A bridge wind vibration quantity injection adaptive control system and method based on an RBF neural network

Abstract

The application relates to a bridge wind vibration momentum injection adaptive control system and method based on an RBF neural network, and belongs to the technical field of bridge engineering. The system comprises a box girder; the momentum injection device comprises at least one pair of rotating cylinders which are respectively rotationally installed on the upper and lower sides of a wind nozzle at the tail of the box girder; a vibration sensor is used for sensing the vibration state of the box girder; an adaptive control unit is configured to receive the signal of the vibration sensor, to perform online approximation on the nonlinear aerodynamic force under the coupling action of the rotating cylinder and the box girder by using a radial basis function neural network, and to generate a cylinder rotating speed control instruction in combination with a sliding mode adaptive control algorithm; and a driving mechanism is connected between the adaptive control unit and the rotating cylinder and is used for driving the rotating cylinder to rotate according to the cylinder rotating speed control instruction. Through the application, the problems that the existing bridge wind vibration active control lacks a momentum injection device and an adaptive control system and cannot effectively and timely suppress the wind-induced unstable vibration of the box girder are solved.

Description

Technical Field

[0001] This invention relates to an adaptive control system and method for injecting wind vibration data into bridges based on RBF neural networks, belonging to the field of bridge engineering technology. Background Technology

[0002] As bridge engineering develops towards longer spans and lighter, more flexible structures, the sensitivity of bridge structures to wind loads has significantly increased. Wind-induced vibration has become a key factor affecting the safety and applicability of long-span bridges. To suppress harmful vibrations of bridges under wind loads and improve their wind resistance stability, various wind vibration control measures have been developed in engineering practice. Based on their mechanisms of action and operation, these measures can be mainly divided into three categories: fixed aerodynamic control measures, movable aerodynamic control measures, and active aerodynamic control measures.

[0003] Fixed aerodynamic control measures, such as the installation of nozzles, deflectors, central stabilizing plates, and central slots, improve aerodynamic performance by optimizing the flow field distribution around the main girder cross-section, thereby increasing the bridge's flutter critical wind speed. These measures offer advantages such as simple structure, no need for external energy, and easy maintenance, and are widely used in traditional bridge wind-resistant design, as seen in bridges like the Akashi Kaikyo Bridge and the Runyang Yangtze River Bridge. However, the aerodynamic optimization effect of fixed measures is often specific to particular wind speeds and directions, exhibiting weak adaptability and difficulty in coping with complex and variable actual wind environments.

[0004] Movable aerodynamic control measures achieve passive or semi-active movement of the control surface through mechanical devices without continuous external energy input. Examples include horizontal sliding devices, nozzle devices driven by the vibration of the main beam, tuned mass dampers (TMDs) and their variants. These measures improve the adaptability to wind-induced vibrations to some extent, but their motion modes are usually fixed or limited by the mechanical design, making it difficult to dynamically adjust according to the real-time wind field and structural conditions. Therefore, the control effect and robustness are still limited.

[0005] Active aerodynamic control measures monitor bridge vibration in real time using sensors, and then calculate and drive actuators to apply control forces via a controller, achieving real-time tracking and active suppression of vibration. This method has potential advantages such as fast response, strong adaptability, and significant control effect, and is considered a cutting-edge direction in bridge wind-induced vibration control. Current research has proposed various active control schemes, such as active control flanges, active control surfaces, and active mass dampers (AMD), and their feasibility has been verified through wind tunnel tests and theoretical analysis. However, the practical application of active control in bridge engineering still faces several key challenges:

[0006] First, active control systems typically involve complex fluid-structure interaction effects between the main beam and the control surface, and their relative motion leads to mutual interference of aerodynamic forces. Existing studies often employ the assumption of "no interference between flow fields," linearly superimposing the aerodynamic forces acting on the main beam and the control surface. This assumption deviates from reality, making it difficult to accurately describe the nonlinear aerodynamic characteristics of the system, thus affecting the accuracy and reliability of the control model.

[0007] Secondly, due to the highly nonlinear and unsteady characteristics of the flow field around the bridge cross-section, the aerodynamic forces acting on the main beam-control surface-airflow coupling system are difficult to express accurately using analytical functions. Traditional control algorithms rely on precise system models, which often fail to guarantee control stability and robustness when facing such highly nonlinear and uncertain systems, thus limiting the applicability and effectiveness of active control methods in practical engineering.

[0008] Furthermore, in the field of active flow control, there is an approach that involves locally introducing momentum to alter boundary layer characteristics, thereby suppressing flow separation and vortex shedding. This method has shown potential in simple fluid flows in aerospace and mechanical fields. However, successfully applying it to the main girder cross-section of bridge box girders with complex aerodynamic shapes, large scale, and low damping characteristics presents unique challenges: how to design effective momentum injection strategies and device placement methods tailored to the unique wake structure and wind-blown areas of the box girder; and how to characterize and model the highly nonlinear aerodynamic forces resulting from the coupling between the momentum injection device and the main girder motion. Currently, a systematic solution is lacking to fully address these challenges, resulting in this approach not yet forming a mature and reliable technical system for bridge wind-induced vibration adaptive control.

[0009] Therefore, the field of active wind-induced vibration control for bridges urgently needs a new technological solution that can overcome the aforementioned limitations. This solution must be able to effectively handle the problem of high-precision modeling of nonlinear aerodynamic forces coupled with complex main girder cross-sections and local momentum injection devices, and on this basis, achieve intelligent vibration control that does not rely on precise mathematical models and possesses online learning and adaptive adjustment capabilities. Summary of the Invention

[0010] The technical problem to be solved by the present invention is to provide an adaptive control system and method for bridge wind vibration injection based on RBF neural network. It solves the problem that the lack of momentum injection device and adaptive control system in the existing active control of bridge wind vibration leads to the inability to effectively suppress wind-induced unstable vibration of box girders in real time.

[0011] The technical problem to be solved by this invention is achieved by the following technical solution:

[0012] An adaptive control system for bridge wind vibration injection based on RBF neural network, including a box girder, and further comprising:

[0013] A momentum injection device, comprising at least a pair of rotating cylinders respectively rotatably mounted on the upper and lower sides of the air nozzle at the tail of the box girder;

[0014] Vibration sensors are used to sense the vibration state of the box girder;

[0015] An adaptive control unit is configured to receive signals from the vibration sensor, approximate the nonlinear aerodynamic forces under the coupling action of the rotating cylinder and the box girder online using a radial basis function neural network, and generate cylinder rotation speed control commands to suppress wind-induced vibrations of the box girder using a sliding mode adaptive control algorithm; and,

[0016] A drive mechanism, connecting the adaptive control unit and the rotating cylinder, is used to drive the rotating cylinder to rotate according to the cylinder speed control command.

