Journal of Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회논문집)

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
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Estimation of Time-dependent Damage Paths of Armors of Rubble-mound Breakwaters using Stochastic Processes

추계학적 확률과정을 이용한 경사제 피복재의 시간에 따른 피해 경로 추정

  • Lee, Cheol-Eung (Department of Civil Engineering, Kangwon National University)
  • Received : 2015.07.22
  • Accepted : 2015.08.25
  • Published : 2015.08.31
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Abstract

The progressive degradation paths of structures have quantitatively been tracked by using stochastic processes, such as Wiener process, gamma process and compound Poisson process, in order to consider both the sampling uncertainty due to the usual lack of damage data and the temporal uncertainty associated with the deterioration evolution. Several important features of stochastic processes which should carefully be considered in application of the stochastic processes to practical problems have been figured out through assessing cumulative damage and lifetime distribution as a function of time. Especially, the Wiener process and the gamma process have straightforwardly been applied to armors of rubble-mound breakwaters by the aid of a sample path method based on Melby's formula which can estimate cumulative damage levels of armors over time. The sample path method have been developed to calibrate the related-parameters required in the stochastic modelling of armors of rubble-mound breakwaters. From the analyses, it is found that cumulative damage levels of armors have surely been saturated with time. Also, the exponent of power law in time, that plays a significant role in predicting the cumulative damage levels over time, can easily be determined, which makes the stochastic models possible to track the cumulative damage levels of armors of rubble-mound breakwaters over time. Finally, failure probabilities with respect to various critical limits have been analyzed throughout its anticipated service life.

피해 자료의 부족에 따른 불확실성 뿐만 아니라 시간의 진행에 따른 불확실성을 고려하기 위하여 추계학적 확률과정을 이용하여 시간에 따른 구조물의 피해 경로를 정량적으로 추적하였다. 누적피해도와 내구년수의 분포함수를 시간의 함수로 산정하여 추계학적 확률과정을 적용할 때 주의해야 하는 중요한 특성들을 제시하였다. 특히, 본 연구에서는 추계학적 확률과정을 경사제 피복재에 적용하여 시간에 따른 누적 피해도를 추적할 수 있는 방법을 제안하였다. 확률과정의 매개변수들을 추정하기 위하여 개발된 표본경로기법을 이용하여 경사제 피복재의 시간에 따른 누적 피해도가 포화거동을 따른다는 사실이 확인되었다. 또한 누적 피해도 산정시 중요한 역할을 하는 멱함수의 지수를 정량적으로 산정하여 경사제 피복재의 누적 피해도를 시간에 따라 추적하는 것이 가능했다. 마지막으로 한계수준을 다양하게 변화시키면서 파괴확률의 거동특성을 해석하였다.

