# Morphological Reconstruction for Variable Wing Leading Edge Based on the Node Curvature Vectors
## 1 Introduction  
The design inspiration for morphing airfoils is derived from the wing structures of birds and other flying animals. It aims to achieve morphing capabilities in aircraft to optimize flight performance and fuel efficiency in different flight phases or conditions [1, 2]. Concurrently, researchers are also dedicated to investigating adaptive control methods for variable wing structures to achieve enhanced maneuverability, stability, and energy efficiency. [PERSON] et al. developed and successfully implemented control laws on a tensegrity morphing airfoil based on reduced order Class-k tensegrity dynamics [3]. [PERSON] et al. proposed an optimal control method based on Markov parameters to achieve wing shape control for tensegrity morphing airfoils [4]. To achieve the \"propagation-shifting\" functionality of aircraft, ensuring their optimal aerodynamic profile, aerodynamic performance, and stealth characteristics in response to complex flight environments and mission requirements, it is essential to synchronize and close the loop control of the wing leading-edge propagation perception and airfoil adjustment [5, 6]. Currently, conventional structural propagation perception technologies mainly include two types: non-contact and contact. Non-contact shape measurement technologies mainly include include methods such as visual measurement and laser scanning [7, 8]. Although this method has high measurement accuracy, it has visual blind spots and presents certainlimitations in terms of volume size, installation calibration, vibration resistance, and real-time response characteristics. Compared to non-contact measurement modes, deformation monitoring methods based on flexible, contact-type strain information perception are more suitable for the real-time shape identification of in-service aircraft structures. For example, the modal superposition method requires the prior acquisition of accurate load or material property information, that is, identifying the strain mode and displacement mode matrices of the target structure through a large number of experiments or finite element modeling. However, due to the complexity of the wing leading-edge structure and material properties, the engineering applicability of this method is limited [9]. For example, the global linear regression prediction or segmented continuous interpolation fitting method, despite having a simple reconstruction process, requires a large number of sensors to ensure the accuracy of structural shape reconstruction, limiting its practical application in the field of variable curvature wing leading-edge propagation perception [10]. To address the above problems, researchers have proposed a linear interpolation-based curvature propagation method (LI-CPM), which reconstructs structural displacement field information by establishing the mathematical relationship between strain, curvature, and displacement without requiring any prior knowledge of material properties or load size, and only using a finite number of discrete strain data [11; 12]. [PERSON] et al. obtained the curvature distribution characteristics along the thickness direction of a structure after loading and the position of the neutral layer of the strain by implanting multiple optical fiber sensors into a 3D composite material plate [13]. [PERSON] et al. achieved structural propagation perception by constructing a function relationship model between measured strain sensor data and beam structure curvature [14]. [PERSON] et al. studied a morphing reconstruction method for thin plates supported by multiple elastic supports based on the curvature-displacement function and the Runge-Kutta solving principle [15]. [PERSON] et al. achieved the displacement field reconstruction of the bed of a gantry boring and milling machine under random loads using a continuous curvature function constructed using the cubic spline interpolation method [16]. [PERSON] et al.