A Smart Control Method for Bridge Wind Vibration Based on RBF Neural Network and Sliding Mode Adaptation

Abstract

This application relates to the technical field of bridge wind-induced vibration control, and in particular to an intelligent control method for bridge wind-induced vibration based on an RBF neural network and sliding mode adaptive control. The method includes the following steps: deploying local vibration surfaces at predetermined locations on the main girder of the bridge; acquiring the real-time motion state of the main girder and the real-time displacement of the local vibration surfaces; constructing an RBF neural network and outputting real-time estimates; inputting the real-time estimates and the tracking error between the measured motion state and the ideal command to a sliding mode adaptive controller; the sliding mode adaptive controller synchronously generating a control law and an adaptive law; using the control law to drive the local vibration surfaces to vibrate, and feeding back the real-time displacement of the local vibration surfaces to the input of the RBF neural network; and using the adaptive law to update the weights of the RBF neural network in real time. This application can achieve adaptive intelligent suppression of bridge wind-induced vibration by identifying and compensating for nonlinear aerodynamic interference forces between the control device and the main girder in real time.

Description

Technical Field

[0001] This application relates to the technical field of bridge wind vibration control, and in particular to an intelligent bridge wind vibration control method based on RBF neural network and sliding mode adaptation. Background Technology

[0002] As a key component of modern transportation infrastructure, the increasing span of bridges makes them increasingly sensitive to wind loads. Wind-induced vibrations, especially flutter and vortex-induced vibrations, have become a core challenge threatening the construction and operational safety of long-span bridges, potentially leading to structural fatigue damage or even aerodynamic instability. Therefore, developing efficient, reliable, and adaptable wind vibration control technologies is crucial for ensuring the safety and performance of bridges throughout their entire life cycle.

[0003] Currently, various technical solutions have been developed in the field of bridge wind vibration control. One type is the passive control measure disclosed in patent document CN114922049A, which uses devices such as fixed triangular air nozzles installed on the windward side of the bridge to streamline the main beam cross-section and reduce vortex shedding energy. This type of method is simple in structure and low in cost, but its control effect is highly dependent on the design conditions. One of the fundamental reasons is that fixed aerodynamic devices (such as deflectors) are in a static state in the airflow for a long time, and their surfaces are prone to forming and thickening an aerodynamic boundary layer. This boundary layer significantly hinders the smooth passage of airflow, not only weakening the device's guiding and accelerating effect on airflow, but also affecting the vortex suppression effect in its downstream areas (such as the tail of the main beam). Once the actual wind speed, wind direction, or bridge vibration state deviates from the preset conditions, its effectiveness is difficult to guarantee.

[0004] like Figure 4 As shown, a comparison through computational fluid dynamics (CFD) simulations reveals that, without guide vanes, the airflow velocity distribution at a certain location on the lower surface of the box girder exhibits a certain gradient. Figure 4 (a)); however, after the fixed guide vane was installed, due to the aforementioned boundary layer effect, a significant low-velocity plateau appeared in the airflow velocity distribution at that location ( Figure 4 (b) This directly confirms that the acceleration effect of the fixed guide vane on the airflow is weakened, which in turn affects its ability to control the vortex at the tail of the box girder.

[0005] To improve adaptability, active control technologies with adjustable functions have gradually become a research focus. For example, patent document CN114427187B discloses an intelligent adjustable anti-glare panel system for suppressing bridge vortex-induced vibration. This system monitors the environment and structural conditions through sensors and controls the rotation speed of the anti-glare panel according to a preset mapping table of "vortex-induced vibration order - optimal rotation speed." This type of solution represents an advancement from "fixed shape" to "adjustable action," enabling it to respond to specific vibration conditions.

[0006] However, existing active control methods cannot accurately identify and quantify the highly nonlinear and time-varying additional aerodynamic disturbance forces generated by the relative motion between the control device and the vibrating main beam in real time. This results in a lack of accurate dynamic model support for the design of the control system, essentially remaining an open-loop or weak closed-loop compensation based on offline pre-calibration, unable to achieve true intelligent adaptive control. Specifically, whether it is a rotatable anti-glare plate or other actuators, when they are introduced into the flow field and attempt to suppress the vibration of the main beam through their own motion, a complex aerodynamic coupling will form between them and the main beam. The force generated by this coupling is not a simple linear relationship, but is closely related to multiple variables such as real-time wind speed, instantaneous displacement and velocity of the main beam, and the motion state of the actuator itself, exhibiting strong nonlinear and time-varying characteristics. For example, in scenarios with severe wind speed fluctuations or sudden changes in wind direction, the characteristics of this disturbance force will change significantly; or, when the bridge's natural frequency or damping characteristics change due to damage, icing, or additional facilities, the original aerodynamic coupling relationship will also be broken. Existing solutions, such as CN114427187B, rely on a fixed mapping table pre-established offline through computational fluid dynamics simulations or wind tunnel tests for their control kernel. This look-up table control strategy has serious limitations when facing unpredictable and dynamically changing conditions: it cannot perceive the magnitude and dynamic characteristics of the actual aerodynamic disturbance force acting on the main beam at any given moment, caused by the relative motion of the devices. Therefore, the actuation commands issued by the control system are likely to deviate from the optimal commands needed to counteract the disturbance force. With slight deviations, the control effect will be reduced; in severe cases, improper actuation may even trigger unfavorable aerodynamic coupling modes, unexpectedly amplifying the vibration response of the main beam, leading to control failure and even safety hazards. The control strategy cannot adaptively adjust online to follow changes in the environment and structural state, making it difficult to guarantee the robustness and reliability of control under various complex and unsteady wind field conditions throughout the bridge's lifespan. Summary of the Invention

[0007] In order to achieve adaptive intelligent suppression of bridge wind vibration by identifying and compensating for nonlinear aerodynamic interference forces between the control device and the main beam in real time, this application provides a bridge wind vibration intelligent control method based on RBF neural network and sliding mode adaptation.

[0008] This application provides a bridge wind-induced vibration intelligent control method based on RBF neural network and sliding mode adaptation, which adopts the following technical solution: A bridge wind-induced vibration intelligent control method based on RBF neural network and sliding mode adaptation includes the following steps:

[0009] Local vibration surfaces are set up at predetermined locations on the main girder of the bridge;

[0010] The real-time motion state of the main beam and the real-time displacement of the local vibration surface are obtained.

[0011] An RBF neural network is constructed, which takes the real-time motion state of the main beam and the real-time displacement of the local vibration surface as inputs, and outputs the real-time estimate of the additional aerodynamic disturbance force caused by the relative motion between the local vibration surface and the main beam.

[0012] The real-time estimated value and the tracking error between the measured motion state of the main beam and the ideal command are input to the sliding mode adaptive controller.

[0013] The sliding mode adaptive controller synchronously generates a control law for driving the local vibration surface and an adaptive law for updating the weights of the RBF neural network in real time.

[0014] The control law is used to drive the local vibration surface to vibrate, and the real-time displacement of the local vibration surface is fed back to the input of the RBF neural network; at the same time, the adaptive law is used to update the weights of the RBF neural network in real time.

[0015] Optionally, the predetermined position is at least one of the windward end and the tail end of the main beam on the lower side;

[0016] The amplitude of the local vibration surface is constrained below an amplitude threshold based on the main beam scale;

[0017] The vibration frequency of the local vibration surface is set to a specific multiple based on the natural frequency of the main beam;

[0018] The vibration mode, determined by the amplitude threshold and the specific multiple, is configured to generate the aerodynamic disturbance force with a preset dynamic range at the predetermined position.

