Optimal Placement of Distributed Optic Fiber Sensors for Online Structural Health Monitoring with the Modified Constitutive Relation Error
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Structural Health Monitoring (SHM) evaluates a structure's health using data from on-board sensors, with sensor placement being a key factor. This paper presents a novel Optimal Sensor Placement strategy tailored to model updating problems based on the modified Constitutive Relation Error (mCRE) functional. Unlike classical functionals, the mCRE searches for structural parameters alongside mechanical fields, leveraging both measured data and physical knowledge without any further a priori assumptions. The approach also integrates mCRE with Bayesian inference to develop a new Fisher Information Matrix (FIM), incorporating the sensitivity of mCRE mechanical fields with respect to updated parameters. While many of the developments made in this work are applicable for different types of sensors, this study focuses on distributed optic fiber sensors due to their spatial accuracy, lightweight, and ability to provide near 1D full-field data in the longitudinal direction of the fiber. The fiber shape is modeled using B-Splines, with design variables being control point coordinates. Constraints like maximum fiber length and minimum curvature radius are handled as penalty terms in the cost function to be optimized using a genetic algorithm. The proposed methodology is then validated for isotropic/orthotropic elasticity using 2D/3D geometries, showing superior performance over the traditional FIM.