[0017] The present invention is further configured such that the ratio of the diameter of the rotating cylinder to the height of the box girder is 0.18 ± 0.02;

[0018] The distance between the outer edge of the rotating cylinder and the outer edge of the tail nozzle of the box girder is 0.3 to 0.4 times the diameter of the rotating cylinder.

[0019] An adaptive control method for bridge wind vibration injection based on RBF neural network, the method being applied to the system described in claim 1 or 2, includes the following steps:

[0020] Monitor the vibration state of the box girder, and when the amplitude of the vibration exceeds a preset safety threshold, obtain the current vibration state of the box girder;

[0021] A radial basis function neural network is used to approximate the nonlinear aerodynamic forces acting on the box girder, which are generated by the coupling of the box girder's own motion and the motion of the rotating cylinder.

[0022] Based on sliding mode adaptive control theory and combined with the approximation results of the radial basis function neural network, the target rotational speed of the rotating cylinder that enables the box girder vibration to track the preset ideal trajectory is calculated.

[0023] The rotating cylinder is controlled to rotate at the target speed.

[0024] The present invention is further configured such that: in the step of controlling the rotating cylinder to rotate at a target speed, based on the comprehensive optimization objective of suppressing efficiency and energy consumption, any one of the following speed control strategies is adaptively selected and executed:

[0025] Based on the current prevailing wind speed range, determine and maintain a constant optimal rotational speed; or,

[0026] The rotational speed of the rotating cylinder is modulated with a periodic component.

[0027] The frequency of the periodic component is set based on the natural frequency of the box girder structure or the frequency of the dominant vibration component in the vibration state.

[0028] The present invention is further configured such that: calculating the target rotational speed of the rotating cylinder that enables the box girder vibration to track a preset ideal trajectory specifically includes:

[0029] Construct a sliding surface based on the error between the actual movement trajectory of the box girder and the preset ideal trajectory;

[0030] Based on the internal state of the sliding surface and the radial basis function neural network, the parameters of the neural network are adjusted online so that the network adapts to system changes in approximation of nonlinear aerodynamic forces.

[0031] The approximation result, the sliding surface information, and the linear dynamics of the system are combined to generate the target rotational speed, which includes a robust compensation term.

[0032] The present invention is further configured such that: the online approximation using a radial basis function neural network specifically includes:

[0033] Build and configure the first and second subnetworks;

[0034] The displacement and velocity signals reflecting the motion state of the box girder are input into the first sub-network to approximate the nonlinear aerodynamic components caused by the motion of the box girder itself.

[0035] The displacement and velocity signals of the box girder's motion state, along with the current rotational speed signal of the rotating cylinder, are input into the second sub-network to approximate the nonlinear aerodynamic control component related to rotational speed caused by the motion of the rotating cylinder.

[0036] The present invention is further configured such that: the online adjustment of the parameters of the neural network specifically includes:

[0037] A first adaptive law is set for the parameters of the first sub-network, the value of which is negatively correlated with the value of the sliding surface and the basis function output of the first sub-network;

[0038] A second adaptive law is set for the parameters of the second sub-network. The value of the second adaptive law is negatively correlated with the value of the sliding surface, the basis function output of the second sub-network, and the value of the target rotational speed.

[0039] The present invention is further configured such that the nonlinear aerodynamic control component caused by the motion of the rotating cylinder includes a higher-order harmonic component related to the fundamental frequency of the rotation of the rotating cylinder.

[0040] The present invention is further configured such that: the method also includes a preparatory step of offline training of the radial basis function neural network;

[0041] A fluid dynamics calculation model including the box girder and the rotating cylinder is established, and the rotation of the rotating cylinder is simulated in the model using the sliding mesh technique;

[0042] In the calculation model, the box girder is set to undergo wind-induced vibration motion, and the rotating cylinder is set to rotate in multiple different speed modes.

[0043] Through fluid dynamics calculations, the motion state data of the box girder, the rotation state data of the rotating cylinder, and the corresponding aerodynamic force data acting on the surface of the box girder are acquired simultaneously.

[0044] The motion state data of the box girder and the rotation state data of the rotating cylinder are combined as input samples, and the corresponding aerodynamic data are used as output samples to form a dataset for training the radial basis function neural network.

[0045] The present invention is further configured such that the preset ideal trajectory is a zero trajectory or an amplitude-controlled reduced vibration trajectory.

[0046] The beneficial effects of this invention are:

[0047] 1. By symmetrically arranging rotating cylinders on the upper and lower sides of the tail vortex nozzles of the box girder, the origin region of the wake vortex shedding from the box girder can be intervened in the most direct and effective way. This specific arrangement is an optimized scheme determined after systematic computational fluid dynamics simulation and comparison. Compared with other methods such as embedding cylinders into the surface of the box girder or arranging them only on one side, it can most effectively promote the convergence of airflow on the upper and lower sides of the tail, thereby significantly disrupting and eliminating the large-scale periodic vortices that cause wind-induced vibrations. It transforms the aerodynamic force acting on the surface of the box girder from a periodic force with a significant and dominant frequency into random fluctuation characteristics, fundamentally destroying the conditions for the generation of aeroelastic instability.

[0048] 2. Through the coordinated optimization of structural design and control strategy, a balance between control efficiency and energy consumption was achieved. Based on the optimal rotating cylinder arrangement and dimensional parameters selected through computational fluid dynamics simulation, the momentum injection device was ensured to achieve maximum flow field control benefits with minimal geometric intervention. In terms of control strategy, the system can adaptively select between maintaining a constant optimal rotational speed or applying periodically modulated rotational speed according to real-time wind vibration characteristics. The former is energy-efficient under stable wind conditions, while the latter is more effective in dealing with strong periodic vibrations. This flexible rotational speed strategy effectively reduces the long-term operating energy consumption of the system while ensuring excellent vibration suppression.

[0049] 3. By introducing a radial basis function neural network and innovatively using a twin network structure to approximate aerodynamic components from different physical sources, the system can accurately fit the strong nonlinear aerodynamic forces that are difficult to describe under the coupling action of a box girder and a rotating cylinder without relying on any precise analytical mathematical model.

