Probability Analysis of Duration of Stochastic Process Exceeding Fixed Threshold and Its Application on Structural Cumulative Damage and Fatigue Reliability Evaluation
Publication: ASCE-ASME Journal of Risk and Uncertainty in Engineering Systems, Part A: Civil Engineering
Volume 10, Issue 2
Abstract
Based on the stochastic process multiple threshold crossings analysis formula, the impact of structural response random process crossing-threshold duration on structural fatigue reliability is studied, which was not involved in fatigue reliability analysis before. This paper considers the type of structural stress stochastic processes with Wiener characteristics in engineering and establishes a novel method considering the random response crossing-threshold duration for fatigue reliability evaluation. The fatigue cumulative damage considering random response crossing-threshold duration is derived analytically based on the assumption that cumulative damage is linear to crossing-threshold duration. This study makes the fatigue reliability analysis closer to the reality.
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Data Availability Statement
All data, models, and code generated or used during the study appear in the published article.
Acknowledgments
This work was jointly supported by the National Key R&G Program of China (Grant No. 2021YFB2600900); the Talent Recruitment Project of Hunan Province, China (Grant No. 2023TJ-Z17); the Research Project of the Educational Commission of Hunan Province, China (Grant No. 22A0239); the Natural Science Foundation of Changsha City, China (Grant No. kq2202210); the Graduate Research and Innovation Project of Changsha University of Science and Technology (Grant No. CX2021SS19); and the Natural Science Foundation of Hunan Province (Grant No. 2022JJ30012).
References
AASHTO. 1990. Guide specifications for fatigue evaluation of existing steel bridges. Washington, DC: AASHTO.
Aeran, A., S. Siriwardane, O. Mikkelsen, and I. Langen. 2017. “A new nonlinear fatigue damage model based only on S-N curve parameters.” Int. J. Fatigue 103 (103): 327–341. https://doi.org/10.1016/j.ijfatigue.2017.06.017.
Alencar, G., J. Hong, A. Jesus, J. Silva, and R. Calçada. 2021. “The master S-N curve approach for fatigue assessment of welded bridge structural details.” Int. J. Fatigue 152 (Nov): 106432. https://doi.org/10.1016/j.ijfatigue.2021.106432.
Andrieu-Renaud, C., B. Sudret, and M. Lemaire. 2004. “The PHI2 method: A way to compute time-variant reliability.” Reliab. Eng. Syst. Saf. 84 (1): 75–86. https://doi.org/10.1016/j.ress.2003.10.005.
Angelo, C., F. Machado, and C. Schön. 2015. “Influence of tire sizes over automobile body spectrum loads and fatigue damage accumulation.” Mater. Des. 67 (15): 385–389. https://doi.org/10.1016/j.matdes.2014.11.060.
Barbosa, A., F. Ribeiro, and L. Neves. 2017. “Influence of earthquake ground-motion duration on damage estimation: Application to steel moment resisting frames.” Earthquake Eng. Struct. Dyn. 46 (Jun): 27–49. https://doi.org/10.1002/eqe.2769.
Benasciutti, D., and R. Tovo. 2007. “On fatigue damage assessment in bimodal random processes.” Int. J. Fatigue 29 (2): 232–244. https://doi.org/10.1016/j.ijfatigue.2006.03.013.
Chandramohan, R., J. Baker, and G. Deierlein. 2016. “Quantifying the influence of ground motion duration on structural collapse capacity using spectrally equivalent records.” Earthquake Spectra 32 (2): 927–950. https://doi.org/10.1193/122813eqs298mr2.
Chau, M., X. Han, C. Jiang, Y. Bai, T. Tran, and V. Truong. 2012. “An efficient PMA-based reliability analysis technique using radial basis function.” Eng. Comput. 31 (6): 1098–1115. https://doi.org/10.1108/EC-04-2012-0087.
Chen, Z., T. Li, X. Xue, Y. Zhou, and S. Jing. 2021. “Fatigue reliability analysis and optimization of vibrator Baseplate based on fuzzy comprehensive evaluation method.” Eng. Fail. Anal. 127 (Jun): 105357. https://doi.org/10.1016/j.engfailanal.2021.105357.
