Iterative matrix algorithm for high precision temperature and force decoupling in multi-parameter FBG sensing

Abstract

A new iterative matrix algorithm has been applied to improve the precision of temperature and force decoupling in multi-parameter FBG sensing. For the first time, this evaluation technique allows the integration of nonlinearities in the sensor's temperature characteristic and the temperature dependence of the sensor's force sensitivity. Applied to a sensor cable consisting of two FBGs in fibers with 80 µm and 125 µm cladding diameter installed in a 7 m-long coiled PEEK capillary, this technique significantly reduced the uncertainties in friction-compensated temperature measurements. In the presence of high friction-induced forces of up to 1.6 N the uncertainties in temperature evaluation were reduced from several degrees Celsius if using a standard linear matrix approach to less than 0.5°C if using the iterative matrix approach in an extended temperature range between -35°C and 125°C.

Strain-Independent Temperature Measurements with Surface-Glued Polarization-Maintaining Fiber Bragg Grating Sensor Elements

“…Assuming a linear change in the Bragg wavelength with temperature is only valid in a small temperature range. In the extended temperature range between −40 °C and 150 °C, the change in Bragg wavelength is commonly expressed with a 3rd order polynomial function [22,25]. Using this approach, the mean wavelength can be written asΔλfalse¯i=aT,iΔT+aT2,iΔT2+aT3,iΔT3=(aT,i+aT2,iΔT+aT3,iΔT2)true︸Kfalse¯T,iglfalse(ΔTfalse)ΔT.…”

“…This would lead to systematic errors in temperature sensing if this nonlinearity was neglected in a large temperature range. The nonlinear sensor characteristic may be taken into account by replacing the constant matrix elements in the sensitivity matrix with temperature-dependent sensitivity constants Kfalse¯T,iglfalse(ΔTfalse) and using the iterative calculation method introduced in [22]. Starting with the sensitivity values for a reference temperature T0, the temperature values of the previous iteration step ΔTk−1 and the corresponding sensitivity values Kfalse¯T,iglfalse(ΔTfalse)k−1 are used to calculate new temperature values ΔTk according to(ΔTkε3k)=1Dfalse(ΔTfalse)k−1(Kfalse¯ε3,s−Kfalse¯ε3,f−Kfalse¯T,sglfalse(Δ…”

“…Here, ε3sim=ε3mech+ε3th describes the simulated strain in the x3-direction at the center of the fiber’s cross section, to which both the thermal strain ε3th and the external strain ε3mech contribute. ξ=6.36·10−6°C−1 is the thermo-optical coefficient of the fiber [22] and Δneff,i,jsimfalse(ΔT,ε3false)=neff,i,jsimfalse(ΔT,ε3false)−neff,0sim (with i∈{s,f} and j∈{90°,0°}) is the simulated change in the effective refractive index, given as the difference of the effective refractive index after temperature changes and the initial refractive index neff,…”

“…Nonlinearities in the temperature characteristics of FBGs are commonly known, and have also to be integrated in the evaluation process by introducing temperature-dependent matrix elements in the sensitivity matrix. The determination of strain and temperature is performed iteratively with the method presented in [22]. For the first time, to our knowledge, the here-presented technique enables temperature measurements with surface-glued FBGs independently of external longitudinal strains.…”

A Novel Recurrent Neural Network-Based Ultra-Fast, Robust, and Scalable Solver for Inverting a “Time-Varying Matrix”

“…In some cases, the accuracy of certain measurements can be significantly improved by involving matrix inversion. For example, a real-time matrix inversion is used to ensure high-precision in multi parameter sensing while using the so-called fiber Bragg grating (FBG)-based sensors [18]. Thereby, in that related approach, the sensor functionality is approximated with a linear system and the problem is thus solved through linear system of equations.…”