Original Article

Wind-resistant stability of bridges with three-force coefficients based on deep learning under mountain conditions

¹ Guangxi Key Laboratory of Green Building Materials and Construction Industrialization, College of Civil Engineering, Guilin University of Technology, Guilin 541004, Guangxi, PR China
² College of Earth and Sciences, Guilin University of Technology, Guilin 541004, Guangxi, PR China
³ College of Agricultural and Hydraulic Engineering, Suihua University, Suihua 152001, Heilongjiang, PR China
⁴ School of Civil Engineering, Liaoning Technical University, Fuxin 123032, Liaoning, PR China
⁵ College of Computer Science and Engineering, Guilin University of Technology, Guilin 541004, Guangxi, PR China

^* e-mail: pengjun20221013@163.com

Received: 22 April 2025
Accepted: 28 August 2025

Abstract

Severe turbulence and nonlinear wind loads in mountainous wind fields make it difficult to predict the lift, drag, and torque coefficients of bridges accurately, thereby affecting the analysis of wind-resistant stability. This paper applies a deep learning framework that combines Diffusion and Fourier Neural Operator (FNO). The diffusion model is used to generate high-fidelity wind field data. FNO is used to efficiently extract spatially relevant features and achieve cross-scale generalization, thereby achieving precise modeling of the three-force coefficients. With the help of this model, the dynamic response and wind-resistant stability of bridges under complex wind fields are deeply evaluated. Based on the physical constraint training diffusion model, a conditional diffusion process is constructed on the WRF (Weather Research and Forecasting Model) large eddy simulation dataset. A three-dimensional pulsating wind speed field containing terrain disturbances is generated through latent space interpolation with a resolution of 0.1D (where D is the beam height). An eight-layer Fourier convolutional branch network is established to capture the vortex evolution law in the 0.5D-5D spatial range around the main beam through frequency domain transformation, and output a quantitative description of the detachment bubble formation position and reattachment length. FNO-ODE (Ordinary Differential Equation) is constructed, and the aerodynamic prediction results are embedded in the Newmark-β method solution process to achieve bidirectional coupling calculation of wind load and bridge torsion/vertical bending vibration mode. The time step is compressed to 0.001 s. The Hilbert spectrum characteristics of the buffeting response time history are analyzed based on the attention mechanism. The divergent vibration starting point is automatically identified, and the probability distribution of the unstable wind speed is output. The experimental results show that the displacement curve and lift frequency are both 0.5 Hz, and the bridge vibration is mainly caused by the periodic excitation of the wind load. When the Lyapunov index is equal to 0, the critical wind speed is about 45 m/s, and the wind speed greater than 60 m/s triggers flutter. The median error of Diffusion+FNO in the critical wind speed prediction is 3.9%, and the interquartile range is 2.9%–4.3%, with extremely high prediction consistency. In the range of 60° to 120° on the circumferential angle of the main beam surface, high pulsating pressure may cause local aerodynamic load mutations and aggravate the structural buffeting response.