Elsevier

Optics Communications

Volume 315, 15 March 2014, Pages 338-346
Optics Communications

Research on non-uniform strain profile reconstruction along fiber Bragg grating via genetic programming algorithm and interrelated experimental verification

https://doi.org/10.1016/j.optcom.2013.11.027Get rights and content

Abstract

A new heuristic strategy for the non-uniform strain profile reconstruction along Fiber Bragg Gratings is proposed in this paper, which is based on the modified transfer matrix and Genetic Programming(GP) algorithm. The present method uses Genetic Programming to determine the applied strain field as a function of position along the fiber length. The structures that undergo adaptation in genetic programming are hierarchical structures which are different from that of conventional genetic algorithm operating on strings. GP regress the strain profile function which matches the ‘measured’ spectrum best and makes space resolution of strain reconstruction arbitrarily high, or even infinite. This paper also presents an experimental verification of the reconstruction of non-homogeneous strain fields using GP. The results are compared with numerical calculations of finite element method. Both the simulation examples and experimental results demonstrate that Genetic Programming can effectively reconstruct continuous profile expression along the whole FBG, and greatly improves its computational efficiency and accuracy.

Introduction

Fiber Bragg grating(FBG) sensors are widely used in health monitor systems. The most commonly measuring method using FBG to get the strain data effectively is to obtain the wavelength shift information at maximum reflectivity, according to a good linear relationship between the wavelength shift and the strain applied to the axis of the FBG. But in practice, the method cannot identify the strain according to the shift of wavelength at maximum reflectivity when a significant strain gradient occurs in the FBG sensor area [1], [2], [3]. Thus, it has become a widespread concern [4], [5], [6], [7] to reconstruct the non-uniform strain distribution along the FBG sensor. However, these above-mentioned methods are based on the intensity and phase of reflection spectrum, and the phase information is also difficult to obtain and expensive in the actual application. The recent results show that heuristic intelligent algorithms perform high effectively in the process of solving this problem [8], [9], [10], [11], [12], [13], [14]. Gill and Peters [8] used the genetic algorithm to reconstruct the strain profile. In their works, the FBG was divided into several homogeneous segments and the strain distribution is assumed to be constant for each segment. Although the approach can improve the speed of reconstruction, but only the strain distribution can be obtained in the form of piecewise function. Shi [9] assumed the strain distribution as the quadratic polynomial function and used an improved simulated annealing algorithm to optimize the parameters of polynomial coefficients. Obviously, this method is more useful for linear, quadratic strain distribution, but it is useless for sine and other forms of higher order polynomial function with large strain gradient, especially for unknown strain distribution form. Zhang et al. [11] used the spline smooth function to approximate the strain profiles along the axis of FBG, and obtained the continuous strain distribution based on the chaos genetic algorithm. So far as is known to the authors, most of past works in the area of non-uniform strain distribution reconstruction have assumed that the strain distribution must be piecewise uniform [8], [10], [12], [13], [14], quadratic polynomial [9] or spline function [11] form. Such an approach is not suitable for sensors to be located in a structure where the form of the strain field is expected to change considerably or become discontinuous, and whose forms are not known a-priori. Another deficiency of the above-mentioned methods is the presence of preprocessing of inputs and postprocessing of strain outputs.

It is worth noting that most of the aforementioned works [8], [9], [10], [12], [13], [14] used the transfer-matrix (T-matrix) formulation to calculate the spectral response of the grating. This formulation regards the grating coupling coefficients as a piecewise constant function along the grating. However, in the presence of remarkable strain gradients, the T-matrix formulation does not closely match the direct solution of the coupled mode equations for a large number of grating segments. Thus, Prabhugoud and Kara proposed a modified T-matrix method in Ref. [15] and demonstrated that the simulated reflection spectrum including the strain gradient in the effective period function converged to the measured spectrum and the numerical solution of the coupled mode equations for non-constant strain fields. However, strain gradients in the local period function of the modified T-matrix formulation bring a new challenge to the reconstruction of strain profiles by piecewise approximation because the strain gradients cannot be precisely got only from the discrete strain data′s corresponding to several segments. As far as the authors are aware, very few works has been reported in the literature for the reconstruction of Bragg grating sensor strain profiles using the modified T-matrix formulation [11].

