An important question in the context of infrastructure management pertains to the Value of Information (VoI) of noisy data and uncertain measurements. Quantification of this value can, for instance, help us assess the impact of a structural health monitoring system over the life-cycle of a structure, or the amount of resources a decision-maker should be willing to spend in order to acquire information prior to a structural intervention.
Accordingly, we can define VoI as a life-cycle or a step-wise metric. It can be shown that POMDPs inherently leverage the step-wise VoI to guide optimal decisions for scheduling of observational actions (e.g. inspection visits) at every decision step. Based on this result and the POMDP optimality properties, it can be also shown that the life-cycle VoI is always non-negative under a POMDP policy. This means that better and/or additional information or data can only improve the efficacy of the decision-maker's choices in the long-run, thus reducing the life-cycle cost of the implemented policy.
Notwithstanding the intuitive nature of non-negativity of VoI, it is worth noting that this is not guaranteed for any locally optimal or otherwise suboptimal policy. Such policies are well-studied in engineering systems decision-making, including, among others, decision assumptions following condition-based, risk-based, and periodic inspection and maintenance schemes with thresholds and interval parameters that are accordingly tuned.
Hence, "better" or "more" information does possibly hurt under a non-POMDP policy, something that tells us that decisions about a highly accurate inspection technique or an expensive permanent monitoring scheme should not be made in isolation of the decision optimization algorithm that will be finally used to prescribe structural interventions. Below is a figure showing the VoI and Value of Structural Health Monitoring (VoSHM) for a deteriorating 3 component system.
We can observe that VoI under the POMDP policy reaches a plateau at lower levels of observation accuracy, without becoming negative. A notable remark is that the optimal condition-based maintenance policy for this system (not shown in the figure) without observation noise would be more expensive than the same policy with a ~5% observation noise (for the observations being freely available in both cases), thus the respective VoI would for this policy be negative.
Policy realizations of a corroding reinforced concrete deck structure under the optimal policy based on inspection visits and the optimal policy based on permanent monitoring information are examined below. Observations from sensor-based inspections and permanent SHM are assumed to be based on the same electrochemical sensors (for the permanent case placed inside the concrete), thus following the same emission model.
For the above structural system, the value of SHM is found to be 8.5% of the life-cycle cost of the policy under optional inspection visits. This amount reflects the estimated upper bound the decision-maker should be willing to pay for the acquirement, installation, and operation of the SHM system.
Andriotis, C.P., Papakonstantinou, K.G., and Chatzi, E.N., “Value of structural health information in partially observable stochastic environments”, Structural Safety (under review), arXiv preprint arXiv:1912.12534, 2020. [Link]
Papakonstantinou K.G., Andriotis C.P., and Shinozuka M., “POMDP and MOMDP solutions for structural life-cycle cost minimization under partial and mixed observability”, Structure and Infrastructure Engineering, 14 (7), 869-882, 2018. [Link]
Papakonstantinou, K.G., Andriotis, C.P., Gao, H., and Chatzi, E.N., “Quantifying the value of information of structural health monitoring for decision making”, 13th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP), Seoul, South Korea, 2019. [Link]
Papakonstantinou, K.G., Andriotis C.P., and Shinozuka M., “POMDP solutions for monitored structures”, Proceedings of IFIP WG-7.5 Conference on Reliability and Optimization of Structural Systems, Pittsburgh, PA, 2016. [Link]
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