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.
Similar content being viewed by others
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.
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.
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.
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.
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.
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.
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.
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.
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.
Ghosh S and Chakraborty S (2020), “Seismic Fragility Analysis of Structures Based on Bayesian Linear Regression Demand Models,” Probabilistic Engineering Mechanics, 61: 103081.
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.
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.
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.
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.
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.
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.
Kim SH and Shinozuka M (2004), “Development of Fragility Curves of Bridges Retrofitted by Column Jacketing,” Probabilistic Engineering Mechanics, 19(1–2): 105–112.
Koutsourelakis PS (2010), “Assessing Structural Vulnerability Against Earthquakes Using Multi-Dimensional Fragility Surfaces: A Bayesian Framework,” Probabilistic Engineering Mechanics, 25(1): 49–60.
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.
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.
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.
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.
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.
Mahmoudi SN and Chouinard L (2016), “Seismic Fragility Assessment of Highway Bridges Using Support Vector Machines,” Bulletin of Earthquake Engineering, 14(6): 1571–1587.
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.
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.
Marano GC, Greco R and Mezzina M (2008), “Stochastic Approach for Analytical Fragility Curves,” KSCE Journal of Civil Engineering, 12(5): 305–312.
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.
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.
Nielson BG (2005), “Analytical Fragility Curves for Highway Bridges in Moderate Seismic Zones,” PhD Thesis, Georgia Institute of Technology, Atlanta, Georgia.
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.
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.
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.
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.
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.
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.
Schmolck A and Everson R (2007), “Smooth Relevance Vector Machine: a Smoothness Prior Extension of the RVM,” Machine Learning, 68(2): 107–135.
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.
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.
Shinozuka M, Feng MQ, Lee J and Naganuma T (2000), “Statistical Analysis of Fragility Curves,” Journal of Engineering Mechanics, 126(12): 1224–1231.
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.
Singhal A and Kiremidjian AS (2002), “Bayesian Updating of Fragilities with Application to RC Frames,” Journal of Structural Engineering, 124(8): 922–929.
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.
Straub D and Der Kiureghian A (2008), “Improved Seismic Fragility Modeling from Empirical Data,” Structural Safety, 30(4): 320–336.
Tipping ME (2001), “Sparse Bayesian Learning and the Relevance Vector Machine,” Journal of Machine Learning Research, 1: 211–244.
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.
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.
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.
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.
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.
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.
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.
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.
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.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
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
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-022-2082-7