Shijie (Jason) Liu 刘士杰

Increasingly slender bridge decks are prone to wind-induced damage, where the complex interactions between the incoming wind, deck, and adjacent wake flows play a deciding role. However, the unsteady wake dynamics at small but realistic angles of attack and their compact reduced-order representation remain insufficiently understood. The unsteady wakes subject to angle of attack from 3° to 5° are investigated via Koopman analysis with the Dynamic Mode Decomposition (DMD), aiming to construct accurate reduced-order models for largely repeated canonical cases, while preserving physical and phenomenological fidelity. Instantaneous velocity and vorticity fields reveal a clear separation-reattachment cycle: leading edge separation bubbles form and migrate upstream at drag peaks, then collapse and reattach at drag valleys. Shear layers roll up into dual vortices that pair, merge with Kelvin–Helmholtz-type shear-layer instabilities, and alternately shed from the deck’s upper and lower surfaces, driving oscillatory wake deflection and attendant drag and lift fluctuations. DMD identifies four dominant modes that together account for over 90% of the turbulent kinetic energy: time averaged base flow, the fundamental vortex shedding mode, and two higher frequency shear-layer modes. Adequate truncation reduces data dimensionality by an order of magnitude while keeping the normalized error below 6%. The results demonstrate that a DMD-based reduced-order model built on Unsteady Reynolds Averaged Navier–Stokes (URANS) data can faithfully preserve both large-scale separation topology and fine-scale vortical structures across small angles of attack, providing a compact and accurate representation of bridge-deck wakes for repeated canonical configurations.

Dynamic Mode Decomposition (DMD) accurately captures growth rates and frequency characteristics of each mode, establishing a reduced-order model for the evolution of the flow field to reconstruct or predict the flow dynamics process. This study applies DMD to analyze the wind pressure distribution problem of cylindrical coal sheds, investigating its accuracy in analyzing pressure fields. First, wind tunnel tests were conducted on cylindrical coal sheds to examine the mean wind pressure coefficient distribution under typical wind directions (defined as θ). Subsequently, the wind pressure field of the coal shed was decomposed using the DMD at θ = 0°. Reconstruction with the first 15 DMD modes can better characterize the wind pressure distribution. Therefore, reconstruction with the first 15 DMD modes was chosen to reconstruct the pressure fields conducted at θ = 30°, 60°, and 90°. The DMD decomposition performance is optimal at θ = 0° for the cylindrical surface. For pressure field reconstruction in the same wind direction, as the number of modes increases, the reconstruction relative error of the pressure field decreases, thereby enhancing reconstruction accuracy and the ability to capture details. Finally, short-term predictions of the coal shed’s wind pressure distribution were conducted, revealing better predictive performance near the incoming flow position. DMD can provide a basis for studying the wind pressure distribution on large-span structures such as coal sheds.

The aerodynamic force is a significant component that influences the stability and safety of structures. It has unstable properties and depends on computer precision, making its long-term prediction challenging. Accurately estimating the aerodynamic traits of structures is critical for structural design and vibration control. This paper establishes an unsteady aerodynamic time series prediction model using Long Short-Term Memory (LSTM) network. The unsteady aerodynamic force under varied Reynolds number and angles of attack is predicted by the LSTM model. The input of the model is the aerodynamic coefficients of the 1 to n sample points and output is the aerodynamic coefficients of the n+1 sample point. The model is predicted by interpolation and extrapolation utilizing Unsteady Reynolds-average Navier-Stokes (URANS) simulation data of flow around a circular cylinder, square cylinder and airfoil. The results illustrate that the trajectories of the LSTM prediction results and URANS outcomes are largely consistent with time. The mean relative error between the forecast results and the original results is less than 6%. Therefore, our technique has a prospective application in unsteady aerodynamic force prediction of structures and can give technical assistance for engineering applications.

Wind loading is a crucial factor affecting the safety and stability of long-span space structures. Therefore, studying the surface wind pressure is important for the design of coal shed structures. The wind tunnel test is the main method for obtaining the surface wind pressure of coal shed structure. However, it is associated with high costs and time-consuming procedures. One of the current research hotspots to develop a rapid wind pressure prediction method is adopting the large amount of data accumulated from wind tunnel test. In this study, a time series prediction model for coal shed structure wind pressure is thusly established upon Long Short-Term Memory (LSTM) neural network. The model utilizes Gaussian smoothing to divide experimental data into smooth and pulsating data, and then trains large-scale and small-scale networks separately. The results show that the multi-scale network prediction model proposed can achieve the rapid wind pressure prediction on the surface of coal shed. Compared to traditional LSTM neural network, the multi-scale LSTM neural network demonstrates advantages such as lower error and higher accuracy. Therefore, the multi-scale network based on LSTM can provide a basis for predicting surface wind pressure for long-span spatial structures such as coal sheds.

