Cable force identification method based on residual adaptive sampling physical information graph neural network

Abstract

The application discloses a cable force identification method based on a residual adaptive sampling physical information graph neural network, and relates to the technical field of bridge health monitoring. The vibration video of a cable is collected by a high-speed camera, and the vibration displacement of the cable is extracted from the video by using a singular value decomposition enhanced phase optical flow method. A PI-GNN model embedded with the cable force to be calculated is constructed according to a cable vibration control differential equation. The physical equation residual of each sampling point is calculated, and the partial derivative of the physical equation residual with respect to the cable force is solved by automatic differentiation. The product of the absolute value of the physical equation residual and the cable force sensitivity is defined as a cable force sensitive residual evaluation index. The candidate sampling points are sorted according to the cable force sensitive residual evaluation index. The whole trainable parameters of the PI-GNN model and the cable force are synchronously updated by optimizing the vibration displacement data loss and the physical equation residual loss until the model converges, and the calculation result of the cable force is output.

Description

Technical Field

[0001] This invention relates to the field of bridge health monitoring technology, and in particular to a cable force identification method based on residual adaptive sampling physical information graph neural network. Background Technology

[0002] Cables are the main load-bearing components of cable-stayed bridges, and their stress state is an important indicator for assessing the health of the bridge. Accurate measurement of cable forces is crucial for ensuring the structural safety of the bridge during construction and operation.

[0003] Currently, commonly used methods for cable force measurement in engineering include the hydraulic pressure gauge method, the pressure sensor method, the magnetic flux method, and the frequency method. While these methods have been applied in practical engineering, each has its limitations. The hydraulic pressure gauge and pressure sensor methods, although providing relatively accurate cable force measurements, are primarily suitable for cable force measurement during the construction phase due to their high cost and complex installation processes. The magnetic flux method estimates cable force by relating it to changes in magnetic flux, offering high accuracy and stability; however, its application is limited by factors such as complex calibration processes and the need to customize electromagnetic sensors based on cable diameter. The frequency method, due to its low cost and simple operation, has been widely used in practical engineering, but its accuracy is easily affected by factors such as boundary conditions, bending stiffness, and effective length, thus limiting its applicability in complex working conditions.

[0004] In recent years, the rapid development of Physics-informed Neural Networks (PINNs) has provided a new approach for cable force identification. This method embeds the cable vibration control differential equation as a physical constraint into the neural network and sets the cable force as a trainable parameter. By optimizing the network weights and cable force, the neural network can fit the measured vibration displacement while satisfying the physical laws of cable vibration. However, existing PINN-based cable force calculation methods typically use uniform or random sampling points before training and maintain the position and number of sampling points during training. This fails to fully consider the different sensitivity differences in cable force calculation across different regions, thus limiting the accuracy of cable force calculation. Summary of the Invention

[0005] The purpose of this invention is to provide a cable force recognition method based on residual adaptive sampling physical information graph neural network to solve the above-mentioned problems.

[0006] 1. To achieve the above objectives, the present invention provides the following technical solution: a cable force recognition method based on a residual adaptive sampling physical information graph neural network, the specific steps of which are as follows:

[0007] S1. Acquire the vibration video of the cable and preprocess the video image;

[0008] S2. The pixel displacement of the cable is extracted from the video based on the singular value decomposition enhanced phase optical flow method. The pixel displacement is converted into physical displacement using the scaling factor method. The lateral vibration displacement at different positions of the cable is obtained through preprocessing. The lateral vibration displacement of the cable is used to build a training dataset, which is used as the training input of the PI-GNN model in S3.

[0009] S3. Construct an embedded cable force calculation based on the differential equation governing cable vibration. The PI-GNN model takes the training dataset established in S2 using the lateral vibration displacement of the cable as input, and inputs it into the PI-GNN model to output the predicted value of the lateral vibration displacement of each node of the cable.

[0010] S4. Calculate the physical equation residuals at each sampling point, and solve the physical equation residuals with respect to the cable force using automatic differentiation. The partial derivatives of the equations are used to define the product of the absolute value of the physical equation residuals and the cable force sensitivity as the cable force sensitivity residual evaluation index.

[0011] S5. All trainable parameters based on the PI-GNN model and cable power Calculate the cable tension-sensitive residual evaluation index for each candidate sampling point in turn, and sort them from largest to smallest; select the top-ranked index. The candidate sampling points are added as new sampling points. At the same time, smaller sampling points in the training set are removed according to a preset ratio. The value of the removal ratio ranges from 5% to 10%, and the training set size is continuously increased to complete the automatic updating and removal of sampling points.

[0012] After the automatic updating and removal of sampling points are completed, the graph structure is reconstructed based on the updated node set, and the edge set and adjacency relationship between nodes are updated synchronously to match the graph topology and sampling point distribution in each adaptive sampling period.

[0013] After each completion of the PI-GNN model The above adaptive sampling and update process is triggered once after each training round, and is updated until the PI-GNN model meets the preset convergence condition.

