A method for constructing a vortex vibration response model of a cable-based photovoltaic support

Abstract

The application provides a cable-supported photovoltaic support vortex vibration response model construction method, and belongs to the technical field of cable-supported photovoltaic support detection. The application extracts modal parameters through fast Fourier transform, performs non-uniform sampling in a six-dimensional parameter space based on a sparse grid point distribution method, performs computational fluid dynamics numerical simulation on the sampling points to establish an aerodynamic force characteristic database, trains a vortex vibration response prediction model to output a vortex-induced lift coefficient, adopts a modal selection criterion based on energy proportion to retain key modes, adopts a symplectic geometry structure-preserving numerical integration algorithm to perform time-domain integration and solving, introduces a corotational coordinate system to perform geometric nonlinear correction, adopts an immersed boundary-lattice Boltzmann coupling method to update a fluid-structure coupling interface, adjusts an artificial intelligence model learning rate through an adaptive adjustment factor, judges convergence, and outputs vortex vibration response results, thereby solving the problem of excessive consumption of resources in vortex vibration response prediction and calculation of cable-supported photovoltaic supports.

Description

Technical Field

[0001] This invention belongs to the field of cable-stayed photovoltaic support technology, and specifically relates to a method for constructing a vortex-induced vibration response model for cable-stayed photovoltaic supports. Background Technology

[0002] Cable-stayed photovoltaic (PV) supports are a novel type of support structure that suspends photovoltaic panels using flexible cable segments. Under wind loads, these cable segments experience vortex-induced vibration (vortex-induced vibration), and accurate prediction of the vortex-induced vibration response is crucial for structural safety. Traditional vortex-induced vibration response prediction methods combine computational fluid dynamics numerical simulation with finite element analysis (FEA). This requires comprehensive sampling in a high-dimensional parameter space comprising amplitude, frequency, Reynolds number, incoming wind speed, cable segment tension, and cable segment diameter. Using tensor product meshes to arrange sampling points presents the curse of dimensionality, as the number of sampling points in a six-dimensional parameter space increases exponentially, leading to enormous computational resource consumption. In current vortex-induced vibration response analysis of cable-stayed PV supports, because independent fluid-structure interaction calculations are required for each operating condition, the prediction of the vortex-induced vibration response for a single project often takes weeks or even months of computation time, severely restricting design efficiency. In other words, existing technologies suffer from the technical problem of excessive computational resource consumption in predicting the vortex-induced vibration response of cable-stayed PV supports. Summary of the Invention

[0003] In view of this, the present invention provides a method for constructing a vortex-induced vibration response model for cable-stayed photovoltaic supports, which can solve the technical problem of excessive resource consumption in the prediction and calculation of vortex-induced vibration response of cable-stayed photovoltaic supports in the prior art.

[0004] This invention is implemented as follows: It provides a method for constructing a vortex-induced vibration response model for cable-stayed photovoltaic (PV) systems. Strain sensors and accelerometers are deployed on the surface of typical cable segments of the PV system to collect vibration displacement time-history data and strain time-history data. The vibration displacement time-history data is converted to the frequency domain using a fast Fourier transform to extract the modal frequencies and corresponding amplitudes, establishing an initial modal parameter set. Based on the sparse grid collocation method, sampling points are arranged in a six-dimensional parameter space consisting of amplitude, frequency, Reynolds number, incoming wind speed, cable segment tension, and cable segment diameter to establish a non-uniformly distributed sampling grid. Computational fluid dynamics numerical simulation is performed on each sampling point in the non-uniformly distributed sampling grid to calculate the vortex shedding frequency and vortex-induced lift coefficient, establishing the aerodynamic force. The aerodynamic feature database is input into the vortex-induced vibration response prediction model for training, and the predicted vortex-induced lift coefficient and vibration response amplitude are output. A modal screening criterion based on energy proportion is established to retain the frequencies of key participating modes to form a simplified mode set. The simplified mode set is solved by time-domain integration using a symplectic geometric-preserving structure numerical integration algorithm to calculate the displacement and velocity responses of the cable segment under the action of the vortex-induced lift coefficient. A corotating coordinate system is introduced to perform geometric nonlinear correction on the large deformation configuration of the cable segment. The fluid-structure interaction interface is updated using the immersed boundary-lattice Boltzmann coupling method. The adaptive adjustment factor is calculated and the learning rate of the vortex-induced vibration response prediction model is adjusted. After determining whether the displacement response has converged, the final vortex-induced vibration response result is output.

[0005] The sparse grid point allocation method uses the Smolyak sparse grid construction algorithm to decompose the six-dimensional parameter space into a combination of multiple one-dimensional discrete spaces, and assigns different discrete levels according to the sensitivity of each dimension parameter to the vortex-induced lift coefficient.

[0006] The non-uniformly distributed sampling grid increases the sampling point density in highly sensitive areas and decreases the sampling point density in low-sensitive areas, reducing the number of sampling points to 0.3% compared to the traditional tensor product grid.

[0007] The aerodynamic feature database is organized in key-value pair format, where the key is a combination of amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter, and the value is the corresponding vortex-induced lift coefficient, vortex shedding frequency, and pressure distribution.

[0008] The aerodynamic feature database is established by adopting an active learning strategy, prioritizing the addition of sampling points in parameter regions with large prediction errors, and gradually improving the prediction accuracy of the aerodynamic feature database in the full parameter space through iterative optimization.

[0009] The vortex-induced vibration response prediction model input layer receives a six-dimensional parameter vector, which is processed by three hidden layers and outputs the vortex-induced lift coefficient and vibration response amplitude. The number of neurons in the three hidden layers are 128, 256 and 128, respectively, and the activation function is a modified linear unit function.

[0010] The vortex-induced vibration response prediction model utilizes a parameter efficiency improvement framework based on weight sharing, which shares the weight matrices of the first and third hidden layers, while only the second hidden layer uses independent weights. The input layer information is directly transmitted to the third hidden layer through residual connections.

[0011] The vortex-induced vibration response prediction model employs a Bayesian uncertainty quantization output calibration mechanism, with two branches connected in parallel at the output layer. One branch outputs the mean prediction, and the other branch outputs the variance prediction. The variance branch parameters are trained through variational inference.

[0012] When establishing the training dataset for the vortex vibration response prediction model, all sampling point data are extracted from the aerodynamic feature database, and the training set and validation set are divided in an 8:2 ratio. The input features are normalized, and the output labels are standardized.

[0013] The symplectic geometric-preserving structure numerical integration algorithm rewrites the cable vibration equation into a regular Hamiltonian form, introduces generalized coordinates and generalized momentum as state variables, and uses the Gaussian-type symplectic Runge-Kutta method for time discretization.

[0014] The training of the vortex-induced vibration response prediction model adopts the stochastic gradient descent optimization algorithm, with an initial learning rate of 0.01, a batch size of 32, a training epoch of 500, and a loss function consisting of a weighted sum of mean squared error and the negative log-likelihood of the variance branch.

[0015] The modal screening criterion based on energy proportion decomposes the vibration displacement time history data into modes, calculates the energy contribution rate corresponding to each modal frequency, stops accumulation when the cumulative energy contribution rate reaches 99.9%, and retains the corresponding modal frequencies to form a simplified mode set.

[0016] The corotating coordinate system is a local coordinate system that rotates with the deformation of the cable segment. The coordinate axes are always aligned with the tangent and normal directions of the current configuration of the cable segment. The nodal displacements are transformed from the global coordinate system to the corotating coordinate system, and a linearized element stiffness matrix is ​​established in the corotating coordinate system.

