Optimal placement of distributed optic fiber sensors with the modified Constitutive Relation Error

This paper presents a novel Optimal Sensor Placement strategy tailored to model updating problems based on the modified Constitutive Relation Error (mCRE) functional. It offers a credible alternative to classical functionals by optimizing structural parameters alongside mechanical fields, achieving the best trade-off between available measured data and physical knowledge without any additional a priori assumption. The proposed approach leverages the strong connection between mCRE and Bayesian inference to develop a new Fisher Information Matrix based on mCRE, incorporating the sensitivity of the mCRE mechanical fields to updated parameters. The mCRE-based optimization strategy leads to increased robustness with respect to measurement noise, deviation in the sensor placement, and modeling bias. While many of the developments in this work apply to various sensor types, additional constraints are included to focus on distributed optic fiber sensors (DOFS). The shape of the fiber is represented using B-Splines, making the control point coordinates the design variables. Constraints on maximum fiber length and minimum curvature radius are treated as penalty terms in the fitness function, optimized using a genetic algorithm. The proposed methodology is validated on isotropic and orthotropic elasticity using 2D and 3D geometries.