## 1 Introduction
However, their algorithm was only verified by simulation data and lacked experimental data support. Swarm intelligence (SI) is another powerful form of computational intelligence (CI) which has been used to solve inverse optimization problems. The authors of [8] used a quantum-behaved Particle Swarm Optimization algorithm to reconstruct FBG sensor strain profiles. In another study, a dynamic Particle Swarm Optimization algorithm was used to reconstruct a non-uniform strain profile for the FBG sensor [9]. Finally, in [10], the reconstruction of non-uniform strain profiles by means of a genetic programming algorithm was described. Researchers have, therefore, confirmed the effectiveness of the optimization algorithm in solving the strain reconstruction problem. However, no experimental verification has yet been obtained with respect to the fatigue testing of aerospace structures. Researchers have also failed to consider the bonding layer effects of FBGs when glued onto such structures, or the cross-sensitivity between strain and temperature effects, so as to determine the best practice for engineering applications. There has also been little to no research into the verification of strain reconstruction algorithms by monitoring fatigue crack propagation in aluminum alloy structures using FBGs. The details of the contributions and limitations of previous research, the advantages of the proposed paper, and future applications are presented in Appendix A. In this study, we use numerical spectral simulations in combination with experimental fatigue crack propagation monitoring using the digital image correlation (DIC) technique. Field strain analysis and damage assessment using DIC was originally developed using a two-dimensional correlation of deformed and undeformed digitized object images [12]. Subsequently, an ex situ DIC technique was developed with the ability to indicate the strain and size of the plastic zone at the crack tip during a single loading cycle. However, this technique cannot provide information on crack tip strain over repeated fatigue loading cycles. In summary, we may say that the areas of interest covered by previous studies have been relatively small. However, clear theoretical analyses using the grey wolf optimizer (GWO) method have been applied in strain reconstruction to detect the actual strain profile of a real structure in a fatigue test. This method [13] has been tailored for a wide variety of optimization problems due to its advantages over other forms of swarm intelligence. GWO involves very few parameters, and no derived information is required in the initial search. In addition, it is simple, easy to use, flexible, scalable, and has a special capability to strike the right balance between exploration and exploitation during the search, which leads to favorable convergence. Consequently, in this study, we aimed to reconstruct full-field macroscopic strain measurements of the fatigue crack growth process in aluminum alloy structures using both FBGs and the GWO method. This approach has four key advantages over the methods used in previous studies. First, the strain obtained by the digital image correlation (DIC) method is used to verify the reconstructed non-uniform strain reported by the FBG sensor. The accuracy of the DIC method has previously been confirmed [14]. Second, the difference in strain transfer caused by the bonding layer between the structure and the FBG sensor is taken into consideration. Third, the cross-sensitivity between the temperature and strain of FBG sensors in practical engineering applications is also taken into account by this method. Finally, and in contrast to traditional algorithmic methods, online performance analysis highlights the efficiency and practicality of GWO methods in solving the inverse problem of FBG. By such means, online analytical processing of strain data using FBGs can detect deformations and crack damage caused to spacecraft by debris impact and fatigue loading.