Optimized Placement of Distributed Optic Fiber Sensors for Structural Health Monitoring via the Modified Constitutive Relation Error

  • Pérez Orozco, José Andrés (LMPS, Safran Tech)
  • Chamoin, Ludovic (LMPS)
  • Cortial, Julien (Safran Tech)
  • De-Buhan, Maya (Safran Tech)
  • Soulier, Bruno (LMPS)

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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 this framework is broadly applicable, our study focuses on distributed optical fiber sensors (DOFS) due to their high spatial resolution, lightweight nature, and ability to provide nearly continuous, one-dimensional strain data along the fiber path. We propose a novel hybrid optimization approach in which, during the global search, fiber paths are modeled using B-Splines to reduce the number of optimization variables. Promising configurations identified via evolutionary algorithms (such as Differential Evolution or Genetic Algorithms) are then refined locally through the Hadamard shape derivative of the FIM/mFIM determinant, allowing for precise geometry adjustment. The effectiveness of the methodology is demonstrated on isotropic and orthotropic elastic structures in two and three dimensions, yielding improved convergence and accuracy compared to traditional FIM-based sensor placement techniques.