On the other hand, many seemingly different problems from fields as diverse as artificial intelligence, symbolic processing, and machine learning can be viewed as requiring discovery of a computer program that produces some desired output for particular inputs. The recently developed genetic programming paradigm provides a way to search the space of possible computer programs (i.e., structure) for an individual computer program that is highly fit in solving (or approximately solving) the problem at hand. The genetic programming paradigm continues the trend of dealing with the problem of representation in genetic algorithms by increasing the complexity of the structures undergoing adaptation. In particular, the structures undergoing adaptation in genetic programming are general, hierarchical computer programs of dynamically varying size and shape. Nevertheless, the conventional genetic algorithm cannot dynamically change the representation scheme during the course of solving the problem. Another important feature of genetic programming is the absence or relatively minor role of preprocessing of inputs and postprocessing of outputs. The inputs, intermediate results, and outputs are typically expressed directly in terms of the natural terminology of the problem domain. The computer programs produced by genetic programming consist of functions that are natural for the problem domain. However, the GP has never been used to reconstruct non-uniform strain distribution. Moreover, to the best knowledge of the authors, most of the present researches about non-uniform strain reconstruction via heuristic intelligent algorithms focus on numerical simulation [8], [9], [10], [11], [12], [13], [14]. Some results were reported about experimental verification of response of embedded optical fiber Bragg grating sensors in non-homogeneous strain fields [2], [3], [16], but very few experimental verification to solve the Bragg grating inverse problem from the reflection spectrum of a fiber Bragg grating (FBG) has been carried out [17]. Hence this, in this paper, a novel approach based on Genetic Programming algorithm which can optimize expressions of any functions by operating individuals expression tree is presented to regress the strain profile function of the FBG directly with no need of any a priori knowledge of strain profile is presented. One of the primary benefits of present method is that the continuous function expression of non-uniform strain distributions with accurate information of the strain gradient can be regressed. Thus, the modified T-matrix formulation can be used to calculate the reflected spectrum and the high spatial strain resolution along the Bragg grating can be reached easily without dividing the grating into too many segments which will enlarge the search space. The design and verification of a specimen which results in desired strain distributions with significant strain gradient along the grating during applied loading is presented. The remainder of this paper is organized as follows. In Section 2, the basic principle of the proposed GP strain profile reconstruction method and its implementation are developed. The numerical simulation results and its experimental verification are given in Section 3 and Section 4, respectively. Finally, the conclusions are provided in Section 5.

Section snippets

Reconstruction algorithm via genetic programming

The limiting effect of the initial selection of the representation method in the conventional genetic algorithm operating on fixed-length strings is one of the sources of the widespread view that the conventional genetic algorithm is very effective for rapidly finding the general neighborhood of the correct answer in a large search space, but not particularly effective at converging to a highly precise final solution. In contrast, in genetic programming, the size and the shape of the solution

Simulation and results

The GP for the reconstruction of Bragg grating sensor non-uniform strain profiles was tested on simulated spectral data for four kinds of strain distribution cases shown in Table 1. The numerical parameters of genetic programming algorithm is set as follows: probability of reproduction Pr is 0.14, probability of crossover Pc is 0.70, probability of mutation Pm is 0.16, population size M is 500, maximum number G of generations to be run is 100, initial tree depth is 19, maximum tree depth is 35.

Experimental validation

In order to verify the reconstruction effect of non-uniform strain profile using GP, the design and verification of a specimen which result in a strain distribution with significant strain gradient along the grating during applied loading is presented. The test rig comprises a cantilever specimen as shown in Fig. 10(a), with an optical Fiber Bragg grating with length 12 mm, which are bonded on the top surface of the specimen using an epoxy adhesive that is curable at room temperature. The left

Conclusion

This paper proposes an approach to reconstruct non-uniform strain profiles in fiber Bragg gratings using a modified genetic programming algorithm. The spatial resolution of FBG sensor using present method is different from that of the classical T-matrix method determined by the number of divided segments, but arbitrary because the strain profile is illuminated in the form of a function expression. The structures undergoing adaptation in genetic programming are active, which are not passive

Acknowledgments

This research is partially supported by the National Natural Science Foundation of China (Grant no. 51075202), the Aeronautical Science Foundation of China (2012ZA52009), the Priority Academic Program Development of Jiangsu Higher Education Institutions and Qing Lan Project.

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