[0017] In the immersion boundary-lattice Boltzmann coupling method, the fluid uses a fixed Cartesian grid, and the structural boundary is achieved by applying virtual forces to the structural surface to make the fluid satisfy the no-slip boundary condition. The lattice Boltzmann method solves the flow field through the collision and migration process of the particle distribution function.

[0018] The adaptive adjustment factor is calculated based on the validation set loss change rate, gradient norm, and number of training rounds, and is summed with weights of 0.5, 0.3, and 0.2. The learning rate decay strategy is selected according to the interval to which the adaptive adjustment factor belongs.

[0019] In determining whether the displacement response has converged, if the rate of change of the displacement response is less than 0.5% within 50 consecutive time steps, it is considered converged and the final vortex-induced vibration response result is output; otherwise, iterative calculation continues.

[0020] This invention employs a sparse grid point allocation method for non-uniform sampling in a six-dimensional parameter space. By utilizing the Smolyak sparse grid construction algorithm to allocate different discrete levels based on the sensitivity of parameters in each dimension, the number of sampling points is reduced to 0.3% of that of traditional tensor product grids, significantly reducing the number of computational fluid dynamics simulations. The vortex-induced vibration response prediction model established in this invention adopts a parameter efficiency improvement framework based on weight sharing. It reduces the model size and improves training speed through a parameter reuse mechanism, and introduces a Bayesian uncertainty quantification output calibration mechanism to automatically provide low-confidence indicators in sparse regions of the parameter space, guiding the active learning sampling strategy of the aerodynamic feature database and avoiding the waste of computational resources caused by blind sampling. This invention solves the technical problem of excessive computational resource consumption in predicting the vortex-induced vibration response of cable-stayed photovoltaic supports by reducing the number of sampling points through the sparse grid point allocation method, rapidly predicting the vortex-induced lift coefficient through the vortex-induced vibration response prediction model, and intelligently expanding the aerodynamic feature database through an active learning strategy. Attached Figure Description

[0021] Figure 1 This is a flowchart of the method of the present invention.

[0022] Figure 2 The time history curves of cable segment vibration displacement under different wind speed conditions are shown.

[0023] Figure 3 This is a scatter plot of the distribution of sparse grid sampling points in the amplitude-Reynolds number two-dimensional parameter space. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below.

[0025] like Figure 1 The diagram shows a flowchart of a method for constructing a vortex-induced vibration response model for a cable-stayed photovoltaic support provided by this invention. This method includes the following steps:

[0026] S01. Strain sensors and acceleration sensors are installed on the surface of typical cable segments of the cable-supported photovoltaic system to collect vibration displacement time history data and strain time history data of the cable segments under different wind speed conditions. At the same time, the corresponding incoming wind speed, wind direction angle, cable segment tension and cable segment diameter are recorded.

[0027] S02. The vibration displacement time history data is converted to the frequency domain through fast Fourier transform, the modal frequencies and corresponding amplitudes of each order are extracted, an initial modal parameter set is established, and the axial stress distribution of the cable segment is calculated based on the strain time history data.

[0028] S03. Based on the sparse grid point arrangement method, sampling points are arranged in a six-dimensional parameter space consisting of amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter. The sampling point density is increased in high-sensitivity areas and decreased in low-sensitivity areas to establish a non-uniformly distributed sampling grid.

[0029] S04. Perform computational fluid dynamics numerical simulation on each sampling point in the non-uniformly distributed sampling grid, calculate the vortex shedding frequency and vortex-induced lift coefficient of the flow field around the cable segment, and record the vortex-induced lift coefficient and the corresponding amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter combination into the aerodynamic characteristic database.

[0030] S05. Input the aerodynamic characteristic database into the vortex-induced vibration response prediction model for training. After training, input the real-time monitored amplitude, frequency, Reynolds number, incoming wind speed, cable tension, and cable diameter, and output the predicted vortex-induced lift coefficient and vibration response amplitude.

[0031] S06. Establish a modal screening criterion based on energy proportion, calculate the energy contribution rate corresponding to each modal frequency in the initial modal parameter set, remove modal frequencies with an energy contribution rate of less than 0.1%, and retain key participating modal frequencies to form a simplified modal set.

[0032] S07. The simplified mode set is solved by time-domain integration using the symplectic geometric-preserving structure numerical integration algorithm. The cable vibration equation is converted into the canonical Hamiltonian form and then discretized by the symplectic Runge-Kutta. The displacement and velocity responses of the cable segment under the action of the vortex-induced lift coefficient are calculated.

[0033] S08. Introduce a corotating coordinate system to perform geometric nonlinear correction on the large deformation configuration of the cable segment, update the cable segment configuration according to the displacement response, and transform the geometric nonlinearity into material nonlinearity for equivalent processing through coordinate transformation.

[0034] S09. The fluid-structure interaction interface is updated by using the immersion boundary-lattice Boltzmann coupling method. The surface boundary conditions of the cable segment are realized by virtual force feedback on the fixed Cartesian fluid grid, so as to avoid the mesh distortion caused by the fluid grid moving with the structure.

[0035] S10. Calculate the adaptive adjustment factor and adjust the learning rate of the vortex vibration response prediction model. Select the learning rate decay strategy according to the range to which the adaptive adjustment factor belongs. When the adaptive adjustment factor belongs to different ranges, use different learning rate update methods.

[0036] S11. Determine whether the displacement response has converged. If the rate of change of the displacement response is less than 0.5% within 50 consecutive time steps, it is determined to be converged, and the final vortex-induced vibration response result is output. Otherwise, return to step S07 to continue iterative calculation.

[0037] The sparse grid point allocation method is a sampling method in a high-dimensional parameter space. By using discretization schemes with different precision in different dimensions, it avoids the curse of dimensionality caused by traditional tensor product grids. In specific implementation, the Smolyak sparse grid construction algorithm is used to decompose the six-dimensional parameter space consisting of amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter into a combination of multiple one-dimensional discrete spaces. Different discretization levels are assigned according to the sensitivity of each dimension parameter to the vortex-induced lift coefficient. Dimensions with high sensitivity are finely discretized, while dimensions with low sensitivity are coarsely discretized. The number of sampling points is reduced to 0.3% of the original number compared to traditional grids.

[0038] The aerodynamic feature database is a data structure that stores the correspondence between vortex-induced lift coefficients and amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter. The aerodynamic feature database is organized in key-value pair form, where the key is a combination of amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter, and the value is the corresponding vortex-induced lift coefficient, vortex shedding frequency, and pressure distribution. The aerodynamic feature database is established using an active learning strategy, which prioritizes adding sampling points in parameter regions with large prediction errors, and gradually improves the prediction accuracy of the aerodynamic feature database in the full parameter space through iterative optimization.

[0039] The specific structure of the vortex-induced vibration response prediction model is as follows: the input layer receives a six-dimensional parameter vector consisting of amplitude, frequency, Reynolds number, incoming wind speed, cable tension, and cable diameter. After processing through three hidden layers, the output is the vortex-induced lift coefficient and vibration response amplitude. The number of neurons in the three hidden layers are 128, 256, and 128, respectively, and the activation function is a modified linear unit function. The vortex-induced vibration response prediction model utilizes a parameter efficiency improvement framework based on weight sharing. In the multi-layer network structure, the model size is reduced while maintaining expressive power through a parameter reuse mechanism. Specifically, the weight matrices of the first and third hidden layers are shared, while the weight matrices of the second and third hidden layers are shared only. The hidden layer uses independent weights and directly transmits the input layer information to the third hidden layer through residual connections, avoiding gradient vanishing and reducing the total number of parameters. The vortex-induced vibration response prediction model adopts a Bayesian uncertainty quantification output calibration mechanism, introducing probability distribution estimation in the output layer and adding confidence intervals to the prediction results. Specifically, two branches are connected in parallel in the output layer, one branch outputs the mean prediction and the other branch outputs the variance prediction. The variance branch parameters are trained through variational inference, so that the vortex-induced vibration response prediction model outputs a larger variance in sparse regions of the parameter space to indicate prediction uncertainty, and outputs a smaller variance in dense regions of the parameter space to indicate high-confidence prediction.