[0050] 4. By deeply integrating sliding mode adaptive control theory with radial basis function neural networks, the system not only utilizes the universal approximation characteristics of neural networks to handle nonlinearities, but also ensures the inherent robustness of the system under parameter perturbations and external disturbances through sliding mode control. The neural network weights are adaptively adjusted online according to the sliding surface error, enabling the entire control system to dynamically track and adapt to changes in wind field conditions, structural frequencies, etc., ensuring that the box girder can be driven to stably track the preset ideal vibration reduction trajectory under different wind speeds and vibration modes, demonstrating superior environmental adaptability and control stability. Attached Figure Description

[0051] Figure 1 This is a schematic diagram of the cross-section of the box girder in the system of the present invention.

[0052] Figure 2 This is a schematic diagram of the numerical calculation region and boundary conditions for the box girder in the system of this invention.

[0053] Figure 3 This is a schematic diagram of the grid near the box girder and rotating cylinder in the system of the present invention.

[0054] Figure 4 This is a schematic diagram of the layout scheme of the momentum injection device in the system of the present invention.

[0055] Figure 5 This is a schematic diagram of the time-averaged flow field around the box girder under different layout methods of the system of the present invention.

[0056] Figure 6 When the rotating cylinder moves at a constant speed in the embodiment of the present invention ( A schematic diagram of the flow field around the box girder.

[0057] Figure 7 When the rotating cylinder moves at a constant speed in the embodiment of the present invention ( A schematic diagram of the aerodynamic forces and their frequency-amplitude characteristics on the surface of the box girder.

[0058] Figure 8 This is a schematic diagram of the aerodynamic forces and frequency-amplitude characteristics on the surface of the box girder when no control measures are applied in an embodiment of the present invention.

[0059] Figure 9 When the rotating cylinder moves at a constant speed in the embodiment of the present invention ( A schematic diagram of the flow field around the box girder.

[0060] Figure 10 When the rotating cylinder moves at a constant speed in the embodiment of the present invention ( A schematic diagram of the aerodynamic forces and their frequency-amplitude characteristics on the surface of the box girder.

[0061] Figure 11 In this embodiment of the invention, the rotating cylinder undergoes variable speed motion as follows: A schematic diagram of the flow field around the box girder.

[0062] Figure 12 In this embodiment of the invention, the rotating cylinder undergoes variable speed motion as follows: A schematic diagram of the aerodynamic forces and frequency-amplitude characteristics on the surface of the box girder.

[0063] Figure 13 In this embodiment of the invention, the rotating cylinder undergoes variable speed motion as follows: A schematic diagram of the flow field around the box girder.

[0064] Figure 14 In this embodiment of the invention, the rotating cylinder undergoes variable speed motion as follows: A schematic diagram of the aerodynamic forces and frequency-amplitude characteristics on the surface of the box girder.

[0065] Figure 15 This is a diagram of the RBF neural network structure in an embodiment of the present invention.

[0066] Figure 16 This is a schematic diagram of the movement of the box girder and the rotating cylinder in an embodiment of the present invention.

[0067] Figure 17 In this embodiment of the invention, the box girder movement is as follows: Cylindrical motion is A schematic diagram of the aerodynamic forces and frequency-amplitude characteristics on the surface of the box girder.

[0068] Figure 18 In this embodiment of the invention, the box girder movement is as follows: Cylindrical motion is A schematic diagram of the aerodynamic forces and frequency-amplitude characteristics on the surface of the box girder.

[0069] Figure 19 In this embodiment of the invention, the box girder movement is as follows: Cylindrical motion is A schematic diagram of the aerodynamic forces and frequency-amplitude characteristics on the surface of the box girder.

[0070] Figure 20 This is a schematic diagram of adaptive control in an embodiment of the present invention.

[0071] Figure 21This is a graph showing the relationship between the vibration response of the box girder and the rotational speed (15m / s) of the cylinder in an embodiment of the present invention.

[0072] Figure 22 This is a graph showing the relationship between the vibration response of the box girder and the rotational speed (25 m / s) of the cylinder in an embodiment of the present invention.

[0073] Figure 23 The vibration response of the box girder and the rotational speed of the cylinder in the embodiments of the present invention are The relationship between the changes is shown in the diagram.

[0074] Figure 24 The vibration response of the box girder and the rotational speed of the cylinder in the embodiments of the present invention are The relationship between the changes is shown in the diagram. Detailed Implementation

[0075] To facilitate a clear understanding of the technical means, creative features, objectives, and effects of this invention, the invention will be further described below in conjunction with specific illustrations.

[0076] Traditional active wind-induced vibration control methods for bridges often suffer from limited control effectiveness when applied to box girder sections due to the difficulty in accurately modeling the complex fluid-structure interaction effect between the main girder and the control surface.

[0077] like Figure 1 As shown, an adaptive control system for bridge wind vibration injection based on RBF neural network includes a box girder, a momentum injection device, a drive mechanism, vibration sensors, and an adaptive control unit, wherein:

[0078] In this embodiment of the invention, for ease of comparison and analysis, the anti-collision railings on the bridge deck and the maintenance track under the beam are not considered when performing calculations.

[0079] The momentum injection device includes at least one pair of rotating cylinders, each rotatably mounted on the upper and lower sides of the wind nozzle at the tail of the box girder. These rotating cylinders can be made of high-strength aluminum alloy or stainless steel, and their surfaces can be treated for corrosion resistance to adapt to the humid and high-wind-load environment of the bridge. The rotating cylinders are fixed to the upper and lower sides of the wind nozzle at the tail of the box girder via bearing seats, which are bolted to the box girder for easy installation and maintenance. The drive end of the rotating cylinder is connected to the output shaft of the drive mechanism via a coupling. The number of rotating cylinders can be increased according to the width of the box girder and the wind vibration mode; for example, multiple pairs of cylinders can be arranged in a wide box girder to enhance the control effect.

[0080] Vibration sensors are used to sense the vibration state of the box girder. High-precision acceleration sensors or displacement sensors can be selected and placed at the mid-span of the box girder or at locations with significant vibration response. The sensors are connected to the adaptive control unit via signal cables to acquire the vibration acceleration or displacement signals of the box girder in real time.