[0014] S6. Construct the total loss function of the PI-GNN model and perform co-optimization until the total loss tends to converge.

[0015] S7. A multi-index collaborative convergence determination mechanism is used to determine whether the PI-GNN model meets the training termination condition, and the calculated cable force is restored to its original dimensions and its reliability is verified. Finally, the cable force calculation result is output.

[0016] Preferably, the preprocessing of the video image in S1 includes cropping, rotating and scaling, and the above preprocessing is used to initially remove noise in the image sequence to eliminate the influence of noise on the identification of cable vibration displacement.

[0017] Preferably, the specific steps in S2 for extracting the vibration displacement of the cable from the video using the singular value decomposition-enhanced phase optical flow method are as follows:

[0018] S21. Target region selection and image gradient calculation:

[0019] In the first frame of the cable vibration video, a rectangular region containing clear edges or texture features is selected along the cable surface as the Region of Interest (ROI). The image grayscale function of the ROI is then analyzed. Find the second-order gradient in the transverse vibration direction to enhance the edge pixels of the image and suppress background interference.

[0020] S22. Construction of an adaptive complex filter based on singular value decomposition:

[0021] The second-order gradient matrix of the horizontal direction of each pixel grayscale value within the ROI of the first frame of the cable vibration video. Perform singular value decomposition;

[0022] Among them, the dominant singular vector corresponding to the maximum singular value represents the strongest and most reliable texture change feature in the row direction of the image; taking this vector as the real part of the filter, performing a Hilbert transform on it yields the phase-orthogonal imaginary part, and the two together constitute a data-driven, adaptive matching one-dimensional complex filter for cable surface texture.

[0023] S23. Phase Calculation and Cable Vibration Displacement Identification:

[0024] First, the complex filter... Convolve with the first frame image to obtain the filter response and phase of the first frame image. Then, a convolution operation is performed on each subsequent frame to obtain the phase of the image. The spatial shift of an image corresponds to the phase change in the frequency domain; therefore, the phase difference between each frame and the first frame is... And convert the phase difference into pixel displacement;

[0025] Then, by setting the amplitude threshold of the cable, the most motion-sensitive effective pixels within the ROI are automatically selected, and the average pixel displacement of all effective pixels is taken to obtain the pixel displacement at the center of the ROI.

[0026] S24. Data post-processing and dataset establishment:

[0027] After obtaining the pixel displacement of the cable, the pixel displacement is converted into physical displacement using the scaling factor method. The lateral vibration displacement at different positions of the cable is obtained through preprocessing. The lateral vibration displacement of the cable is used to build a training dataset, which is used as the training input of the PI-GNN model.

[0028] The preferred S3 is to construct the embedded cable force to be calculated. The specific process of the PI-GNN model is as follows:

[0029] First, the spatiotemporal computational domain of the cable is discretized into a graph structure, which is represented as follows: ,in, For a set of nodes, The edge set is defined; each training sampling point is set as a graph node, and the corresponding spatial coordinates and time coordinates are used as node features. The nearest neighbor relationship is determined and the edge is constructed according to the spatial distance or time interval between sampling points. Then, the neighbor node information is aggregated layer by layer through the message passing mechanism of the PI-GNN model and the hidden state of each node is updated. Finally, the readout layer outputs the predicted value of the cable lateral vibration displacement at each node.

[0030] Preferably, S4 includes:

[0031] S41. Physical residual calculation: Substitute the predicted values ​​of the cable lateral vibration displacement output by the PI-GNN model into the cable vibration control differential equation to calculate the physical residual at each training sampling point.

[0032] S42. Cable Force Sensitivity Calculation: Utilizing the automatic differentiation mechanism of a deep learning model, calculate the physical residual at each sampling point with respect to the cable force to be calculated. The absolute value of the first-order partial derivative is defined as the cable force sensitivity coefficient at that point;

[0033] S43. Establish a residual evaluation index sensitive to cable tension: Multiply the absolute value of the physical residual by the cable tension sensitivity to construct a residual evaluation index sensitive to cable tension.

[0034] Preferably, S6 is as follows:

[0035] The total loss function for constructing the PI-GNN model includes:

[0036] S61, Data Error Loss Calculate the predicted value of the lateral vibration displacement of the cable. Compared with measured values The mean square error between them is used to ensure the accuracy of the predicted cable lateral vibration displacement output by the PI-GNN model;

[0037] S62, Physical Residual Loss Calculate the physical residual at each sampling point. The mean square error is calculated to ensure that the predicted lateral vibration displacement of the cable output by the PI-GNN model satisfies the differential equation governing cable vibration.

[0038] S63, Boundary and Regularization Constraint Loss This includes boundary condition loss, initial condition loss, and cable force. The range of values ​​is constrained, which will affect the cable force. The optimization process should be limited to a reasonable range in practical engineering to avoid convergence to physically impossible cable force values, such as negative values.

