A deep neural network methods to predict aeroelastic responses of a shape memory alloy hysteretic springs based typical airfoil section

Abstract

The main dangerous phenomenon in aeroelasticity exists as flutter which occurs through the combined forces of aerodynamic, structural, and inertial leading to uncontrollable airfoil oscillations. The phenomenon results in catastrophic structural collapses alongside the severe destruction of aircraft structures. Shape memory alloys (SMA) possess a unique property which allows them to retrieve their original shape from beneficial deformed states. The material properties of SMAs enable them to reverse the deformed forms that result from external loadings to their initial state. The unique property enables both energy dissipation and passive vibration control. The main objective of this research involves modeling and numerical analysis along with verification of the effects on two and three degrees of freedom (DOF) two-dimensional (2D) aeroelastic airfoil sections through replacing linear steel springs with SMA springs. The primary goal focuses on studying and forecasting how superelastic hysteresis in SMA affects aircraft wing section aeroelastic behavior using deep neural network (DNN) methods. The research investigates three scenarios that include aeroelastic analysis of SMA integrated typical airfoil sections and two cases of aeroelastic response prediction through long short-term memory (LSTM) and feedforward neural network (FFNN) network models for 2 DOF 2D SMA integrated aeroelastic typical airfoil models and 3 DOF 2D aeroelastic typical airfoil models, respectively. The unique nonlinear characteristics of SMAs distinguish them from other materials which scientists call superelasticity and the shape memory effect (SME). The phase transformation that occurs during specific thermal and mechanical loadings to the SMA leads to this property because it uses an approved model for validation. SMAs demonstrate the ability to return their shape to its original form after undergoing various loads. This property allows for energy dissipation and passive vibration control. The superelastic properties of SMAs function as a tool to reduce harmful wing oscillations that could occur during flight. The high energy absorption capabilities of oscillations delay flutter formation while transforming it into limit cycle oscillations (LCO). The research explores how the SMA spring affects the equation of motion for a 2 DOF 2D linear aeroelastic airfoil section. The unsteady aerodynamic model served to establish aerodynamic loads during this investigation. The state-space form of the complete model enabled the solution of the equation of motion, where the fourth-order Runge-Kutta method served as the chosen integration scheme for the complete model. The SMA material selected for this research utilized the nickel-titanium (NiTi) alloy because it provides the best response and excellent structural and workability properties. The researchers transformed the NiTi alloy into helical spring form to replace traditional linear steel springs in standard aeroelastic configurations. The solution process continues for both spring types before researchers compare their linear steel spring and SMA spring responses. External loads were applied to the SMA spring to demonstrate its natural damping characteristics. The research later investigates how the NiTi SMA spring exhibits nonlinear behavior through its analysis of flutter and post-flutter behaviors in the aeroelastic system. The results obtained undergo comparative analysis to verify their consistency with existing research findings. The numerical results demonstrated that SMA springs with their superelastic hysteresis properties successfully controlled unstable growing oscillations by producing acceptable LCOs at various airflow speeds. The application of artificial intelligence (AI) through neural network models has become widespread across academic and industrial research fields during recent years. This research investigates aeroelastic phenomena while predicting flutter speeds through DNN algorithms without requiring costly experimental or computational methods. The DNN algorithm serves as a fundamental method for dealing with the complexities of aeroelastic systems through multiple layers of the network. Flight data is interpreted through this structured network design from neurons. The research uses state-space models and Theodorsen's unsteady aerodynamic theory to build a complete database of flutter speed variations with different wing configurations. An FFNN model based on neural network with sigmoid hidden neurons and linear output neuron has been proposed to forecast the flutter speeds for the conditions mentioned above. The proposed model obtained a regression value of 0.92 for flutter speeds based on experimental findings. The suggested FFNN model demonstrates a successful performance that makes it suitable for flutter speed estimation predictions. The proposed FFNN structure maintains consistency with previous research on aeroelastic flutter speed analysis reported in the literature. The research reveals that the FFNN model developed in this study achieves high accuracy in predicting flutter speeds based on numerical aeroelastic structure results from unsteady aerodynamic theory. The correct prediction of the flutter speeds indicates that future analysis will become possible through tests without requiring costly equipment or extensive computational power. The study presents an innovative method to predict aeroelastic responses and LCO through DNN for a typical 2D airfoil section with SMA springs. The unique capacity of SMAs to convert aeroelastic vibrations into stable LCO through crystal structure phase transformation makes them suitable for enhancing structural stability in aeroelastic applications. The material transforms its pseudoelastic properties to deform under specific load and temperature conditions before returning to its original state. The hysteresis loop results from this process enables passive control of aeroelastic instabilities. The LSTM architecture enables the prediction of complex nonlinear aeroelastic responses from SMA-based airfoils by capturing long-term dependencies in their behavior. DNN models with an LSTM architecture serve as subtypes that enable the model to retain past information, enhancing its ability to make accurate predictions across prolonged time sequences. Time-dependent data and time series prediction require this particular architecture as its most suitable choice. The LSTM network learns from data obtained from numerical aeroelastic simulations that include unsteady aerodynamics with SMA springs. The DNN model demonstrates exceptional accuracy in predicting LCO onset and amplitude and frequency for various preloaded Nitinol or NiTi SMA properties which leads to successful outcomes for passive control and design of aeroelastic systems. The calculated flutter speed reaches 11.6 m/s while the superelastic effect above the preload 2 N applied to the NiTi SMA spring leads to LCO responses from the flutter regime. The results show that the prediction accuracy is high with a root mean square error (RMSE) of 0.97. The predictions and forecast trends for the flutter and post-flutter regime are precise. The DNN-based method provides a fast computational solution to traditional analysis and testing methods, which enhances predictive capabilities in aeroelastic systems containing SMA components. The promising model demonstrates its ability to perform efficient future forecasting without requiring testing or computational expenses.