[0081] The adaptive control unit is configured to receive signals from vibration sensors, use a radial basis function neural network to approximate the nonlinear aerodynamic forces under the coupling action of the rotating cylinder and the box girder online, and combine a sliding mode adaptive control algorithm to generate cylinder speed control commands to suppress wind-induced vibration of the box girder.

[0082] The drive mechanism connects the adaptive control unit to the rotating cylinder and drives the cylinder to rotate according to the cylinder's speed control command. The drive mechanism can be a servo motor or a stepper motor, which is connected to the rotating shaft of the cylinder through a reducer. The drive mechanism receives speed commands from the adaptive control unit and achieves precise adjustment of the cylinder's speed through closed-loop control.

[0083] The ratio of the diameter of the rotating cylinder to the height of the box girder is 0.18 ± 0.02. Based on numerical simulation and wind tunnel test results, the optimal ratio of the rotating cylinder diameter D0 to the box girder height H is 0.18. For example, when the box girder height is 2.5m, the cylinder diameter should preferably be 0.45m. This ratio ensures that the cylinder has sufficient momentum injection capacity without excessively increasing structural drag and energy consumption. In practical applications, this ratio can be fine-tuned according to the actual aerodynamic shape of the box girder; this embodiment of the invention does not impose any limitations on this.

[0084] The distance between the outer edge of the rotating cylinder and the outer edge of the tail nozzle of the box girder is 0.3 to 0.4 times the diameter of the rotating cylinder. For example, when the cylinder diameter is 0.45m, the spacing d0 can be between 0.135m and 0.18m. This distance range ensures that the cylinder can effectively influence the tail flow field while avoiding interference with the box girder structure. In practical applications, this distance can be adjusted according to specific installation conditions, and this embodiment of the invention does not limit this.

[0085] To determine the optimal arrangement and parameter range of the aforementioned rotating cylinder, this invention conducted a systematic comparative study using computational fluid dynamics (CFD) numerical simulation methods. A system was established as follows... Figure 1 The box girder cross-section model shown is configured as follows. Figure 2 The computational domain and boundary conditions are shown. The computation was performed using the RANS-based method provided by the commercial software Fluent. A two-equation model and sliding mesh technique were used to simulate the flow field control effect of a rotating cylinder under different layout schemes.

[0086] like Figure 3 As shown, quadrilateral meshes were used to improve computational accuracy, with a total of 145,000 meshes. To simulate momentum injection, this embodiment of the invention uses a sliding mesh method to realize the rotation of the cylinder, avoiding mesh distortion caused by large displacements of the cylinder's motion.

[0087] The calculation parameters are set as follows: momentum, turbulent kinetic energy and energy dissipation are discretized using a two-order upwind scheme, pressure-velocity coupling is performed using the SIMPLE algorithm, the solver is a split-type solver, and the calculation mode is a two-order implicit scheme.

[0088] The boundary conditions were set as follows: velocity inlet, initial inlet wind speed 7.5 m / s, turbulence intensity 0.5%, pressure outlet, and the upper and lower edges of the computational domain were set as no-slip fixed wall conditions. The computation time step was set to... The residual calculated in each iteration is less than The calculation results are considered to have converged.

[0089] like Figure 4 As shown, in order to compare and analyze the control effect of the spatial arrangement of the momentum injection device on the flow field of the box girder, the embodiments of the present invention conducted numerical simulation calculations under the following five scenarios:

[0090] (1) No control measures are implemented, such as Figure 4 As shown in (a);

[0091] (2) Install separate rotating cylinders at the windward and rear ends of the underside of the box girder, such as Figure 4 As shown in (b);

[0092] (3) Install embedded rotating cylinders at the windward and rear ends of the underside of the box girder, such as... Figure 4 As shown in (c);

[0093] (4) Install embedded rotating cylinders at the windward end, tail end, and tail vent of the box girder, such as... Figure 4 As shown in (d);

[0094] (5) Install separate rotating cylinders on the upper and lower sides of the air nozzle at the tail of the box girder, such as Figure 4 As shown in (e).

[0095] When performing calculations for the above five operating conditions, the incoming air velocity is 7.5 m / s, the box girder remains stationary, only the rotating cylinder rotates, the cylinder diameter D0 is taken as 0.18 times the height of the box girder, the distance from the edge of the cylinder to the outer edge of the box girder is d0 = 1 / 3 * D0, the rotational speed of the cylinder is 2500 rad / s, and the direction of rotation is as follows. Figure 4 (b)- Figure 4 As shown in (e).

[0096] like Figure 5 As shown, the flow field distribution around the box girder under the above five working conditions is given:

[0097] Without control measures, two vortices of similar size form near the vent at the tail of the box girder, such as... Figure 5 As shown in (a).

[0098] When the momentum control device is deployed using method 1, the momentum injection increases the distance between the tail vortex and the tail end of the box girder, but it cannot eliminate the tail vortex. Figure 5 As shown in (b).

[0099] When the momentum injection device is installed in an embedded manner, the vortex at the tail of the box girder cannot be effectively controlled, and the introduction of the momentum injection device also causes large-scale vortices to form on the lower surface of the box girder, such as... Figure 5 (c) and Figure 5 As shown in (d).

[0100] When the momentum injection device is installed in mode 4, the vortex at the tail of the box girder is effectively controlled, and the airflow above and below the tail nozzles converges through the momentum injection device, such as... Figure 5 As shown in (e).

[0101] The comparative studies described above demonstrate that separating the rotating cylinders and placing them on the upper and lower sides of the tail nozzles of the box girder can specifically inject momentum into the initial region of wake vortex shedding, directly intervening in the formation process of the most destructive large-scale vortices. Combined with optimized size and spacing parameters, this maximizes both energy injection efficiency and control effectiveness.

[0102] Through systematic numerical comparison, the arrangement and parameter range claimed in the embodiments of the present invention have been determined to have clear technical advantages. Compared with other possible arrangements, this scheme can more effectively eliminate tail vortices and disrupt the periodicity of aerodynamic forces, providing a stable and efficient aerodynamic control foundation for subsequent adaptive control based on RBF neural networks.

[0103] Based on the above analysis, it can be seen that when the momentum injection device adopts the arrangement method of mode 4, the large-scale vortex at the tail of the box girder can be effectively controlled. The following analysis examines the influence of the rotational cylinder's motion mode on the flow field around the box girder and the aerodynamic forces on the model surface when using this arrangement method. This paper presents calculations and analyses under two motion modes: one where the rotating cylinder maintains a constant speed, and the other where the rotational speed of the rotating cylinder changes periodically.