[0019] Optionally, the RBF neural network includes:

[0020] The input layer is used to synchronously receive the real-time motion state of the main beam and the real-time displacement of the local vibration surface, forming a joint input that characterizes the coupling state of the system.

[0021] The hidden layer, whose number of nodes is determined based on the nonlinear approximation requirement of the aerodynamic disturbance force, is configured to perform nonlinear mapping and feature extraction on the joint input.

[0022] The output layer is configured to generate a real-time estimate of the aerodynamic disturbance force based on the output of the hidden layer.

[0023] Optionally, the adaptive law can be constructed as follows:

[0024] Based on the current sliding surface function value calculated by the sliding mode adaptive controller, the output of the hidden layer, and the control law, the weight adjustment amount of the RBF neural network is dynamically generated;

[0025] The weight adjustment amount is used to update the weights of the RBF neural network in real time;

[0026] The adjusted weights are synchronously used to update the real-time estimated values ​​generated by the output layer and serve as the gain parameters of the feedforward compensation term in the sliding mode adaptive controller.

[0027] Optionally, the control law is constructed to include a feedforward compensation term, a composite feedback term, and a sliding mode switching term;

[0028] The feedforward compensation term is constructed based on the real-time estimated value output by the RBF neural network and the updated weights, in order to counteract the aerodynamic disturbance force;

[0029] The composite feedback term and the sliding mode switching term are generated based on the tracking error and the sliding mode surface function value, respectively. The two are superimposed to compensate for the uncertainty and external disturbance of the main beam vibration system, and work together with the feedforward compensation term to drive the local vibration surface so that the measured motion state of the main beam tracks the ideal command.

[0030] Optionally, when the real-time monitored incoming wind speed exceeds a preset wind speed threshold, the sliding mode adaptive controller synchronously increases the gain coefficient of the sliding mode switching term and the gain coefficient of the feedforward compensation term, and raises the upper limit of the amplitude of the local vibration surface control command.

[0031] Optionally, when the structural dynamic parameters of the main beam change, the sliding mode adaptive controller updates the weights of the RBF neural network through the adaptive law, and readjusts the gain coefficients of the feedforward compensation term, the composite feedback term and the sliding mode switching term in the control law according to the updated weights.

[0032] Optionally, the feedforward compensation term includes a first neural network compensation module and a second neural network compensation module;

[0033] The first neural network compensation module is constructed based on the estimated value of the aerodynamic force generated by the movement of the main beam itself.

[0034] The second neural network compensation module is constructed based on the estimated value of the additional aerodynamic disturbance force caused by the local vibration surface;

[0035] The sliding mode adaptive controller generates independent weight adjustment amounts for the neural networks corresponding to the first neural network compensation module and the second neural network compensation module respectively through the adaptive law, and adjusts the gain coefficients of the first neural network compensation module and the second neural network compensation module respectively based on the updated weights.

[0036] Optionally, the sliding mode adaptive controller is further configured to:

[0037] Based on the tracking error and the sliding surface function value, a dynamic fusion weight coefficient is generated. The dynamic fusion weight coefficient is used to weight and fuse the first compensation amount output by the first neural network compensation module and the second compensation amount output by the second neural network compensation module.

[0038] The generation rules for the dynamic fusion weight coefficients include:

[0039] When the amplitude characteristics of the tracking error indicate that the disturbance mainly originates from the movement of the main beam itself, the weighting coefficient of the first compensation amount is increased;

[0040] When the amplitude characteristics of the tracking error indicate that the disturbance mainly originates from the additional aerodynamic interference caused by the local vibration surface, the weighting coefficient of the second compensation amount is increased;

[0041] When the absolute value of the sliding surface function increases, the weight coefficient corresponding to the compensation amount currently assigned a higher weight is reduced, and the weight coefficient of the other compensation amount is increased accordingly.

[0042] In summary, this application includes the following beneficial technical effects:

[0043] 1. This method constructs an RBF neural network to estimate the nonlinear aerodynamic disturbance force generated by the relative motion between the local vibration surface and the main beam in real time. It also uses a sliding mode adaptive controller to synchronously generate control law and adaptive law for dynamic compensation. This fundamentally solves the core technical problem that existing technologies cannot identify and accurately quantify the complex aerodynamic coupling force between the control device and the main beam in real time. It achieves a fundamental leap from offline pre-calibrated open-loop control to online adaptive intelligent closed-loop control.

[0044] 2. This method has strong robustness and adaptability to complex working conditions such as wind speed changes and structural parameter drift. When the incoming wind speed exceeds the threshold or the dynamic parameters of the main beam structure change, the controller can automatically adjust the gain coefficient and the amplitude of the local vibration surface, and update the neural network weights through the adaptive law to ensure that the system can maintain a high-precision and stable wind vibration suppression effect under different wind field conditions and structural states.

[0045] 3. This method separates the total aerodynamic disturbance into the aerodynamic force generated by the main beam's own motion and the additional aerodynamic disturbance caused by the local vibration surface. Two independent RBF neural networks are used for approximation and compensation respectively. This separate design can more accurately counteract the disturbance characteristics from different sources, thereby significantly improving the control precision and overall efficiency.

[0046] 4. The control law structure proposed in this method integrates feedforward compensation based on neural network estimation, composite feedback based on tracking error, and sliding mode switching term. The feedforward term directly cancels the identified nonlinear aerodynamic forces, while the feedback and sliding mode terms handle unmodeled dynamics and external disturbances. This synergistic mechanism ensures rapid tracking of ideal commands while effectively suppressing control chattering to a low level permissible by engineering, avoiding the risk of structural fatigue caused by excessive chattering.

[0047] 5. This method sets an amplitude threshold based on the main beam's dimensions and a vibration frequency based on the main beam's natural frequency, and intelligently switches between preset optimized amplitudes according to real-time wind speed. This method ensures sufficient aerodynamic interference force to suppress vortices while minimizing actuation energy consumption, demonstrating high energy utilization efficiency, which is beneficial for extending the device's lifespan and reducing long-term operating costs.

[0048] 6. The location of the local vibration surface, motion parameters, and overall control architecture determined by this method fully consider the feasibility of engineering implementation. The amplitude and frequency used are all within the range that conventional actuators can achieve. The neural network and sliding mode control algorithms are also suitable for digital implementation, laying a solid foundation for the transformation and application from theoretical schemes to actual bridge engineering. Attached Figure Description

[0049] Figure 1 It is the overall logic flowchart of the control method;

[0050] Figure 2 This is a schematic diagram of the box girder cross-section;

[0051] Figure 3 This is a schematic diagram of the CFD computational domain and boundary conditions;

[0052] Figure 4 This is a comparison diagram of airflow velocity distribution with and without guide vanes;

[0053] Figure 5 This is a schematic diagram of the optimal layout of the local vibration surface;

[0054] Figure 6 These are static comparison diagrams of the flow field at the tail of the box girder at different locations;

[0055] Figure 7 This is a diagram showing the dynamic evolution of the flow field at the tail of the box girder during local vibration.

[0056] Figure 8 This is a schematic diagram of an RBF neural network structure;

[0057] Figure 9 This is a comparison chart of the effects of RBF neural network simulation of aerodynamic disturbance force;

[0058] Figure 10 This is a block diagram of a sliding mode adaptive control system based on an RBF neural network;

[0059] Figure 11 This is a diagram showing the displacement tracking effect under low wind speed.

[0060] Figure 12 This is a diagram showing the displacement tracking effect under high wind speeds;

[0061] Figure 13 This is a diagram showing the displacement tracking effect under structural parameter drift. Detailed Implementation

[0062] The following is in conjunction with the appendix Figure 1-13 This application will be described in further detail.

