Bayesian Optimal Sensor Placement for Damage Detection in Frequency-Domain Dynamics

Abstract

Identification and monitoring of structural damage have a growing importance in the maintenance of aging structures. Specifically, an optimal sensor configuration capable of fully identifying structural damage is desired. One innovative approach is casting the optimal sensor placement problem as a decision-centric, utility-maximization framework. By choosing mutual information (or relative entropy) as the utility criteria, sensor placements are chosen to maximize information about structural damage parameters. To accelerate this optimal experimental design (OED) problem, we propose the parameterization of damage using binary variables and the corresponding integration of the Bernoulli prior into this Bayesian OED framework. By limiting the damage parameter design space, we can direct the computational effort toward optimizing over informative and practical structural damage scenarios. Additionally, we convert the OED problem into a convex optimization problem, ensuring that sensor placement solutions contain the maximum information. We evaluate our proposed modified OED framework using a deterministic damage estimator also informed by the Bernoulli prior. We quantify the performance of sensor placements using a mean-squared error (MSE) metric, and we show that optimally selected sensors outperform randomly selected sensors, in general. We also provide a potential heuristic in selecting a sensor budget through the consideration of utility. In this work, we present a theoretical framework that identifies a set of optimal locations for sensor placement for damage detection in large structures. Given a sufficiently defined finite element model of a structure, this framework can identify a set of optimal sensor placements. Then, physically placing any sensor that can measure field data (e.g., displacements or accelerations) at these positions will yield experimental data that is most informative about potential damage scenarios at key components. Sensors can include and are not limited to accelerometers, strain gauges, fiber optic sensors, and laser vibrometers, among others. Ideally, sensors should minimally interfere with the structure’s dynamics. Furthermore, any measurement data should be processed to displacements in the frequency domain to seamlessly fit in the theoretical framework with minimal modifications. We expect practitioners to use the framework to numerically model and design experimental sensor configurations before physically placing any sensors on a structure to minimize any experimental burden.