[0040] The parameter efficiency improvement framework based on weight sharing reduces the number of parameters in the vortex-induced vibration response prediction model, increases training speed, and avoids the risk of overfitting. The output calibration mechanism based on Bayesian uncertainty quantization ensures that the output of the vortex-induced vibration response prediction model includes not only the predicted value but also confidence information. When the input amplitude-frequency-Reynolds number-incoming wind speed-cable tension-cable diameter falls in an area with insufficient training data coverage, the vortex-induced vibration response prediction model automatically provides a low confidence indicator, prompting the need to supplement computational fluid dynamics numerical simulation data in that area. This guides the active learning sampling strategy of the aerodynamic feature database. The synergistic effect of these two mechanisms significantly reduces computational resource consumption while ensuring prediction accuracy. At the same time, uncertainty quantization enables intelligent expansion of the aerodynamic feature database, avoiding the waste of computational resources caused by blind sampling.

[0041] The steps for establishing the training dataset of the vortex-induced vibration response prediction model specifically include: extracting all sampling point data from the aerodynamic feature database; using amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter as input features; and using the corresponding vortex-induced lift coefficient and vibration response amplitude as output labels; dividing the training set and validation set in an 8:2 ratio; normalizing the input features to unify the range of parameters in each dimension to the interval between 0 and 1; and standardizing the output labels to make the mean 0 and the variance 1, thus establishing the training dataset and validation dataset.

[0042] The specific steps for training the vortex-induced vibration response prediction model include using a stochastic gradient descent optimization algorithm, setting the initial learning rate to 0.01, the batch size to 32, the number of training epochs to 500, and the loss function to be a weighted sum of mean squared error and negative log-likelihood of variance branch, with weight coefficients set to 0.7 and 0.3. Every 50 epochs, the performance of the vortex-induced vibration response prediction model is evaluated on the validation set, and the model parameters with the minimum loss on the validation set are recorded as the optimal model. During training, the gradient norm is monitored to avoid gradient explosion, and the gradient is clipped when the gradient norm exceeds 10.

[0043] The modal selection criterion based on energy proportion is a method for selecting modes based on the contribution rate of each modal frequency to the total vibration energy. Specifically, the vibration displacement time history data is decomposed into modes, the sum of kinetic and potential energy corresponding to each modal frequency is calculated, and the sum is divided by the total energy of all modal frequencies to obtain the energy contribution rate corresponding to the modal frequency. The energy contribution rates are sorted from largest to smallest, and accumulation stops when the cumulative energy contribution rate reaches 99.9%. The corresponding modal frequencies are retained to form a simplified mode set.

[0044] The symplectic geometry-preserving numerical integration algorithm utilizes the symplectic geometric properties of Hamiltonian systems to construct a symplectic Runge-Kutta integration scheme that maintains the invariance of phase space volume. This ensures that the energy conservation error of the system does not accumulate during long-term integration. Specifically, the cable vibration equation is first rewritten in canonical Hamiltonian form, and generalized coordinates and generalized momentum are introduced as state variables. A Hamiltonian function is established to express the sum of the kinetic and potential energy of the cable segment. Then, a Gaussian-type symplectic Runge-Kutta method is used for time discretization. This method implicitly ensures that the discretized numerical mapping satisfies the symplectic condition, that is, the product of the transpose of the Jacobian matrix and itself equals the identity matrix. This ensures that the phase space volume is strictly conserved during numerical integration, avoiding artificial energy dissipation or growth caused by traditional explicit integration methods.

[0045] The proposed symplectic geometry-preserving numerical integration algorithm prevents spurious amplitude decay or growth during long-term free vibration simulation of cable segments with low damping. The total system energy remains at its initial value after thousands of vibration cycles, fundamentally solving the amplitude distortion problem caused by numerical damping in the traditional Newmark method. This is crucial for accurately predicting the long-term vortex-induced vibration response of cable segments under continuous wind loads, especially when assessing the fatigue life of cable segments. Spurious numerical damping can severely underestimate the stress cycle amplitude, while the symplectic geometry-preserving numerical integration algorithm ensures that the long-term statistical characteristics of the stress time history are not distorted, providing a reliable numerical basis for fatigue assessment. At the same time, the energy conservation characteristics of the symplectic geometry-preserving numerical integration algorithm also significantly improve the stability of the numerical solution, allowing for larger time steps without causing computational divergence and improving computational efficiency.

[0046] The co-rotating coordinate system is a local coordinate system that rotates with the deformation of the cable segment. The coordinate axes are always aligned with the tangent and normal directions of the current configuration of the cable segment. In the co-rotating coordinate system, the geometric nonlinear deformation of the cable segment is equivalent to the material nonlinearity problem, avoiding repeated updates of the stiffness matrix in the global coordinate system. In specific implementation, the axial direction of the cable segment is calculated based on the displacement of the nodes at both ends of the cable segment, a co-rotating coordinate system is established, the node displacements are transformed from the global coordinate system to the co-rotating coordinate system, a linearized element stiffness matrix is ​​established in the co-rotating coordinate system, the nodal forces in the co-rotating coordinate system are solved, and then the system is transformed back to the global coordinate system for overall equilibrium iteration.

[0047] The immersion boundary-lattice Boltzmann coupling method is a fluid-structure interaction computation method. The fluid uses a fixed Cartesian grid, and the structural boundary is not aligned with the Cartesian grid. Virtual forces are applied to the structural surface to make the fluid satisfy the no-slip boundary condition. The lattice Boltzmann method solves the flow field through the collision and migration process of the particle distribution function. In specific implementation, at each time step, a lattice Boltzmann collision step is first performed to calculate the local equilibrium state, and then a migration step is performed to update the particle distribution of adjacent nodes. Then, the required boundary force is calculated according to the surface position and velocity response of the cable segment, and the boundary force is distributed to the surrounding fluid grid nodes in the form of volume force to update the fluid velocity field. The multi-relaxation BGK collision operator improves numerical stability and accuracy by introducing multiple relaxation time parameters to control the relaxation process of different physical quantities.

[0048] The adaptive adjustment factor is used to adjust the learning rate of the vortex-induced vibration response prediction model. The adaptive adjustment factor is calculated based on the validation set loss change rate, gradient norm, and number of training epochs. Specifically, the validation set loss change rate is obtained by comparing the current validation set loss with the average of the losses in the previous 10 epochs; the normalized gradient norm is obtained by dividing the current gradient norm by the initial gradient norm; and the training progress is obtained by dividing the current number of training epochs by the total number of training epochs. These three factors are then weighted and summed with weights of 0.5, 0.3, and 0.2 to obtain the adaptive adjustment factor value. When the adaptive adjustment factor α∈[0, 0.3), the learning rate remains at its initial value of 0.01. When α∈[0.3, 0.6), the learning rate decays to 0.005. When α∈[0.6, 0.85), the learning rate decays to 0.001. When α∈[0.85, 1], the learning rate decays to 0.0001. By dynamically adjusting the learning rate through the adaptive adjustment factor, the vortex vibration response prediction model can converge quickly in the early stage of training and be finely tuned in the later stage of training, avoiding oscillations caused by an excessively large learning rate or slow convergence caused by an excessively small learning rate.

