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

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.

The attached matlab code is an implementation of the proposed methods, and provides a comparison to other existing methods.

Related publications

1. Calculation of the Mean Strain of Non-uniform Strain Fields Using Conventional FBG Sensors
   Aydin Rajabzadeh; Richard Heusdens; Richard C. Hendriks; Roger M. Groves;
   Journal of Lightwave Technology,
   Volume 36, Issue 17, pp. 3716-3725, September 2018.
   document

2. Analysis of FBG reflection spectra under anti-symmetrical strain distributions using the approximated transfer matrix model
   A. Rajabzadeh; R.C. Hendriks; R. Heusdens; R.M. Groves;
   In Proc. SPIE 10680, Optical Sensing and Detection V,
   May 2018. DOI: 10.1117/12.2306381
   document