D’Angelo, L., and A. Nussbaumer. 2015. “Reliability based fatigue assessment of existing motorway bridge.” Struct. Saf. 57 (57): 35–42. https://doi.org/10.1016/j.strusafe.2015.07.001.
Ding, Y., Y. Song, B. Cao, G. Wang, and A. Li. 2016. “Full-range S-N fatigue-life evaluation method for welded bridge structures considering hot-spot and welding residual stress.” J. Bridge Eng. 21 (12): 04016096. https://doi.org/10.1061/(ASCE)BE.1943-5592.0000969.
Dong, Y., A. P. Teixeira, and C. Guedes Soares. 2018. “Time-variant fatigue reliability assessment of welded joints based on the PHI2 and response surface methods.” Reliab. Eng. Syst. Saf. 177 (Aug): 120–130. https://doi.org/10.1016/j.ress.2018.05.005.
Fang, T., and R. Landelma. 2016. “Optimization of combined heat and power production with heat storage based on sliding time window method.” Appl. Energy 162 (10): 723–732. https://doi.org/10.1016/j.apenergy.2015.10.135.
Feng, Y., B. Ma, T. J. Zhang, T. Zhang, and Y. He. 2021. “Reliability fatigue life and a new S-N curve model of composite laminates under tensile-tensile fatigue load.” Appl. Compos. Mater. 28 (1): 129–148. https://doi.org/10.1007/s10443-020-09847-x.
Fu, B., J. Zhao, B. Li, J. Yao, M. Teifouet, A. Robinson, L. Sun, and Z. Wang. 2020. “Fatigue reliability analysis of wind turbine tower under random wind load.” Struct. Saf. 87 (Apr): 101982. https://doi.org/10.1016/j.strusafe.2020.101982.
Gao, K., and G. Liu. 2021. “Novel nonlinear time-varying fatigue reliability analysis based on the probability density evolution method.” Int. J. Fatigue 149 (Aug): 106257. https://doi.org/10.1016/j.ijfatigue.2021.106257.
Gao, R., J. Li, and A. H. S. Ang. 2019. “Stochastic analysis of fatigue of concrete bridges.” Struct. Infrastruct. Eng. 15 (7): 925–939. https://doi.org/10.1080/15732479.2019.1569073.
Gong, G. L., and M. P. Qian. 2004. Tutorial on applying stochastic process and stochastic model in algorithm and intelligent computing. Beijing: Tsinghua University Press.
Hao, S., J. Yang, and C. Berenguer. 2019. “Degradation analysis based on an extended inverse Gaussian process model with skew-normal random effects and measurement errors.” Reliab. Eng. Syst. Saf. 189 (Jun): 261–270. https://doi.org/10.1016/j.ress.2019.04.031.
He, W., J. Liu, and D. Xie. 2015. “Probabilistic life assessment on fatigue crack growth in mixed-mode by coupling of Kriging model and finite element analysis.” Eng. Fract. Mech. 139 (Mar): 56–77. https://doi.org/10.1016/j.engfracmech.2015.03.040.
Heng, J., K. Zheng, S. Kaewunruen, J. Zhu, and C. Baniotopoulos. 2019. “Dynamic Bayesian network-based system-level evaluation on fatigue reliability of orthotropic steel decks.” Eng. Fail. Anal. 105 (Apr): 1212–1228. https://doi.org/10.1016/j.engfailanal.2019.06.092.
Kaleva, O., and H. Orelma. 2021. “Modeling stress history as a stochastic process.” Int. J. Fatigue 143 (56): 105–996. https://doi.org/10.1016/j.ijfatigue.2020.105996.
Kim, H., and B. Jang. 2021. “Fatigue life prediction of ship and offshore structures under wide-banded non-Gaussian random loadings: Part II: Extension to wide-banded non-Gaussian random processes.” Appl. Ocean Res. 106 (Jan): 102480. https://doi.org/10.1016/j.apor.2020.102480.
Kim, H., B. Jang, and J. Kim. 2020. “Fatigue-damage prediction for ship and offshore structures under wide-banded non-Gaussian random loadings Part I: Approximation of cycle distribution in wide-banded gaussian random processes.” Appl. Ocean Res. 101 (Aug): 102294. https://doi.org/10.1016/j.apor.2020.102294.
