{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,11]],"date-time":"2026-01-11T01:36:45Z","timestamp":1768095405729,"version":"3.49.0"},"reference-count":38,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2017,4,24]],"date-time":"2017-04-24T00:00:00Z","timestamp":1492992000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003565","name":"Ministry of Land, Infrastructure and Transport","doi-asserted-by":"publisher","award":["16SCIP-B066018-04"],"award-info":[{"award-number":["16SCIP-B066018-04"]}],"id":[{"id":"10.13039\/501100003565","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Railway bridges are exposed to repeated train loads, which may cause fatigue failure. As critical links in a transportation network, railway bridges are expected to survive for a target period of time, but sometimes they fail earlier than expected. To guarantee the target bridge life, bridge maintenance activities such as local inspection and repair should be undertaken properly. However, this is a challenging task because there are various sources of uncertainty associated with aging bridges, train loads, environmental conditions, and maintenance work. Therefore, to perform optimal risk-based maintenance of railway bridges, it is essential to estimate the probabilistic fatigue life of a railway bridge and update the life information based on the results of local inspections and repair. Recently, a system reliability approach was proposed to evaluate the fatigue failure risk of structural systems and update the prior risk information in various inspection scenarios. However, this approach can handle only a constant-amplitude load and has limitations in considering a cyclic load with varying amplitude levels, which is the major loading pattern generated by train traffic. In addition, it is not feasible to update the prior risk information after bridges are repaired. In this research, the system reliability approach is further developed so that it can handle a varying-amplitude load and update the system-level risk of fatigue failure for railway bridges after inspection and repair. The proposed method is applied to a numerical example of an in-service railway bridge, and the effects of inspection and repair on the probabilistic fatigue life are discussed.<\/jats:p>","DOI":"10.3390\/s17040936","type":"journal-article","created":{"date-parts":[[2017,4,24]],"date-time":"2017-04-24T13:10:11Z","timestamp":1493039411000},"page":"936","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":16,"title":["Probabilistic Fatigue Life Updating for Railway Bridges Based on Local Inspection and Repair"],"prefix":"10.3390","volume":"17","author":[{"given":"Young-Joo","family":"Lee","sequence":"first","affiliation":[{"name":"School of Urban and Environmental Engineering, Ulsan National Institute of Science and Technology (UNIST), Ulsan 44919, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Robin","family":"Kim","sequence":"additional","affiliation":[{"name":"Fire Research Institute, Korea Institute of Civil Engineering and Building Technology, Hwaseong 18544, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Wonho","family":"Suh","sequence":"additional","affiliation":[{"name":"Department of Transportation and Logistics Engineering, Hanyang University ERICA Campus, Ansan 15588, Korea"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Kiwon","family":"Park","sequence":"additional","affiliation":[{"name":"Department of Mechanical and Aerospace Engineering, Trine University, Angola, IN 46703, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,4,24]]},"reference":[{"key":"ref_1","first-page":"157","article-title":"Wind and earthquake protection of cable-supported bridges","volume":"169","author":"Domaneschi","year":"2015","journal-title":"Bridge Eng."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"475","DOI":"10.1016\/j.engfailanal.2008.06.009","article-title":"Crack-growth arrest by redirecting crack growth by drilling stop holes and inserting pins into them","volume":"16","author":"Makabe","year":"2009","journal-title":"Eng. Fail. Anal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"785","DOI":"10.1111\/j.1460-2695.2004.00777.x","article-title":"Fatigue behaviour of welded joints with cracks, repaired by hammer peening","volume":"27","author":"Branco","year":"2004","journal-title":"Fatigue Fract. Eng. Mater. Struct."