## 1 Introduction  
Cracking is a common form of damage in engineering applications, especially in aerospace structures. A recent report by the NASA Spacecraft Fault Management Workshop described small cracks found in the NZRYA module of the International Space Station (ISS). These fissures were described as superficial, but with the potential to spread over time. The authors of the report were unsure whether the cracks were responsible for any air leaks from the orbiting lab [1]. Such reports indicate the importance of detecting structural damage to spacecraft as early as possible, and this is now a matter of considerable interest to researchers. Fracture mechanics are now routinely applied in the early stages of structure design for the purpose of life prediction using damage tolerance design methods [2]. In addition, because structures only need to be repaired when a crack propagates to a certain dangerous length, conventional non-destructive detection techniques are unsuited for the requirements of long-term online monitoring. For this reason, it is necessary to detect crack propagation using structural health monitoring (SHM) techniques. Fiber Bragg grating (FBG) sensors have exhibited great potential in structural health monitoring. In this regard, their light weight, high resolution, multiplexing capability, and immunity to electromagnetic fields can all be seen as advantageous. In SHM applications,FBG sensors can monitor any damage or environmental impact during the operation process without compromising their structural strength, because shifts in central wavelength correspond to changes in strain/temperature. A uniform strain sensed along the axial direction of an FBG sensor leads to a Bragg wavelength shift, and this shift is linearly proportional to the constantly applied strain. In this way, FBG sensors can be used to identify the local strains upon a structure [3]. In spacecraft, cracks usually occur around holes in the mechanical structure, and a stress concentration zone involving stress singularity distribution and a strain gradient appears at the crack tip during the crack propagation process. Such an inhomogeneous crack-tip strain field phenomenon affects the response of FBGs. A deformation reflection spectrum response is indicated when the non-uniform axial force sensed by the FBGs varies along the grating direction [3]. However, a determination of structural strain distribution cannot be achieved by the Bragg wavelength shift algorithm alone when significant strain gradients appear around the FBGs [4]. Determining the best means of using a high-precision reconstruction algorithm to reconstruct axial non-uniform strain distribution from the reflection spectrum of FBGs can, therefore, be seen as an inverse problem, which many researchers have so far attempted to resolve [5]. The key to solving the inverse problem is to establish a database--including various simulation deformation spectra for sections of FBGs under different strains--by application of a modified transfer-matrix method (TMM). Previous studies have found good agreement between target reflection spectra profiles and reconstructed profiles obtained using modified TMM methods under strain field conditions [4]. A reconstructed strain may be considered as a simulation strain whose spectrum matches that of an experimental reflection with a high degree of accuracy and a minimal level of error tolerance. An optimization algorithm can then be adapted to deal with the problem of matching the simulation and experimental spectra, and can determine the strain with the minimum spectrum error. The reconstruction of the inhomogeneous strain field, or the fluctuations in stress-strain behavior, can be used to identify structural damage, such as cracks or impact damage [6]. A growing body of research suggests that intelligent heuristic algorithms perform well in solving this inverse reconstruction problem [7; 8; 9; 10; 11]. The authors of [7] demonstrated that a differential evolution algorithm was able to solve the inverse strain problem of FBGs.