[0049] Optionally, the present invention also provides a computer-based method for forming a cable-stayed photovoltaic support vortex-induced vibration response analysis system. The computer is equipped with a readable storage medium, which stores program instructions. When the program instructions are run on the computer, they execute the above-mentioned method for constructing the cable-stayed photovoltaic support vortex-induced vibration response model.

[0050] The specific implementation methods of the above steps are described in detail below.

[0051] The specific implementation of step S01 is as follows: First, determine the location of the typical cable segment to be monitored in the cable-stayed photovoltaic support. Select a cable segment with a large span and prone to vortex-induced vibration as the monitoring object. Distribute strain sensors evenly along the axial direction on the surface of the cable segment, with the sensor spacing being one-tenth of the cable segment length. Place an accelerometer at the midpoint of the cable segment. Set the sensor sampling frequency to 200Hz to capture the high-frequency components of the cable segment vibration. Simultaneously record the vibration displacement time history data and strain time history data under different wind speed conditions through a data acquisition system. At the same time, collect the incoming wind speed and wind direction angle in real time through an anemometer and wind vane. Measure the cable segment tension through a tension sensor and measure the cable segment diameter through a vernier caliper. Store all monitoring data aligned with timestamps to form an original dataset. The purpose of this step is to obtain the dynamic response characteristics of the cable segment under real wind field conditions to provide a data foundation for subsequent model construction.

[0052] The specific implementation of step S02 involves importing the vibration displacement time history data into a fast Fourier transform algorithm for frequency domain conversion. The fast Fourier transform algorithm performs spectral analysis by decomposing the time domain signal into superimposed sine waves of different frequencies. Peak frequencies with amplitudes exceeding three times the background noise are identified from the spectrum as the modal frequencies of each order. The amplitude value corresponding to each modal frequency is recorded. The extracted modal frequencies and amplitude data are organized into an initial modal parameter set. Simultaneously, the axial stress distribution of the cable segment is calculated using Hooke's law based on the strain time history data. When calculating the stress, the strain value is multiplied by the elastic modulus of the cable segment material to obtain the axial stress. Interpolation along the length of the cable segment yields a continuous stress distribution curve. The purpose of this step is to extract modal parameters from the time domain vibration data and obtain the stress state of the cable segment to provide a basis for subsequent energy analysis.

[0053] The specific implementation of step S03 is a sampling strategy based on the sparse grid collocation method to construct a six-dimensional parameter space. The sparse grid collocation method uses the Smolyak algorithm to decompose the high-dimensional tensor product space into a linear combination of one-dimensional node sets. First, sampling nodes are set for the amplitude dimension in the range of 0 to 10 times the cable segment diameter; for the frequency dimension, sampling nodes are set in the range of 0.1Hz to 50Hz; and for the Reynolds number dimension... arrive Sampling nodes are set within a specified range: for the incoming wind speed dimension, sampling nodes are set within the range of 0 to 30 m / s; for the cable segment tension dimension, sampling nodes are set within the range of 0.5 to 1.5 times the design tension; and for the cable segment diameter dimension, sampling nodes are set within the range of 0.9 to 1.1 times the actual diameter. Sensitivity analysis is used to determine the degree of influence of each dimension on the vortex-induced lift coefficient. Fifth-order precision discretization is used for dimensions with sensitivity higher than 0.3, third-order precision discretization is used for dimensions with sensitivity between 0.1 and 0.3, and first-order precision discretization is used for dimensions with sensitivity lower than 0.1. Finally, a non-uniformly distributed sampling grid is generated in six-dimensional space. The purpose of these steps is to minimize the number of sampling points and reduce computational costs while ensuring parameter space coverage.

[0054] The specific implementation of step S04 involves establishing a computational fluid dynamics numerical simulation model for each sampling point in a non-uniformly distributed sampling grid. A Reynolds-averaged Navier-Stokes equation solver is used to simulate the flow field around the cable segment. The computational domain is set to 50 times the cable segment diameter. The inlet boundary condition is set to the incoming air velocity at the corresponding sampling point, the outlet boundary condition is set to a pressure outlet, and the cable segment surface is set as a no-slip wall boundary. During mesh generation, a boundary layer mesh is used near the cable segment surface to capture the shear layer. The height of the first layer of the boundary layer mesh is set to a fraction of the cable segment diameter. The process involves calculating the lift time history curve of the cable segment through time-domain simulation, extracting the vortex shedding frequency by performing a fast Fourier transform on the lift time history curve, and calculating the root mean square value of the lift coefficient as the vortex-induced lift coefficient. The amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter corresponding to each sampling point are associated with the calculated vortex-induced lift coefficient and vortex shedding frequency and stored in the aerodynamic feature database. The purpose of this step is to establish a mapping relationship from the six-dimensional parameter space to the aerodynamic response to provide sample data for surrogate model training.

[0055] The specific implementation of step S05 involves dividing the data in the aerodynamic feature database into a training set and a validation set. The training set is used for parameter learning of the vortex-induced vibration response prediction model, while the validation set is used for evaluating the model's generalization ability. The input layer of the vortex-induced vibration response prediction model receives a normalized six-dimensional vector of amplitude, frequency, Reynolds number, incoming wind speed, cable tension, and cable diameter. Features are extracted through nonlinear transformation of three hidden layers. The output layer is divided into a mean branch and a variance branch to predict the expected value and uncertainty of the vortex-induced lift coefficient and vibration response amplitude, respectively. The training process uses a stochastic gradient descent optimization algorithm to iteratively update the network weights. The loss function comprehensively considers the prediction error and the quality of uncertainty estimation. After training, the vortex-induced vibration response prediction model receives the amplitude, frequency, Reynolds number, incoming wind speed, cable tension, and cable diameter parameters from the real-time monitoring system and quickly predicts the vortex-induced lift coefficient and vibration response amplitude under the current working condition. The purpose of this step is to use deep learning methods to establish a fast prediction tool to replace time-consuming computational fluid dynamics simulation and achieve real-time response prediction.

[0056] The specific implementation of step S06 involves simplifying the initial modal parameter set according to the modal screening criterion based on energy proportion. First, the vibration displacement time history data is decomposed into a linear combination of modal responses of each order according to the modal superposition principle. The modal displacement amplitude corresponding to each modal frequency is calculated. The modal kinetic energy is obtained by multiplying the square of the modal displacement amplitude by the modal mass, and the modal potential energy is obtained by multiplying the square of the modal displacement amplitude by the modal stiffness. The modal kinetic energy and modal potential energy are added together to obtain the total energy corresponding to the modal frequency of that order. The sum of the total energies of all modal frequencies in the initial modal parameter set is then calculated. To calculate the total vibration energy of the system, the energy contribution rate is obtained by comparing the total energy of each modal frequency with the total vibration energy of the system. The modal frequencies are sorted in descending order of energy contribution rate, and the accumulation starts from the modal frequency with the largest energy contribution rate. The accumulation stops when the accumulated energy contribution rate reaches 99.9%. The modal frequencies involved in the accumulation process are retained to form a simplified modal set, and high-order modal frequencies with an energy contribution rate of less than 0.1% are removed. The purpose of this step is to reduce the number of modes involved in the calculation and reduce the computational complexity of subsequent time-domain integration while ensuring the accuracy of vibration energy characterization.

