Reflection Intensity Spectra Research Articles

Non-uniform strain field reconstruction of FBG using an adaptive Nelder–Mead algorithm

This paper presents an adaptive Nelder–Mead algorithm to inversely reconstruct the non-uniform strain field from the reflected intensity spectrum of the fiber grating sensor. In this algorithm, the standard operating parameters are modified to adapt to the variable strain profiles, and an improved transfer matrix method is adopted to rapidly calculate the reflected intensity spectrum with a high precision. Thus, the performance of high-dimensional optimization involved in the reconstruction of complex strain distributions is significantly improved. Several numerical examples firstly demonstrate the advantages of the proposed algorithm compared with the standard Nelder–Mead algorithm. Then, experimental investigations are conducted on aluminum alloy plates with central circular hole under tensile and bending loading. A penalty function is added to the objective function to meet the constraints of the optimization variables under experimental conditions. The experimental results are compared with the finite element analysis results, which verifies the effectiveness and accuracy of the proposed algorithm. Finally, we provide some insights about the strain distribution and the resulting spectral distortion. Based on the measured spectrum, a spectral feature parameter (slope of the deflection–intensity ratio) is proposed as an indicator to reveal the size of the hole.

Investigation on Characteristic Variation of the FBG Spectrum with Crack Propagation in Aluminum Plate Structures.

In order to monitor the crack tip propagation of aluminum alloy, this study investigates the variation of the spectrum characteristics of a fiber Bragg grating (FBG), combined with an analysis of the spectrum simulation. The results identify the location of the subordinate peak as significantly associated with the strain distribution along the grating, corresponding to the different plastic zones ahead of the crack tip with various crack lengths. FBG sensors could observe monotonic and cyclic plastic zones ahead of the crack tip, with the quadratic strain distribution along the grating at the crack tip-FBG distance of 1.2 and 0.7 mm, respectively. FBG sensors could examine the process zones ahead of the crack tip with the cubic strain distribution along the grating at the crack tip-FBG distance of 0.5 mm. The spectrum oscillation occurs as the crack approaches the FBG where the highly heterogeneous strain is distributed. Another idea is to use a finite element method (FEM), together with a T-matrix method, to analyze the reflection intensity spectra of FBG sensors for various crack sizes. The described crack propagation detection system may apply in structural health monitoring.

Probabilistic Model Updating for Sizing of Hole-Edge Crack Using Fiber Bragg Grating Sensors and the High-Order Extended Finite Element Method.

This paper presents a novel framework for probabilistic crack size quantification using fiber Bragg grating (FBG) sensors. The key idea is to use a high-order extended finite element method (XFEM) together with a transfer (T)-matrix method to analyze the reflection intensity spectra of FBG sensors, for various crack sizes. Compared with the standard FEM, the XFEM offers two superior capabilities: (i) a more accurate representation of fields in the vicinity of the crack tip singularity and (ii) alleviation of the need for costly re-meshing as the crack size changes. Apart from the classical four-term asymptotic enrichment functions in XFEM, we also propose to incorporate higher-order functions, aiming to further improve the accuracy of strain fields upon which the reflection intensity spectra are based. The wavelength of the reflection intensity spectra is extracted as a damage sensitive quantity, and a baseline model with five parameters is established to quantify its correlation with the crack size. In order to test the feasibility of the predictive model, we design FBG sensor-based experiments to detect fatigue crack growth in structures. Furthermore, a Bayesian method is proposed to update the parameters of the baseline model using only a few available experimental data points (wavelength versus crack size) measured by one of the FBG sensors and an optical microscope, respectively. Given the remaining data points of wavelengths, even measured by FBG sensors at different positions, the updated model is shown to give crack size predictions that match well with the experimental observations.

Polarization interferometry for real-time spectroscopic plasmonic sensing.

We present quantitative, spectroscopic polarization interferometry phase measurements on plasmonic surfaces for sensing applications. By adding a liquid crystal variable wave plate in our beam path, we are able to measure phase shifts due to small refractive index changes on the sensor surface. By scanning in a quick sequence, our technique is extended to demonstrate real-time measurements. While this optical technique is applicable to different sensor geometries-e.g., nanoparticles, nanogratings, or nanoapertures-the plasmonic sensors we use here consist of an ultrasmooth gold layer with buried linear gratings. Using these devices and our phase measurement technique, we calculate a figure of merit that shows improvement over measuring only surface plasmon resonance shifts from a reflected intensity spectrum. To demonstrate the general-purpose versatility of our phase-resolved measurements, we also show numerical simulations with another common device architecture: periodic plasmonic slits. Since our technique inherently measures both the intensity and phase of the reflected or transmitted light simultaneously, quantitative sensor device characterization is possible.