[0104] In analyzing the first type of motion mode, for comparative analysis, the rotational speed of the cylinder was taken as follows: and These two values.

[0105] like Figure 6 As shown, the rotational speed is given. The flow field diagram around the box girder is shown in the figure. It can be seen from the figure that at this rotational speed, the large-scale vortices at the tail of the box girder are effectively controlled. The aerodynamic time-history curves on the model surface further illustrate the effect of momentum injection.

[0106] like Figure 7 As shown, the aerodynamic forces acting on the surface of the box girder and their frequency-amplitude characteristics at this rotational speed are presented, such as... Figure 8 As shown, the aerodynamic forces and frequency-amplitude characteristics of the action model surface of the box girder in a static state (without control measures) are presented.

[0107] contrast Figure 7 and Figure 8 It can be seen that the aerodynamic force acting on the model surface after momentum injection exhibits random fluctuation characteristics. The aerodynamic force does not have a dominant frequency. Without control measures, due to the periodic shedding of vortices, the aerodynamic force formed on the box girder surface has obvious periodic characteristics.

[0108] like Figure 9 As shown, the rotational speed is given. The flow field diagram around the box girder is shown in the figure. It can be seen from the figure that at this rotational speed, the airflow on the upper and lower sides of the box girder's tail converges at one point through the momentum injection device, the large-scale vortices near the tail nozzle disappear, and the aerodynamic forces acting on the box girder surface exhibit random fluctuation characteristics (e.g., ...). Figure 10 As shown in the figure, there is no dominant frequency. Therefore, increasing the rotational speed of the rotating cylinder can more effectively control the flow field at the tail of the box girder.

[0109] In analyzing the second type of motion mode, two different equations of motion were used for the cylinder's rotational speed for comparison:

[0110] One of the equations is: , ;

[0111] Another equation of motion is: , .

[0112] like Figure 11 As shown, the equation for rotational speed is given as follows: The flow field characteristics around the box girder are shown in the figure. As can be seen from the figure, after the momentum injection from the rotating cylinder, the large-scale vortices at the tail of the box girder are effectively eliminated, leaving only some smaller vortices. The aerodynamic forces acting on the surface of the box girder are significantly affected by the rotating cylinder (e.g., Figure 12 As shown in the figure, since the rotation of the rotating cylinder is periodic, the aerodynamic force acting on the surface of the box girder also exhibits periodic variation characteristics, and under this working condition, the dominant frequency of the aerodynamic force is equal to the frequency of the rotor motion.

[0113] like Figure 13 As shown, the rotational speed is given. The flow field distribution around the box girder is shown in the figure. It can be seen from the figure that the flow field at the tail of the box girder is effectively controlled. Large-scale vortices in the flow field at the tail of the box girder effectively disappear. However, under this condition, the periodic motion of the rotating cylinder causes the aerodynamic forces on the surface of the box girder to exhibit complex frequency components, including higher-order harmonics of the rotor's motion frequency, and the aerodynamic forces have obvious nonlinear characteristics (e.g., Figure 14 (As shown).

[0114] An adaptive control method for bridge wind vibration injection based on RBF neural network includes the following steps:

[0115] S1. Monitor the vibration state of the box girder. When the vibration amplitude exceeds the preset safety threshold, obtain the current vibration state of the box girder.

[0116] Vibration safety thresholds can be set according to bridge design specifications and actual operational requirements; for example, the torsional angle amplitude threshold can be set to 0.5°. When the sensor detects that the vibration amplitude exceeds the threshold, the system enters active control mode and collects real-time displacement and velocity signals of the box girder.

[0117] S2. Using a radial basis function (RBF) neural network, the nonlinear aerodynamic forces acting on the box girder, generated by the coupling of the box girder's own motion and the motion of the rotating cylinder, are approximated online.

[0118] like Figure 15 As shown, RBF neural networks generally have an input layer, a hidden layer, and an output layer. They can approximate any nonlinear function, handle the difficult-to-analyze regularities within a system, have good generalization ability, and have a fast learning and convergence speed.

[0119] To verify the ability of the RBF neural network to simulate the nonlinear aerodynamics of the momentum injection device-box girder-fluid system, a fluid dynamics calculation model including the box girder and the rotating cylinder was established, and the rotation of the rotating cylinder was simulated in the model using the sliding mesh technique.

[0120] In this embodiment of the invention, a box girder is subjected to wind-induced vibration motion. Through fluid dynamics calculations, motion state data of the box girder, rotation state data of the rotating cylinder, and corresponding aerodynamic force data acting on the surface of the box girder are acquired simultaneously. The motion state data of the box girder and the rotation state data of the rotating cylinder are combined as input samples, and the corresponding aerodynamic force data are used as output samples to form a dataset for training a radial basis function neural network.

[0121] Specifically, CFD numerical calculations were used to obtain the results when the box girder underwent torsional motion. When a rotating cylinder undergoes amplitude-varying motion At that time, the aerodynamic forces acting on the surface of the box girder have the following computational domain: Figure 16 As shown.

[0122] The torsional motion of the box girder and the rotation of the rotating cylinder are both simulated using a sliding mesh. The torsional motion equation of the main girder is as follows: Torque Amplitude Taken as 3 degrees, frequency The frequency is 6.60Hz. The rotating cylinder is also set to rotate at various speeds; the equations of motion for the rotating cylinder are compared in three cases, with the specific formulas as follows:

[0123] (1-a)

[0124] (1-b)

[0125] (1-c)

[0126] Based on the aerodynamic forces obtained from CFD calculations, the following analysis uses an RBF neural network to fit the numerically calculated aerodynamic forces. The neural network structure used in this embodiment is 3-20-1, meaning the input layer has 3 grid nodes, the hidden layer has 20 nodes, and the output layer has 1 grid node. The input of the neural network... The displacements of the box girder are respectively Speed ​​item and the rotational speed of the cylinder ;

[0127] The relevant parameters of the Gaussian function in the RBF neural network are:

[0128] The center vector of a neuron , ,in , The maximum and minimum values ​​related to the input; This represents the number of hidden layer nodes. ; Neural network basis width vector

[0129] , Initial weights of the network The value is a random number within the range [0, 1]. The learning rate of the neural network. Momentum factor .