[0057] The specific implementation of step S07 involves using a symplectic geometric-preserving structure numerical integration algorithm to solve the simplified mode set in the time domain. First, the cable vibration equation is rewritten in canonical Hamiltonian form. Generalized coordinates are introduced to represent the modal displacements at each modal frequency in the simplified mode set, and generalized momentum is introduced to represent the modal velocity multiplied by the modal mass at each modal frequency. The Hamiltonian function is established as the sum of the system's kinetic and potential energies. Kinetic energy is calculated by dividing the square of the generalized momentum by the modal mass, and potential energy is calculated by multiplying the square of the generalized coordinates by the modal stiffness. The Gaussian-type symplectic Runge-Kutta method is then used to solve the Hamiltonian function. The system is discretized over time. The discretization scheme ensures the symplectic property of the numerical mapping, namely the conservation of phase space volume, through implicit iteration. The vortex-induced lift coefficient is converted into a generalized force applied to the right-hand side of the Hamilton equation. The generalized coordinates and generalized momentum at each moment are solved step by step through the symplectic integral scheme. The generalized coordinates are converted into the displacement response in physical space through modal superposition. The generalized momentum is divided by the modal mass and then converted into the velocity response through modal superposition. The purpose of these steps is to accurately simulate the continuous vibration process of the cable segment under the action of vortex-induced force by utilizing the long-term energy conservation characteristics of the symplectic geometric algorithm, and to avoid response distortion caused by numerical damping.

[0058] The specific implementation of step S08 is to update the geometric configuration of the cable segment based on the displacement response to handle the large deformation nonlinear effect. Geometric nonlinearity correction is performed in the co-rotating coordinate system. First, the axial direction vector of the current configuration of the cable segment is calculated based on the displacement response of the nodes at both ends of the cable segment. The local coordinate axis of the co-rotating coordinate system is established based on the axial direction vector. The nodal displacements in the global coordinate system are mapped to the co-rotating coordinate system through coordinate rotation transformation. In the co-rotating coordinate system, the large rotation of the cable segment is absorbed by the coordinate system rotation, and the remaining deformation is manifested as small deformation. The nodal internal forces in the co-rotating coordinate system are calculated through the linearized element stiffness matrix. The nodal internal forces are mapped back to the global coordinate system through the inverse transformation of coordinate rotation. They are assembled with the external vortex-induced force to form the overall equilibrium equation. The equilibrium equation is solved by the preconditional conjugate gradient method to obtain the corrected nodal displacements. The purpose of this step is to transform the geometric nonlinear problem into a material nonlinear equivalent problem by rotating the coordinate system, thereby avoiding repeated updates of the stiffness matrix and improving computational efficiency.

[0059] The specific implementation of step S09 involves updating the fluid-structure interaction interface using the immersion boundary-lattice Boltzmann coupling method. Flow field calculations are performed on a fixed Cartesian grid. The cable segment surface, acting as the immersion boundary, is not aligned with the Cartesian grid. First, the spatial position and velocity of the cable segment surface are updated based on the displacement and velocity responses. In the collision step of the lattice Boltzmann method, a multi-relaxation BGK collision operator is used to calculate the relaxation of the particle distribution function towards a local equilibrium state. The multi-relaxation BGK collision operator improves numerical stability by introducing independent relaxation time parameters to control the relaxation processes of density, momentum, and energy. In the migration step, the particle distribution function is transferred to adjacent grid nodes along the discrete velocity direction. The required virtual boundary force is calculated based on the no-slip boundary condition of the cable segment surface. The virtual boundary force is dispersed to the fluid grid nodes near the cable segment surface through the Dirac function. The virtual boundary force is added to the momentum equation in the form of a volume force to update the fluid velocity field. The purpose of these steps is to achieve fluid-structure interaction on a fixed grid, avoid grid update overhead, and adapt to the large vibration conditions of the cable segment.

[0060] The specific implementation of step S10 involves calculating an adaptive adjustment factor to dynamically adjust the learning rate of the vortex-induced vibration response prediction model. First, the current loss value of the vortex-induced vibration response prediction model is evaluated on the validation set. The current loss value is divided by the average loss of the validation set from the previous 10 training rounds to obtain the validation set loss change rate. The norm of the current gradient is calculated and divided by the gradient norm at the initial training time to obtain the normalized gradient norm. The number of training rounds completed is divided by the total number of training rounds to obtain the training progress. The validation set loss change rate is multiplied by a weight of 0.5, the normalized gradient norm is multiplied by a weight of 0.3, and the training progress is multiplied by a weight of 0.2. These three are added together to obtain the adaptive adjustment factor value. The corresponding learning rate value is selected based on the range to which the adaptive adjustment factor belongs. When the adaptive adjustment factor is small, a larger learning rate is maintained to accelerate convergence; when the adaptive adjustment factor is large, the learning rate is reduced for fine-tuning. The purpose of this step is to improve the training efficiency of the vortex-induced vibration response prediction model by balancing training speed and convergence accuracy through an adaptive learning rate adjustment strategy.

[0061] The specific implementation of step S11 is to determine whether to terminate the iteration by judging the convergence of the displacement response. First, the maximum displacement response value of each time step within 50 consecutive time steps is recorded. The difference between the maximum displacement response values ​​of adjacent time steps is calculated. The difference is divided by the maximum displacement response value of the previous time step to obtain the displacement response change rate. The maximum displacement response change rate within 50 time steps is counted. If the maximum displacement response change rate is less than 0.5%, it is determined that the displacement response has converged to a steady state. The displacement response and velocity response at the current moment are output as the final vortex-induced vibration response result. At the same time, the vortex-induced lift coefficient and vibration response amplitude are output for engineering evaluation. If the maximum displacement response change rate is greater than or equal to 0.5%, it is determined that the displacement response has not converged. The process returns to step S07 to continue the time-domain integration solution. The purpose of this step is to ensure that the vortex-induced vibration response calculation reaches a steady state through convergence judgment to avoid premature termination or over-calculation.

[0062] It should be noted that the key technical approach of this invention includes a high-dimensional parameter space adaptive sampling strategy based on the sparse grid point allocation method. By dynamically adjusting the sampling density in the six-dimensional parameter space according to sensitivity, dense sampling is performed in high-sensitivity areas and sparse sampling is performed in low-sensitivity areas. Compared with traditional uniform grid sampling, this significantly reduces the number of computational fluid dynamics simulations while ensuring effective coverage of the parameter space. This solves the problem of exploding computational load in the construction of the eddy current coefficient database, shortening the database construction time from several months to an acceptable range. It provides a high-quality sample dataset for subsequent surrogate model training. The core advantage of this strategy is that it uses parameter sensitivity information to guide the placement of sampling points, avoiding wasting computational resources in parameter areas with weak influence on the response, and achieving the optimal balance between computational cost and prediction accuracy.

[0063] Another key technical approach of this invention is to use a symplectic geometric structure-preserving numerical integration algorithm for long-term integration of the cable vibration equation. By rewriting the cable vibration equation into Hamiltonian canonical form and adopting a symplectic Runge-Kutta discretization scheme, the symplectic structure in phase space and the energy conservation of the system are strictly maintained. Compared with the traditional Newmark method, it does not produce false numerical damping or energy drift during long-term integration, ensuring the long-term stability and physical realism of the vibration response simulation of the cable segment under low-damping continuous vortex-induced action. The core advantage of this algorithm is that it uses the geometric properties of Hamiltonian systems to design numerical schemes, allowing discrete systems to inherit the conservation laws of continuous systems, avoiding the underestimation of stress amplitude caused by numerical dissipation in traditional algorithms, and providing reliable stress time history data for cable segment fatigue life assessment.

[0064] The third key technical idea of ​​this invention is to construct a vortex-induced vibration response prediction model that integrates a weight-sharing mechanism and Bayesian uncertainty quantization. The weight-sharing mechanism reduces the model size and accelerates the training process by reusing parameters. The Bayesian uncertainty quantization mechanism provides a confidence interval while outputting the predicted value. When the input parameters fall in a sparse region of the training data, the model automatically outputs a low-confidence indicator to guide the aerodynamic feature database to supplement computational fluid dynamics simulation data in that region, thereby realizing the active learning-based intelligent expansion of the database. The core advantage of this model is that it combines prediction capability with uncertainty assessment, avoiding the problem of traditional proxy models giving unreliable predictions in areas with insufficient training data coverage but failing to identify them. This transforms the database construction process from blind full-space sampling to intelligent on-demand sampling.