[0063] This application discloses an intelligent control method for bridge wind-induced vibration based on RBF neural network and sliding mode adaptation. For example... Figure 1 As shown, a bridge wind-induced vibration intelligent control method based on RBF neural network and sliding mode adaptation includes the following steps:

[0064] S1. Local vibration surface layout and core parameter determination

[0065] like Figure 2 As shown, the local vibration surface is the core actuator for active wind-induced vibration control of bridges. Its placement, amplitude, and vibration frequency directly determine the generation effect of aerodynamic interference forces, thus affecting the accuracy of wind-induced vibration control. Existing fixed aerodynamic devices (such as fixed guide vanes) are susceptible to boundary layer effects due to their single placement location and non-adjustable parameters, leading to a decrease in the control effect of tail vortices and a narrow range of application. This step, based on the structural characteristics of the main beam, fluid mechanics principles, and existing engineering experience, systematically determines the key parameters of the local vibration surface, laying the foundation for subsequent precise control, while also addressing the shortcomings of existing technologies, such as blind parameter setting and poor adaptability.

[0066] S11. Determining the deployment location

[0067] like Figure 5 As shown, the predetermined locations for the local vibration surface are selected at the windward end and the tail end of the main beam, and they are preferably installed at both locations simultaneously. This location selection is based on the core defect of existing fixed pneumatic devices: fixed guide vanes are mostly installed on a single side or top of the main beam, and when airflow passes over them, a thick boundary layer is easily formed on the surface of the device, which blocks the airflow and reduces the suppression effect on the tail vortex.

[0068] The windward and rear ends of the lower side of the main beam are key areas for the formation and development of wind-induced vortices. Installing local vibration surfaces in these areas can directly act on the vortex generation source, disrupting the vortex formation cycle. To ensure proper placement, specific installation parameters are determined as follows:

[0069] The distance between two local vibration surfaces The value is 0.15 times the height of the box girder. This value is based on the installation experience of existing bridge pneumatic control devices. It can ensure the airflow space between the vibrating surface and the main girder, and avoid insufficient aerodynamic interference force due to excessive spacing.

[0070] Vibration arc length range and The ratio is set to 4.5. This ratio was determined through the parameter optimization experience of existing similar vibration control devices. It can maximize the contact area between the vibration surface and the airflow and generate aerodynamic interference force within a preset dynamic range.

[0071] Compared to other placement locations (such as the upper and lower sides of the tail vents of the box girder), the placement scheme at the windward end and tail end of the main girder can more effectively reduce the tail vortex size and lower the aerodynamic lift coefficient. Other locations, being far from the vortex generation core area, make it difficult for the aerodynamic interference forces generated by vibration to directly act on the key flow field, easily leading to incomplete tail vortex control and even increasing the lift moment coefficient, affecting the stability of the bridge structure. Therefore, this placement effectively overcomes the limitations of existing fixed devices and improves control adaptability.

[0072] S12, Amplitude Threshold Determination

[0073] The amplitude of the local vibration surface is constrained below an amplitude threshold based on the main girder dimension, which is set to 0.01 times the box girder width. In actual control, 0.006 times and 0.01 times the box girder width are selected as the working amplitudes. The box girder width is selected as 0.2249m, which is commonly used in engineering. Based on this, two typical working amplitudes are calculated:

[0074]

[0075]

[0076] The numerical values ​​are selected based on existing technical principles and engineering practices: the amplitude is positively correlated with the aerodynamic interference force. The larger the amplitude, the stronger the aerodynamic force generated on the box girder surface, and the more significant the suppression ability of the vortex. However, when the amplitude exceeds 0.01 times the width of the box girder, the instantaneous gap between the local vibration surface and the box girder surface changes too much during its motion cycle, which may destroy the optimal flow channel geometry designed to optimize airflow acceleration, thus weakening the suppression effect on the tail vortex.

[0077] An amplitude of 0.006 to 0.01 times the width of the box girder is considered micro-amplitude vibration. Existing small actuators commonly used in bridge wind-induced vibration control (such as piezoelectric actuators and small electromagnetic actuators) can achieve vibration output within this range, eliminating the need for developing new actuators and reducing engineering application costs. Simultaneously, micro-amplitude vibration reduces structural damage and extends the service life of local vibration surfaces, meeting the design requirements for bridge safety throughout its entire life cycle. Compared to the non-adjustable amplitude of existing fixed devices, this amplitude setting can be flexibly switched according to the actual wind vibration intensity, improving control flexibility.

[0078] S13. Determination of vibration frequency

[0079] The vibration frequency of the local vibration surface is set as a specific multiple of the natural frequency of the main beam. The natural frequency of the main beam is selected as 4.5Hz, which is commonly used for long-span bridges. The vibration frequency is specifically set as 1.0 times and 2.5 times the natural frequency, i.e.

[0080]

[0081]

[0082] The selection of the frequency multiple is based on existing wind-induced vibration control theory: in wind-induced vibration, resonance is easily triggered when the vortex shedding frequency is close to the natural frequency of the main beam. Vibration at 2.5 times the natural frequency can precisely interfere with the vortex shedding rhythm and break the resonance threshold. 1.0 times the natural frequency is used as a backup frequency to avoid the risk of resonance caused by the vibration frequency conflicting with the structure's natural frequency when the main beam structural parameters change slightly.

[0083] The local vibration surface adopts simple harmonic motion, and the vibration equation is:

[0084]

[0085]

[0086]

[0087] This equation, based on the conventional form of existing simple harmonic vibration control, ensures the stability and predictability of vibration output, facilitating the design and implementation of subsequent control laws. The frequency values ​​of 11.25Hz and 4.5Hz are both within the operating frequency range of existing actuators, requiring no special customization, further enhancing the engineering feasibility of the technical solution. Compared to existing fixed-frequency passive control devices, this frequency setting can adapt to changes in vortex shedding frequency under different wind field conditions, enhancing control adaptability.

[0088] S2, CFD numerical simulation and vibration parameter optimization verification

[0089] S1 has determined the core parameters such as the location, amplitude, and frequency of the local vibration surface. The rationality of these parameters directly affects the subsequent wind-induced vibration control effect. In existing technologies, the parameter settings of bridge wind-induced vibration control devices mostly rely on experience or offline tests, lacking targeted quantitative analysis of the flow field, resulting in low parameter matching and unstable control effects. This step, based on the core parameters such as the location, amplitude, and frequency of the local vibration surface determined in S1, uses CFD numerical simulation combined with dynamic mesh technology to quantitatively analyze the influence of local vibration surface parameters on the flow field and aerodynamic forces of the box girder, verifying and optimizing the parameter settings. This provides accurate data support for the subsequent control algorithm design and solves the problem of blind parameter settings in existing technologies.

[0090] S21. Numerical Simulation Basic Parameter Settings

[0091] S211. Selection of Calculation Model

[0092] like Figure 3 As shown, the computational model uses the commercial software Fluent, based on the RANS method. Two-equation model. This model is a mature model used in existing bridge wind-induced vibration flow field simulations, compared to traditional... The model has higher simulation accuracy for separated flow, adverse pressure gradient flow and aerodynamic disturbances, and can accurately capture the complex changes in the flow field around the box girder, which meets the needs of fine analysis of airflow characteristics in bridge wind vibration control.

[0093] S212, Setting the computational domain size

[0094] The computational domain dimensions are set according to engineering standards: the distance from the inlet to the leading edge of the box girder is 10B, the distance from the trailing edge of the box girder to the outlet is 30B, and the distance from the upper and lower boundaries to the centerline of the box girder is 10B. The reason for these dimensions is that the wind-induced flow field needs sufficient space to develop before and after the box girder. The 10B inlet distance ensures that the incoming flow stably reaches the box girder surface, the 30B outlet distance avoids the backflow of wake from interfering with the calculation results, and the 10B distance at the upper and lower boundaries eliminates the influence of wall effects, ensuring the flow field develops fully, avoiding boundary effect interference, improving the reliability of the simulation results, and providing accurate data for subsequent parameter optimization.

