## 1 Introduction  
Load monitoring techniques for wing structures are a promising technology for enhancing the flight performance of future aircrafts. Load monitoring is beneficial in terms of structural safety and reliability. There has been significant demand for high-aspect-ratio wings for efficient long-endurance flight, and the loading for such structurally challenging designs is critical [1]. Monitoring results of loading history can be utilized for structural fatigue analysis. By controlling applied loads to wings based on real-time load monitoring, it could be feasible to alleviate undesirable large moments at the wing root. When wings are flexible, aerodynamic loads cause large deflections, which affect the aeroelastic stability and response [2; 3; 4]. Load monitoring is beneficial to estimate structural deformation and conduct reliable structural analysis based on practical assumptions of deflected wing shape. Another potential benefit of load monitoring is stable and efficient control of an aircraft, including unmanned air vehicles (UAVs). Considering the gust perturbation process for example, the load variations from incoming gusts result in attitude and flight path variations, and there is a theoretical phase-lag between the cause (load) and effect (attitude and flight path) [5; 6; 7]. The load is a \"phase-advanced\" phenomena in this sense, and, therefore, its observation in addition to the conventional inertia observations could potentially enhance vehicle controllability. Aerodynamic loads are not always directly measurable. The wing structure is complex and space in wings is limited. It is difficult to install sufficient pressure sensors and tubes. To overcome these engineering obstacles, studies have been conducted to estimate, as opposed to directly measure, the loads using a measurable parameter, which is a strain. In a mechanical sense, load causes strain. When strain is used to identify loads, it creates an inverse problem [8; 9; 10]. Inverse analyses tend to be ill-conditioned, specifically when distributed aerodynamic loads are to be calculated. The solution becomes highly unstable for the strain measurement errors. There have been a number of studies to obtain stable solutions. For example, using the inverse interpolation method, [PERSON] et al. assumed polynomial functions, whereas [PERSON] et al. used Fourier cosine series terms for spatial load distribution functions [11; 12]. [PERSON] et al. reported a finite-element-based inverse analysis in which aerodynamic restriction was coupled with elastic equations [13]. These techniques to assume functions for aerodynamic load distributions are effective in improving the identification accuracy. There have been other studies to identify loads by using neural networks. Using strain as an input and load as an output of the neural network, the strain-to-load transfer is represented by the neural network that is optimized through a learning algorithm. The optimization through a learning algorithm contributes to stable solutions. [PERSON] et al. conducted numerical simulations of a cantilever beam to validate the neural network applicability [14]. [PERSON] et al. used strain gauge data to estimate loads in fatigue tests that simulated maneuver and buffet loads [15]. They reported successful results, although they focused primarily on the load identification in the form of a limited number of concentrated forces. [PERSON] et al. reported that the approach was applicable for the identification of distributed loads by using a number of strain gauges bonded on a flat panel [16]. These techniques remain limited to a level of conceptual demonstration, and validation of the applicability in the aerodynamic environment needs to be conducted. Currently, one of the primary challenges is the collection of sufficient amounts of strain data from the wing structure under flight conditions. It is not practical to install a myriad strain gauges on the surface of the wings considering the amount of wiring required.