## 1 Introduction  
To ensure the safety of marine equipment during operation, Structural Health Monitoring (SHM) technology has been developed. This technology utilizes various sensors to collect parameters related to structural mechanics. By using pre-designed algorithms, it evaluates the structure's condition, reliability, and durability, and triggers early alerts when the structural condition is severely abnormal. This helps to provide a basis and guidance for structural maintenance and support management decisions [1]. However, in engineering applications, the SHM system can only provide primary safety warnings, since the limited number of sensors cannot cover all areas where structural failure may occur. Therefore, researchers have conducted extensive research to explore methods to reconstruct the global stress of structures using a few discrete stress sensors. This is done with the aim of obtaining more mechanical response details under operational conditions. In 1995, [PERSON] et al. proposed the modal method [2], which uses the modal coordinates of the structure as weighting values for the overall structural modes. This method allows one to obtain a transformation matrix from the stress to the displacement field. By utilizing discrete stress sensors placed at specific points, the structural deformation can be reconstructed. The key concept is to view structural deformation as a linear combination of various modal orders. The accuracy of the reconstruction is significantly influenced by the accuracy of modal analysis, and this method is typically used for damage identification in structures that have been damaged. In 2007, [PERSON] et al. introduced the Ko displacement theory [3, 4, 5], which is based on the classical Bernoulli-Euler beam theory. This theory assumes that the bending deformation of each small section of the beam is solely caused by the bending moment, and it establishes a relationship between the bending moment and strain. By integratingthe measured axial strain twice, the deformation of the beam structure can be determined. This method is applicable to the reconstruction of unidirectional structural deformation. In 2003 and 2005, [PERSON] and [PERSON] proposed the inverse Finite Element Method (iFEM) [6; 7; 8; 9]. This method divides the structure into one-dimensional, two-dimensional, and three-dimensional elements, conducts discrete solutions by placing stress sensors at specific locations, and then assembles them into an overall matrix to obtain the global stress field through restructuring [6; 7; 8; 9]. [PERSON] et al. [10] utilized the iFEM method to calculate the global stress and bending of a parallel center body of an overturned bulk carrier using the iQS4 element [11], which demonstrated the practicality of the iFEM technology for bulk carriers. In addition, numerous researchers have explored the deformation reconstruction of beams, frames, plates, and shells using the iFEM method [12]. Despite the potential benefits of the iFEM method, such as its ability to reconstruct the stress and strain fields of various structures, the high reconstruction cost for the strain field of complex curved surface structures is a challenging issue. In recent years, alternative approaches have been proposed to overcome this issue [13; 14; 15; 16; 17]. For example, [PERSON] et al. [18] analyzed the steel structure of a gymnasium and established a mapping relationship between measured and estimated points through structural correlation analysis, providing an alternative approach for stress field reconstruction. In 2021, [PERSON] et al. [19] developed a two-dimensional stress distribution algorithm along a pipeline based on the stress monitoring data of oil and gas pipelines, utilizing a BP neural network and the particle swarm optimization algorithm. The algorithm's accuracy was validated through examples, and it required no manual boundary establishment, with a smaller sensor quantity and fast solution speed.