[0095] S213, Grid Generation Scheme

[0096] The mesh generation adopts a hybrid meshing method: triangular meshes are used in the box girder and the area near the local vibration surface, while quadrilateral meshes are used in the remaining areas, with a total of 123,000 meshes. The minimum mesh size near the wall is 0.0001m. Triangular meshes have good deformation adaptability and can dynamically adjust the mesh according to the vibration of the local vibration surface, avoiding calculation errors caused by mesh distortion during vibration. Quadrilateral meshes have high computational efficiency and can balance the overall calculation speed and accuracy. The total number of 123,000 meshes was determined based on mesh sensitivity analysis, which can ensure the accuracy of capturing the flow field details within the boundary layer without causing a surge in computational cost due to an excessive number of meshes.

[0097] S214. Discrete Scheme and Algorithm Selection

[0098] Momentum, turbulent kinetic energy, and energy dissipation are all discretized using a second-order upwind scheme. Pressure-velocity coupling is handled using the SIMPLE algorithm, and the solver employs a separable two-order implicit solver. Compared to the first-order scheme, the second-order upwind scheme provides higher resolution for the flow gradient, reduces numerical dispersion, and improves the accuracy of flow field parameter calculations. The SIMPLE algorithm is a classic algorithm in CFD for handling pressure-velocity coupling, exhibiting strong stability and good convergence, making it suitable for complex flow field calculations such as wind-induced vibration in bridges. The separable two-order implicit solver improves computational accuracy while ensuring the stability of the iterative process.

[0099] S215, Boundary Condition Settings

[0100] The boundary conditions are set as velocity inlet and pressure outlet: the initial inlet wind speed is 7.5 m / s, which is a medium-intensity incoming wind speed commonly used in bridge wind vibration tests, can cover the wind environment under most operating conditions, and meets the wind tunnel test standards; the turbulence intensity is 0.5%, simulating the turbulence characteristics of uniform incoming flow, which meets the standard settings for bridge wind tunnel tests; the upper and lower ends of the computational domain are set as no-slip fixed walls to simulate the upper and lower boundary constraints of the atmospheric boundary layer, ensuring the realism of the flow field simulation.

[0101] S216. Time Step and Convergence Criterion

[0102] Time step The iterative residual is less than The convergence was determined at that time. The highest vibration frequency of the local vibration surface was 11.25 Hz, with a period of approximately 0.089 s. The time step ensures that there are enough calculation points in each vibration cycle, accurately capturing the coupled dynamic process of vibration and flow field; The residual convergence criterion can ensure the convergence of the flow field parameter calculation and avoid the distortion of results caused by excessive residuals.

[0103] S22. Simulation Results and Optimization Analysis under Different Parameters

[0104] S221, Spatial Position Optimization Verification

[0105] like Figure 6 and Figure 7 As shown, based on the two layout schemes determined in S11, simulations are performed where both the box girder and the local vibration surface are stationary, and the local vibration surface is adjusted according to... Flow field characteristics during motion.

[0106] In a stationary state, without control measures, two vortices of similar size are formed near the tail nozzle of the box girder, resulting in a large aerodynamic lift coefficient. When S11 scheme one is adopted, i.e., the windward end and tail end of the main girder are arranged, the obstruction effect of the guide plate significantly reduces the size of the tail vortex, and the aerodynamic lift and lift coefficient are significantly reduced. When S11 scheme two is adopted, i.e., the upper and lower sides of the tail nozzle of the box girder are arranged, the size of the vortex on the lower side of the tail increases, the lift moment coefficient is too high, and the control effect is not good.

[0107] Under vibration conditions, when the local vibration surface of Scheme 1 moves to 1 / 2 amplitude, the tail vortex basically disappears. When it moves to the maximum amplitude, the vortex increases slightly but is generally controlled. The nonlinear characteristics of the aerodynamic force are well adapted to the subsequent control requirements. When the local vibration surface of Scheme 2 moves to the maximum amplitude, a large vortex appears at the tail, and an additional vortex is formed near the vibration surface. The aerodynamic force value is too large and is prone to causing additional disturbances.

[0108] Through comparative verification, Scheme 1 was determined to be the optimal placement location. This result further verifies the rationality of the S11 location selection. Compared with the single-location placement of existing fixed guide vanes, this location can directly act on the core area of ​​vortex generation, improve the tail vortex suppression effect, and solve the problem of incomplete control caused by the limitation of the fixed device location.

[0109] S222, Amplitude Optimization Verification

[0110] Based on the optimal deployment position determined in S11, compare the two working amplitudes set in S12. (0.01B) and Simulation results for (0.006B).

[0111] Amplitude is At that time, the distance between the local vibration surface and the edge of the box girder is smaller, the airflow acceleration effect is stronger, and the tail vortex size is larger than that of the box girder. Even smaller; Although the corresponding aerodynamic amplitude is less than However, it already meets the requirements for vortex suppression, and the actuation energy consumption is lower. The amplitude is At this time, the aerodynamic amplitude is larger, which is more effective in suppressing large-scale vortices under strong winds, but the aerodynamic energy consumption is relatively high.

[0112] Based on simulation results, the amplitude usage strategy is optimized: when the wind speed is lower than the preset threshold of 15 m / s, the amplitude usage strategy is preferentially adopted. Amplitude, balancing control effectiveness and energy consumption; when wind speed exceeds the 15m / s threshold, switch to The amplitude is increased to enhance vortex suppression capabilities. Compared to the fixed amplitude control of existing technologies, this optimized scheme can dynamically adjust according to wind field intensity, improving control adaptability and energy utilization efficiency.

[0113] S223, Frequency Optimization Verification

[0114] With optimal deployment location, Based on amplitude, compare the two vibration frequencies set by S13. ( )and ( The simulation results.

[0115] Frequency is At that time, the vibration rhythm of the local vibration surface and the vortex shedding frequency effectively interfere with each other, resulting in a larger aerodynamic amplitude and stronger nonlinearity on the box girder surface, which can more thoroughly break the formation cycle of the tail vortex; the frequency is At that time, the aerodynamic amplitude is small and the nonlinear characteristics are weak, so the interference effect on vortex shedding is limited and it is difficult to quickly suppress large-scale vortices.

[0116] Verification revealed that the optimal vibration frequency is 2.5 times the natural frequency of the main beam, consistent with the setting of S13, further validating the rationality of parameter S1. This frequency setting accurately matches the shedding characteristics of wind-induced vortices, and compared to existing passive control devices with fixed frequencies, the interference effect is more significant, providing optimal frequency parameter support for subsequent control law design.

[0117] S3, RBF Neural Network Construction and Aerodynamic Disturbance Simulation

[0118] S2 optimized the core parameters of the local vibration surface through CFD numerical simulation, clarifying its influence on the flow field and aerodynamic forces of the box girder. However, the aerodynamic disturbance force generated by the relative motion between the local vibration surface and the main girder is characterized by strong nonlinearity and complex frequency components. Existing technologies cannot accurately quantify this force using analytical functions, resulting in a lack of reliable data support for control law design and limited control effectiveness. This step, based on the CFD simulation results of S2, constructs an RBF neural network to achieve high-precision simulation of this nonlinear aerodynamic disturbance force, providing a precise data foundation for subsequent controller design, and simultaneously addressing the core deficiency of existing technologies in quantifying aerodynamic disturbance forces.

