# Morphological Reconstruction for Variable Wing Leading Edge Based on the Node Curvature Vectors
## 1 Introduction
studied a method for calculating the curvature of a driving beam based on the measured axial strain of optical fiber sensors, achieving the shape perception of a medical robotic arm [17]. [PERSON] et al. studied a continuous equation-solving method based on the relationship model between strain-curvature-displacement and reconstructed the displacement field of beam structures according to the curvature value [18]. It is worth noting that the conventional curvature propagation method described above, which establishes the strain-curvature function relationship, is primarily applicable to flat-plate structures. However, the variable curvature of the wing leading edge, being a curved surface structure, results in changes in the arc angle during deformation. This variation leads to significant discrepancies between the curvature information calculated based on this function at measured points and the actual curvature. To address this issue, a strain-arc curvature function suitable for dynamically changing surface curvature angles of the wing leading edge is proposed based on the curvature radius of the leading-edge surface and measured strain, aiming to improve the accuracy of the curvature information for sensing points [19]. Conventional curvature propagation methods require linear interpolation to obtain curvature information for unattached sensor positions. However, the linear interpolation function, being a first-order linear function, accumulates errors between the interpolated curvature features and the actual curvature distribution, thereby affecting the accuracy of propagation reconstruction. Therefore, this study proposes a curvature propagation method based on node curvature vectors (NCV-CPM). By adding nodes within the segmented leading-edge arc sections, the aim is to enhance the order of curvature fitting functions. By constructing a least squares error function between theoretical curvature and actual curvature, node curvature vectors are solved to address the cumulative error problem. Additionally, by establishing a curvature-strain mapping function relationship, it is possible to achieve the inverse reconstruction of the leading-edge strain field based on the curvature distribution [20]. The higher the accuracy requirement for the morphing of the variable wing leading-edge morphological reconstruction, the greater the number of sensors needed, leading to a significant increase in the complexity of the monitoring system. To address this, researchers utilize optimization algorithms to obtain the optimal sensor layout, such as genetic algorithms [21], simulated annealing [22], and particle swarm optimization [23]. Genetic algorithms require determining suitable crossover and mutation rate parameters based on the size of the established sample library, while simulated annealing exhibits slow convergence and is influenced by multiple parameters to be optimized. In contrast, particle swarm optimization requires fewer optimization parameters and does not necessitate constructing a sample library. Therefore, this study proposes the adoption of particle swarm optimization to iteratively determine the optimal number of virtual sensing points, thereby simplifying the complexity of the sensor network. The remainder of this study is organized as follows. Section 2 outlines the principles of the wing leading-edge morphological reconstruction method based on NCV-CPM. Section 3 describes the simulation model of the variable wing leading-edge structure and presents the simulation verification results of the NCV-CPM. Section 4 discusses the strain monitoring system for the variable wing leading-edge structure and presents the experimental verification results of the NCV-CPM. Section 5 concludes by summarizing the innovations and implementation outcomes of the NCV-CPM.