[0039] The total loss function is,

[0040] ;

[0041] In the formula, , and These are data error loss, physical residual loss, and boundary and regularization constraint loss, respectively. , and These are the weighting coefficients for data error loss, physical residual loss, and boundary and regularization constraint loss, respectively; with data error loss as the baseline loss, the following settings are applied. , The value range is 0.1 to 10. The value range is 1 to 100; within this range, the minimum mean square error of the lateral vibration displacement of the cable on the verification dataset is used as the criterion for determination. and Preferred, , , .

[0042] Using either the Adam or L-BFGS optimizer, all trainable parameters of the PI-GNN model are updated synchronously in each iteration. and cable power This continues until the total loss function converges.

[0043] The technical effects and advantages of this invention are as follows:

[0044] 1. A cable force sensitivity residual evaluation index was constructed by multiplying the physical residual with the cable force sensitivity, which is used to quantify the contribution of different sampling points to the cable force calculation.

[0045] 2. An adaptive sampling strategy based on the ranking of cable force-sensitive residual evaluation index is used to automatically update the sampling points during the training of the PI-GNN model. The graph structure and adjacency relationship are reconstructed according to the updated sampling points, so that the newly added sampling points are preferentially distributed in the region that contributes the most to the calculation of cable force.

[0046] 3. Within the model, the sparse spatiotemporal displacement points obtained visually are constructed into a dynamically updatable graph structure, and irregular nearest neighbor information is aggregated through message passing; cable tension. As globally trainable physical parameters embedded in the vibration control equations, rather than ordinary network inputs or post-processing quantities dependent on mode shapes / half-wavelengths, direct cable force inversion can be achieved without extracting higher-order mode shapes.

[0047] 4. Larger nodes are added and smaller nodes are removed, and the graph adjacency relationship is reconstructed simultaneously. This allows the sampling resource allocation and the information propagation path within the graph to be updated together around the cable identification target, forming a closed-loop computing mechanism that is different from the fixed topology PI-GNN model and the ordinary residual adaptive PINN. Attached Figure Description

[0048] Figure 1 This is a flowchart of the cable force calculation process of the present invention;

[0049] Figure 2 This is a diagram illustrating the cable vibration displacement identification and dataset creation for this invention.

[0050] Figure 3 This is a schematic diagram of the PI-GNN model architecture of the present invention. Detailed Implementation

[0051] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0052] This invention provides, for example Figures 1-3 The cable force recognition method based on residual adaptive sampling physical information graph neural network shown in the figure firstly acquires the vibration displacement of the cable using computer vision technology, that is, by acquiring vibration video of the cable through a high-speed camera, and extracting the vibration displacement of the cable from the video using a singular value decomposition-enhanced phase optical flow method; secondly, it constructs an embedded cable force of the cable to be calculated based on the cable vibration control differential equation. The PI-GNN model is used; next, the physical equation residuals at each sampling point are calculated, and the physical equation residuals with respect to the cable force are solved by automatic differentiation. The partial derivatives of the partial derivatives are used to define the product of the absolute value of the physical equation residuals and the cable force sensitivity as the cable force sensitivity residual evaluation index. Subsequently, candidate sampling points are sorted according to the cable force sensitivity residual evaluation index, and sampling points are added in the region with a larger cable force sensitivity residual evaluation index to achieve adaptive updating of the training sampling point set. Finally, by optimizing the vibration displacement data loss and the physical equation residual loss, the neural network weights and cable force are updated synchronously until the PI-GNN model converges, and the calculation result of the cable force is output.

[0053] Step 1: Acquisition and preprocessing of cable vibration video;

[0054] High-speed cameras were used to capture vibration videos of the cables under environmental excitation, and digital image processing software was used to preprocess the video images, including cropping, rotating, and scaling. This preprocessing initially removed noise from the image sequence to eliminate its influence on the identification of cable vibration displacement.

[0055] Step 2: Cable vibration displacement identification and dataset establishment based on singular value decomposition-enhanced phase optical flow method;

[0056] The process of cable vibration displacement identification based on singular value decomposition enhanced phase optical flow method is as follows: Figure 2 As shown, the main steps are as follows:

[0057] (1) Target region selection and image gradient calculation:

[0058] In the first frame of the cable vibration video, a rectangular region containing clear edges or texture features is selected along the cable surface as the Region of Interest (ROI). The image grayscale function of the ROI is then applied. Find the second-order gradient in the transverse vibration direction to enhance the edge pixels of the image and suppress background interference. The expression is,

[0059] ;

[0060] In the formula, The direction is the lateral vibration direction of the cable; This represents the grayscale value of the first frame of the video. This represents the second-order gradient in the horizontal direction of the first frame of the video.