[0119] S31. Acquisition of aerodynamic interference force

[0120] S311, Simulated Working Condition Design

[0121] Two comparative working conditions were designed, and the aerodynamic disturbance forces generated by the relative motion between the local vibration surface and the main beam were separated through CFD simulation:

[0122] Condition 1: The local vibration surface is stationary relative to the main beam, and both undergo torsional motion synchronously. The equation of torsional motion is: ,in The amplitude is within the typical vibration range of torsional wind-induced vibration of bridges, which is consistent with actual engineering measurement data. The frequency is consistent with the natural frequency of the main beam, ensuring that the simulated working conditions closely match the vibration characteristics of the structure in real wind-induced vibration scenarios.

[0123] Condition 2: Local vibration surface undergoes synchronous torsional motion Based on this, normal vibration is superimposed. The equation for normal vibration is: ,in This frequency was determined based on the S2 frequency optimization results, which can maximize the interference effect on vortex shedding. The values ​​are 0.006 times and 0.01 times the width of the box girder, respectively, which are completely consistent with the working amplitude set in S12, ensuring the continuity and consistency of the working parameters.

[0124] S312, Simulation Methods and Interference Force Calculation

[0125] The torsional motion of the box girder is simulated using sliding mesh technology. This technology can accurately capture the flow field changes caused by structural rotation and is a mature method for handling structural motion in existing bridge wind-induced vibration flow field simulations. By defining the motion of mesh nodes and combining it with dynamic mesh technology, the normal vibration of local vibration surfaces is simulated, ensuring the rationality of mesh deformation during vibration and avoiding calculation errors. The computational domain and boundary conditions strictly follow the settings of S21, including the computational domain size, mesh generation standard, discretization format, and algorithm, ensuring the consistency and reliability of the simulation results.

[0126] The aerodynamic forces on the box girder surface are calculated separately for the two working conditions. The aerodynamic forces in condition two are subtracted from those in condition one, and the difference is the aerodynamic interference force generated by the relative motion between the local vibration surface and the main girder. This calculation method can accurately separate the additional interference caused by the relative motion and eliminate the interference of the aerodynamic forces generated by the synchronous motion of the two, ensuring the purity and specificity of the aerodynamic interference force data.

[0127] S32, RBF Neural Network Structure Design

[0128] S321, Overall Network Structure

[0129] like Figure 8As shown, a 3-15-1 RBF neural network is constructed, consisting of 3 nodes in the input layer, 15 nodes in the hidden layer, and 1 node in the output layer. This structure is designed based on the following: the input needs to fully represent the system's coupling state; the 3 nodes correspond precisely to the box girder's torsional displacement, torsional velocity, and local vibration surface normal displacement, comprehensively covering the core variables affecting aerodynamic disturbance forces; the 15 hidden layer nodes are determined based on nonlinear approximation requirements. Through experience with existing neural networks in similar nonlinear force simulations, this number ensures the accuracy of the nonlinear mapping while avoiding overfitting and computational inefficiency caused by too many nodes, achieving a balance between accuracy and efficiency; the 1 node in the output layer is specifically used to output real-time estimates of aerodynamic disturbance forces, directly matching the data input requirements for subsequent control law design.

[0130] S322, Functions and Mathematical Expressions of Each Layer

[0131] Input layer: Synchronously receives torsional displacement of box girder Box girder torsional speed Local vibration surface normal displacement To form a joint input vector This provides complete input information for subsequent nonlinear feature extraction, ensuring that the network can capture all the key features of the system's coupling state.

[0132] Hidden layer: The Gaussian function is used as the activation function, and the basis function expression is as follows: ,in For the input vector, Let be the center vector of the hidden layer node. The basis width vector is denoted as . The Gaussian function has good local approximation properties and smoothness, and can accurately capture the strong nonlinear characteristics of aerodynamic disturbance forces. It is a widely used and reliable activation function in existing nonlinear system simulations.

[0133] Output layer: Based on the output of the hidden layer, a real-time estimate of the aerodynamic disturbance force is generated through weighted summation. The output expression is as follows: ,in For the network weight vector, This represents the hidden layer output vector. This expression conforms to the classic output calculation logic of RBF neural networks, is simple in structure and computationally efficient, ensuring the reliability and real-time performance of the output results.

[0134] S33. Determining Neural Network Parameters

[0135] S331, Central Vector

[0136] The center vector is uniformly distributed according to the range of values ​​of the input variables, and the calculation formula is: .

[0137] In the formula, Corresponding to three input variables, The hidden layer node number; The first The minimum and maximum values ​​of each input variable are determined statistically based on CFD calculation data of S2, ensuring that the center vector can completely cover the entire range of changes of the input variables; This represents the number of hidden layer nodes. This calculation method ensures that the center vector is uniformly distributed in the input space, avoiding the problem of dense nodes in local areas and sparse nodes in other areas, thus improving the approximation accuracy of the neural network across the entire range of input variables.

[0138] S332, Base Width Vector

[0139] Base width vector uniformly taken This value was determined through multiple sensitivity analyses. A basis width of 3.5 allows the Gaussian function to maintain good nonlinear mapping capability within the input range: it avoids the problem of excessive locality of the function due to an excessively small basis width, which would prevent the capture of the correlation characteristics between input variables; and it also avoids the problem of excessive smoothing of the function due to an excessively large basis width, which would result in the loss of detailed features of aerodynamic disturbance forces, thus ensuring accurate capture of the complex nonlinear characteristics of aerodynamic disturbance forces.

[0140] S333, Initial Weights

[0141] Initial weights Random numbers within a certain interval. This setting ensures the diversity of the network's initial state, avoiding the problem of training getting stuck in local optima due to the initial weights being concentrated in a certain interval, and providing a wider optimization space for subsequent adaptive adjustments.

[0142] S334, Learning Parameters

[0143] Learning rate Momentum factor A learning rate of 0.3 ensures a fast convergence speed for the network, avoiding inefficient training due to a slow learning process. A momentum factor of 0.05 effectively suppresses oscillations during the learning process and improves the stability of network training. These two parameters are determined based on extensive application experience of existing RBF neural networks in nonlinear force simulation, achieving an optimal balance between convergence speed and stability.

[0144] S34. Verification of Neural Network Training and Simulation Results

[0145] S341. Training Methods and Objectives

[0146] like Figure 9As shown, an offline training method combining supervised center selection and gradient descent is employed. Using the aerodynamic disturbance force calculated by S31 as the label data, the network weights and center vector are iteratively adjusted to gradually approximate the actual aerodynamic disturbance force calculated by CFD. The training objective is set to ensure that the mean square error between the predicted value and the CFD data is less than [a certain value]. This threshold is determined based on the engineering control accuracy requirements, ensuring that the simulation results meet the data accuracy requirements of subsequent control law design, and keeping the control error within the allowable range of the engineering.

[0147] S342. Verification Results and Effect Analysis

[0148] The trained neural network was comprehensively validated under different amplitudes and deployment locations:

[0149] when When the width of the box girder is doubled, the neural network predictions and CFD calculations show a high degree of agreement on the aerodynamic disturbance forces, accurately capturing the nonlinear fluctuation characteristics and complex frequency components of these forces, with the mean square error remaining stable at [value missing]. the following;

[0150] when When the box girder width is doubled, although the aerodynamic disturbance force amplitude increases and the nonlinear characteristics become more pronounced, the neural network can still maintain good simulation accuracy, and the deviation between the predicted value and the CFD data is controlled within a certain range. within;

[0151] Even when the local vibration surface is located in a non-optimal position, the simulation effect of the neural network does not significantly decrease, further demonstrating its generalization ability.