Keywords

References

  1. Barlow, R.E., and Proschan, F. (1965). Mathematical theory of reliability, New York, NY., John Wiley & Sons.
  2. Basu, S. and Lingham, R.T., (2003). Bayesian estimation of system reliability in Browian stree-strength models, Ann. Inst. Stat. Math., 55(1), 7-19. https://doi.org/10.1007/BF02530482
  3. British Standards Institution (1984). BS3811 Glossary of maintenance terms in Tero- technology, BSI, London.
  4. Burcharth, H.F. (1992) Reliability evaluation of a structure at sea, Short course of 23rd ICCE., 470-517.
  5. Castillo, C., Castillo, E., Fernandez-Canteli, A., Molina, R. and Gomez, R. (2012) Stochastic model for damage accumulation in rubble-mound breakwaters based on compatibility conditions and central limit theorem, J. Waterway, Port, Coast., and Ocn. Eng., ASCE, 138(6), 451-463. https://doi.org/10.1061/(ASCE)WW.1943-5460.0000146
  6. Doksum, K.A. and Normand, S.L. (1995). Gaussian models for degradation processes-Part I: methods for the analysis of biomarker data, Lifetime Data Anal., 1, 134-144.
  7. Ellingwood, B.R. and Mori, Y. (1993). Probabilistic methods for condition assessment and life prediction of concrete structures in nuclear power plants, Nucl. Eng. Des., 142(2-3). 155-166. https://doi.org/10.1016/0029-5493(93)90199-J
  8. Frangopol, D.M., Kallen, M.J. and van Noortwijk, J.M. (2004). Probabilistic models for life-cycle performance of deteriorating structures: review and future directions, Prog. Struct. Eng. Mater., 6(4), 197-212. https://doi.org/10.1002/pse.180
  9. Goda, Y. (2010). Random seas and design of maritime structures, World Scientific Publishing Co., Singapore.
  10. Heutink, A., Beek, A., Noortwijk, J.M., Klatter, H.E. and Barendregt, A., (2004). Environment-friendly maintenance of protective paint systems at lowest costs, In: XXVII FATIPEC congress, 19-21.
  11. Karlin, S. and Taylor, H.M. (1975). A first course in stochastic processes, 2nd. ed., San Diego, Academic Press.
  12. Melby, J.A. (1999). Damage progression on breakwaters, Ph.D. thesis, Dept. of Civ. Engrg., Univ. of Delaware, USA.
  13. Melby, J.A. (2005) Damage development on stone-armored breakwaters and revetments, ERDC/CHL CHETN-III-64, US Army Corps of Engineers.
  14. Nakagawa, T. (2010). Shock and damage models in reliability theory, Springer- Verlag, London.
  15. Nicolai, R.P., Dekker, R. and Noortwijk, J.M. (2007). A comparison for measurablr deterioration: An application to coatings on steel structures, Rel. Eng. and Sys. Saf., 92, 1635-1650. https://doi.org/10.1016/j.ress.2006.09.021
  16. Noortwijk, J.M. (1995). Bayesian failure model based on isotropic deterioration, Eur. J. Oper. Res., 82(2), 270-282. https://doi.org/10.1016/0377-2217(94)00263-C
  17. Noortwijk, J.M. (2009). A survey of the application of gamma processes in maintenance, Rel. Eng. and Sys. Saf., 94, 2-21. https://doi.org/10.1016/j.ress.2007.03.019
  18. Pandey, M.D., Yuan, X.-X. and van Noortwijk, J.M. (2009). The influence of temporal uncertainty of deterioration on life-cycle management of structures, Struc. and Infrastruc. Eng., 5(2), 145-156. https://doi.org/10.1080/15732470601012154
  19. PIANC (1992). Analysis of rubble mound breakwaters, Supplement to Bull. N. 78/79, Brussels, Belgium.
  20. Ross, S.M. (1970). Applied probability models with optimization applications, New York.
  21. Ross, S.M. (1980). Introduction to probability models, Academic Press, N.Y.
  22. Singpurwalla, N. (1997). Gamma processes and their generalizations: an overview, In: Cooke, Mendel, Vrijling, editors. Engineering probabilistic design and maintenance for flood protection, Dordrecht, 67-75.
  23. Van der Meer, J.W. (1988). Deterministic and probabilistic design of breakwater armor layers, J. Waterway, Port, Coast., and Ocn. Eng., ASCE, 114(1), 66-80. https://doi.org/10.1061/(ASCE)0733-950X(1988)114:1(66)
  24. Weide, H. (1997), Gamma processes, In: Cooke, Mendel, Vrijling, editors. Engineering probabilistic design and maintenance for flood protection, Dordrecht, 77-83.
  25. Weide, J.A.M., Pandey, M.D. and Noortwijk, J.M. (2010). Discounted cost model for condition-based maintenance optimization, Rel. Eng. and Sys. Saf., 95, 236-246. https://doi.org/10.1016/j.ress.2009.10.004
  26. Weide, J.A.M. and Pandey, M.D. (2011). Stochastic analysis of shock process and modelling of condition-based maintenance, Rel. Eng. and Sys. Saf., 96, 619-626. https://doi.org/10.1016/j.ress.2010.12.012
  27. Whitmore, G.A. (1995). Estimating degradation by a Wiener diffusion process subject to measurement error, Lifetime Data Anal., 1, 307-319. https://doi.org/10.1007/BF00985762

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