[0065] The synergistic effect of the three key technical approaches mentioned above forms a complete system for constructing vortex-induced vibration response models for cable-stayed photovoltaic (PV) systems. The sparse grid collocation method provides efficient training data for the vortex-induced vibration response prediction model, while the uncertainty quantification mechanism of the vortex-induced vibration response prediction model guides the optimization of the sampling strategy of the sparse grid collocation method. The two form a closed-loop iterative process to gradually improve the database quality. The symplectic geometry-preserving structure numerical integration algorithm uses the vortex-induced force coefficients predicted by the vortex-induced vibration response prediction model to perform long-term and accurate dynamic response simulation. The synergy of these three approaches enables the entire vortex-induced vibration response model construction method to achieve excellent levels in terms of computational efficiency, prediction accuracy, and long-term stability. Compared with traditional methods, it significantly reduces computational resource consumption and significantly improves prediction reliability, providing a practical and efficient analytical tool for the wind-resistant design and safety assessment of cable-stayed PV systems.

[0066] It should be noted that this invention also solves the following technical problem: the problem of amplitude distortion caused by numerical damping in the simulation of long-term free vibration of cable segments with low damping. Traditional explicit integration methods such as the Newmark method introduce artificial damping during long-term integration, leading to amplitude decay distortion, severely underestimating the stress cycle amplitude, and affecting the accuracy of fatigue life assessment. This invention adopts a symplectic geometry-preserving numerical integration algorithm to convert the cable vibration equation into a regular Hamiltonian form, and uses a Gaussian-type symplectic Runge-Kutta method for time discretization. The implicit scheme ensures that the discretized numerical mapping satisfies the symplectic condition, ensuring that the phase space volume is strictly conserved during numerical integration, avoiding artificial energy dissipation or growth, and keeping the total system energy at its initial value after thousands of vibration cycles. This provides a reliable numerical basis for fatigue assessment, while allowing for a larger time step to improve computational efficiency.

[0067] The large deformation configuration of cable segments presents a technical challenge due to the geometric nonlinearity that hinders the updating of the fluid-structure interaction (FSI) interface. Traditional methods, handling geometric nonlinearity in a global coordinate system, require repeated updates to the stiffness matrix, resulting in low computational efficiency. Furthermore, the fluid mesh undergoes distortion due to structural motion, impacting computational accuracy. This invention introduces a corotating coordinate system to correct the geometric nonlinearity of the large deformation cable segment configuration. By transforming the coordinates, the geometric nonlinearity is converted into material nonlinearity for equivalent processing, avoiding repeated updates to the stiffness matrix in the global coordinate system. An immersed boundary-lattice Boltzmann coupling method is employed to update the FSI interface. The fluid uses a fixed Cartesian mesh, and the structural boundary achieves no-slip boundary conditions through virtual force feedback, preventing mesh distortion caused by fluid mesh movement and improving the efficiency and accuracy of FSI calculations.

[0068] Specifically, the principle of this invention is as follows: This invention solves the technical problem of excessive computational resource consumption in predicting the vortex-induced vibration response of cable-stayed photovoltaic supports. Traditional methods use uniform sampling in the six-dimensional parameter space, resulting in an excessive number of sampling points. This invention, however, employs a sparse grid point allocation method to perform non-uniform sampling based on parameter sensitivity. Sampling points are denser in highly sensitive areas and less dense in low-sensitivity areas, avoiding the curse of dimensionality. The vortex-induced vibration response prediction model established by this invention reduces the number of parameters through a weight-sharing mechanism and avoids gradient vanishing through residual connections, resulting in high training efficiency and rapid prediction of the vortex-induced lift coefficient of unsampled points, reducing the number of computational fluid dynamics numerical simulations. The Bayesian uncertainty quantification mechanism introduced in this invention can identify parameter regions with high prediction uncertainty, guiding the active learning strategy to prioritize supplementing sampling points in these regions, achieving intelligent expansion of the aerodynamic feature database, and avoiding blind sampling that wastes computational resources. The technical solution of this invention, through the synergistic effect of reducing the number of sampling points, improving model prediction efficiency, and achieving intelligent sampling, aligns with the logic of reducing computational resource consumption.

[0069] The following provides a specific embodiment 1 of the present invention. The specific implementation of the calculation steps involved in this embodiment 1 is described in detail below.

[0070] The specific implementation of step S02 involves converting the vibration displacement time history data to the frequency domain using a fast Fourier transform, extracting the modal frequencies and corresponding amplitudes, establishing an initial modal parameter set, and calculating the axial stress distribution of the cable segment based on the strain time history data. The formula for calculating the axial stress distribution of the cable segment is as follows:

[0071] ;

[0072] In the formula, This represents the dimensionless expression for the axial stress of the cable segment; This is the elastic modulus of the cable segment, expressed in Pa. For strain time history data, dimensionless; The reference stress is set to 1 Pa. Here are the axial coordinates of the cable segment, in meters (m). The time unit is seconds (s).

[0073] The specific implementation of step S03 is based on the sparse grid point allocation method, which arranges sampling points in a six-dimensional parameter space consisting of amplitude, frequency, Reynolds number, incoming wind speed, cable tension, and cable diameter. The sampling point density is increased in high-sensitivity areas and decreased in low-sensitivity areas to establish a non-uniformly distributed sampling grid. The sparse grid point allocation method uses the Smolyak sparse grid construction algorithm. The formula for calculating the total number of sampling points is as follows:

[0074] ;

[0075] In the formula, The total number of sampling points in the sparse grid is dimensionless. For the first The discrete levels of the dimension parameter are assigned according to sensitivity, are dimensionless, and range from 1 to 5. This is a dimensionless index for the parameter, ranging from 1 to 6. The number of sampling points in the traditional tensor product grid is dimensionless.

[0076] The specific implementation of step S06 involves establishing a modal screening criterion based on energy proportion, calculating the energy contribution rate corresponding to each modal frequency in the initial modal parameter set, removing modal frequencies with an energy contribution rate lower than 0.1%, and retaining the key participating modal frequencies to form a simplified modal set. The formula for calculating the energy contribution rate is expressed as follows:

[0077] ;

[0078] In the formula, For the first The energy contribution rate corresponding to the first modal frequency is dimensionless. For the first The energy corresponding to the first modal frequency is dimensionless. The total number of modes in the initial modal parameter set, dimensionless; This is a modal order index, dimensionless; Let be the current modal order, which is dimensionless. Where is the th... Energy corresponding to the first modal frequency The calculation formula is expressed as follows:

[0079] ;

[0080] In the formula, For the first The kinetic energy corresponding to the first modal frequency, expressed in J; For the first Potential energy corresponding to the first modal frequency, in J; The reference energy is set to 1 J.

[0081] The specific implementation of step S07 involves using a symplectic geometry-preserving numerical integration algorithm to solve the simplified mode set through time-domain integration. After converting the cable vibration equation into a canonical Hamiltonian form, it is discretized using a symplectic Runge-Kutta method. The displacement and velocity responses of the cable segment under the action of the vortex-induced lift coefficient are then calculated. The Hamiltonian function is expressed as follows:

[0082] ;

[0083] In the formula, It is a Hamiltonian function, dimensionless; These are generalized coordinates, with units in meters (m). Generalized momentum, with units of kg·m / s; The mass per unit length of the cable segment is expressed in kg / m. For reference speed, the value is taken as 1 m / s; This is the stiffness coefficient of the cable segment, in N / m; For reference force, the value is 1N; For reference length, the value is 1m.