[0061] (2) Construction of an adaptive complex filter based on singular value decomposition;

[0062] The second-order gradient matrix of the horizontal direction of each pixel grayscale value within the ROI of the first frame of the cable vibration video. Perform singular value decomposition:

[0063] ;

[0064] In the formula, Let be the second-order gradient matrix of the image sequence; It is a left singular matrix, composed of image column feature vectors; It is a singular diagonal matrix, and the non-negative real numbers on the diagonal are arranged in descending order. The larger the value, the more reliable the corresponding image and the less noise it has. It is a right singular matrix, composed of image row feature vectors; For matrix The transpose of .

[0065] Among them, the dominant singular vector corresponding to the largest singular value (i.e. This vector represents the strongest and most reliable texture change feature along the row direction of the image. Using this vector as the real part of the filter, a Hilbert transform (HT) is performed to obtain the phase-orthogonal imaginary part. Together, these two vectors form a data-driven, adaptive one-dimensional complex filter that matches the texture of the cable surface. Its expression is,

[0066] ;

[0067] In the formula, It is a one-dimensional complex filter; The dominant singular vector corresponding to the maximum singular value is taken as the real part of the filter. The imaginary unit (i.e.) ); for HT is the imaginary part of the filter.

[0068] Complex filter Unlike Gabor filters, which have fixed parameters, complex filters... The weights are determined by the image features of the cable. Therefore, this filter can enhance the edge pixels of the cable and suppress background interference in the image.

[0069] (3) Phase calculation and cable vibration displacement identification;

[0070] First, the complex filter... Convolve with the first frame image to obtain the filter response and phase of the first frame image. Then, a convolution operation is performed on each subsequent frame to obtain the phase of the image. The spatial shift of an image corresponds to the phase change in the frequency domain. Therefore, the phase difference between each frame and the first frame is... The phase difference can be converted into pixel displacement using the following formula:

[0071] ;

[0072] In the formula, Pixel displacement; Phase difference; This represents the gradient of the phase along the transverse vibration direction.

[0073] By setting the amplitude threshold of the cable, the most motion-sensitive effective pixels within the ROI can be automatically selected. The average pixel displacement of all effective pixels can then be used to obtain the pixel displacement at the center of the ROI.

[0074] (4) Data post-processing and dataset creation;

[0075] After obtaining the pixel displacement of the cable, the pixel displacement is converted into physical displacement using the scaling factor method. Then, the lateral vibration displacement at different positions of the cable is obtained through preprocessing such as filtering and noise reduction, zero-point correction, and trend term elimination. A training dataset was established using the lateral vibration displacement of the cables. , which serves as the training input for the PI-GNN model.

[0076] Step 3: Construct a PI-GNN model embedding cable forces

[0077] A physical-informed graph neural network (PI-GNN) is constructed to predict cable vibration displacement. First, the spatiotemporal computational domain of the cable is discretized into a graph structure, represented as follows: ,in, For a set of nodes, The set is defined as an edge set. Each training sampling point is set as a graph node, and its corresponding spatial and temporal coordinates are used. As node features, nearest neighbor relationships are determined and edges are constructed based on the spatial distance or time interval between sampling points. Subsequently, the neighbor node information is aggregated layer by layer and the hidden state of each node is updated through the message passing mechanism of the PI-GNN model. Finally, the readout layer outputs the predicted values ​​of lateral vibration displacement at each node of the cable. ,in, These are all the trainable parameters for the PI-GNN model.

[0078] The cable force to be calculated Defined as a trainable global physics parameter tensor. Cable force. Instead of using them as input features for the PI-GNN model, they are embedded in the physical constraint loss function and used as input features along with all trainable parameters. Global optimization variables are synchronously involved in backpropagation and gradient update, thereby simultaneously calculating cable forces when predicting the lateral vibration displacement of the cable.

[0079] Compared to traditional fully connected PINN, each message passing layer of this invention no longer treats each sampling point as an independent sample, but instead achieves information sharing between neighboring nodes through graph edges. Specifically, each message passing layer includes: generating edge messages based on the hidden states of the nodes at both ends of the edge and the relative spatiotemporal coordinate difference; aggregating the neighboring edge messages of the same target node; and fusing the aggregated message with the hidden state of the node in the previous layer to obtain the updated hidden state of the node. Thus, a local displacement observation of a certain ROI or at a certain moment can affect its nearest neighboring nodes through graph edges without interpolating all observations to a regular grid.

[0080] Based on the aforementioned message transmission mechanism, this invention further realizes the direct calculation of cable force, characterized in that: the input does not require modal frequencies, mode order, mode node positions, or intermediate half-wavelengths; and the output cable force is not calculated through the analytical formulas of the aforementioned intermediate quantities. During training, the displacement prediction values ​​are obtained by automatic differentiation with respect to spatial and temporal derivatives, forming a formula containing the cable force. The physical residuals; the total loss on the cable force Calculate the gradient and update the cable force. After the model converges, the cable force is directly read from the optimal model state and its dimensions are restored. .

