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

Korean Society of Coastal and Ocean Engineers (한국해안·해양공학회)
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Condition-Based Model for Preventive Maintenance of Armor Units of Rubble-Mound Breakwaters using Stochastic Process

추계학적 확률과정을 이용한 경사제 피복재의 예방적 유지관리를 위한 조건기반모형

  • Lee, Cheol-Eung (Department of Civil Engineering, Kangwon National University)
  • Received : 2016.07.18
  • Accepted : 2016.08.10
  • Published : 2016.08.31
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Abstract

A stochastic process has been used to develop a condition-based model for preventive maintenance of armor units of rubble-mound breakwaters that can make a decision the optimal interval at which some repair actions should be performed under the perfect maintenance. The proposed cost model in this paper based on renewal reward process can take account of the interest rate, also consider the unplanned maintenance cost which has been treated like a constant in the previous studies to be a time-dependent random variable. A function for the unplanned maintenance cost has been mathematically proposed so that the cumulative damage, serviceability limit and importance of structure can be taken into account, by which a age-based maintenance can be extended to a condition-based maintenance straightforwardly. The coefficients involved in the function can also be properly estimated using a method expressed in this paper. Two stochastic processes, Wiener process and gamma process have been applied to armor stones of rubble-mound breakwaters. By evaluating the expected total cost rate as a function of time for various serviceability limits, interest rates and importances of structure, the optimal period of preventive maintenance can easily determined through the minimization of the expected total cost rate. For a fixed serviceability limit, it shows that the optimal period has been delayed while the interest rate increases, so that the expected total cost rate has become lower. In addition, the gamma process tends to estimate the optimal period more conservatively than the Wiener process. Finally, it is found that the more crucial the level of importance of structure becomes, the more often preventive maintenances should be carried out.

추계학적 확률과정을 이용하여 경사제 피복재를 예방적으로 유지관리할 수 있는 조건기반모형을 개발하였다. 완전 보수보강 조건에서 가장 경제적으로 보수보강이 수행되어야 하는 최적의 시점을 결정할 수 있는 모형이다. 본 연구에서 개발된 RRP(Renewal Reward Process) 기반 경제성 모형은 이자율을 고려할 수 있을 뿐만 아니라 기존 연구에서 상수로 취급하던 비용을 시간에 따른 확률변수로 고려할 수 있다. 누적피해와 사용한계 그리고 구조물의 중요도를 모두 고려할 수 있는 함수식을 제시하여 ABM(Age-Based Maintenance)을 CBM(Condition-Based Maintenance)으로 쉽게 확장할 수 있게 하였다. 또한 함수식에 포함된 계수들을 수학적으로 산정할 수 있는 방법도 제시하였다. 두 가지 추계학적 확률과정, WP(Wiener Process)와 GP(Gamma Process)를 이용하여 경사제 사석재를 해석하였다. 사용한계, 이자율 그리고 구조물의 중요도에 따라 시간에 따른 기대총비용율을 산정하여 기대총비용율이 최소가 되는 예방적 유지관리의 최적 시점을 쉽게 추정할 수 있었다. 동일한 사용한계에서 이자율이 높을수록 최적시점은 늦어지고 그에 따라 기대총비용율도 낮아졌다. 또한 상대적으로 GP가 WP보다 더 보수적으로 최적시점을 예측하였다. 마지막으로 동일한 조건에서 구조물의 중요도가 높을수록 더 자주 예방적 보수보강을 실시하여야 한다는 것을 알았다.

Keywords

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