# Nonlinear Aeroelastic System Identification Based on Neural Network
## 1 Introduction  
Early investigation treated the aeroelastic system as purely linear [1]. However, many sources of nonlinearity exist in the actual aeroelastic system, such as structural nonlinearity or aerodynamic nonlinearity, both of which affect performance of the system. The effects of three types of structural nonlinearity on the flutter of a two-degree-of-freedom system were calculated on an analog computer [2; 3]. Describing functions and harmonic balance were adopted to approach nonlinear flutter problems [4; 5; 6; 7; 8; 9], as both can be used to predict some nonlinear behavior. However, the aeroelastic system is dynamic and its response is dependent on initial conditions. Subsequently, the describing function approach does not permit a full exploration of the effect of nonlinear behavior [10].  
The system identification method, which predicts the response of the nonlinear system via establishing an approximate model of the system, has been adopted in the last decades. Volterra kernels were used to represent the system, which can estimate uncertainties by considering only the linear component of flight data [11]. Block-oriented identification, a non-iterative identification algorithm that divides the system into linear and nonlinear subsections, was utilized to approach characterization of nonlinear dynamics [12]. A frequency domain identification method was presented to estimate physical poles of the dynamic system [13]. A parameter-varying estimation framework was proposed to predict flutter speed [14]. Computational fluid dynamics (CFD) based reduced-order-models, were used to study the control surface limit cycle oscillation (LCO) and the structure of aerodynamic model equations, as a combination of linear and nonlinear contributions [15; 16]. Unfortunately, the actual wing is a complex nonlinear system, influenced by many uncertain factors. It is difficult for traditional identification methods to establish an accurate model for such a complex system.  
The neural network identification method, which does not need to establish the precise model of the system, has been developed in recent years. An artificial neural network (ANN) can approximateany nonlinear function and adapt to environmental changes by learning. Neural network identification can be used to identify linear or nonlinear systems and is a very effective method to identify nonlinear aeroelastic systems. The neural network identification method has been applied to predict aerodynamic force, flutter critical speed, and LCO speed of the system [17; 18].  
The purpose of this work is to study the nonlinear aeroelastic system identification method based on the ANN and verify the effectiveness of the neural network. A typical three-degree-of-freedom wing section model in two-dimensions is established. Two types of structural nonlinearity, including cubic-spring and friction, are studied in this work. The standard Runge-Kutta algorithm is used to compute the response of the cubic-spring-nonlinear aeroelastic system and the friction-nonlinear aeroelastic system. Then, a time-delay recurrent neural network (TDRNN) is established and the neural network model is trained by the simulated data. The chirp and sine excitation signals are used to verify the identification model.