[0081] Upon reaching the preset adaptive sampling period, the cable force-sensitive residual evaluation index for each candidate sampling point is first calculated. ,Will Larger candidate sampling points are added to the sampling point set and then removed according to a preset ratio. Smaller sampling points are used. Then, based on the updated sampling point coordinates, the nearest neighbor relationships are recalculated and an edge set is generated. This closed loop of "evaluation-addition / deletion-reconstruction-continued joint optimization" ensures that the message propagation path within the graph network remains consistent with the spatial distribution of force-sensitive information.

[0082] The vibration governing differential equation considering the bending stiffness of the cable is:

[0083] ;

[0084] In the formula, The mass per unit length of the cable; The bending stiffness of the cable; For cable tension; This is the predicted value of the lateral vibration displacement of the cable.

[0085] The network architecture, total loss function, and adaptive sampling mechanism of the PI-GNN model are as follows: Figure 3 As shown.

[0086] Step 4: Construct evaluation indicators for physical residuals and cable tension-sensitive residuals;

[0087] (1) Physical residual calculation: The predicted values ​​of the lateral vibration displacement of the cable output by the PI-GNN model are calculated. Substituting into the differential equation governing cable vibration, the physical residual at each training sampling point is calculated, and its expression is:

[0088] ;

[0089] In the formula: For physical residuals; The coordinates of the sampling point; This is the differential operator for the differential equation governing cable vibration.

[0090] The physical residuals reflect the degree to which the PI-GNN model's predictions violate physical laws at the sampling points. The larger the residual, the less the vibration displacement at that point conforms to the cable's vibration control equations.

[0091] (2) Cable tension sensitivity calculation: Calculate the sensitivity of each sampling point using the automatic differentiation mechanism of the deep learning model. Physical residual at the location Regarding the cable force to be calculated The absolute value of the first-order partial derivative is defined as the cable tension sensitivity coefficient at that point, and its expression is:

[0092] ;

[0093] In the formula: Sampling points Sensitivity coefficient at the location; For the physical residuals calculated by automatic differentiation Cable tension The first-order partial derivative of .

[0094] Cable force sensitivity quantitatively describes the degree to which the physical residual at a given location fluctuates with changes in cable force. Higher sensitivity indicates that the residual at that point is more sensitive to changes in cable force, and that the point contains more cable force information.

[0095] (3) Establish an evaluation index for cable tension-sensitive residuals: Multiply the absolute value of the physical residuals by the cable tension sensitivity to construct an evaluation index for cable tension-sensitive residuals. And record it as Its expression is,

[0096] ;

[0097] In the formula, Sampling points Evaluation index of cable tension-sensitive residuals at the location. This also considers information from both the physical equation residuals and the cable force sensitivity. The larger the value, the greater the residual of the physical equation at that sampling point, and the more sensitive it is to changes in cable force, meaning that the sampling point contributes more information to the calculation of cable force.

[0098] Step 5: Dynamic adaptive sampling update based on the evaluation index of cable tension-sensitive residuals;

[0099] Within the LAC spatiotemporal computational domain, candidate sampling point sets are generated using random sampling or Latin hypercube sampling methods to improve the uniformity of candidate point coverage across the entire spatiotemporal domain. All trainable parameters based on the PI-GNN model are used. and cable power The cable tension-sensitive residual evaluation index corresponding to each candidate sampling point is calculated sequentially. and in accordance with Sort by largest to smallest. Select the top-ranked items. The candidate sampling points were selected as new sampling points. The value depends on the size of the training set. Determined according to a preset ratio, that is .in The value range is 5% to 10%. New sampling points are added to the physical residual sampling point set for the calculation of physical residual loss.

[0100] To control the size of the training set and avoid the computational cost from continuously increasing with the number of iterations, when increasing... While sampling a large number of points, remove samples from the training set according to a preset ratio. Smaller sampling points, elimination ratio The value range is 5% to 10%, and is based on... Control the continuous increase of the training set size. For example, when the training set size is... At that time, if taken , Then 1000 more will be added. Larger sampling points, 500 of which were removed simultaneously. For smaller sampling points, the training set is increased by 500 nodes.

[0101] After the automatic updating and removal of sampling points are completed, the graph structure is reconstructed based on the updated node set, and the edge set and adjacency relationship between nodes are updated synchronously to match the graph topology and sampling point distribution in each adaptive sampling period.

[0102] After each completion of the PI-GNN model The above adaptive sampling and update process is triggered once every training epoch. For example, it can be set to... To balance adaptive sampling performance with PI-GNN model training efficiency, the PI-GNN model training, metric calculation, sampling point update, and graph structure reconstruction are repeated until the PI-GNN model meets the preset convergence criteria.