Structures with square cross-sections are widely used in engineering, thusly it is important to investigate the wind loading and wind-induced vibration characteristics of the flow around one square cylinder. The unsteady flow field of flow around the square cylinder usually involve a variety of complex flow phenomena. It is significant to capture the main modes of flow for the analysis of the flow field characteristics and the control of flow. In this study, a Reduced Order Model (ROM) is established upon the Dynamic Mode Decomposition (DMD) method to extract the main modes of the flow field and to reconstruct the flow field. The snapshots of the unsteady flow field are obtained upon numerical simulations. The main modes are extracted using DMD. The extracted modes are utilized to reconstruct the unsteady flow field. The results show that the first fourth modes extracted by the DMD method can accurately reconstruct the original flow field and provide a reference for flow control and structure design.

Aerodynamic force affects the stability and safety of bridge structures significantly. The understanding of its evolution is influenced by its unsteady characteristics and by computer accuracy, making it difficult to achieve long-term predictions. The accurate prediction of the aerodynamic properties of bridge structures is essential for structural design and vibration control. Wind tunnel tests and numerical simulations are currently the most widely used methods in aerodynamic research. However, wind tunnel tests are expensive, simulating complex wind field conditions is difficult, and numerical simulations depend strongly on computational resources. Therefore, to achieve a balance between computational volume and computational accuracy, in this study, an unsteady aerodynamic time-series prediction model for bridges at different angles of attack was developed using a long short-term memory (LSTM) network. For the model, aerodynamic coefficients of 0 to n moments under different wind attack angles were the input and the aerodynamic coefficients of the n+1 moments were the output. First, an LSTM network framework was constructed based on the open-source TensorFlow library. Second, training and test sets were constructed based on the numerical simulation results of the unsteady aerodynamic forces on a bridge at three angles of attack (3°, 4°, and 5°), and the models were trained. Finally, in the interpolation prediction, a dataset was constructed from the aerodynamic coefficients at angles of attack of 3° and 5° to train the model, and the aerodynamic coefficient of 4° was predicted. For extrapolation prediction, a dataset was constructed from the aerodynamic coefficients at angles of attack of 3° and 4° to train the model, and the aerodynamic coefficient of 5° was predicted. The results show that the LSTM prediction results are basically consistent with the trajectory, amplitude, and period of the numerical simulation results over time. To verify the generalization of the model further, the trained LSTM extrapolation prediction model was used to predict the aerodynamic coefficients at angles of attack of 0° and -3°. The results show that the model can predict the original results better. Therefore, this algorithm has potential applications in predicting the unsteady aerodynamics of bridge structures and can provide technical support for engineering applications.

Structures with square sections are widely used in engineering, so it is important to investigate the wind load and wind-induced vibration characteristics of flow around square cylinder. The unsteady flow field of flow around square cylinder usually involve a variety of complex flow phenomena. It is significant to capture the main modes of flow for analysis of the flow field characteristics and control of flow. In this paper, a Reduced Order Model (ROM) is established based on Dynamic Mode Decomposition (DMD) method to extract the main modes of the flow field and reconstruct the flow field. Firstly, the snapshots of the unsteady flow field are obtained based on numerical simulations. Secondly, the main modes are extracted using DMD. Finally the extracted modes are used to reconstruct the unsteady flow field. The results show that the first to four modes extracted by the DMD method can accurately reconstruct the original flow field and provide a reference for flow control and structure design.

Computational Fulid Dynamics (CFD) simulation method is one of the main research methods in the field of wind engineering, but its cost is high for flow fields with significant unsteady effects. This paper perform a rapid time-series lift-drag prediction model of two-dimensional unsteady flow around a circular cylinder based on the Long short-term memory (LSTM) neural network. First, the LSTM framework is constructed based on the open source Tensorflow library. After that, training set and testing set are generated based on the numerical simulation results with Reynolds numbers of 300, 600 and 1000, and the LSTM is trained to learn the time evolution of the mapping and the information of Reynolds number. Finally, the trained model is used to perform interpolation prediction and extrapolation prediction based on the Reynolds number distribution. The prediction results show that the LSTM model can accurately predict the lift and drag coefficients of two-dimensional flow around circular cylinder outside the Reynolds number distribution, and provide a reliable prediction for nonlinear fluid flow.

Wind load is one of the key factors affecting the safety and stability of long-span space structure, so it is of great significance to study the surface wind pressure of structure for the design of coal shed structure. Wind tunnel test is the main method to obtain the surface wind pressure of coal shed structure, but it is costly and time-consuming. It is one of the research hotspots to develop a rapid prediction method of wind pressure based on the large amount of data accumulated in wind tunnel test. Based on the Long Short-Term Memory (LSTM) neural network, a wind pressure time series prediction model of coal shed structure is established. The model uses Gaussian smoothing to divide experimental data into smooth data and pulsating data, and then trains large-scale network and small-scale network respectively. The results show that the proposed multi-scale network prediction model can realize the rapid prediction of coal shed surface wind pressure, and compared with the traditional LSTM neural network, the multi-scale LSTM neural network has the advantages of smaller error and higher precision. Therefore, the multi-scale network based on LSTM can provide a basis for the surface wind pressure of coal shed and other long-span spatial structures.