[0084] The specific implementation of step S10 involves calculating the adaptive adjustment factor and adjusting the learning rate of the vortex vibration response prediction model. A learning rate decay strategy is selected based on the interval to which the adaptive adjustment factor belongs. The formula for calculating the adaptive adjustment factor is as follows:

[0085] ;

[0086] In the formula, The adaptive adjustment factor is dimensionless. The loss for the current validation set is dimensionless. This is the average value of the loss on the first 10 rounds of validation set, which is dimensionless. The current gradient norm is dimensionless. The initial gradient norm is dimensionless; This is the current training round number, dimensionless. This represents the total number of training rounds, with an empirical value of 500.

[0087] The specific implementation of step S11 is to determine whether the displacement response has converged. If the rate of change of the displacement response is less than 0.5% within 50 consecutive time steps, it is determined to be converged, and the final vortex-induced vibration response result is output. Otherwise, return to step S07 to continue iterative calculation. The formula for calculating the rate of change of displacement response is as follows:

[0088] ;

[0089] In the formula, The displacement response rate is dimensionless. For the first Displacement response over a time step, in meters; For the first Displacement response over a time step, in meters; The time step is numbered and is dimensionless.

[0090] It should be noted that the variables involved in this embodiment are explained in detail in Table 1.

[0091] Table 1. Variable Explanation Table

[0092]

[0093] To better understand and implement this invention, a specific application scenario of the invention is provided below as Example 2: To verify the effectiveness of the invention, technicians set up a test environment and conducted vortex-induced vibration response monitoring and predictive analysis on a typical cable segment of a large cable-stayed photovoltaic support system. The cable segment is 45m long, with an initial tension of 85kN, a diameter of 62mm, and is made of high-strength steel wire bundle. Technicians deployed a total of 5 strain sensors and 3 triaxial accelerometers at the middle and quarter points of the cable segment, with a sampling frequency set to 200Hz and a continuous monitoring time of 72 hours. During the monitoring period, the ambient wind speed ranged from 3 to 18m / s, and the wind direction angle varied from 0 to 90°, covering the main wind load conditions that the cable segment might encounter.

[0094] like Figure 2 As shown, technicians first collected vibration displacement time history data under different wind speed conditions. Under the condition of a wind speed of 8 m / s and a wind direction angle of 45°, the cable segment exhibited significant vortex-induced vibration, with a maximum amplitude of 127 mm. By converting the time history data to the frequency domain using Fast Fourier Transform, five significant modal frequencies were identified: 1.32 Hz, 2.68 Hz, 4.05 Hz, 5.41 Hz, and 6.78 Hz, corresponding to amplitudes of 127 mm, 68 mm, 34 mm, 19 mm, and 12 mm, respectively. Simultaneously, the axial stress distribution of the cable segment was calculated based on strain sensor data, with the peak stress occurring in the middle of the segment at a value of 215 MPa. Technicians calculated the energy contribution rate of each modal frequency according to the modal selection criterion based on energy proportion, as shown in Table 2.

[0095] Table 2 Distribution of Modal Frequency Energy Contribution Rate

[0096]

[0097] As shown in Table 1, the cumulative energy contribution rate of the first three modal frequencies has reached 95.5%, while the energy contribution rate of the fifth modal frequency is only 0.7%, which is lower than the elimination threshold of 0.1%. Therefore, the technicians retained the first four modal frequencies to form a simplified modal set, and the fifth modal frequency was eliminated.

[0098] Technicians used a sparse grid sampling method to arrange sampling points in a six-dimensional parameter space consisting of amplitude, frequency, Reynolds number, incoming wind speed, cable segment tension, and cable segment diameter. The amplitude ranged from 10 to 200 mm, the frequency ranged from 0.5 to 10 Hz, and the Reynolds number ranged from... ~ The incoming wind velocity ranged from 2 to 20 m / s, the cable tension ranged from 60 to 120 kN, and the cable diameter ranged from 50 to 80 mm. The Smolyak sparse mesh construction algorithm was used, and the discretization levels were assigned based on the sensitivity of each dimension parameter to the vortex-induced lift coefficient. Sensitivity analysis showed that amplitude and Reynolds number had the highest sensitivity, reaching 0.78 and 0.72 respectively; therefore, 5 layers of fine discretization were used in these two dimensions. The sensitivity of the cable diameter was only 0.23, so 3 layers of coarse discretization were used. Finally, 2847 sampling points were generated, a reduction of 0.30% compared to the 956,000 sampling points of the traditional tensor product mesh.

[0099] like Figure 3 As shown, technicians performed computational fluid dynamics numerical simulations at each sampling point to calculate the vortex shedding frequency and vortex-induced lift coefficient of the flow field around the cable segment. The simulation employed Reynolds-averaged Navier-Stokes equations combined with... The SST turbulence model has a total of 3.85 million mesh elements in the fluid domain, with the first mesh layer near the wall having a height of 0.08 mm. The value is approximately 1.2, and the time step is set to 0.002 s. Through 15 days of parallel computation, flow field simulations were completed for all sampling points, establishing an aerodynamic characteristic database containing 2847 sets of data. The database is organized in key-value pair format, with the key being a six-dimensional parameter combination, and the values ​​including vortex-induced lift coefficient, vortex shedding frequency, and pressure distribution data.

[0100] Technicians divided the aerodynamic feature database into training and validation sets at an 8:2 ratio, containing 2278 and 569 data sets respectively. Input features were normalized to unify the parameter range of each dimension to the 0-1 interval, and output labels were standardized to have a mean of 0 and a variance of 1. The vortex-induced vibration response prediction model employs a three-layer hidden layer structure with 128, 256, and 128 neurons respectively, using a modified linear unit function as the activation function. To improve parameter efficiency, the weight matrices of the first and third hidden layers are shared, and input layer information is directly passed to the third hidden layer through residual connections. A Bayesian uncertainty quantization mechanism is introduced in the output layer, with two parallel branches outputting mean and variance predictions respectively. This allows the model to output a larger variance in sparse regions of the parameter space, indicating prediction uncertainty. Training employs a stochastic gradient descent optimization algorithm with an initial learning rate of 0.01, a batch size of 32, and 500 training epochs. The loss function is a weighted sum of the mean squared error and the negative log-likelihood of the variance branch, with weight coefficients set to 0.7 and 0.3 respectively. During training, the adaptive adjustment factor dynamically adjusts the learning rate based on the validation set loss rate of change, gradient norm, and training progress. At 150 epochs, the adjustment factor reaches 0.32, and the learning rate decays to 0.005. At 380 epochs, the adjustment factor reaches 0.68, and the learning rate further decays to 0.001. Finally, at 472 epochs, the validation set loss reaches its minimum value of 0.0087, and model training is complete.

[0101] Technicians input real-time monitored data on amplitude, frequency, Reynolds number, incoming wind speed, cable segment tension, and cable segment diameter into a trained vortex-induced vibration response prediction model, which quickly outputs the predicted vortex-induced lift coefficient. Under conditions of wind speed of 12 m / s, tension of 85 kN, and amplitude of 95 mm, the model predicts a vortex-induced lift coefficient of 1.38, with a confidence interval of 1.32–1.44 and an uncertainty variance of 0.0036, indicating that this parameter combination has high prediction confidence in areas with sufficient training data coverage. A symplectic geometric-preserving numerical integration algorithm is used to solve the simplified mode set in the time domain, transforming the cable vibration equation into a canonical Hamiltonian form. Generalized coordinates and generalized momentum are introduced as state variables, and a Hamiltonian function is established to express the sum of the cable segment's kinetic and potential energy. A Gaussian-type symplectic Runge-Kutta method is used for time discretization, with a time step set to 0.01 s to ensure that the discretized numerical mapping satisfies the symplectic condition. The displacement and velocity responses of the cable segment under the action of the vortex-induced lift coefficient were calculated. The maximum displacement response was 98 mm and the maximum velocity response was 0.86 m / s.

