# Breaking the Cross-Sensitivity Degeneracy in FBG Sensors: A Physics-Informed Co-Design Framework for Robust Discrimination

## TL;DR

This paper introduces a new framework to improve the accuracy of Fiber Bragg Grating sensors by combining sensor design and machine learning.

## Contribution

The paper introduces a physics-informed co-design framework that combines sensor architecture and machine learning to overcome cross-sensitivity issues.

## Key findings

- A standard Quadratically Chirped FBG fails to distinguish measurements due to high feature space collapse (Kcond>4600).
- Two robust co-designs are validated: an Amplitude-Modulated Superstructure FBG with ANN and a Polarization-Diverse Inverse-Gaussian FBG with a 4 × 4 K-matrix.

## Abstract

The simultaneous measurement of strain and temperature using Fiber Bragg Grating (FBG) sensors presents a significant challenge due to the intrinsic cross-sensitivity of the Bragg wavelength. While recent studies have increasingly employed “black-box” machine learning algorithms to address this ambiguity, such approaches often overlook the physical limitations of the sensor’s spectral response. This paper challenges the assumption that advanced algorithms alone can compensate for data that is physically ambiguous. We propose a “Sensor-Algorithm Co-Design” methodology, demonstrating that robust discrimination is achievable only when the sensor architecture exhibits a unique, orthogonal physical signature. Using a rigorous Transfer Matrix Method (TMM) and 4 × 4 polarization analysis, we evaluate three distinct architectures. Quantitative analysis reveals that a standard Quadratically Chirped FBG (QC-FBG) functions as an “ill-conditioned baseline” failing to distinguish measurands due to feature space collapse (Kcond>4600). Conversely, we validate two robust co-designs: (1) An Amplitude-Modulated Superstructure FBG (S-FBG) paired with an Artificial Neural Network (ANN), utilizing thermally induced duty-cycle variations to achieve high accuracy (~3.4 °C error) under noise; and (2) A Polarization-Diverse Inverse-Gaussian FBG (IG-FBG) paired with a 4 × 4 K-matrix, exploiting strain-induced birefringence (Kcond≈64). Furthermore, we address the data scarcity issue in AI-driven sensing by introducing a Physics-Informed Neural Network (PINN) strategy. By embedding TMM physics directly into the loss function, the PINN improves data efficiency by 2.2× compared to standard models, effectively bridging the gap between physical modeling and data-driven inference, addressing the critical data scarcity bottleneck identified in recent optical sensing roadmaps.