Reconstruction of structural damage based on reflection intensity spectra of fiber Bragg gratings

We present an approach for structural damage reconstruction based on the reflection intensity spectra of fiber Bragg gratings (FBGs). Our approach incorporates the finite element method, transfer matrix (T-matrix), and genetic algorithm to solve the inverse photo-elastic problem of damage reconstruction, i.e. to identify the location, size, and shape of a defect. By introducing a parameterized characterization of the damage information, the inverse photo-elastic problem is reduced to an optimization problem, and a relevant computational scheme was developed. The scheme iteratively searches for the solution to the corresponding direct photo-elastic problem until the simulated and measured (or target) reflection intensity spectra of the FBGs near the defect coincide within a prescribed error. Proof-of-concept validations of our approach were performed numerically and experimentally using both holed and cracked plate samples as typical cases of plane-stress problems. The damage identifiability was simulated by changing the deployment of the FBG sensors, including the total number of sensors and their distance to the defect. Both the numerical and experimental results demonstrate that our approach is effective and promising. It provides us with a photo-elastic method for developing a remote, automatic damage-imaging technique that substantially improves damage identification for structural health monitoring.

Analytical coherency matrix treatment of shear strained fiber Bragg gratings

Reconstruction of the strain tensor at the position of an embedded fiber Bragg grating sensor has been the goal of recent research. However, ambiguities in the measurand--the polarization resolved reflected intensity spectrum--upon occurrence of shear strain hinder its achievement due to lack of an invertible model. In this work, we derive such a model using coherency matrix properties of unpolarized light. We deduce simplified sensor parameters for the ambiguous shear strain loading case, which possibly lead to a practical inversion of the problem.

Strain profile reconstruction of fiber Bragg grating with gradient using chaos genetic algorithm and modified transfer matrix formulation

In this paper, a new heuristic approach based on chaos genetic algorithm and modified transfer matrix method is presented to demodulate the fiber Bragg grating strain sensors. To facilitate accurate calculation of the grating reflected intensity spectrum, the modified transfer matrix approach is applied. The motivation for using the spline smooth function scheme is to provide nice approximation of strain profiles from a scattered data set and overcome the difficulty of calculating the strain gradients in local period function of the modified T-matrix formulation for the piecewise constant strain field assumption. The chaos genetic algorithm is developed to improve the performance of GA and optimize the data of control nodes of the spline smooth function, and more valuably, the reconstructed strain profile is continuous with discretionary spatial resolution. The proposed method is verified through numerical example reconstructions of Bragg grating sensor simulated strain profile cases.

Reconstruction of phase-shifted fiber Bragg grating parameters using genetic algorithm over thermally-modulated reflection intensity spectra

This paper presents a numerical method for the inverse extraction of the multiple physical parameters of phase-shifted fiber Bragg gratings (FBGs). In the proposed approach, the reflection intensity spectra produced by two known temperature distributions are taken as objective functions and a genetic algorithm is then employed to perform an iterative search for the corresponding parameters of the phase-shifted FBG, including the grating period, the grating position, the grating length, the refractive-index modulation depth, the apodize factor, and the phase-shift position. The numerical results confirm that the proposed method successfully synthesizes the parameters of phase-shifted FBGs with various structures with a high degree of accuracy. Furthermore, the method has the advantages of simplicity, low cost and a nondestructive nature. Accordingly, the method is suitable for widespread application in the fiber communications and fiber laser components fields.

OS18-1-4 Arbitrary strain distribution sensing using two FBGs and a genetic algorithm with considering the attenuation factors

We propose and verify a simple, convenient, and low cost method to inversely measure arbitrary strain distributions by applying a genetic algorithm approach to analyze the reflection intensity spectra of two fiber Bragg gratings (FBGs). The proposed method involves bonding one uniform FBG and one chirped FBG to the same location of the structure of interest such that they both encounter the same strain field. The arbitrary strain distribution within the fiber gratings is then determined inversely from the two Bragg intensity spectra by means of a genetic algorithm population-based optimization process. Also, we include the reflection power attenuation factors into the genetic algorithm and make this approach more useful in practical. Several strain distributions along the fiber Bragg gratings are reconstructed numerically. The proposed measurement method is suitable for many smart structure-monitoring applications.