[0102] Technicians introduced a cosine coordinate system to perform geometric nonlinear correction on the large deformation configuration of the cable segment. The cable segment's axial direction was calculated based on the nodal displacements at both ends, establishing a cosine coordinate system whose axes were always aligned with the tangent and normal directions of the current cable segment configuration. The nodal displacements were transformed from the global coordinate system to the cosine coordinate system, and a linearized element stiffness matrix was established in the cosine coordinate system. The nodal forces in the cosine coordinate system were then solved, and the system was transformed back to the global coordinate system for overall equilibrium iteration. An immersed boundary-lattice Boltzmann coupling method was used to update the fluid-structure interaction interface. The fluid used a fixed Cartesian grid with a grid spacing of 5 mm. The lattice Boltzmann method solved the flow field through the collision and migration processes of the particle distribution function. The required boundary forces were calculated based on the cable segment's surface position and velocity response. These boundary forces were then distributed as volume forces to the surrounding fluid grid nodes, updating the fluid velocity field. A multi-relaxation BGK collision operator was used, incorporating five relaxation time parameters to control the relaxation process of different physical quantities, thus improving numerical stability. After iterative calculations for 68 consecutive time steps, the rate of change of the displacement response within 50 consecutive time steps decreased to 0.42%, satisfying the convergence criterion, and the final vortex-induced vibration response result was output.

[0103] The advancements of this invention compared to traditional methods are mainly reflected in the following aspects: Traditional methods employ uniform grid sampling across the entire parameter space, generating millions of sampling points in the six-dimensional parameter space. This results in computational fluid dynamics numerical simulations taking months or even years. In contrast, this invention uses a sparse grid allocation method, adaptively allocating discrete layers based on the sensitivity of parameters in each dimension. Sampling is increased in highly sensitive regions and decreased in low-sensitivity regions, reducing the number of sampling points to three-thousandths of that of traditional methods, significantly reducing computational resource consumption. Traditional neural network prediction models have a large number of parameters and are prone to overfitting. This invention achieves parameter reuse through a weight sharing mechanism, reducing model size while maintaining expressive power, improving training speed, and avoiding overfitting risks. Traditional prediction models only output a single value and cannot determine prediction reliability. This invention introduces a Bayesian uncertainty quantification mechanism, connecting mean and variance branches in parallel at the output layer, and adding confidence intervals to the prediction results. When input parameters fall into regions with insufficient training data coverage, a low-confidence flag is automatically given, guiding the active learning sampling strategy of the aerodynamic feature database and achieving intelligent expansion. Traditional time-domain integration methods, such as the Newmark method, suffer from numerical damping, leading to amplitude distortion in long-term vibration simulations and a significant underestimation of stress cycle amplitude. In contrast, this invention employs a symplectic geometry-preserving numerical integration algorithm. By utilizing the symplectic geometric properties of Hamiltonian systems, an integration scheme is constructed that maintains the constant volume of the phase space. This ensures that energy conservation errors do not accumulate during long-term integration, avoids spurious amplitude decay or growth, and provides a reliable numerical basis for fatigue assessment.

[0104] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for constructing a vortex-induced vibration response model for cable-stayed photovoltaic supports, characterized in that, Strain sensors and accelerometers were deployed on the surface of typical cable segments of the cable-stayed photovoltaic system to collect vibration displacement time history data and strain time history data. The vibration displacement time history data were converted to the frequency domain using fast Fourier transform to extract the modal frequencies and corresponding amplitudes to establish an initial modal parameter set. Based on the sparse grid collocation method, sampling points were arranged in a six-dimensional parameter space consisting of amplitude, frequency, Reynolds number, incoming wind speed, cable segment tension, and cable segment diameter to establish a non-uniformly distributed sampling grid. Computational fluid dynamics numerical simulation was performed on each sampling point in the non-uniformly distributed sampling grid to calculate the vortex shedding frequency and vortex-induced lift coefficient to establish an aerodynamic characteristic database. The aerodynamic characteristic database was then input into... After training the vortex-induced vibration response prediction model, the predicted vortex-induced lift coefficient and vibration response amplitude are output. A modal screening criterion based on energy proportion is established to retain the frequencies of key participating modes and form a simplified mode set. The simplified mode set is solved by time-domain integration using a symplectic geometric-preserving structure numerical integration algorithm to calculate the displacement and velocity responses of the cable segment under the action of the vortex-induced lift coefficient. A co-rotating coordinate system is introduced to perform geometric nonlinear correction on the large deformation configuration of the cable segment. The fluid-structure interaction interface is updated using the immersion boundary-lattice Boltzmann coupling method. The adaptive adjustment factor is calculated and the learning rate of the vortex-induced vibration response prediction model is adjusted. After determining whether the displacement response has converged, the final vortex-induced vibration response result is output.

2. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 1, characterized in that, The sparse grid point allocation method uses the Smolyak sparse grid construction algorithm to decompose the six-dimensional parameter space into a combination of multiple one-dimensional discrete spaces, and assigns different discrete levels according to the sensitivity of each dimension parameter to the vortex-induced lift coefficient.

3. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 2, characterized in that, The non-uniformly distributed sampling grid increases the sampling point density in highly sensitive areas and decreases the sampling point density in low-sensitive areas, reducing the number of sampling points to 0.3% compared to the traditional tensor product grid.

4. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 3, characterized in that, The aerodynamic characteristic database is organized in key-value pair form, where the key is a combination of amplitude-frequency-Reynolds number-incoming wind speed-cable segment tension-cable segment diameter, and the value is the corresponding vortex-induced lift coefficient, vortex shedding frequency, and pressure distribution.

5. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 4, characterized in that, The aerodynamic feature database is established using an active learning strategy, prioritizing the addition of sampling points in parameter regions with larger prediction errors, and gradually improving the prediction accuracy of the aerodynamic feature database across the entire parameter space through iterative optimization.

6. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 5, characterized in that, The input layer of the vortex-induced vibration response prediction model receives a six-dimensional parameter vector, which is processed by three hidden layers to output the vortex-induced lift coefficient and vibration response amplitude. The number of neurons in the three hidden layers are 128, 256, and 128, respectively, and the activation function is a modified linear unit function.

7. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 6, characterized in that, The vortex-induced vibration response prediction model utilizes a parameter efficiency improvement framework based on weight sharing, which shares the weight matrices of the first and third hidden layers, while only the second hidden layer uses independent weights. The input layer information is directly transmitted to the third hidden layer through residual connections.

8. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 7, characterized in that, The vortex-induced vibration response prediction model adopts a Bayesian uncertainty quantization output calibration mechanism, with two branches connected in parallel at the output layer. One branch outputs the mean prediction, and the other branch outputs the variance prediction. The variance branch parameters are trained through variational inference.

9. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 8, characterized in that, When establishing the training dataset for the vortex-induced vibration response prediction model, all sampling point data are extracted from the aerodynamic feature database, and the training set and validation set are divided in an 8:2 ratio. The input features are normalized, and the output labels are standardized.

10. The method for constructing the vortex-induced vibration response model of a cable-stayed photovoltaic support according to claim 9, characterized in that, The symplectic geometry-preserving structure numerical integration algorithm rewrites the cable vibration equation into a regular Hamiltonian form, introduces generalized coordinates and generalized momentum as state variables, and uses the Gaussian-type symplectic Runge-Kutta method for time discretization.

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