Modeling nonlinear flutter behavior of long‐span bridges using knowledge‐enhanced long short‐term memory network

Abstract

AbstractThe nonlinear characteristics of bridge aerodynamics preclude a closed‐form solution of limit‐cycle oscillation (LCO) amplitude and frequency in the post‐flutter stage. To address this issue, a long short‐term memory (LSTM) network is utilized as the reduced‐order modeling of nonlinear aeroelastic forces on the bridge deck section, and it is repeatedly employed to generate force inputs at spanwise nodes of a three‐dimensional (3D) finite element model (FEM) of the long‐span bridge (using spatial beam elements). All LSTM networks are dynamically coupled through FEM, and the 3D nonlinear flutter response is accordingly obtained. To improve the simulation accuracy and reduce the required training data of the standard LSTM network, both general knowledge (motivated by the gating mechanism and mathematical models for information processing) and domain knowledge (resulting from the basic understanding of bridge aerodynamics) are leveraged to, respectively, customize the LSTM cell and network architecture. In addition, a fast‐training algorithm effectively combining the linear convergence of stochastic gradient descent and superlinear convergence of modified Broyden–Fletcher–Goldfarb–Shanno is developed to improve the training efficiency of the obtained knowledge‐enhanced LSTM network. To further advance the computational efficiency of the coupled LSTM‐FEM nonlinear flutter analysis, the convolution‐based numerical integration is adopted in the finite element modeling of long‐span bridge dynamics. A case study of a long‐span suspension bridge under strong winds demonstrates the proposed 3D nonlinear flutter analysis presents high simulation efficiency and accuracy and can be utilized to effectively obtain the nonlinear LCO characteristics in a wide range of post‐flutter wind speeds.