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"159","DOI":"10.1115\/1.4009458","article-title":"Cumulative damage in fatigue","volume":"12","author":"Miner","year":"1945","journal-title":"J. Appl. Mech."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1199","DOI":"10.1016\/j.jcsr.2006.06.007","article-title":"Fatigue reliability of welded steel structures","volume":"62","author":"Chryssanthopoulos","year":"2006","journal-title":"J. Constr. Steel Res."},{"key":"ref_6","unstructured":"Fisher, J.W. (1984). Fatigue and Fracture in Steel Bridges: Case Studies, John Wiley & Sons."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1061\/(ASCE)0733-9445(1999)125:2(152)","article-title":"Fatigue in steel highway bridges under random loading","volume":"125","author":"Agerskov","year":"1999","journal-title":"ASCE J. Struct. Eng."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"320","DOI":"10.1061\/(ASCE)1084-0702(2006)11:3(320)","article-title":"Fatigue damage of steel bridges due to dynamic vehicle loads","volume":"11","author":"MacDougall","year":"2006","journal-title":"J. Bridg. Eng."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1016\/j.ijfatigue.2005.07.017","article-title":"Fatigue cracks in longitudinal ribs of steel orthotropic deck","volume":"28","author":"Xiao","year":"2006","journal-title":"Int. J. Fatigue"},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Lee, Y.J., and Cho, S. (2016). SHM-based probabilistic fatigue life prediction for bridges based on FE model updating. Sensors, 16.","DOI":"10.3390\/s16030317"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"299","DOI":"10.12989\/sss.2007.3.3.299","article-title":"Issues in structural health monitoring employing smart sensors","volume":"3","author":"Nagayama","year":"2007","journal-title":"Smart Struct. Syst."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1016\/j.jsv.2015.07.012","article-title":"Methodology for model updating of mechanical components with local nonlinearities","volume":"357","author":"Kurt","year":"2015","journal-title":"J. Sound Vib."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"111","DOI":"10.1016\/j.ymssp.2016.10.016","article-title":"Nonlinear model updating applied to the IMAC XXXII Round Robin benchmark system","volume":"88","author":"Kurt","year":"2017","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.ymssp.2013.12.014","article-title":"Experimental system identification of the dynamics of a vibro-impact beam with a view towards structural health monitoring and damage detection","volume":"46","author":"Chen","year":"2014","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"04013074","DOI":"10.1061\/(ASCE)ST.1943-541X.0000836","article-title":"System reliability updating of fatigue-induced sequential failures","volume":"140","author":"Lee","year":"2014","journal-title":"J. Struct. Eng."},{"key":"ref_16","first-page":"51","article-title":"An effective approximation to evaluate multinormal integrals","volume":"20","author":"Paris","year":"1963","journal-title":"Struct. Saf."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"185","DOI":"10.1016\/0013-7944(81)90116-8","article-title":"An empirical stress intensity factor equation for the surface crack","volume":"15","author":"Newman","year":"1981","journal-title":"Eng. Fract. Mech."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"2712","DOI":"10.1016\/j.ymssp.2009.05.010","article-title":"Determination of fragments of multiaxial service loading strongly influencing the fatigue of machine components","volume":"23","author":"Nieslony","year":"2009","journal-title":"Mech. Syst. Signal Process."},{"key":"ref_19","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1115\/1.1286601","article-title":"Implications of inspection updating on system fatigue reliability of offshore structures","volume":"122","author":"Moan","year":"2000","journal-title":"J. Offshore Mech. Arct. Eng."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"684","DOI":"10.1061\/(ASCE)0733-9445(1992)118:3(684)","article-title":"Systems reliability approach to fatigue of structures","volume":"118","author":"Karamchandani","year":"1992","journal-title":"J. Struct. Eng."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"459","DOI":"10.1115\/1.3609637","article-title":"Numerical Analysis of Crack Propagation in Cyclic Loaded Structures","volume":"89","author":"Forman","year":"1967","journal-title":"J. Basic Eng."