[0103] Step 6: Construct the total loss function and perform co-optimization;

[0104] The total loss function for constructing the PI-GNN model includes the following three items:

[0105] (1) Data error loss Calculate the predicted value of cable vibration displacement Compared with measured values The mean square error between the two values ​​is used to ensure the accuracy of the cable vibration predictions output by the PI-GNN model. Its expression is as follows:

[0106] ;

[0107] In the formula, This dataset contains measured values ​​of lateral vibration displacement of cables obtained using visual technology. For dataset The total number of displacement points is used to normalize and average the cable vibration displacement error; For Lasso's Measured values ​​of transverse vibration displacement; To utilize the PI-GNN model in The predicted value of the lateral vibration displacement of the cable is output at the location; for The measured value of the lateral vibration displacement of the cable at the point.

[0108] (2) Physical residual loss Calculate the physical residual at each sampling point. The mean square error is calculated to ensure that the predicted lateral vibration displacement of the cable output by the PI-GNN model satisfies the cable vibration control differential equation, the expression of which is as follows.

[0109] ;

[0110] In the formula, This is the set of sampling points used to calculate the physical residuals after adaptive updating. This represents the total number of sampling points in the central sampling area, used to normalize and average the physical residual loss. To sample points Predicted lateral vibration displacement of the cable at the location The physical residual value is obtained by substituting it into the differential equation for the control of cable vibration.

[0111] (3) Boundary and regularization constraint loss This includes boundary condition loss, initial condition loss, and cable force. The range of values ​​is constrained. The optimization process should be limited to a reasonable range in practical engineering to avoid convergence to physically impossible cable force values, such as negative values.

[0112] The total loss function is,

[0113] ;

[0114] In the formula, , and These are data error loss, physical residual loss, and boundary and regularization constraint loss, respectively. , and These are the weighting coefficients for data error loss, physical residual loss, and boundary and regularization constraint loss, respectively.

[0115] Using either the Adam or L-BFGS optimizer, all trainable parameters of the PI-GNN model are updated synchronously in each iteration. and cable power This continues until the total loss function converges.

[0116] Step 7: Convergence judgment of PI-GNN model and output of cable force calculation results;

[0117] After joint optimization and iteration, a multi-index collaborative convergence judgment mechanism is adopted to determine whether the PI-GNN model meets the training termination condition, and the calculated cable force is restored to its original dimensions and its reliability is verified. Finally, the cable force calculation result is output.

[0118] (1) Multi-indicator collaborative convergence determination;

[0119] During the training of the PI-GNN model, the total loss and cable tension are calculated, and the maximum number of training epochs is used to determine whether to terminate training. The specific criteria for this determination are as follows:

[0120] 1) Total Loss Stabilization Criterion: Calculate the relative change of total loss over several consecutive training epochs. When the relative rate of decrease of total loss is continuously lower than a preset threshold, it indicates that the total loss has stabilized, meaning that the PI-GNN model training has entered the convergence phase.

[0121] 2) Cable Stability Criterion: Establish a sliding window for cable force and record the cable force within each window. The mean, standard deviation, or relative fluctuation range of the cable force is used. When the relative fluctuation range of the cable force is lower than the preset stability threshold within multiple consecutive sliding windows, the cable force calculation result is considered to be stable. This criterion directly reflects the convergence state of the cable force to be calculated, avoiding misjudgments based solely on changes in total loss.

[0122] 3) Maximum training epoch criterion: Set the maximum number of training epochs. When the training rounds reach Regardless of whether the aforementioned criteria are met, the PI-GNN model training is terminated to prevent the PI-GNN model from continuing to iterate under abnormal conditions. Adaptive sampling update interval. Based on the maximum number of training rounds Configure settings to control the number of updates during adaptive sampling during training.

[0123] When both the total loss stability criterion and the cable stability criterion are satisfied, or when the maximum number of training rounds is reached. When the training time is reached, the PI-GNN model training is terminated. During training, the total loss of the PI-GNN model is continuously recorded, and the PI-GNN model parameters corresponding to the minimum total loss are saved, including all trainable parameters of the PI-GNN model. and cable power .

[0124] In addition, a training state protection mechanism is set up. When the total loss is observed to increase continuously over several consecutive training rounds, or when the fluctuation of the loss value exceeds a preset threshold, it is determined that the training process has diverged or oscillated violently, and the PI-GNN model is reloaded to the optimal model state saved during training to avoid the cable force calculation results being deviated due to training instability.

[0125] (2) Cable tension calculation and reliability verification;

[0126] After the PI-GNN model training terminates, the cable forces are extracted from the saved optimal model state. When the cable force is used in optimization during training in a normalized or dimensionless form, inverse normalization or dimension restoration is performed according to a preset scale transformation relationship to obtain the calculated cable force value with actual physical units. To ensure the reliability of the cable force calculation results, Perform the following verifications:

[0127] 1) Consistency Verification of Results from Multiple Measurement Areas: Multiple ROIs or measurement points are set for the same cable, and the cable force calculation results for different ROIs or measurement points are obtained. The relative deviation between the different results is then calculated. If the relative deviation does not exceed a preset tolerance threshold, the cable force calculation results from different measurement areas are considered consistent, and the final cable force is calculated using an arithmetic mean or weighted average method. If the relative deviation exceeds a preset allowable threshold, the cable force calculation result is marked as a low-confidence abnormal result, and an anomaly message is output.