Kwon, K., and D. Frangopol. 2010. “Bridge fatigue reliability assessment using probability density functions of equivalent stress range based on field monitoring data.” Int. J. Fatigue 32 (8): 1221–1232. https://doi.org/10.1016/j.ijfatigue.2010.01.002.
Larsen, C., and L. Lutes. 1991. “Predicting the fatigue life of offshore structures by the single-moment spectral method.” Probab. Eng. Mech. 6 (2): 96–108. https://doi.org/10.1016/0266-8920(91)90023-W.
Li, J., and J. Chen. 2008. “The principle of preservation of probability and the generalized density evolution equation.” Struct. Saf. 30 (1): 65–77. https://doi.org/10.1016/j.strusafe.2006.08.001.
Li, J., J. Chen, W. Sun, and Y. Peng. 2012. “Advances of the probability density evolution method for nonlinear stochastic systems.” Probab. Eng. Mech. 28 (Apr): 132–142. https://doi.org/10.1016/j.probengmech.2011.08.019.
Li, Y., P. Zhi, Y. Zhang, B. Chen, and Y. Wang. 2020. “Fatigue reliability analysis of motor hanger for high-speed train based on bayesian updating and subset simulation.” Adv. Mater. Sci. Eng. 2020 (Mar): 1–10. https://doi.org/10.1155/2020/3012471.
Liang, J., R. Li, S. Bai, Q. Li, F. Ning, and S. Kang. 2019. “Compliance and fatigue life analysis of U-shape flexure hinge.” Mechanika 25 (6): 501–510. https://doi.org/10.5755/j01.mech.25.6.22686.
Lin, Y., and G. Cai. 1995. Probabilistic structural dynamics: Advanced theory and applications. New York: McGraw-Hill Press.
Ling, J., and J. Pan. 1997. “A maximum likelihood method for estimating P-S-N curves.” Int. J. Fatigue 19 (5): 415–419. https://doi.org/10.1016/S0142-1123(97)00037-6.
Liu, M., D. Frangopol, and K. Kwon. 2010. “Fatigue reliability assessment of retrofitted steel bridges integrating monitored data.” Struct. Saf. 32 (1): 77–89. https://doi.org/10.1016/j.strusafe.2009.08.003.
Liu, Y., L. Deng, W. Zhong, J. Xu, and W. Xiong. 2020. “A new fatigue reliability analysis method for steel bridges based on peridynamic theory.” Eng. Fract. Mech. 236 (Sep): 107214. https://doi.org/10.1016/j.engfracmech.2020.107214.
Mahmouda, H., and G. Riveros. 2014. “Fatigue reliability of a single stiffened ship hull panel.” Eng. Struct. 66 (1): 89–99. https://doi.org/10.1016/j.engstruct.2014.02.007.
Meshii, L. 1999. “Near-threshold fatigue: A review.” Int. J. Fatigue 21 (1): 15–34. https://doi.org/10.1016/S0142-1123(99)00053-5.
Mohabeddine, A., J. Correia, P. Montenegro, A. Jesus, J. Castro, and F. Berto. 2021. “Probabilistic S-N curves for CFRP retrofitted steel details.” Int. J. Fatigue 148 (Jun): 106205. https://doi.org/10.1016/j.ijfatigue.2021.106205.
Murakami, Y., T. Nomoto, and T. Ueda. 1999. “Factors influencing the mechanism of super long fatigue failure in steels.” Fatigue Fract. Eng. Mater. Struct. 22 (7): 581–590. https://doi.org/10.1046/j.1460-2695.1999.00187.x.
Murakami, Y., T. Takagi, K. Wada, and H. Matsunaga. 2021. “Essential structure of S-N curve: Prediction of fatigue life and fatigue limit of defective materials and nature of scatter.” Int. J. Fatigue 146 (Jun): 106138. https://doi.org/10.1016/j.ijfatigue.2020.106138.
Nabizadeh, A., and H. Tabatabai. 2020. “Development of nonlinear probabilistic S-N curves using survival analysis techniques with application to steel bridges.” Int. J. Fatigue 141 (Dec): 105892. https://doi.org/10.1016/j.ijfatigue.2020.105892.
National Standard of the People’s Republic of China. 2017. Standard for design design of steel steel structures structures. Beijing: China Architecture and Building Press.