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Walker, K. (1970). The effect of stress ratio during crack propagation and fatigue for 2024-T3 and 7075-T6 aluminum. Effects of Environment and Complex Load History on Fatigue Life, ASTM International.","DOI":"10.1520\/STP32032S"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1016\/0167-4730(90)90005-A","article-title":"Methods of reliability model updating through additional events","volume":"9","author":"Jiao","year":"1990","journal-title":"Struct. Saf."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"254","DOI":"10.1016\/j.probengmech.2010.08.003","article-title":"Reliability updating with equality information","volume":"26","author":"Straub","year":"2011","journal-title":"Probab. Eng. Mech."},{"key":"ref_25","unstructured":"Madsen, H.O. (1987, January 25\u201329). Model updating in reliability theory. Proceedings of the 5th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP5), Vancouver, BC, Canada."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/0167-4730(82)90024-8","article-title":"First-order concepts in system reliability","volume":"1","author":"Hohenbichler","year":"1983","journal-title":"Struct. Saf."},{"key":"ref_27","unstructured":"Melchers, R.E. (1999). Structural Reliability Analysis and Prediction, John Wiley & Son Ltd."},{"key":"ref_28","unstructured":"Der Kiureghian, A. (2005). First- and second-order reliability methods. Engineering Design Reliability Handbook, CRC Press. Chapter 14."},{"key":"ref_29","unstructured":"Sudret, B., and Der Kiureghian, A. (2000). Stochastic Finite Element Methods and Reliability: A State-of-the-Art Report, Department of Civil and Environmental Engineering, University of California."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"627","DOI":"10.1061\/(ASCE)0733-9399(2003)129:6(627)","article-title":"Bounds on system reliability by linear programming","volume":"129","author":"Song","year":"2003","journal-title":"J. Eng. Mech."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"148","DOI":"10.1016\/j.strusafe.2008.06.012","article-title":"System reliability and sensitivity under statistical dependence by matrix-based system reliability method","volume":"31","author":"Song","year":"2009","journal-title":"Struct. Saf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"683","DOI":"10.12989\/sss.2015.15.3.683","article-title":"System identification of an in-service railroad bridge using wireless smart sensors","volume":"15","author":"Kim","year":"2015","journal-title":"Smart Struct. Syst."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"e1863","DOI":"10.1002\/stc.1863","article-title":"Railroad bridge monitoring using wireless smart sensors","volume":"24","author":"Moreu","year":"2016","journal-title":"Struct. Control Health Monit."},{"key":"ref_34","unstructured":"Crossbow Technology Inc. (2017, January 17). Imote2\u2014High-Performance Wireless Sensor Network Node. Available online: http:\/\/wsn.cse.wustl.edu\/images\/e\/e3\/Imote2_Datasheet.pdf."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"04016066","DOI":"10.1061\/(ASCE)ST.1943-541X.0001530","article-title":"Hybrid model for railroad bridge dynamics","volume":"142","author":"Kim","year":"2016","journal-title":"J. Struct. Eng."},{"key":"ref_36","doi-asserted-by":"crossref","unstructured":"Tada, H., Paris, P.C., and Irwin, G.R. (2000). The Stress Analysis of Cracks Handbook, ASME.","DOI":"10.1115\/1.801535"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"997","DOI":"10.1016\/0013-7944(89)90015-5","article-title":"Crack growth rates of structural steel in air and aqueous environments","volume":"32","author":"Yazdani","year":"1989","journal-title":"Eng. Fract. Mech."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1016\/j.ress.2012.05.007","article-title":"Finite-element-based system reliability analysis of fatigue-induced sequential failures","volume":"108","author":"Lee","year":"2012","journal-title":"Reliab. Eng. Syst. Saf."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/936\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:33:17Z","timestamp":1760207597000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/17\/4\/936"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,4,24]]},"references-count":38,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2017,4]]}},"alternative-id":["s17040936"],"URL":"https:\/\/doi.org\/10.3390\/s17040936","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,4,24]]}}}