[0130] like Figure 17 As shown, the torsional motion of the box girder is given as follows: The rotational speed of the cylinder is The figure shows the fitting effect of the RBF neural network on the nonlinear aerodynamic forces acting on the surface of the box girder. As can be seen from the figure, the fitted values ​​of the RBF for the aerodynamic forces agree well with the CFD numerical calculation results. This provides a foundation for designing an adaptive control law for the momentum injection device-box girder-fluid system by comprehensively applying the RBF neural network and sliding mode control method.

[0131] Torsional motion law of box girder Keeping constant, when the rotational frequency of the rotating cylinder increases to Twice the time, that is, the cylinder rotates according to During rotation, under this working condition, the aerodynamic force acting on the surface of the box girder is as follows: Figure 18 As shown in the figure, under this working condition, the fitted value of RBF to aerodynamic forces still matches the CFD numerical calculation results well.

[0132] Torsional motion law of box girder Assuming that the rotational frequency of the rotating cylinder remains constant, if the rotational frequency continues to increase to Three times the time, that is, the cylinder rotates according to During rotation, under these conditions, the aerodynamic forces acting on the surface of the box girder, such as... Figure 19 As shown.

[0133] Therefore, as can be seen from the figure, under this working condition, the RBF neural network can still simulate the nonlinear aerodynamic forces of the fluid-structure interaction system quite well.

[0134] The above analysis shows that the RBF neural network can effectively simulate the nonlinear aerodynamic forces of the momentum injection device-box girder-fluid system. The following section discusses an adaptive control method for wind-induced vibration of box girders based on momentum injection, combining the RBF neural network and sliding mode control.

[0135] In practical engineering, the vortex-induced vibration of box girders is a single-degree-of-freedom vibration. Therefore, to simplify the analysis, this embodiment of the invention takes the single-degree-of-freedom torsional vibration of a box girder under wind load as an example to carry out adaptive control design of the vibration system. The equation for the single-degree-of-freedom torsional vibration of the box girder is shown in the following formula (2):

[0136] (2)

[0137] In the formula: , , These are the mass moment of inertia of the box girder, the damping of the vibration system, and the stiffness, respectively. This represents the torsional displacement of the system. This refers to the aerodynamic force generated on the surface of the box girder during its movement. It is related to the torsional displacement and velocity of the box girder, that is ; , These represent the aerodynamic forces generated on the surface of the box girder when the rotating cylinder at the tail of the model moves up and down. The torsional displacement and velocity of the box girder and the rotational speed of the cylinder Related, that is ; The rotational speed of the cylinder. The diameter of the rotating cylinder.

[0138] To simplify the calculation, the above formula can be further written as: (3-a)

[0139] (3-b)

[0140] Because in actual analysis, it is not necessary to determine , The function expression only needs to determine The expression is sufficient. To rewrite the above formula (3) in the form of a state equation, let:

[0141] , (4)

[0142] Then formula (3) can be expressed as the following state equation:

[0143] (5)

[0144] In the formula: , , .

[0145] As can be seen from the previous analysis, the aerodynamic forces of the momentum injection device-box girder-fluid system have obvious nonlinear characteristics. Therefore, the control equation (5) above... and Both should be nonlinear functions, but these two functions are difficult to describe using analytical mathematical expressions. Therefore, in this embodiment, a first sub-network and a second sub-network are constructed and configured. Both the first and second sub-networks are radial basis function neural networks used to describe the nonlinear functions. , .

[0146] First Sub-network It is configured to approximate the nonlinear aerodynamic components directly generated by the wind-induced vibration of the box girder itself.

[0147] (6-a)

[0148] Second Subnetwork It is configured to approximate the rotational speed-dependent nonlinear aerodynamic control component introduced by the rotation of a rotating cylinder. The nonlinear aerodynamic control component caused by the motion of the rotating cylinder includes higher-order harmonic components related to the fundamental frequency of the rotating cylinder's rotation.

[0149] (6-b)

[0150] In the formula: For network input, , This is the output of the Gaussian function. , These are the ideal weights for the neural network.

[0151] S3. Based on sliding mode adaptive control theory and combined with the approximation results of radial basis function neural networks, the target rotational speed of the rotating cylinder that enables the box girder vibration to track the preset ideal trajectory is calculated. The preset ideal trajectory is either a zero trajectory or a reduced-amplitude vibration trajectory with controlled amplitude.

[0152] For the aforementioned control system based on RBF, the key issue lies in how to determine the weights of the neural network. , and control laws This invention employs a sliding mode adaptive control method for designing the control law of a vibration system. Figure 20 ).

[0153] A sliding surface is constructed based on the error between the actual motion trajectory of the box girder and the preset ideal trajectory. The ideal trajectory is defined as follows: The actual trajectory output by the neural network is The tracking error of the calculation system The sliding surface is designed as follows: , For the specified parameter, for example, take =3.0. This sliding surface can simultaneously reflect the magnitude and trend of the error.

[0154] Based on the internal state of the sliding mode surface and radial basis function neural network, the parameters of the neural network are adjusted online to make the network adapt to system changes in approximation of nonlinear aerodynamic forces.

[0155] According to formula (5) and combined with the Lyapunov stability criterion, a first adaptive law is set for the parameters of the first subnetwork. The value of the first adaptive law is negatively correlated with the value of the sliding surface and the basis function output of the first subnetwork. A second adaptive law is set for the parameters of the second subnetwork. The value of the second adaptive law is negatively correlated with the value of the sliding surface, the basis function output of the second subnetwork, and the value of the target rotational speed.

[0156] (7-a)

[0157] (7-b)

[0158] In the formula: , To specify parameters.

[0159] Then the RBF neural network pairs , The approximate output is:

[0160] (8-a)

[0161] (8-b)

[0162] The approximation result, the sliding surface information, and the linear dynamics of the system are combined to generate the target rotational speed, which includes a robust compensation term. Its control law... Calculate according to the following formula (9):

[0163] (9)

[0164] in: For parameters, For symbolic functions, specifically:

[0165] (10)

[0166] For detailed derivations of the first adaptive law, the second adaptive law, and the control law, please refer to the reference "A Review and Reflection on Wind Vibration Control of Long-Span Cable-Rolled Bridges - Passive Control Effect and Active Control Strategy of Main Girder" - Zhao Lin, Ge Yaojun, Guo Zengwei, Li Ke - Journal of Civil Engineering, 2015, 48(12):91-98.

