## 1 Introduction  
Long-endurance low-speed aircraft, represented by solar aircraft, has the advantage of high cruise efficiency and is widely used in low-speed reconnaissance [1, 2, 3]. For such aircraft, the traditional rigid skin cannot meet the requirements of rigidity and weight at the same time, so the skin material is usually flexible membrane [4, 5, 6]. In the design and flight experiment of a solar unmanned aerial vehicle (UAV), the project team discovered that the deviation between aerodynamic data and numerical results is larger than that of conventional UAV, and the uncertain effect of membrane deformation should be an important reason for this phenomenon. The influence of membrane deformation on wing aerodynamic characteristics is reflected in multiple dimensions. On the two-dimensional level, the aerodynamic load presents asymmetric suction and pressure on the upper and lower surfaces, respectively, and the chamber and thickness of the cross-section airfoil will change. On the three-dimensional level, the wing surface is no longer regular, and the spanwise disturbance caused by the periodic fluctuation will affect the K-H instability, resulting in three-dimensional effects on the flow behavior [7]. In an early study of fluid structure coupling of membrane wings, the deformation measurement was generally realized by numerical method [8; 9]. [PERSON] et al. [10] carried out numerical simulation of airship membrane structure by using the nonlinear finite element method and improved the accuracy of nonlinear calculation by updating the incremental method of Lagrange scheme. [PERSON] et al. [11] used the four-node reduced integral membrane element to simulate the deformation of inflatable wing under internal pressure, and obtained the influence of internal and external pressure difference on wing surface stiffness and buckling characteristics. Currently, with the progress of measurement technology, the research of membrane wing is generally performed based on deformation real-time capture technology, and the mainstream measurement methods include the stereo vision measurement method and the optical fiber sensing method. [PERSON] et al. [12] installed two cameras with an angle of 40\({}^{\circ}\) between the optical axes on the upper surface of the membrane wing and solved the three-dimensional coordinates of 230 points on the membrane by using the direct linear transformation method (DLT), so as to realize the measurement of the deformation behavior through the stereo photogrammetry technology. [PERSON] et al. [13] used the optical fiber sensing method to monitor the polyimide skin and performed the sensing and reconstruction the membrane shape based on the surface-fitting algorithm of the sensing point curvature. The error between the monitoring results and photogrammetry is less than 5%. With respect to numerical calculation of aerodynamic characteristics, with the maturity of computational fluid dynamics (CFD) method, the algorithm based on Reynolds's averaged N-S equation has become the mainstream solution method. Among them, the \(\gamma\)-_Re_ transition model is commonly used to solve the aerodynamic characteristics of solar aircraft, which was proposed by [PERSON] and [PERSON] et al. [14; 15] by combining the SST \(k\)-\(\omega\) model with a transition equation. [PERSON] et al. [16] used the S-A turbulence model to conduct static and dynamic analysis on fluid structure-coupling characteristics of large aspect ratios and large flexible wings. The results indicate that the S-A model can improve the calculation efficiency on the premise of ensuring the calculation accuracy. Large eddy simulation (LES) and direct numerical simulation (DNS) have higher accuracy than the above methods, but they also have the disadvantage of a large amount of calculation [17]. With respect to experiments, the PIV method is the mainstream method to observe the flow field structure. [PERSON] et al. [18] observed the unsteady flow field of the rectangular membrane wing with a small aspect ratio via the PIV method.