Development of Stochastic Decision Model for Estimation of Optimal In-depth Inspection Period of Harbor Structures

- Journal title : Journal of Korean Society of Coastal and Ocean Engineers
- Volume 28, Issue 2, 2016, pp.63-72
- Publisher : Korean Society of Coastal and Ocean Engineers
- DOI : 10.9765/KSCOE.2016.28.2.63

Title & Authors

Development of Stochastic Decision Model for Estimation of Optimal In-depth Inspection Period of Harbor Structures

Lee, Cheol-Eung;

Lee, Cheol-Eung;

Abstract

An expected-discounted cost model based on RRP(Renewal Reward Process), referred to as a stochastic decision model, has been developed to estimate the optimal period of in-depth inspection which is one of critical issues in the life-cycle maintenance management of harbor structures such as rubble-mound breakwaters. A mathematical model, which is a function of the probability distribution of the service-life, has been formulated by simultaneously adopting PIM(Periodic Inspection and Maintenance) and CBIM(Condition-Based Inspection and Maintenance) policies so as to resolve limitations of other models, also all the costs in the model associated with monitoring and repair have been discounted with time. From both an analytical solution derived in this paper under the condition in which a failure rate function is a constant and the sensitivity analyses for the variety of different distribution functions and conditions, it has been confirmed that the present solution is more versatile than the existing solution suggested in a very simplified setting. Additionally, even in that case which the probability distribution of the service-life is estimated through the stochastic process, the present model is of course also well suited to interpret the nonlinearity of deterioration process. In particular, a MCS(Monte-Carlo Simulation)-based sample path method has been used to evaluate the parameters of a damage intensity function in stochastic process. Finally, the present stochastic decision model can satisfactorily be applied to armor units of rubble mound breakwaters. The optimal periods of in-depth inspection of rubble-mound breakwaters can be determined by minimizing the expected total cost rate with respect to the behavioral feature of damage process, the level of serviceability limit, and the consequence of that structure.

Keywords

harbor structures;optimal period of in-depth inspection;stochastic decision model;damage intensity function;sample path method;

Language

Korean

References

1.

Barlow, R.E., and Proschan, F. (1965). Mathematical theory of reliability, New York, NY., John Wiley & Sons.

2.

Burcharth, H.F. (1992) Reliability evaluation of a structure at sea, Short course of 23rd ICCE., 470-517.

3.

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.

4.

Cheng, T., Pandey, M.D., and Van der Weide, J.A.M., (2012). The probability distribution of maintenance cost of a system affected by the gamma process of degradation : finite time solution, Rel. Eng. and Sys. Saf., 108, 65-76.

5.

CIRIA. (2007). The rock manual, The use of rock in hydraulic engineering(2nd. ed.) C683, London.

6.

Gassandras, C.G. and Han, Y. (1992). Optimal inspection policies for a manufacturing station, European J. of Op. Res., 63, 35-53.

7.

Goda, Y. (2010) Random seas and design of maritime structures, World Scientific Pub. Co.,

8.

Kahle, W., and Wendt, H. (2004) On a cumulative damage process and resulting first passage times, Appl. Stochastic Models Bus. Ind., 20, 17-26.

9.

Kaio, N. and Osaki, S. (1984). Some remarks on optimal inspection policies, IEEE Trans. on Reliability, R-33, 277-279.

10.

Kaio, N. and Osaki, S. (1986). Optimal inspection policy with two types of imperfect inspection probabilities, Micro-elect. and Reli., 26, 935-942.

11.

Lee, C.-E. (2013). Development of stochastic expected cost model for preventive optimal maintenance of armor units of rubble-mound breakwaters, Journal of the Korean Society of Coastal and Ocean Engineers, 25(5), 276-284. (in Korean).

12.

Lee, C.-E. (2015). Estimation of time-dependent damage paths of armors of rubble-mound breakwaters using stochastic processes, Journal of the Korean Society of Coastal and Ocean Engineers, 27(4), 246-257. (in Korean).

13.

Melby, J.A. (1999). Damage progression on breakwaters, Ph.D. thesis, Dept. of Civ. Engrg., Univ. of Delware, USA.

14.

Melby, J.A. (2005) Damage development on stone-armored break-waters and revetments, ERDC/CHL CHETN-III-64, US Army Corps of Engineers.

15.

Munford, A.G. and Shahani, A.K. (1972). A nearly optimal inspection policy, Oper. Res. Quarterly, 23, 373-379.

16.

Munford, A.G. and Shahani, A.K. (1973). An inspection policy for the Weibull case, Oper. Res. Quarterly, 24, 453-458.

17.

Nakagawa, T. (2005). Maintenance theory of reliability, Springer-Verlag, London.

18.

Nakagawa, T. and Yasui, K. (1979). Approximate calculation of inspection policy with Weibull failure times, IEEE Trans. on reliability, R-28, 403-404.

19.

Noortwijk, J.M. and Frangopol, D.M. (2004). Deterioration and main-tenance models for insuring safety of civil infrastructures at lowest life-cycle cost, Proc. of Life- Cycle Performance of Deteriorating Structures: Assessment, Design and Management, ASCE, 384-391.

20.

Noortwijk, J.M. and Klatter, H.E. (1999). Optimal inspection decisions for the block mats of the Eastern-Scheldt, Rel. Eng. and Sys. Saf., 65, 203-211.

21.

PIANC (1992). Analysis of rubble mound breakwaters, Supplement to Bull. N. 78/79, Brussels, Belgium.

22.

Ramchandani, P (2009). Stochastic renewal process model for condition-based maintenance, Master thesis, University of Waterloo.

23.

Ross, S.M. (1980). Introduction to probability models, Academic Press, N.Y.

24.

Sandoh, H. and Igaki, N. (2003). Optimal inspection policies for a scale, Comp. and Math. with Applic., 46, 1119-1127.

25.

Tadikamalla, P.R. (1979). An inspection policy for gamma failure distributions, Naval Re. Log. Quarterly, 25. 243-255.

26.

Thuesen, G.J. and Fabrycky, W.J. (1994). Engineering economy, Prentice-Hall Inc, N.J.

27.

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.

28.

Van der Troon, A. (1994). The maintenance of civil engineering structures, Heron Journal, TRB, 39, 3-34.

29.

Van der Weide, J.A.M., Pandey, M.D. (2011). Stochastic analysis of shock process and modelling of condition-based maintenance, Rel. Eng. and Sys. Saf., 96, 619-626.

30.

Wattanapanom, N. and Shaw, L. (1979). Optimal inspection schedules for failure detection in a model where tests hasten failures, Oper. Res., 27, 303-317.