Simultaneous strain and temperature distribution sensing using two fiber Bragg grating pairs and a genetic algorithm

This study uses two pairs of FBGs to perform simultaneous strain and temperature field measurements. The first pair of FBGs, comprising one uniform FBG and one chirped FBG, measures the strain and temperature fields, while the second pair of FBGs, also comprising one uniform FBG and one chirped FBG, measures the temperature field only. A genetic algorithm is applied to reconstruct the arbitrary strain and temperature distribution profiles simultaneously from the measured reflection intensity spectra of the four FBGs. Various examples of nonmonotonic variations in the strain and temperature fields are considered for illustration purposes. It is found that the proposed scheme successfully reconstructs the applied strain and temperature fields.

Reconstruction of chirped fiber Bragg grating parameters and phase spectrum using two thermally modulated intensity spectra and a genetic algorithm

This study presents a synthesis method for reconstructing the multiple parameters such as grating position, length, period profile, refractive index modulation, and phase response of a chirped fiber Bragg grating (FBG) and its phase spectrum using two thermally modulated reflection intensity spectra and a genetic algorithm. In the proposed approach, the FBG parameters are determined using the genetic algorithm and are then used to reconstruct the phase response. The advantages of the proposed method include its simplicity, low cost, and nondestructive nature. Furthermore, the proposed method does not require a prior knowledge of the sign of the chirp of the grating period distribution of FBGs.

The synthesis of multiple parameters of arbitrary FBGs via a genetic algorithm and two thermally modulated intensity spectra

This paper describes the use of a genetic algorithm and two thermally modulated fiber Bragg grating (FBG) reflection intensity spectra to perform the inverse extraction of multiple physical parameters of arbitrary FBGs, including the grating period, grating position, grating length, chirped direction, and refractive-index modulation. The developed numerical approach is applied to synthesize the parameters of uniform and chirped FBGs. The experimental results confirm the ability of the proposed method to recover the grating period, grating length, grating position, refractive-index modulation depth, and apodize factor of a 10-mm-length uniform FBG. The proposed method is suitable for fiber communication applications and smart structure-monitoring systems.

Genetic algorithm for the reconstruction of Bragg grating sensor strain profiles

This paper presents a genetic algorithm for the interrogation of optical fibre Bragg grating strain sensors. The method encodes the axial strain distribution along the Bragg grating, here represented through the local period distribution, into a gene. To facilitate rapid calculation of the grating reflected intensity spectrum, the transfer-matrix approach is applied. The genetic algorithm inversion method presented requires only intensity information from the sensor and reconstructs non-linear and discontinuous distributions well, including regions with significant gradients. The development of this algorithm will permit the use of Bragg grating sensors for structural damage identification, allowing them to be located in regions where strong strain non-uniformities occur.

Arbitrary strain distribution measurement using a genetic algorithm approach and two fiber Bragg grating intensity spectra

This paper proposes and verifies a simple, convenient, and low cost method to inversely measure arbitrary strain distributions by applying a genetic algorithm approach to analyze the reflection intensity spectra of two fiber Bragg gratings (FBGs). The proposed method involves bonding one uniform FBG and one chirped FBG to the same location of the structure of interest such that they both encounter the same strain field. The arbitrary strain distribution within the fiber gratings is then determined inversely from the two Bragg intensity spectra by means of a genetic algorithm population-based optimization process. The proposed measurement method is suitable for many smart structure-monitoring applications.

Linear spatial temperature distribution fibre Bragg grating sensor

A study is presented of the application of commercially available FBGs (fibre Bragg gratings) to measure temperature gradients. The optical measurement system is based on an electronically tuned solid-state laser, S-TLD. FBG sensor calibration is carried out using a dual Peltier water-cooled system, with which linear temperature gradients are applied to the FBG, resulting in chirping along the grating. Spectral parameters are extracted from reflection intensity spectra using LabView software. A 'look-up table' approach is then used as a means of solving the inverse problem. Quantified worst-case errors associated with each estimated temperature value are presented, and in this way the accuracy of the temperature measurements are discussed. Based on our experimental results a novel proposal to use pre-chirped FBGs to optimize temperature gradient sensing is made.