# VoI-Based Optimization of Structural Assessment for Spatially Degrading RC Structures
###### Abstract
It requires the calculation of two expected values of the life-cycle cost, i.e., the prior and the posterior cost. To evaluate the posterior costs, the expected value of the life-cycle costs is evaluated by taking the average over all possible monitoring outcomes. In this analysis, for the different monitoring outcomes, posterior distributions of the model parameters and the corresponding updated probability of failure should be calculated. Calculating this posterior distribution is often based on sampling based methods, where many model evaluations are required. Applications of the VoI analysis can be found in several works. For example, in [5] the methodology is applied to steel structures and the VoI is calculated based on partially observable Markov decision processes. The influence of the time to damage, availability and inaccuracy of the data, reaction time, repair costs, and discount factor is investigated for application on a wind turbine structure under continuous damage monitoring. Also in [6], the VoI is explained in a clear way and its benefit of a rational way of making decisions is illustrated. In [7], transition probabilities between different damage states and probabilities of monitoring outcomes are assumed together with repair costs for application in a Bayesian network for the example of a wind farm. Also in [8], the VoI is determined for the application of structural health monitoring to a wind farm. Finally, in [9], assumptions are made on utilities and prior probabilities of bridge states. In general, all the referred works have contributed greatly to the introduction of the VoI as an objective tool in decision-making. However, it is not always clear how sensitive the computed VoI is to different choices for the relevant input parameters. The literature is especially lacking applications for the optimization of monitoring strategies in the case of reinforced concrete structures. Some publications can be found where the influence of some assumptions on the input variables is investigated. However, this is often very limited and applied to simplified conceptual models of structures. In [10], the effects of different system properties on the VoI are demonstrated. In addition, Reference [11] illustrates how the decision problem is influenced by the assumed probabilistic models, i.e., the type of probability distribution, the level of uncertainty, the choice of degradation law, the quantity and quality of information, and the probabilistic dependencies between components of systems. The influence of the measurement accuracy on the VoI is investigated in [12]. In [12], the challenges in the selection of suitable monitoring thresholds for action alternatives are also pointed out. This concerns both defining the threshold values for monitoring outcomes triggering an action and the choice among different actions. In [13], the influence of the threshold on the annual probability of component fatigue failure is investigated, and in [14], the influence of the inspection time and monitoring plan is studied, together with the influence of the number of monitoring years. In [15], the computational burden of the VoI is pointed out as one of the main challenges in real world applications. From this work and others, it can be concluded that computational cost is an important bottleneck in the calculation of the VoI since calculations over the whole service life of the bridge are required. In [16], the VoI analysis is applied to a reinforced concrete structure to determine the cost effectiveness of measuring the chloride content as an alternative to visual inspections. The work provides a valuable basis for the application of VoI analysis to reinforced concrete structures affected by chloride ingress.