[0152] The verification results demonstrate that the constructed RBF neural network can stably and accurately simulate the nonlinear aerodynamic disturbance force generated by the relative motion between the local vibration surface and the main beam, completely solving the core defect of existing technologies that cannot quantify this force, and providing reliable data support for the subsequent design of sliding mode adaptive controllers. Compared with existing simulation methods using fixed models, this neural network has stronger generalization ability and adaptability, and can adapt to changes in aerodynamic disturbance force characteristics under different working conditions.

[0153] S4. Sliding Mode Adaptive Controller Design and Control Law Derivation

[0154] like Figure 10As shown, S3 achieves high-precision simulation of nonlinear aerodynamic disturbance forces through an RBF neural network, providing reliable data support for controller design. Existing bridge wind-induced vibration active control technologies mostly rely on fixed control strategies or offline calibration mapping tables, which cannot adapt to complex working conditions such as wind speed changes and structural parameter drift, resulting in insufficient control robustness. Based on the aerodynamic disturbance force simulation results of S3, this step designs a sliding mode adaptive controller, simultaneously generating control and adaptive laws to achieve precise driving of local vibration surfaces. This also addresses the core shortcomings of existing technologies, such as fixed weights and poor adaptability to working conditions, ensuring that the main beam's motion state stably tracks the ideal command.

[0155] S41. Establishment of System Dynamics Equations

[0156] Taking the single-degree-of-freedom torsional vibration of the box girder as the control object, torsional vibration is a key mode affecting bridge safety in wind-induced vibration, and this selection aligns with the actual control requirements of the project. Based on Newton's second law, considering the effects of box girder inertia, damping, stiffness, and aerodynamic forces, the following dynamic equations are established:

[0157] (1)

[0158] The symbols in the formula are defined as follows:

[0159] The moment of inertia is the mass of the box girder, expressed in kg·m² / m. The initial value is 0.012 kg·m² / m, which is a typical engineering value for the torsional moment of inertia of a large-span box girder and conforms to the actual structural characteristics.

[0160] The damping of the vibration system is expressed in N·s / m, and the standard for structural damping values ​​commonly used in engineering is adopted (generally 0.5% to 2% of the critical damping).

[0161] The stiffness of the vibration system is expressed in N / m and is calculated based on the elastic modulus of the box girder material, the moment of inertia of the cross section, and the support conditions.

[0162] The displacement is the torsional displacement of the box girder, in rad. The torsional acceleration of the box girder is expressed in rad / s². The torsional velocity of the box girder is expressed in rad / s.

[0163] The aerodynamic force generated by the movement of the box girder itself. That is, it is directly related to torsional displacement and velocity;

[0164] , This refers to the additional aerodynamic disturbance force component caused by the local vibration surface. This encompasses the coupling state between the main beam and the local vibration surface;

[0165] The control displacement of the local vibration surface, in meters;

[0166] A constant related to the size of the local vibration surface itself, in units Values This value is determined based on the ratio of the width to the thickness of the local vibration surface and aerodynamic efficiency analysis, which can maximize the control force output efficiency.

[0167] To simplify the control law design, the additional aerodynamic disturbance force components are combined, and equation (1) is rewritten as:

[0168] (2-a)

[0169] (2-b)

[0170] This simplification process does not change the essential characteristics of the system; it only integrates similar terms to facilitate subsequent state equation transformation and control law derivation.

[0171] S42, State Equation Transformation

[0172] Defining state variables transforms the second-order dynamic equations into a system of first-order linear equations, which conforms to the conventional approach in modern control theory and facilitates controller design.

[0173]

[0174] (3)

[0175] Due to torsional acceleration Substituting it into equation (2-a) and rearranging, we obtain the state equation:

[0176] (4)

[0177] The symbols in the formula are defined as follows:

[0178] The known linear part of the system reflects the combined effects of inertia, damping, and stiffness;

[0179] This refers to the nonlinear disturbance term corresponding to the aerodynamic forces of the box girder itself.

[0180] This is the nonlinear disturbance term corresponding to the aerodynamic interference force on the local vibration surface;

[0181] This is the system output, specifically the torsional displacement feedback value of the box girder, in rad.

[0182] The state equations clearly separate the known parts of the system from the unknown disturbance terms, providing a clear mathematical model for subsequent nonlinear disturbance approximation and control compensation.

[0183] S43, RBF neural network approximates nonlinear terms

[0184] Two independent RBF neural networks are used to approximate the... and This design can specifically capture the characteristics of different perturbation terms, thereby improving the approximation accuracy.

[0185] (5-a)

[0186] (5-b)

[0187] The symbols in the formula are defined as follows:

[0188] To approach The ideal weight vector for the neural network has a dimension of 15×1, which is consistent with the number of hidden layer nodes in the RBF neural network of S3.

[0189] To approach The ideal weight vector for a neural network has a dimension of 15×1;

[0190] , These are the hidden layer output vectors of the two neural networks, each with a dimension of 15×1, calculated using the Gaussian function defined by S3.

[0191] In practical applications, ideal weights , The values ​​cannot be obtained directly; they must be estimated. , Therefore, an approximation error is introduced. and The corresponding approximate output and error relationship are as follows:

[0192]

[0193]

[0194] In the formula, , For the neural network approximation error, satisfying The accuracy of neural network simulation based on S3, The threshold of 0.01 ensures that the error is within the allowable range for engineering applications.

[0195] For ease of subsequent controller design, let the real-time estimated output of the RBF neural network be denoted as:

[0196] (6-a)

[0197] (6-b)

[0198] S44, Sliding surface design

[0199] The sliding surface is designed to ensure that the system tracking error converges quickly. Sliding mode control has the characteristics of strong robustness and can effectively suppress disturbances and uncertainties.

[0200] (7)

[0201] The symbols in the formula are defined as follows:

[0202] This is the system tracking error. For ideal instructions, For system output;

[0203] , where is the derivative of the tracking error, in rad / s;

[0204] , which are the sliding surface parameters, determined through Lyapunov stability analysis. These values ​​ensure the accessibility of the sliding surface and the system response speed, while controlling the chattering amplitude within 0.01 rad to avoid affecting structural safety.

[0205] Ideal Instructions Set as The unit is rad. This command simulates the typical simple harmonic vibration trajectory of a bridge under wind. The amplitude and frequency are both within the actual range of engineering practice, which can effectively verify the tracking performance of the control algorithm.

[0206] S45, Derivation of Adaptive Law

[0207] To achieve real-time updates of the weights in the RBF neural network, an adaptive law is derived based on the Lyapunov stability criterion to ensure global system stability. The Lyapunov function is defined as follows:

[0208] (8)

[0209] The symbols in the formula are defined as follows:

[0210] To approach The neural network weight estimation error vector;

[0211] To approach The neural network weight estimation error vector;

[0212] , where is the adaptive law gain coefficient. The setting prioritizes ensuring the approximation accuracy of the aerodynamic disturbance terms of the box girder itself. This value is determined through simulation and is used to balance the convergence speed and steady-state accuracy.

[0213] right Differentiate and let Combining the state equation (4) and the definition of the sliding surface (7), the adaptive law is derived:

[0214] {9-a}

[0215] {9-b}

[0216] In the formula, These are the estimated weight vectors. Update rate; Adaptive gain coefficient ; The function value of the sliding surface; This is the Gaussian function output vector of the hidden layer of the RBF neural network; This is the control law for the local vibration surface. This adaptive law can dynamically adjust the weights based on the sliding mode surface function value and the hidden layer output, solving the problem of insufficient adaptability caused by fixed weights in existing technologies, and ensuring that the neural network continuously and accurately approximates nonlinear disturbances.

[0217] S46. Control Law Design

[0218] The control law is constructed as a combination of feedforward compensation terms, composite feedback terms, and sliding mode switching terms, with each component working together to achieve high-precision control.

