## 1 Introduction  
The hull, serving as a complex mechanical structure, operates in harsh maritime environments and is subject to various interacting loads, such as wind loads, wave loads, ice loads, and deoperator-pressure loads. The hull structure is prone to experiencing torsional fatigue, bending fatigue, and corrosion fatigue from seawater, leading to a decrease in the structural load-bearing capacity and even the occurrence of catastrophic accidents [1]. Therefore, the reconstruction of the dynamic/static strain field responses and distribution characteristics of the hull's reinforced panels through finite discrete strain data is crucial. This capability enables the assessment of the operational and health status of the hull structure, providing essential technical support for the development of scientifically sound maintenance strategies in maritime environments [2]. Resistance strain gauges are commonly used to gather strain information from key ship components [3, 4], but they have drawbacks such as complex wiring, susceptibility to electromagnetic interference, and unstable signal transmission. They struggle to handle the tough conditions found in ship structures. Meanwhile, Digital Image Correlation technology (DIC) can measure displacement, vibration, and strain in 3D with full-field, non-contact optical measurements [5]; yet it faces challenges in meeting service process monitoring needs due to visual blind areas and its heavy weight. In contrast, fiber Bragg grating sensors have distinct advantages, including high temperature and corrosion resistance, immunity to electromagnetic interference, high sensitivity, and the ability to form a space or wavelength-division multiplexing monitoring array. This makes them highly suitable for real-time monitoring and the reconstruction of a ship's structural strain [6; 7]. Recently, researchers have proposed various methods for reconstructing structural strain fields, such as the modal superposition principle, the Radon transform principle, and the neural network construction method. [PERSON] et al., employed a strain-load superposition method based on the modal principle to reconstruct strain field distribution information for the structure [8]. [PERSON] et al. utilized a Bragg-edge strain imaging technique based on the Radon transform principle to reconstruct the residual strain in the structure [9]. [PERSON] et al. applied the K-BP neural network construction method to reconstruct both the strain and load fields in the structure [10]. However, these methods still have certain limitations in practical engineering applications. For instance, the modal superposition method requires obtaining precise information about the load or material properties in advance. Due to the complexity of actual constraints and structural properties, this method faces significant limitations in engineering applicability. Similarly, the neural network construction method, while having a straightforward reconstruction process, necessitates the configuration of a large number of sensors to achieve structural strain reconstruction. In response to the above problems, many experts offered their insights. [PERSON] from NASA's Langley Center proposed the inverse finite element method (iFEM) [11], which, based on the variational principle, uses different error functionals to approximate a finite element model to reconstruct the displacement field and strain field. [PERSON] et al. investigated the impact of three different element meshing forms--three-node shell element, four-node shell element, and eight-node body element--on the reconstruction of the structural displacement field, strain field, and the accuracy of damage location. They also proposed an element meshing strategy applicable to any structure [12]. [PERSON] et al., examined a plate damage localization method based on the inverse finite element strain field reconstruction principle [13]. [PERSON] et al.