    Article  Google Scholar 

  • Jeon J-S, Mangalathu S, Song J and Desroches R (2019), “Parameterized Seismic Fragility Curves for Curved Multi-Frame Concrete Box-Girder Bridges Using Bayesian Parameter Estimation,” Journal of Earthquake Engineering, 23(6): 954–979.

    Article  Google Scholar 

  • Kefayati S, Baghbanan A, Torkan M, Hashemolhosseini H and Dehnavi RN (2020), “Static and Dynamic Analysis on Slope Stability using a DFN-DEM Approach on the Right Abutment of the Karun 4 Dam,” Earthquake Engineering and Engineering Vibration, 19(4): 937–951.

    Article  Google Scholar 

  • Kim SH and Feng MQ (2003), “Fragility Analysis of Bridges Under Ground Motion with Spatial Variation,” International Journal of Non-Linear Mechanics, 38(5): 705–721.

    Article  Google Scholar 

  • Kim SH and Shinozuka M (2004), “Development of Fragility Curves of Bridges Retrofitted by Column Jacketing,” Probabilistic Engineering Mechanics, 19(1–2): 105–112.

    Article  Google Scholar 

  • Koutsourelakis PS (2010), “Assessing Structural Vulnerability Against Earthquakes Using Multi-Dimensional Fragility Surfaces: A Bayesian Framework,” Probabilistic Engineering Mechanics, 25(1): 49–60.

    Article  Google Scholar 

  • Kwon O-S and Elnashai A (2006), “The Effect of Material and Ground Motion Uncertainty on the Seismic Vulnerability Curves of RC Structure,” Engineering Structures, 28(2): 289–303.

    Article  Google Scholar 

  • Li J, Spencer Jr BF and Elnashai AS (2013), “Bayesian Updating of Fragility Functions Using Hybrid Simulation,” Journal of Structural Engineering, 139(7): 1160–1171.

    Article  Google Scholar 

  • Li Z, Li Y and Li N (2014), “Vector-Intensity Measure Based Seismic Vulnerability Analysis of Bridge Structures,” Earthquake Engineering and Engineering Vibration, 13(4): 695–705.

    Article  Google Scholar 

  • Lu D, Yu X, Jia M and Wang G (2014), “Seismic Risk Assessment for a Reinforced Concrete Frame Designed According to Chinese Codes,” Structure and Infrastructure Engineering, 10(10): 1295–1310.

    Article  Google Scholar 

  • Mackie KR and Stojadinović B (2007), “Performance-Based Seismic Bridge Design for Damage and Loss Limit States,” Earthquake Engineering and Structural Dynamics, 36(13): 1953–1971.

    Article  Google Scholar 

  • Mahmoudi SN and Chouinard L (2016), “Seismic Fragility Assessment of Highway Bridges Using Support Vector Machines,” Bulletin of Earthquake Engineering, 14(6): 1571–1587.

    Article  Google Scholar 

  • Maikol Del Carpio R, Hashemi MJ and Mosqueda G (2017), “Evaluation of Integration Methods for Hybrid Simulation of Complex Structural Systems Through Collapse,” Earthquake Engineering and Engineering Vibration, 16(4): 745–759.

    Article  Google Scholar 

  • Mangalathu S, Heo G and Jeon JS (2018), “Artificial Neural Network Based Multi-Dimensional Fragility Development of Skewed Concrete Bridge Classes,” Engineering Structures, 162: 166–176.

    Article  Google Scholar 

  • Marano GC, Greco R and Mezzina M (2008), “Stochastic Approach for Analytical Fragility Curves,” KSCE Journal of Civil Engineering, 12(5): 305–312.

    Article  Google Scholar 

  • Marano GC, Greco R and Morrone E (2011), “Analytical Evaluation of Essential Facilities Fragility Curves by Using a Stochastic Approach,” Engineering Structures, 33(1): 191–201.

    Article  Google Scholar 

  • Moehle JP and Eberhard MO (2000), “Earthquake Damage to Bridges,” in Chen W-F and Duan L, Editors, Bridge Engineering Handbook, Boca Raton, CRC Press.

    Google Scholar 

  • Nielson BG (2005), “Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones,” PhD Thesis, Georgia Institute of Technology, Atlanta, Georgia.

    Google Scholar 

  • Nielson BG and DesRoches R (2007), “Seismic Fragility Methodology for Highway Bridges Using a Component Level Approach,” Earthquake Engineering and Structural Dynamics, 36(6): 823–839.

    Article  Google Scholar 

  • Padgett JE, Nielson BG and DesRoches R (2008), “Selection of Optimal Intensity Measures in Probabilistic Seismic Demand Models of Highway Bridge Portfolios,” Earthquake Engineering and Structural Dynamics, 37(5): 711–725.

    Article  Google Scholar 

  • Pujari NN, Ghosh S and Lala S (2015), “Bayesian Approach for the Seismic Fragility Estimation of a Containment Shell Based on the Formation of Through-Wall Cracks,” ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering, 2(3): B4015004.

    Article  Google Scholar 

  • Raffaele D, Porco F, Fiore A and Uva G (2014), “Simplified Vulnerability Assessment of Reinforced Concrete Circular Piers in Multi-Span Simply Supported Bridges,” Structure and Infrastructure Engineering, 10(8): 950–962.