Niu, Q., S. Yang, and X. Li. 2018. “An empirical mode decomposition-based frequency-domain approach for the fatigue analysis of nonstationary processes.” Fatigue Fract. Eng. Mater. Struct. 41 (9): 1980–1996. https://doi.org/10.1111/ffe.12836.
Niu, X., R. Wang, D. Liao, S. Zhu, X. Zhang, and B. Keshtegar. 2021. “Probabilistic modeling of uncertainties in fatigue reliability analysis of turbine bladed disks.” Int. J. Fatigue 142 (Jan): 105912. https://doi.org/10.1016/j.ijfatigue.2020.105912.
Ou, J., and G. Wang. 1998. Random vibration of structures. Beijing: Higher Education Press.
Pana, Y., C. Venturaa, W. Finn, and H. Xiong. 2019. “Effects of ground motion duration on the seismic damage to and collapse capacity of a mid-rise woodframe building.” Eng. Struct. 197 (Apr): 109451. https://doi.org/10.1016/j.engstruct.2019.109451.
Pastorcic, D., G. Vukelic, and Z. Bozic. 2019. “Coil spring failure and fatigue analysis.” Eng. Fail. Anal. 99 (Feb): 310–318. https://doi.org/10.1016/j.engfailanal.2019.02.017.
Raghunandan, M., and A. Liel. 2013. “Effect of ground motion duration on earthquake-induced structural collapse.” Struct. Saf. 41 (Mar): 119–133. https://doi.org/10.1016/j.strusafe.2012.12.002.
Roberts, J. 1986. “First-passage probabilities for randomly excited systems: Diffusion methods.” Probab. Eng. Mech. 1 (2): 66–81. https://doi.org/10.1016/0266-8920(86)90029-9.
Ross, S. 1996. Stochastic processes. 2nd ed. New York: Wiley.
Seddik, R., R. Sghaier, A. Atig, and R. Fathallah. 2017. “Fatigue reliability prediction of metallic shot peened-parts based on Wöhler curve.” J. Constr. Steel Res. 130 (Jun): 222–233. https://doi.org/10.1016/j.jcsr.2016.12.015.
Shittu, A., A. Mehmanparast, P. Hart, and A. Kolios. 2021. “Comparative study between S-N and fracture mechanics approach on reliability assessment of offshore wind turbine jacket foundations.” Reliab. Eng. Syst. Saf. 215 (Apr): 107838. https://doi.org/10.1016/j.ress.2021.107838.
Sina, S., S. Mandegarian, and F. Taheri-Behrooz. 2019. “A nonlinear FE analysis to model progressive fatigue damage of cross-ply laminates under pin-loaded conditions.” Int. J. Fatigue 119 (Feb): 290–301. https://doi.org/10.1016/j.ijfatigue.2018.10.010.
Singh, S., S. Abdullah, and N. Nikabdullah. 2017. “The needs of understanding stochastic fatigue failure for the automobile crankshaft: A review.” Eng. Fail. Anal. 80 (Oct): 464–471. https://doi.org/10.1016/j.engfailanal.2017.06.023.
Stanzle, S. E., E. K. Tschegy, and H. Mayer. 1986. “Lifetime measurements for random loading in very high cycle fatigue range.” Int. J. Fatigue 8 (4): 195–200. https://doi.org/10.1016/0142-1123(86)90021-6.
Tovo, R. 2002. “Cycle distribution and fatigue damage under broad-band random loading.” Int. J. Fatigue 24 (11): 1137–1147. https://doi.org/10.1016/S0142-1123(02)00032-4.
Wang, C., D. Wagner, Q. Wang, and C. Bathias. 2012. “Gigacycle fatigue initiation mechanism in Armco iron.” Int. J. Fatigue 45 (Jun): 91–97. https://doi.org/10.1016/j.ijfatigue.2012.06.005.
Wang, X., Y. Ma, L. Wang, X. Geng, and D. Wu. 2017. “Composite laminate oriented reliability analysis for fatigue life under non-probabilistic time-dependent method.” Comput. Methods Appl. Mech. Eng. 137 (1): 1–58. https://doi.org/10.1016/0045-7825(96)01054-7.
Weibring, M., L. Gondecki, and P. Tenberge. 2019. “Simulation of fatigue failure on tooth flanks in consideration of pitting initiation and growth.” Tribol. Int. 131 (Jun): 299–307. https://doi.org/10.1016/j.triboint.2018.10.029.
