Deep Neural Network-based Method For Calculating Nonlinear Aerodynamic Forces And Responses Of Bridge Sections

Flutter instability is a key design factor that restricts the main span’s further growth of long-span bridges.Theoretical analysis frameworks for bridge flutter are now being transferred from calculating traditional linear critical flutter wind speed to nonlinear flutter analysis considering nonlinear aerodynamic forces with amplitude dependence.At present,the analytical method and potential mechanism of nonlinear flutter under uniform flow have been extensively explored,while the investigation of nonlinear flutter-buffeting characteristics and nonlinear aerodynamic forces of bluff bodies under turbulent flow conditions has not yet been involved.Since the actual wind environment of the bridge is basically turbulent,how to reasonably model the nonlinear aerodynamic forces and obtain the potential large-amplitude motion states of bluff bridge sections under different turbulent conditions are the current urgent tasks both for prohibiting the occurrence of bridge flutter as well as for establishing the windresistant design specification.Under the BARC(a Benchmark on the Aerodynamics of a Rectangular 5:1 Cylinder)framework,this paper takes a typical 5:1 rectangular cylinder section as the research object to synchronously measure the vibration displacements and the surface pressure by sectional wind tunnel free-vibration tests.The nonlinear flutter-buffeting vibration under both uniform flow and two grid-generated turbulent flows are systematically carried out.Based on the experimental data,the nonlinear aerodynamic characteristics and nonlinear flutter-buffeting characteristics under different wind fields are studied in detail.A unified method for modeling nonlinear aerodynamic forces based on neural network technology is proposed.Based on this,a unified Encoder-Decoder framework applicable for the identification of nonlinear aerodynamic forces and for the analysis of nonlinear flutter-buffeting under different incoming flow conditions is proposed.The research results of this paper reveal the nonlinear characteristics of aerodynamic forces and nonlinear response of the bluff body section under different incoming flows,which make up for the shortcomings of the existing methods for identifying nonlinear aerodynamic forces and improve the nonlinear flutter analysis framework of bluff body section as well as provide significant theoretical references for windresistant design of long-span and super-long span bridges.The main research works in this paper are as follows:(1)A uniform flow field and two types of wind fields with different turbulence characteristics are simulated by using or not using passive grids;the nonlinear properties of the structural damping and stiffness of sectional model free vibration system with varying amplitudes(or varying displacement)are studied;based on the self-developed signal trigger device,the nonlinear aerodynamic forces,nonlinear response and fluctuating wind speeds of the 5:1 rectangular section under different motion states are obtained.(2)The nonlinear response characteristics of the 5:1 rectangular section under the uniform flow and the two turbulent flows in the full range wind speed process are studied,mainly including the amplitude’s statistical and time-varying characteristics,as well as the probability density characteristics of displacement time history.And the effects of different turbulent flows on nonlinear flutter characteristics are discussed.(3)The nonlinear evolution characteristics of aerodynamic forces of 5:1 rectangular section under uniform flow and two kinds of turbulent flows are studied,including spanwise correlation properties,frequency spectrum characteristics,and amplitude-dependent characteristics of aerodynamic forces,revealing the difference and connection of evolution characteristics of aerodynamic forces covering the full range of incoming wind speeds.(4)The existing linear and non-linear aerodynamic modeling and parameter identification methods are fully discussed.Based on the deep neural network(DNN)and long short-term memory network(LSTM)technology,a new unified strategy for modeling the nonlinear aerodynamic forces of bluff bodies suitable for both uniform flow and turbulent flow is proposed and its feasibility is verified.The influence of choosing the input variables’ order during aerodynamic force modeling is discussed and the two models are fully compared by this.(5)Taking the neural network methods and Hidden Markov Model as the starting point,a unified Encoder-Decoder analysis framework for extracting nonlinear aerodynamic forces under different wind field conditions and analyzing nonlinear flutter-buffeting responses in the time domain is proposed with no limitation of section type and section geometry.This framework can complete the aerodynamic force identification and time-domain analysis of the nonlinear response of a 5:1 rectangular section under the state of nonlinear flutter-buffeting vibration only by relying on free vibration time history data.The analysis and identification results of this framework and the wind tunnel test results of pressure measurement and vibration measurement are in good agreement.A typical box girder bridge section is used as an engineering example to carry out the analysis of nonlinear flutter-buffeting response.The analytical results further verifies the accuracy of the Encoder-Decoder framework as well as confirmed its applicablity to bridge sections.