[0128] 2) Physical rationality verification: Based on the design value of cable force, allowable variation range, and bridge operating conditions, preset allowable cable force range. . judge Does it meet the allowable range of cable tension?

[0129] ;

[0130] If the calculated cable force meets the physical rationality requirements, it is determined that the calculated cable force meets the requirements. If it exceeds the allowable range, the calculated cable force is marked as abnormal and is not output as a valid cable force result. The system will then prompt the user to check the vibration data quality, model parameter settings, or training status.

[0131] The cable force calculation result that passes the credibility verification is recorded as the cable force calculation value;

[0132] In summary, this invention constructs a cable force sensitivity residual evaluation index by multiplying the physical residual and the cable force sensitivity, which is used to quantify the contribution of different sampling points to the cable force calculation. An adaptive sampling strategy based on the cable force sensitivity residual evaluation index is used to automatically update sampling points during the PI-GNN model training process, and the graph structure and adjacency relationships are reconstructed according to the updated sampling points, so that newly added sampling points are preferentially distributed in the regions that contribute the most to the cable force calculation. Internally, the sparse spatiotemporal displacement points obtained visually are constructed into a dynamically updatable graph structure, and irregular nearest neighbor information is aggregated through message passing. (Cable force...) As globally trainable physical parameters embedded in the vibration control equations, rather than ordinary network inputs or post-processing quantities dependent on mode shapes / half-wavelengths, direct cable force inversion is achieved without extracting higher-order mode shapes. Larger nodes are added, smaller nodes are removed, and graph adjacency relationships are reconstructed simultaneously, ensuring that sampling resource allocation and intra-graph information propagation paths are updated around the cable force identification target. This forms a closed-loop computation mechanism distinct from fixed-topology PI-GNN models and ordinary residual adaptive PINNs. The distinguishing techniques include placing visually acquired cable vibration displacement, cable vibration control equations, graph structure neighborhood relationships, and the cable force to be calculated within the same inversion framework, allowing the cable force to be updated synchronously with network weights and directly output as a globally trainable physical parameter. The partial derivative of the physical residual with respect to the cable force characterizes the cable force sensitivity, and "absolute value of physical residual × cable force sensitivity" serves as the common basis for adding / removing sampling points and reconstructing the graph topology. This combination is not simply adding an input parameter or replacing an ordinary fully connected network with a graph neural network.

[0133] Finally, it should be noted that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A cable force recognition method based on residual adaptive sampling physical information graph neural network, characterized in that: The specific steps are as follows: S1. Acquire the vibration video of the cable and preprocess the video image; S2. The pixel displacement of the cable is extracted from the video based on the singular value decomposition enhanced phase optical flow method. The pixel displacement is converted into physical displacement using the scaling factor method. The lateral vibration displacement at different positions of the cable is obtained through preprocessing. The lateral vibration displacement of the cable is used to build a training dataset, which is used as the training input of the PI-GNN model in S3. S3. Construct an embedded cable force calculation based on the differential equation governing cable vibration. The PI-GNN model takes the training dataset established in S2 using the lateral vibration displacement of the cable as input, and inputs it into the PI-GNN model to output the predicted value of the lateral vibration displacement of each node of the cable. S4. Calculate the physical equation residuals at each sampling point, and solve the physical equation residuals with respect to the cable force using automatic differentiation. The partial derivatives of the equations are used to define the product of the absolute value of the physical equation residuals and the cable force sensitivity as the cable force sensitivity residual evaluation index. S5. All trainable parameters based on the PI-GNN model and cable power Calculate the cable tension-sensitive residual evaluation index for each candidate sampling point in turn, and sort them from largest to smallest; select the top-ranked index. The candidate sampling points are added as new sampling points. At the same time, smaller sampling points in the training set are removed according to a preset ratio. The value of the removal ratio ranges from 5% to 10%, and the training set size is continuously increased to complete the automatic updating and removal of sampling points. After the automatic updating and removal of sampling points are completed, the graph structure is reconstructed based on the updated set of nodes, and the edge set and adjacency relationship between nodes are updated synchronously to match the graph topology and sampling point distribution in each adaptive sampling period. After each completion of the PI-GNN model The above adaptive sampling and update process is triggered once after each training round, and is updated until the PI-GNN model meets the preset convergence condition. S6. Construct the total loss function of the PI-GNN model and perform co-optimization until the total loss tends to converge. S7. A multi-index collaborative convergence determination mechanism is used to determine whether the PI-GNN model meets the training termination condition, and the calculated cable force is restored to its original dimensions and its reliability is verified. Finally, the cable force calculation result is output.

2. The cable force recognition method based on residual adaptive sampling physical information graph neural network according to claim 1, characterized in that: S1 performs preprocessing on the video images, including cropping, rotating, and scaling. This preprocessing is used to initially remove noise from the image sequence to eliminate the impact of noise on the identification of cable vibration displacement.