Xu, Y. 2015. “Fatigue reliability evaluation using probability density evolution method.” Probab. Eng. Mech. 42 (Sep): 1–6. https://doi.org/10.1016/j.probengmech.2015.09.005.
Xue, X., and N. Chen. 2018. “Fracture mechanics analysis for a mooring system subjected to Gaussian load processes.” Eng. Struct. 162 (1): 188–197. https://doi.org/10.1016/j.engstruct.2018.02.040.
Yan, Y. 2020. “Load characteristic analysis and fatigue reliability prediction of wind turbine gear transmission system.” Int. J. Fatigue 130 (Jan): 105259. https://doi.org/10.1016/j.ijfatigue.2019.105259.
Yang, L., J. Zhang, Y. Guo, and P. Wang. 2016. “A Bayesian-based reliability estimation approach for corrosion fatigue crack growth utilizing the random walk.” Qual. Reliab. Eng. Int. 32 (7): 2519–2535. https://doi.org/10.1002/qre.1954.
Yao, W., and S. Guo. 2008. “VHCF test and life distribution and life distribution of aluminum alloy LC4CS.” Int. J. Fatigue 30 (1): 172–177. https://doi.org/10.1016/j.ijfatigue.2007.02.004.
Zhang, C., and K. Tee. 2019. “Application of gamma process and maintenance cost for fatigue damage of wind turbine blade.” Energy Procedia 158 (Feb): 3729–3734. https://doi.org/10.1016/j.egypro.2019.01.884.
Zhang, H., Y. Liu, and Y. Deng. 2020a. “Fatigue crack assessment for orthotropic steel deck based on compound Poisson process.” J. Bridge Eng. 25 (8): 04020057. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001575.
Zhang, X., W. Zhao, and Y. Xie. 2019a. “Fatigue failure analysis of semi-open impeller with mistuning considered.” Eng. Fail. Anal. 95 (8): 127–139. https://doi.org/10.1016/j.engfailanal.2018.09.002.
Zhang, Z., Q. Li, and C. Zhang. 2019b. “Research on bogie reliability based on probabilistic cumulative damage and Wiener process.” J. South China Univ. Technol. 47 (7): 90–98. https://doi.org/10.12141/j.issn.1000-565X.180506.
Zhang, Z., M. Liu, M. Zhou, and J. Chen. 2020b. “Dynamic reliability analysis of nonlinear structures using a Duffing-system-based equivalent nonlinear system method.” Int. J. Approx. Reason. 126 (Apr): 84–97. https://doi.org/10.1016/j.ijar.2020.08.006.
Zhang, Z., X. Liu, Y. Zhang, M. Zhou, and J. Chen. 2020c. “Time interval of multiple crossings of the Wiener process and a fixed threshold in engineering.” Mech. Syst. Signal Process. 135 (1): 106389. https://doi.org/10.1016/j.ymssp.2019.106389.
Zhang, Z., M. Zhou, and M. Fang. 2019c. “First-passage probability analysis of Wiener process using different methods and its applications in the evaluation of structural durability degradation.” Eur. J. Environ. Civ. Eng. 25 (10): 1–19. https://doi.org/10.1080/19648189.2019.1601134.
Zhu, S., D. Liao, Q. Liu, J. Correia, and A. Jesus. 2019. “Nonlinear fatigue damage accumulation: Isodamage curve-based model and life prediction aspects.” Int. J. Fatigue 128 (Nov): 108185. https://doi.org/10.1016/j.ijfatigue.2019.105185.
Zhu, S., Q. Liu, and H. Huang. 2017. “Probabilistic modeling of damage accumulation for fatigue reliability analysis.” Procedia Struct. Integrity 4 (12): 3–10. https://doi.org/10.1016/j.prostr.2017.07.012.
Zhuang, M., and C. Miao. 2020. “Fatigue reliability assessment for hangers of a special-shaped CFST arch bridge.” Structures 28 (9): 235–250. https://doi.org/10.1016/j.istruc.2020.08.067.
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© 2024 American Society of Civil Engineers.
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Received: Jul 11, 2023
Accepted: Nov 2, 2023
Published online: Jan 24, 2024
Published in print: Jun 1, 2024
Discussion open until: Jun 24, 2024
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