[0167] By employing a sliding mode adaptive control method based on RBF neural networks, the vibration of the box girder can be controlled by adjusting the rotational speed of the cylinder, ensuring that the girder's motion trajectory closely follows the preset ideal command. This means that under different wind speeds, adaptive control can guarantee that the box girder's vibration follows the specified ideal motion trajectory, ensuring the stability and safety of the vibration system.

[0168] Based on the control method established above, the tracking effect of the box girder's motion trajectory on the ideal command is discussed under different wind speeds and natural frequencies, verifying the reliability of the method. The basic parameters of the vibration system are as follows: width of the box girder... Moment of inertia Torsional vibration frequency Torsional damping ratio Assume the ideal trajectory of the vibration system is .

[0169] Using RBF neural networks to simulate nonlinear functions and Among them, simulation The function uses a 2-20-1 neural network structure, and the network input is the torsional displacement of the box girder. and speed The number of hidden neurons is 20; simulation The function uses a 3-20-1 neural network structure, and the network input is the torsional displacement of the box girder. ,speed and the rotational speed of the cylinder The number of hidden neurons is also 20. The relevant parameters of the Gaussian function in the RBF neural network include the center vector of the neuron. Neural network basis width vector Initial weights of the network The learning rate of neural networks and momentum factor The initial values ​​should be set according to the parameters in Section 4.1. and Adaptive law and The calculation is performed according to formula (7), and the control law is calculated according to formula (9), where , , , .

[0170] Based on the physical parameters of the vibration system and the relevant parameters of the adaptive control system, the following sliding mode adaptive control algorithm based on the RBF neural network is used as an example to verify the effectiveness of the adaptive control method established in this embodiment of the invention. In the specific calculations, the control effect of the adaptive control system and the rotational speed of the rotating cylinder under different wind speeds and natural frequencies were considered.

[0171] like Figure 21 As shown in the figure, the tracking displacement, tracking velocity, and rotational speed input of the rotating cylinder of the box girder vary with time at a wind speed of 15 m / s. The figure shows that the displacement of the box girder can track the preset ideal displacement signal well at this wind speed, and the velocity of the box girder exhibits only minor fluctuations, generally matching the ideal velocity time history well. The rotational speed of the rotating cylinder shows a periodic variation.

[0172] When the wind speed further increases to 25 m / s, the control effect of the vibration system is as follows: Figure 22As shown in the figure, under this wind speed, the displacement time history of the box girder still matches the ideal displacement signal very well, while the velocity time history of the box girder differs somewhat from the ideal velocity command. The velocity of the box girder exhibits a certain degree of fluctuation at its peak. The root cause of this problem lies in the presence of a sliding mode variable structure term in the controller when using sliding mode control for adaptive control design, resulting in a discontinuous control law. However, because the velocity fluctuation amplitude is relatively small, the adaptive control based on the RBF neural network can effectively control the vibration of the box girder, ensuring that the motion trajectory of the box girder matches the preset ideal command well.

[0173] To more comprehensively analyze the control effect of the adaptive control algorithm established in this embodiment of the invention on system vibration, the motion characteristics of the box girder when the natural frequency of the vibration system changes are compared and analyzed below. In specific calculations, the change in the system's natural frequency is achieved by altering the mass moment of inertia of the box girder.

[0174] like Figure 23 As shown, the moment of inertia is reduced to 0.5 times its initial value when the wind speed is 25 m / s. The figure shows the relationship between the tracking displacement and tracking velocity of the box girder, and the rotational speed of the rotating cylinder over time. It can be seen from the figure that the displacement and velocity of the box girder track the ideal signal command quite well. The rotational speed of the rotating cylinder exhibits a periodic change over time.

[0175] With the wind speed maintained at 25 m / s, the moment of inertia of the vibrating system becomes 3.5 times its initial value. When the tracking displacement, tracking velocity, and rotational speed input of the rotating cylinder of the box girder change with time, the relationship is as follows: Figure 24 As shown. Under this working condition, the displacement and velocity of the box girder match the given ideal signal command well. The rotational speed of the rotating cylinder exhibits a periodic change over time, and the curve is relatively smooth.

[0176] S4. Control the rotating cylinder to rotate at the target speed.

[0177] Based on the comprehensive optimization objective of suppression efficiency and energy consumption, the following rotation speed control strategy is adaptively selected and implemented: determine and maintain a constant optimal rotation speed based on the current dominant wind speed range; or control the rotation speed of the rotating cylinder to be modulated with a periodic component.

[0178] The frequency of the periodic component is set based on the natural frequency of the box girder structure or the frequency of the dominant vibration component in the vibration state.

[0179] The implementation principle of this invention is as follows:

[0180] The system of this invention utilizes a pair of independently rotating cylinders symmetrically installed above and below the wind-induced vibration nozzles at the tail of a bridge box girder as momentum injection devices, which activate upon sensing that the wind-induced vibration of the box girder exceeds the limit. Its core lies in using two parallel radial basis function neural networks to approximate the nonlinear aerodynamic excitation components caused by the box girder's own motion and the nonlinear aerodynamic control components caused by the rotational cylinders' motion in real-time online. Based on this approximation result, combined with sliding mode adaptive control theory, the system dynamically calculates a target rotational speed of the rotating cylinder that enables the box girder's vibration trajectory to accurately track a preset ideal vibration reduction trajectory, and executes this speed command through a drive mechanism. After the rotating cylinders rotate, they inject momentum into the flow field at the tail of the box girder, thereby interfering with and disrupting the periodic vortex shedding that causes vibration, changing the aerodynamic distribution acting on the box girder, and ultimately achieving the purpose of suppressing or eliminating harmful vibrations. The entire system forms a closed-loop adaptive control loop of "sensing-identification-decision-execution".

