Journal of Bionic Engineering (2025) 22:1126–1142https://doi.org/10.1007/s42235-025-00692-x

Modeling of Flapping Wing Aerial Vehicle Using Hybrid Phasefunctioned Neural Network Based on Flight Data

Zhihao Zhao1,2  · Zhiling Jiang1,2 · Chenyang Zhang1,2 · Guanghua Song1,2

1 School of Aeronautics and Astronautics, Zhejiang University, Hangzhou 310027, China 

2 Huanjiang Laboratory, Zhuji 311800, China

Abstract 

Modeling the dynamics of flapping wing aerial vehicle is challenging due to the complexity of aerodynamic effects and mechanical structures. The aim of this work is to develop an accurate dynamics model of flapping wing aerial vehicle based on real flight data. We propose a modeling framework that combines rigid body dynamics with a neural network to predict aerodynamic effects. By incorporating the concept of flapping phase, we significantly enhance the network’s ability to analyze transient aerodynamic behavior. We design and utilize a phase-functioned neural network structure for aerodynamic predictions and train the network using real flight data. Evaluation results show that the network can predict aerodynamic effects and demonstrate clear physical significance. We verify that the framework can be used for dynamic propagation and is expected to be utilized for building simulators for flapping wing aerial vehicles. 

Keywords Flapping wing aerial vehicle · Flapping phase · Modeling · Neural networks