    Article  Google Scholar 

  • Ramamoorthy SK, Gardoni P and Bracci JM (2006), “Probabilistic Demand Models and Fragility Curves for Reinforced Concrete Frames,” Journal of Structural Engineering, 132(10): 1563–1572.

    Article  Google Scholar 

  • Ramanathan K, Padgett JE and DesRoches R (2015), “Temporal Evolution of Seismic Fragility Curves for Concrete Box-Girder Bridges in California,” Engineering Structures, 97: 29–46.

    Article  Google Scholar 

  • Schmolck A and Everson R (2007), “Smooth Relevance Vector Machine: a Smoothness Prior Extension of the RVM,” Machine Learning, 68(2): 107–135.

    Article  Google Scholar 

  • Seo J and Linzell DG (2013), “Use of Response Surface Metamodels to Generate System Llevel Fragilities for Existing Curved Steel Bridges,” Engineering Structures, 52: 642–653.

    Article  Google Scholar 

  • Shamsabadi A, Rollins KM and Kapuskar M (2007), “Nonlinear Soil—Abutment—Bridge Structure Interaction for Seismic Performance-Based Design,” Journal of Geotechnical and Geoenvironmental Engineering, 133(6): 707–720.

    Article  Google Scholar 

  • Shinozuka M, Feng MQ, Lee J and Naganuma T (2000), “Statistical Analysis of Fragility Curves,” Journal of Engineering Mechanics, 126(12): 1224–1231.

    Article  Google Scholar 

  • Shinozuka M, Kim SH, Kushiyama S and Yi JH (2002), “Fragility Curves of Concrete Bridges Retrofitted by Column Jacketing,” Earthquake Engineering and Engineering Vibration, 1(2): 195–205.

    Article  Google Scholar 

  • Singhal A and Kiremidjian AS (2002), “Bayesian Updating of Fragilities with Application to RC Frames,” Journal of Structural Engineering, 124(8): 922–929.

    Article  Google Scholar 

  • Song S, Qian Y, Liu J, Xie X and Wu G (2019), “Time-Variant Fragility Analysis of the Bridge System Considering Time-Varying Dependence Among Typical Component Seismic Demands,” Earthquake Engineering and Engineering Vibration, 18(2): 363–377.

    Article  Google Scholar 

  • Straub D and Der Kiureghian A (2008), “Improved Seismic Fragility Modeling from Empirical Data,” Structural Safety, 30(4): 320–336.

    Article  Google Scholar 

  • Tipping ME (2001), “Sparse Bayesian Learning and the Relevance Vector Machine,” Journal of Machine Learning Research, 1: 211–244.

    Google Scholar 

  • Tolentino D, Márquez-Domínguez S and Gaxiola-Camacho JR (2020), “Fragility Assessment of Bridges Considering Cumulative Damage Caused by Seismic Loading,” KSCE Journal of Civil Engineering, 24(2): 551–560.

    Article  Google Scholar 

  • Tsompanakis Y, Lagaros ND and Stavroulakis GE (2008), “Soft Computing Techniques in Parameter Identification and Probabilistic Seismic Analysis of Structures,” Advances in Engineering Software, 39(7): 612–624.

    Article  Google Scholar 

  • Wang Qa, Wu Z and Liu S (2012), “Seismic Fragility Analysis of Highway Bridges Considering Multi-Dimensional Performance Limit State,” Earthquake Engineering and Engineering Vibration, 11(2): 185–193.

    Article  Google Scholar 

  • Xia Z, Li A, Shi H and Li J (2021), “Model Updating of a Bridge Structure Using Vibration Test Data Based on GMPSO and BPNN: Case Study,” Earthquake Engineering and Engineering Vibration, 20(1): 213–221.

    Article  Google Scholar 

  • Xu H and Gardoni P (2016), “Probabilistic Capacity and Seismic Demand Models and Fragility Estimates for Reinforced Concrete Buildings Based on Three-Dimensional Analyses,” Engineering Structures, 112: 200–214.

    Article  Google Scholar 

  • Zhang J and Huo Y (2009), “Evaluating Effectiveness and Optimum Design of Isolation Devices for Highway Bridges Using the Fragility Function Method,” Engineering Structures, 31(8): 1648–1660.

    Article  Google Scholar 

  • Zhang J, Huo Y, Brandenberg SJ and Kashighandi P (2008), “Effects of Structural Characterizations on Fragility Functions of Bridges Subject to Seismic Shaking and Lateral Spreading,” Earthquake Engineering and Engineering Vibration, 7(4): 369–382.

    Article  Google Scholar 

  • Zhong J, Gardoni P and Rosowsky D (2009), “Bayesian Updating of Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents,” Journal of Earthquake Engineering, 13(5): 716–735.

    Article  Google Scholar 

  • Zhong J, Gardoni P, Rosowsky D and Haukaas T (2008), “Probabilistic Seismic Demand Models and Fragility Estimates for Reinforced Concrete Bridges with Two-Column Bents,” Journal of Engineering Mechanics, 134(6): 495–504.

    Article  Google Scholar 

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Correspondence to Swarup Ghosh.

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Ghosh, S., Chakraborty, S. Seismic fragility analysis of bridges by relevance vector machine based demand prediction model. Earthq. Eng. Eng. Vib. 21, 253–268 (2022). https://doi.org/10.1007/s11803-022-2082-7

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