[0181] The specific working process of this invention begins with the offline training phase. First, a high-fidelity computational fluid dynamics model is established, including a box girder and a rotating cylinder, and the rotational motion of the cylinder is accurately simulated using sliding mesh technology. In this model, the box girder is pre-programmed to undergo wind-induced torsional motion with different amplitudes and frequencies, while various working conditions, including constant rotational speed and multiple periodic speed-changing modes, are set for the rotating cylinder. Through extensive numerical simulation calculations, motion state data of the box girder, rotational speed data of the cylinder, and corresponding aerodynamic data of the box girder surface are simultaneously collected to construct a sample database for training the radial basis function neural network. In the online control phase, the system is activated when the vibration sensor installed on the box girder detects that the vibration amplitude exceeds a safety threshold. The vibration sensor collects the displacement and velocity signals of the box girder in real time and transmits them to the adaptive control unit. The two radial basis function sub-networks in this unit then begin to operate: the first sub-network receives the displacement and velocity signals and outputs an approximation value of the aerodynamic force generated by the box girder's own motion; the second sub-network additionally receives real-time rotational speed feedback from the rotating cylinder and outputs an approximation value of the aerodynamic control component generated by the cylinder's motion. Meanwhile, the control unit constructs a sliding surface based on the error between the actual trajectory of the box girder and the preset ideal trajectory. Based on the sliding surface information and the internal state of the neural network, it fine-tunes the weight parameters of the two neural networks online using a pre-designed adaptive law, enabling their approximation capability to adapt to real-time changes in the wind field and structural state. Subsequently, the approximation results of the two networks, the sliding surface information, and the linear dynamic model parameters of the box girder structure are comprehensively calculated to determine the target rotational speed command for the rotating cylinder, including a robust compensation term. This command is sent to the drive mechanism, which precisely controls the rotating cylinder to rotate at the target speed, thereby achieving active intervention in the flow field at the tail of the box girder. The system continuously cycles through the above monitoring, approximation, calculation, and drive steps until the box girder vibration is suppressed to a safe range.

[0182] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments, and various changes and modifications can be made without departing from the spirit and scope of the invention, all of which fall within the scope of protection claimed by the present invention. The scope of protection of the present invention is defined by the appended claims and their equivalents.

Claims

1. An adaptive control system for bridge wind vibration injection based on RBF neural network, comprising a box girder, characterized in that, Also includes: A momentum injection device, comprising at least a pair of rotating cylinders respectively rotatably mounted on the upper and lower sides of the air nozzle at the tail of the box girder; Vibration sensors are used to sense the vibration state of the box girder; An adaptive control unit is configured to receive signals from the vibration sensor, approximate the nonlinear aerodynamic forces under the coupling action of the rotating cylinder and the box girder online using a radial basis function neural network, and generate cylinder speed control commands to suppress wind-induced vibrations of the box girder using a sliding mode adaptive control algorithm; and, A drive mechanism, connecting the adaptive control unit and the rotating cylinder, is used to drive the rotating cylinder to rotate according to the cylinder speed control command.

2. The adaptive control system for bridge wind vibration injection based on RBF neural network according to claim 1, characterized in that, The ratio of the diameter of the rotating cylinder to the height of the box girder is 0.18 ± 0.02; The distance between the outer edge of the rotating cylinder and the outer edge of the tail nozzle of the box girder is 0.3 to 0.4 times the diameter of the rotating cylinder.

3. An adaptive control method for bridge wind vibration injection based on RBF neural network, characterized in that, The method, when applied to the system of claim 1 or 2, includes the following steps: Monitor the vibration state of the box girder, and when the amplitude of the vibration exceeds a preset safety threshold, obtain the current vibration state of the box girder; A radial basis function neural network is used to approximate the nonlinear aerodynamic forces acting on the box girder, which are generated by the coupling of the box girder's own motion and the motion of the rotating cylinder. Based on sliding mode adaptive control theory and combined with the approximation results of the radial basis function neural network, the target rotational speed of the rotating cylinder that enables the box girder vibration to track the preset ideal trajectory is calculated. The rotating cylinder is controlled to rotate at the target speed.

4. The method according to claim 3, characterized in that, The step of controlling the rotating cylinder to rotate at the target speed involves adaptively selecting one of the following speed control strategies based on the comprehensive optimization objective of suppressing efficiency and energy consumption: Based on the current prevailing wind speed range, determine and maintain a constant optimal rotational speed; or, The rotational speed of the rotating cylinder is modulated with a periodic component. The frequency of the periodic component is set based on the natural frequency of the box girder structure or the frequency of the dominant vibration component in the vibration state.

5. The method according to claim 3, characterized in that, The calculation of the target rotational speed of the rotating cylinder that enables the box girder to track a preset ideal trajectory specifically includes: Construct a sliding surface based on the error between the actual movement trajectory of the box girder and the preset ideal trajectory; Based on the internal state of the sliding surface and the radial basis function neural network, the parameters of the neural network are adjusted online so that the network adapts to system changes in approximation of nonlinear aerodynamic forces. The approximation result, the sliding surface information, and the linear dynamics of the system are combined to generate the target rotational speed, which includes a robust compensation term.

6. The method according to claim 5, characterized in that, The online approximation using a radial basis function neural network specifically includes: Build and configure the first and second subnetworks; The displacement and velocity signals reflecting the motion state of the box girder are input into the first sub-network to approximate the nonlinear aerodynamic components caused by the motion of the box girder itself. The displacement and velocity signals of the box girder's motion state, along with the current rotational speed signal of the rotating cylinder, are input into the second sub-network to approximate the nonlinear aerodynamic control component related to rotational speed caused by the motion of the rotating cylinder.

7. The method according to claim 6, characterized in that, The online adjustment of the neural network parameters specifically includes: A first adaptive law is set for the parameters of the first sub-network, the value of which is negatively correlated with the value of the sliding surface and the basis function output of the first sub-network; A second adaptive law is set for the parameters of the second sub-network. The value of the second adaptive law is negatively correlated with the value of the sliding surface, the basis function output of the second sub-network, and the value of the target rotational speed.

8. The method according to claim 6, characterized in that, The nonlinear aerodynamic control component caused by the motion of the rotating cylinder includes higher-order harmonic components related to the fundamental frequency of the rotation of the rotating cylinder.

9. The method according to claim 3, characterized in that, The method further includes a preparatory step of offline training of the radial basis function neural network: A fluid dynamics calculation model including the box girder and the rotating cylinder is established, and the rotation of the rotating cylinder is simulated in the model using the sliding mesh technique; In the calculation model, the box girder is set to undergo wind-induced vibration motion, and the rotating cylinder is set to rotate in multiple different speed modes. Through fluid dynamics calculations, the motion state data of the box girder, the rotation state data of the rotating cylinder, and the corresponding aerodynamic force data acting on the surface of the box girder are acquired simultaneously. The motion state data of the box girder and the rotation state data of the rotating cylinder are combined as input samples, and the corresponding aerodynamic data are used as output samples to form a dataset for training the radial basis function neural network.

10. The method according to claim 3, characterized in that, The preset ideal trajectory is either a zero trajectory or a reduced-amplitude vibration trajectory with controlled amplitude.

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