3. The cable force recognition method based on residual adaptive sampling physical information graph neural network according to claim 1, characterized in that: The specific steps for extracting cable vibration displacement from the video using the singular value decomposition-based enhanced phase optical flow method in S2 are as follows: S21. Target region selection and image gradient calculation: In the first frame of the cable vibration video, a rectangular region containing clear edges or texture features is selected along the cable surface as the region of interest. The image grayscale function of the region of interest is then analyzed. Find the second-order gradient in the transverse vibration direction to enhance the edge pixels of the image and suppress background interference. S22. Construction of an adaptive complex filter based on singular value decomposition: The second-order gradient matrix of the horizontal direction of each pixel grayscale value in the region of interest of the first frame of the cable vibration video. Perform singular value decomposition; Among them, the dominant singular vector corresponding to the maximum singular value represents the strongest and most reliable texture change feature in the row direction of the image; taking this vector as the real part of the filter, performing a Hilbert transform on it yields the phase-orthogonal imaginary part, and the two together constitute a data-driven, adaptive matching one-dimensional complex filter for cable surface texture. S23. Phase Calculation and Cable Vibration Displacement Identification: First, the complex filter... Convolve with the first frame image to obtain the filter response and phase of the first frame image. Then, a convolution operation is performed on each subsequent frame to obtain the phase of the image. The spatial shift of an image corresponds to the phase change in the frequency domain; therefore, the phase difference between each frame and the first frame is... And convert the phase difference into pixel displacement; Then, by setting the amplitude threshold of the cable, the most motion-sensitive effective pixels in the region of interest are automatically selected, and the average pixel displacement of all effective pixels is taken to obtain the pixel displacement at the center of the region of interest. S24. Data post-processing and dataset establishment: After obtaining the pixel displacement of the cable, the pixel displacement is converted into physical displacement using the scaling factor method. The lateral vibration displacement at different positions of the cable is obtained through preprocessing. The lateral vibration displacement of the cable is used to build a training dataset, which is used as the training input of the PI-GNN model.

4. The cable force recognition method based on residual adaptive sampling physical information graph neural network according to claim 1, characterized in that: Construct an embedded cable force to be calculated in S3. The specific process of the PI-GNN model is as follows: First, the spatiotemporal computational domain of the cable is discretized into a graph structure, which is represented as follows: ,in, For a set of nodes, The edge set is defined; each training sampling point is set as a graph node, and the corresponding spatial coordinates and time coordinates are used as node features. The nearest neighbor relationship is determined and the edge is constructed according to the spatial distance or time interval between sampling points. Then, the neighbor node information is aggregated layer by layer through the message passing mechanism of the PI-GNN model and the hidden state of each node is updated. Finally, the readout layer outputs the predicted value of the cable lateral vibration displacement at each node.

5. The cable force recognition method based on residual adaptive sampling physical information graph neural network according to claim 1, characterized in that: S4 includes: S41. Physical residual calculation: Substitute the predicted values ​​of the cable lateral vibration displacement output by the PI-GNN model into the cable vibration control differential equation to calculate the physical residual at each training sampling point. S42. Cable Force Sensitivity Calculation: Utilizing the automatic differentiation mechanism of a deep learning model, calculate the physical residual at each sampling point with respect to the cable force to be calculated. The absolute value of the first-order partial derivative is defined as the cable force sensitivity coefficient at that point; S43. Establish a residual evaluation index sensitive to cable tension: Multiply the absolute value of the physical residual by the cable tension sensitivity to construct a residual evaluation index sensitive to cable tension.

6. The cable force recognition method based on residual adaptive sampling physical information graph neural network according to claim 1, characterized in that: S6 specifically refers to: The total loss function for constructing the PI-GNN model includes: S61, Data Error Loss Calculate the predicted value of the lateral vibration displacement of the cable. Compared with measured values The mean square error between them is used to ensure the accuracy of the predicted cable lateral vibration displacement output by the PI-GNN model; S62, Physical Residual Loss Calculate the physical residual at each sampling point. The mean square error is used to ensure that the predicted lateral vibration displacement of the cable output by the PI-GNN model satisfies the differential equation for cable vibration control. S63, Boundary and Regularization Constraint Loss This includes boundary condition loss, initial condition loss, and cable force. The range of values ​​is constrained, which will affect the cable force. The optimization process should be limited to a reasonable range in practical engineering to avoid convergence to physically impossible cable force values, such as negative values. The total loss function is, ； In the formula, , and These are data error loss, physical residual loss, and boundary and regularization constraint loss, respectively. , and These are the weighting coefficients for data error loss, physical residual loss, and boundary and regularization constraint loss, respectively. Using either the Adam or L-BFGS optimizer, all trainable parameters of the PI-GNN model are updated synchronously in each iteration. and cable power This continues until the total loss function converges.

Images