Calculation of the Mean Strain of Smooth Non-uniform Strain Fields Using Conventional FBG Sensors

TL;DR

This paper introduces a new algorithm for accurately estimating the mean strain in smooth non-uniform strain fields using FBG sensors, addressing errors caused by non-uniform stress distributions.

Contribution

It proposes an approximated transfer matrix model and a maximum likelihood estimator to improve strain measurement accuracy in non-uniform fields.

Findings

The method reduces strain estimation errors from tens of microstrains to around 60 microstrains.

Validation with simulations and experiments confirms improved accuracy over existing methods.

The approach effectively compensates for non-uniform strain effects in FBG sensor measurements.

Abstract

In the past few decades, fibre Bragg grating (FBG) sensors have gained a lot of attention in the field of distributed point strain measurement. One of the most interesting properties of these sensors is the presumed linear relationship between the strain and the peak wavelength shift of the FBG reflected spectra. However, subjecting sensors to a non-uniform stress field will in general result in a strain estimation error when using this linear relationship. In this paper we propose a new strain estimation algorithm that accurately estimates the mean strain value in the case of smooth non-uniform strain distributions. To do so, we first introduce an approximation of the classical transfer matrix model, which we will refer to as the approximated transfer matrix model (ATMM). This model facilitates the analysis of FBG reflected spectra under arbitrary strain distributions, particularly by providing a closed-form approximation of the side-lobes of the reflected spectra. Based on this new formulation, we derive a maximum likelihood estimator of the mean strain value. The algorithm is validated using both computer simulations and experimental FBG measurements. Compared to state-of-the-art methods, which typically introduce errors of tens of microstrains, the proposed method is able to compensate for this error. In the typical examples that were analysed in this study, mean strain errors of around 60 microstrains were compensated.