[0219] (10)

[0220] The functions and parameters of each part in the formula are explained as follows:

[0221] For RBF neural network pairs Real-time estimated value; For RBF neural network pairs Real-time estimated value; The linear dynamics of the system are known. The second derivative of the ideal instruction; These are the parameters of the sliding surface; The derivative of the tracking error; This refers to the gain coefficient of the sliding mode switching term; For symbolic functions, defined as .

[0222] S47. Dynamic fusion weights and adaptive adjustment based on operating conditions

[0223] S471, Generation of Dynamic Fusion Weight Coefficients

[0224] Sliding mode adaptive controller based on tracking error With sliding surface function value The dynamic fusion weight coefficient λ is generated and used to weight and fuse the outputs of the two neural network compensation modules.

[0225] when This indicates that the disturbance mainly originates from the movement of the main beam itself, thus increasing the weight of the first neural network compensation module. This enhances the compensation effect on the aerodynamic forces of the box girder itself;

[0226] when and This indicates that the disturbance mainly originates from additional aerodynamic interference caused by local vibration surfaces, thus increasing the weight of the second neural network compensation module. It precisely counteracts additional aerodynamic interference forces;

[0227] when When this occurs, it indicates that the system deviates significantly from the sliding surface. The weights of the two compensation modules are balanced to avoid the over-exertion of a single module that could lead to control instability.

[0228] This design can dynamically adjust the compensation priority according to the source of the disturbance, further improving control accuracy.

[0229] S472, Adaptive Adjustment of Wind Speed ​​Threshold and Structural Parameter Changes

[0230] The preset wind speed threshold is 15 m / s. This threshold is determined based on S2's CFD simulation and engineering experience. Below this wind speed, small amplitude and low gain are sufficient to meet the control requirements. Above this wind speed, the control intensity needs to be increased.

[0231] When monitoring the incoming airflow speed Simultaneously increase the gain of the sliding mode switching term. Up to 0.08, the gain of the feedforward compensation term The amplitudes of the local vibration surface control command were increased to 6.0 and 1.2 respectively, and the upper limit of the amplitude was increased to 0.015B to cope with large disturbances under strong winds.

[0232] When wind speed When the initial parameters are restored, the control effect and energy consumption are balanced.

[0233] When the dynamic parameters of the main beam structure change, the controller updates the weights of the RBF neural network in real time through adaptive laws (9-a) and (9-b), and readjusts the gain coefficients of the feedforward compensation term, composite feedback term and sliding mode switching term in the control law according to the updated weights, so as to ensure that the system maintains good control performance under the condition of structural parameter drift, and solves the defect of insufficient robustness of the existing technology.

[0234] S5. Control Effect Verification

[0235] S4 has completed the design of a sliding mode adaptive controller and the derivation of its control law, constructing a complete control system that includes dynamic fusion weights and adaptive adjustment under different operating conditions. Existing technologies often rely on verification under single operating conditions, lacking comprehensive testing under complex scenarios such as wind speed changes and structural parameter drift, making it difficult to prove control robustness. This step, based on S4's control strategy, sets different operating conditions for simulation verification: box girder width... Moment of inertia (Base value); Torsional frequency Damping ratio Ideal instructions ; RBF neural network structure: approximation The network is a 2-15-1 network, approximating The network is a 3-15-1 network; controller parameters: .

[0236] S51, Verification of Operating Conditions

[0237] S511, Operating Condition 1: Low Wind Speed ​​with Conventional Structural Parameters

[0238] Set wind speed The wind speed is lower than the preset wind speed threshold of 15m / s, simulating the normal wind environment during bridge operation; the structural parameters are the above basic values.

[0239] S512, Operating Condition 2: High Wind Speed ​​with Conventional Structural Parameters

[0240] Set wind speed The wind speed is higher than the 15m / s wind speed threshold, simulating a strong wind disturbance scenario; the structural parameters are the above basic values.

[0241] S513, Operating Condition 3: High Wind Speed ​​Structural Parameter Drift Condition

[0242] Set wind speed Maintain a high-wind-speed disturbance environment; adjust the moment of inertia of the box girder mass to The adjustment ratio simulates the drift of structural parameters of the bridge caused by icing, installation of additional facilities, etc., with a change of more than 50%, verifying the robustness of the controller to changes in structural dynamic parameters.

[0243] The three sets of operating conditions cover core scenarios such as normal wind, strong wind, and changes in structural parameters, comprehensively testing the adaptability of the control strategy under different actual operating conditions, which meets the engineering verification requirements for bridge wind vibration control.

[0244] S52. Verification Results and Effect Analysis

[0245] S521, Operating Condition 1: Low Wind Speed ​​with Conventional Structural Parameters

[0246] like Figure 11 As shown, displacement tracking: box girder torsional displacement and ideal command. The results are largely consistent, with a maximum tracking error of 0.008 rad. Existing fixed guide vanes typically have a maximum tracking error of 0.02 rad due to boundary layer effects and unadjustable parameters. This solution reduces the error by 60%, thanks to the synergistic effect of the feedforward compensation term and the composite feedback term, which accurately counteracts the aerodynamic disturbances generated by the movement of the box girder itself.

[0247] Speed ​​Response: The jitter amplitude at the peak of the tracked speed is 0.01 rad / s, far less than the 0.03 rad / s of passive TMD control. Sliding Mode Switching Gain The reasonable settings effectively suppress approximation errors and external disturbances, while successfully controlling the amplitude of chattering and avoiding fatigue damage to the structure caused by chattering.

[0248] Local vibration surface motion: The vibration exhibits a stable periodicity, with the amplitude automatically maintained at 0.006B, consistent with the amplitude strategy under low and medium wind speeds in S472. This amplitude satisfies the vortex suppression requirements while reducing actuation energy consumption, achieving an energy reduction of over 25% compared to existing fixed amplitude control.

[0249] S522, Operating Condition 2: High Wind Speed ​​with Conventional Structural Parameters

[0250] like Figure 12 As shown, displacement tracking: the maximum tracking error of the box girder's torsional displacement is 0.01 rad, maintaining high control accuracy. Existing fixed guide vanes experience increased aerodynamic interference under strong winds, resulting in a tracking error of 0.035 rad. This solution, by synchronously increasing the sliding mode switching term gain to 0.08 and the feedforward compensation term gain to 6.0 and 1.2 respectively, effectively counteracts large disturbances under strong winds. Even with an aerodynamic interference increase exceeding 50%, stable control is maintained, and the error is reduced by 71%.

[0251] Speed ​​Response: The peak chattering amplitude at the tracking speed is 0.015 rad / s, which is within the allowable range for engineering applications. The chattering control performance is superior to existing active control schemes, demonstrating the strong robustness of sliding mode control and the effectiveness of adaptive gain adjustment.

[0252] Local vibration surface motion: The amplitude is automatically adjusted to 0.01B, consistent with the amplitude upper limit adjustment strategy under medium and high wind speeds in S472. This adjustment precisely matches the aerodynamic interference force requirements under strong winds, ensuring control effectiveness while avoiding excessive actuation, thus balancing control accuracy and energy consumption.

[0253] S523, Operating Condition 3: High Wind Speed ​​Structural Parameter Drift Condition

[0254] like Figure 13 As shown, displacement tracking: the maximum tracking error of the box girder's torsional displacement is 0.009 rad, which is basically consistent with the error levels of working conditions 1 and 2, and there is no significant decrease in accuracy due to structural parameter drift. Existing technologies typically increase the control error by more than double when structural parameters change by more than 30%. This scheme updates the RBF neural network weights in real time through an adaptive law, readjusting the gain coefficients of the control law to ensure stable tracking of the ideal command, significantly improving robustness.

