Planning maintenance over a finite time horizon is valuable in the maintenance strategy design phase, and this plan can be used to allocate resources, make investment decisions and identify most cost-effectively maintenance choices. This section aims to utilise the developed models and extend them to evaluate the effectiveness of different maintenance plans. We
present a simplified maintenance plan and show how to use it to analyse the life-cycle cost of the maintenance as an example.
Since inspection and maintenance activities for bridges are performed periodically with time intervals as discussed in Section 2.2.1, to perform life cycle cost analysis over a finite time horizon on bridges, we can discretise the time horizon into several cycles, where each cycle models an intervention process. For simplicity, this section illustrates this idea using a fixed interval of every two years over a hundred-year lifetime. However, notes that it is possible to implement with a dynamic intervention schedule by integrating with an optimisation technique.
In each cycle, we model the repair decision-making process together with its deterioration prediction up till to its next intervention cycle. Intervention model from Section 6.3.2 is employed to infer the effectiveness of maintenance. The choice of repair option is a decision node that relies on the anticipated conditions post-repair. Since we cannot directly observe the future condition of a structure as we showed in Figure 6.6, instead, we predict its future condition by learning their deterioration. By repeatedly linking the posterior of each cycle’s model as the prior of the next cycle’s model using the model from Section 4.5, the maintenance whole life cycle is modelled.
We continue using the deck repair example from in the section. In general, a deck bottom surface deteriorates slower than its top surface. Among the available repair actions, deck replacement is the only action in Table 6.2 that can improve the condition of the deck bottom surface, but it is also the most expensive action according to Table 6.3. Hence, in the example maintenance plan, deck replacement is assumed to be the last resort of maintenance. Instructed by Michigan Department of Transportation [116], its trigger is when both deck top and bottom surface are deficient with a rating of less or equal to 3 and a rating of 2 or 3, respectively. Similarly, the use of other repair actions requires both top and bottom surface are within the range of deck condition listed in Table 6.2. Notes that when deck top surface is rated less or equal to 3, HMA Cap repair action shares the same trigger conditions. As instructed from Michigan Department of Transportation [116], since HMA Cap is a temporary repair with low expected service life, a replacement is often scheduled in the next five years after an HMA Cap is performed.
Within an asset’s whole life cycle, a structure may be maintained by multiple actions. A maintenance strategy is used to decide what action to take at what time. Here we use a simple strategy as an example to show how we can evaluate the cost of different maintenance actions over its lifetime. In this maintenance strategy, if the deck conditions fall into the trigger condition of the repair options, a repair action from Table 6.2 will be performed; otherwise,
Figure 6.8 Deck top and bottom surface conditions with repairs in a 100 years horizon.
if the deck conditions satisfy the trigger condition of replacement, deck replacement will be performed; otherwise, no action will be taken.
In each cycle, depending on the number of required transitions, the model contains observations ranging from 100 to more than 1000 with a computational time from seconds to overnight. After the inference on the repaired condition, we can further predict its condition up to its next intervention. To model multiple intervention cycles sequentially, we can link the predicted condition in this intervention cycle as the input of the following intervention cycle. This can be modelled by multiple sequentially arranged BN objects from Section 4.5, where the predicted state at intervention i becomes the prior of previous state variable at intervention i+ 1, and used to reason the repaired condition as well as to predict its further deterioration as shown in Figure 6.7. Unlike the model in Figure 6.6, where the previous structure state is observed as hard evidence (e.g. 100% at S6). In each object, the previous state is a future event that cannot be observed directly but only predicted probabilistically as soft evidence (e.g. 80% at S6 and 20% at S5). This problem is resolved by the employment of multiple binary factorisations discussed in Section 4.5, where each state’s further deterioration is modelled as a Markov model. The cost of all actions is recorded using a cumulative cost function and sequentially becomes the prior of the previous repair cost node for the next intervention.
Figure 6.8 shows an example of condition changes of the deck top and the bottom surface (with an initial state of S7 and S6 respectively) in the next 100-year horizon. The maintenance strategy comprised of maintenance action HMA Cap and deck replacement. If the state of deck top surface deteriorates to a state of 4 or 5 and the bottom surface is in a state of 2 or
3, or the deck top surface deteriorates to a state less or equal to 3, and the bottom surface is in a state of 2 or 3, HMA Cap is triggered. Since HMA Cap is a temporal repair action with a short expected service life of 1 to 3 years, as the footnote in Table 6.2 suggested, the deck is scheduled for replacement in the next five years. For example, in 14 years, the top surface is predicted with a state of 3 the same as the bottom surface. Therefore, an HMA Cap is performed that restores the condition of the top surface to 8 while the bottom surface remains the same. After five years, the deck is replaced with both top and bottom surface back to state 9. In the next 100 years, implementing this maintenance strategy requires three HMA Cap actions and three replacements. Together with the cost presented in Table 6.3, in this example, for a 57.7 f t length and 31.8 f t width deck, we estimated it has an overall repair cost of $ 392,201.33.
Figure 6.9 Repair cost with different maintenance strategy in the next 100 years.
Different maintenance action-based strategies are evaluated, and their cumulative costs are presented in Figure 6.9. Epoxy Overlay and patching are the two most costly strategies since they prefer to repair the deck top surface while they are still in fair conditions. Other strategies share similar costs; among them, HMA Overlay with waterproofing membrane strategy has the lowest cost. Though deck replacement strategy (only repair with replacement) has a lower cost than some strategies, the deck stays in poor condition most of the time. In some cases, keeping structures staying in better conditions throughout its lifetime, even in the cost of a higher expenditure, is still desired due to safety and reliability reasons.
The repair decisions in this example are simplified, only a limited type of actions are considered in each strategy, and the repairs are triggered by the asset conditions only. However, usually, there are more constraints in deciding repair decisions, such as repair action availability, cost and reliability - this form a multi-criteria decision problem. Our model gives a framework to integrate deterioration prediction with repair decisions. Together with an optimisation technique, by providing a set of constraints, we can make optimal decisions for maintenance. For example, along with the model shown in Figure 6.7, we can use a Genetic Algorithm (GA) to generate a maintenance strategy that takes both asset deterioration and maintenance effectiveness into consideration. We can therefore optimally select different repair actions to restore an asset condition to a suitable condition at an appropriate time with an objective of minimum cost and high level of reliability. The strategy can be implemented in the decision node Repair Options in Figure 6.7, and further used to estimate its life cycle cost for maintenance planning.