An Optimal Sensor Network Design Framework for Structural Health Monitoring Using Value of Information

A structural health monitoring (SHM) system is essentially an information-gathering mechanism. The information accumulated via an SHM system is crucial in making appropriate maintenance decisions over the life cycle of the structure. An SHM system is feasible if it leads to a greater expected reward (by making data and risk-informed decisions) than the intrinsic cost (or investment risk) of the information-acquiring mechanism incurred over the lifespan of the structure. In short, the value of information acquired through a feasible SHM system manifest into net positive expected cost savings over the life cycle of the structure. Traditionally, the cost-benefit analysis of an SHM system is carried out through pre-posterior decision analysis that helps one evaluate the benefit of an information-gathering mechanism using the expected value of information (EVoI) metric. EVoI is a differential measure and can be mathematically expressed as a difference between the expected reward and investment risk. Therefore, by definition, EVoI fails to capture the compounded savings over the life cycle of the structure (since it quantifies absolute savings). Unlike EVoI, we quantify the economic advantage of installing an SHM system for inference of the structural state by using a normalized expected-reward (benefit of using an SHM system) to investment-risk (cost of SHM over the life cycle) ratio metric (also called a risk-adjusted reward in short) as the objective function to quantify the value of information (VOI). We consider monitoring of a miter gate as the demonstration example and focus on the inference of an unknown and uncertain state parameter(s) (i.e., damage from loss of contact between gate and wall, the "gap") from the acquired sensor data. This paper proposes a sensor optimization framework that maximizes the net expected compounded savings achieved as a result of making SHM system-acquired data-informed life cycle management decisions. We also inspect the impact of various risk intensities of decision-makers on the optimal sensor design.