[0255] Speed ​​response: The tracking speed is stable with no obvious distortion, and the chattering amplitude is controlled within 0.012 rad / s, further verifying the adaptability of sliding mode adaptive control to changes in structural parameters.

[0256] Local vibration surface motion: The amplitude automatically decreases to 0.005B. Due to the increased structural inertia, the system's inherent stability is enhanced, and the required control force is reduced. This dynamic adjustment demonstrates the controller's ability to perceive and adapt to changes in structural parameters, achieving energy consumption optimization. Compared to the condition with constant parameters, energy consumption is further reduced by 17%.

[0257] The verification results of three sets of operating conditions show that the proposed solution, through the sliding mode adaptive control strategy designed with S4, can achieve high-precision, low-bounce, and low-energy-consumption control effects under different wind speeds and structural parameter variations. Compared with existing fixed control, passive control, and traditional active control schemes, this solution effectively solves the core defects such as narrow adaptability, insufficient robustness, and significant bounce, providing an efficient and reliable technical solution for bridge wind vibration control.

[0258] The implementation principle of the intelligent control method for bridge wind vibration based on RBF neural network and sliding mode adaptive control in this application embodiment is as follows: This invention arranges local vibration surfaces at key positions of the main beam and constructs an RBF neural network to estimate the nonlinear aerodynamic disturbance force generated by the relative motion between the vibration surface and the main beam in real time. Then, the estimated value and the main beam motion tracking error are input into the sliding mode adaptive controller. The controller synchronously generates the control law driving the vibration surface and the adaptive law updating the neural network weights, thereby forming a closed-loop control system that can identify and compensate for complex aeroelasticity online. This fusion mechanism directly addresses the core defect of existing technologies that cannot quantify and compensate for the nonlinear aerodynamic coupling force between the device and the main beam in real time. Through the self-learning of the neural network and the strong robustness of the sliding mode control, it realizes adaptive and high-precision suppression of bridge wind vibration under complex working conditions such as sudden wind speed changes and structural parameter drift. It effectively overcomes the narrow range of application, poor control robustness, and safety hazards of traditional methods that rely on fixed mapping tables or offline calibration methods, as well as the possibility of amplifying vibration due to improper compensation under non-preset conditions.

[0259] The above are all preferred embodiments of this application, and are not intended to limit the scope of protection of this application. Therefore, all equivalent changes made in accordance with the structure, shape and principle of this application should be covered within the scope of protection of this application.

Claims

1. A bridge wind-induced vibration intelligent control method based on RBF neural network and sliding mode adaptation, characterized in that, Includes the following steps: Local vibration surfaces are set up at predetermined locations on the main girder of the bridge; The real-time motion state of the main beam and the real-time displacement of the local vibration surface are obtained. An RBF neural network is constructed, which takes the real-time motion state of the main beam and the real-time displacement of the local vibration surface as inputs, and outputs the real-time estimate of the additional aerodynamic disturbance force caused by the relative motion between the local vibration surface and the main beam. The real-time estimated value and the tracking error between the measured motion state of the main beam and the ideal command are input to the sliding mode adaptive controller. The sliding mode adaptive controller synchronously generates a control law for driving the local vibration surface and an adaptive law for updating the weights of the RBF neural network in real time. The control law is used to drive the local vibration surface to vibrate, and the real-time displacement of the local vibration surface is fed back to the input of the RBF neural network; at the same time, the adaptive law is used to update the weights of the RBF neural network in real time.

2. The method according to claim 1, characterized in that, The predetermined position is at least one of the windward end and the tail end of the main beam on the lower side. The amplitude of the local vibration surface is constrained below an amplitude threshold based on the main beam scale; The vibration frequency of the local vibration surface is set to a specific multiple based on the natural frequency of the main beam; The vibration mode, determined by the amplitude threshold and the specific multiple, is configured to generate the aerodynamic disturbance force with a preset dynamic range at the predetermined position.

3. The method according to claim 1, characterized in that, The RBF neural network includes: The input layer is used to synchronously receive the real-time motion state of the main beam and the real-time displacement of the local vibration surface, forming a joint input that characterizes the coupling state of the system. The hidden layer, whose number of nodes is determined based on the nonlinear approximation requirement of the aerodynamic disturbance force, is configured to perform nonlinear mapping and feature extraction on the joint input. The output layer is configured to generate a real-time estimate of the aerodynamic disturbance force based on the output of the hidden layer.

4. The method according to claim 3, characterized in that, The adaptive law is constructed as follows: Based on the current sliding surface function value calculated by the sliding mode adaptive controller, the output of the hidden layer, and the control law, the weight adjustment amount of the RBF neural network is dynamically generated; The weight adjustment amount is used to update the weights of the RBF neural network in real time; The adjusted weights are synchronously used to update the real-time estimated values ​​generated by the output layer and serve as the gain parameters of the feedforward compensation term in the sliding mode adaptive controller.

5. The method according to claim 4, characterized in that, The control law is constructed to include a feedforward compensation term, a composite feedback term, and a sliding mode switching term. The feedforward compensation term is constructed based on the real-time estimated value output by the RBF neural network and the updated weights, in order to counteract the aerodynamic disturbance force; The composite feedback term and the sliding mode switching term are generated based on the tracking error and the sliding mode surface function value, respectively. The two are superimposed to compensate for the uncertainty and external disturbance of the main beam vibration system, and work together with the feedforward compensation term to drive the local vibration surface so that the measured motion state of the main beam tracks the ideal command.

6. The method according to claim 5, characterized in that, When the real-time monitored incoming wind speed exceeds the preset wind speed threshold, the sliding mode adaptive controller synchronously increases the gain coefficient of the sliding mode switching term and the gain coefficient of the feedforward compensation term, and raises the upper limit of the amplitude of the local vibration surface control command.

7. The method according to claim 5, characterized in that, When the structural dynamic parameters of the main beam change, the sliding mode adaptive controller updates the weights of the RBF neural network through the adaptive law, and readjusts the gain coefficients of the feedforward compensation term, the composite feedback term and the sliding mode switching term in the control law according to the updated weights.

8. The method according to claim 5, characterized in that, The feedforward compensation term includes a first neural network compensation module and a second neural network compensation module; The first neural network compensation module is constructed based on the estimated value of the aerodynamic force generated by the movement of the main beam itself. The second neural network compensation module is constructed based on the estimated value of the additional aerodynamic disturbance force caused by the local vibration surface; The sliding mode adaptive controller generates independent weight adjustment amounts for the neural networks corresponding to the first neural network compensation module and the second neural network compensation module respectively through the adaptive law, and adjusts the gain coefficients of the first neural network compensation module and the second neural network compensation module respectively based on the updated weights.

9. The method according to claim 8, characterized in that, The sliding mode adaptive controller is also configured to: Based on the tracking error and the sliding surface function value, a dynamic fusion weight coefficient is generated. The dynamic fusion weight coefficient is used to weight and fuse the first compensation amount output by the first neural network compensation module and the second compensation amount output by the second neural network compensation module. The generation rules for the dynamic fusion weight coefficients include: When the amplitude characteristics of the tracking error indicate that the disturbance mainly originates from the movement of the main beam itself, the weighting coefficient of the first compensation amount is increased; When the amplitude characteristics of the tracking error indicate that the disturbance mainly originates from the additional aerodynamic interference caused by the local vibration surface, the weighting coefficient of the second compensation amount is increased; When the absolute value of the sliding surface function increases, the weight coefficient corresponding to the compensation amount currently assigned a higher weight is reduced, and the weight coefficient of the other compensation amount is increased accordingly.

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