Modelling and optimizing imperfect maintenance of coatings on steel structures

Steel structures such as bridges, tanks and pylons are exposed to outdoor weathering conditions. In order to prevent them from corrosion they are protected by an organic coating system. Unfortunately, the coating system itself is also subject to deterioration. Imperfect maintenance actions such as spot repair and repainting can be done to extend the lifetime of the coating. This paper considers the problem of finding the set of actions that minimizes the expected (discounted) maintenance costs over both a finite horizon and an infinite horizon. To this end the size of the area affected by corrosion is modelled by a non-stationary gamma process. An imperfect maintenance action is to be done as soon as a fixed threshold is exceeded. The direct effect of such an action on the condition of the coating is assumed to be random. On the other hand, due to maintenance the parameters of the gamma deterioration process may also change. It is shown that the optimal maintenance decisions related to this problem are a solution of a continuous-time renewal-type dynamic programming equation. To solve this equation time is discretized and it is verified theoretically that this discretization induces only a small error. Finally, the model is illustrated with numerical examples.