Double-fusion neural network bridge cable force prediction method and system based on physical data

Abstract

The invention discloses a double-fusion neural network bridge cable force prediction method and system based on physical data, and belongs to the field of bridge health monitoring. Comprising the following steps: acquiring input features of a bridge cable to be predicted, and preprocessing the input features to obtain standardized input features; inputting the standardized input features into a pre-trained hybrid neural network model to obtain a standardized cable force predicted value; wherein the hybrid neural network model comprises a physical guiding path, a data driving path and a fusion gating module. Compared with the prior art, high-precision and high-robustness prediction of the cable force of the bridge cable under different boundary conditions is realized through the pre-constructed hybrid neural network model fusing the physical mechanism and data driving.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of bridge health monitoring, and more particularly, to a double fusion neural network bridge cable force prediction method and system based on physical data. BACKGROUND

[0002] Cable force is a core index for evaluating the safety state of cable-supported bridge structures such as cable-stayed bridges and suspension bridges. Accurate measurement of cable force is crucial for bridge maintenance, safety warning and life assessment.

[0003] Currently, the most commonly used non-destructive testing method for cable force in engineering practice is the frequency method, which measures the vibration frequency of the cable and then uses the vibration theory formula to calculate the cable force. However, existing formulas are only for single boundary conditions (e.g., hinged at both ends, fixed at both ends, or fixed at one end and hinged at the other end), and are limited to ideal environments. The accuracy is not accurate. In actual engineering, the working environment of the bridge is much more complex than the ideal assumption, and is affected by the constraints provided by the anchor, the damping of the damper, the bending stiffness of the cable itself, and temperature changes and other non-ideal factors, which leads to systematic deviation between the calculation results of the theoretical formula and the actual cable force, and the accuracy often cannot meet the needs of modern bridge engineering maintenance and management.

[0004] In recent years, to overcome the limitations of traditional formula methods, some studies have begun to use machine learning or traditional neural network methods to directly build an end-to-end mapping model from "frequency" to "cable force". These purely data-driven methods can theoretically fit any complex non-linear relationship. However, their success is heavily dependent on "massive, high-quality, and full-conditions" labeled data. In the field of bridge health monitoring, obtaining such a large amount of training samples is extremely costly and impractical. In addition, such "black box" models usually have poor physical interpretability, and the model decision-making process is not transparent, which can easily lead to overfitting in new conditions not covered by the training data, resulting in unstable prediction performance, poor generalization ability and physical interpretability, and overfitting, making it difficult to predict the performance of unseen data samples. As can be seen from the above, the existing technology has not effectively solved the problem of accurately and robustly predicting bridge cable force under different boundary conditions. SUMMARY

[0005] 1. Technical problems to be solved To solve the above problems in the prior art, the present application provides a double fusion neural network bridge cable force prediction method and system based on physical data, which can realize high-precision and high-robustness prediction of bridge cable force under different boundary conditions through a hybrid neural network model that combines physical mechanisms and data-driven methods.

[0006] 2. Technical solutions The object of the present application is achieved by the following technical solutions.

[0007] The summary section of this application is intended to provide a brief overview of the concepts, which will be described in detail in the detailed description section below. This summary section is not intended to identify key or essential features of the claimed technical solutions, nor is it intended to limit the scope of the claimed technical solutions.

[0008] Some embodiments of this application propose a method and system for predicting bridge cable forces based on dual-fusion neural networks using physical data, in order to solve the technical problems mentioned in the background section above.

[0009] As a first aspect of this application, some embodiments of this application provide a method for predicting bridge cable forces based on a dual-fusion neural network using physical data, comprising the following steps: The input features of the bridge cable to be predicted are obtained, including the vibration frequency, cable length, bending stiffness and linear density of the bridge cable to be predicted. The input features are preprocessed to obtain standardized input features; The standardized input features are fed into a pre-trained hybrid neural network model to obtain standardized cable force prediction values. The hybrid neural network model includes a physical guidance path, a data-driven path, and a fusion gating module. The hybrid neural network model processes input features through the physical guidance path to generate physical prediction values; processes input features through the data-driven path to generate data-driven correction values; and dynamically fuses the physical prediction values ​​and data-driven correction values ​​through the fusion gating module to output standardized cable force prediction values.

[0010] Furthermore, the physical guidance path includes parallel physical computing units and attention networks; The parallel physical computing unit, based on the first three vibration frequencies, cable length, bending stiffness and linear density, combined with trainable physical parameters, calculates the preliminary cable force prediction values ​​corresponding to the first three frequencies in parallel according to the modified physical formula. The attention network performs weighted fusion of the initial cable force predictions to generate physical predictions.

[0011] Furthermore, the physics guidance path is configured to generate physics predictions based on an adjustable physics formula, which is expressed as: ; In the formula, f is the vibration frequency. For frequency order, To correct the cable force value calculated by the physical formula, α and β are both trainable physical parameters, EI is the bending stiffness, L is the cable length, and m is the linear density.

[0012] Furthermore, the data-driven path uses a deep residual network to process the input features; the deep residual network consists of several sequentially connected residual blocks, and the output feature dimension of the residual blocks gradually decreases along the network propagation direction.

[0013] Furthermore, the fusion gating module includes a fully connected neural network and a sigmoid function; The fusion gating module calculates a dynamic gating weight between 0 and 1 using a fully connected neural network and a sigmoid activation function, and obtains the standardized cable force prediction value based on the following formula: ; in, This is a physical prediction value. Data-driven correction values, To standardize the predicted cable force, For dynamic gating weights.

[0014] Furthermore, the pre-trained hybrid neural network model is obtained through the following training steps: Several sets of bridge cable input features and actual cable forces are obtained, and feature engineering is used to construct enhanced features based on the input features; The enhanced features and the true cable force are preprocessed to obtain standardized input features and standardized true cable forces, forming a standardized dataset; the standardized dataset is then divided into a training set and a validation set. Initialize the parameters of the hybrid neural network model, including the physical guidance path, the data-driven path, and the trainable parameters in the fusion gating module; The model parameters are iteratively updated on the training set with the composite loss function as the optimization objective, and the model performance is monitored on the validation set. When the model performance no longer improves within several consecutive training cycles, training is terminated and the parameters of the best-performing model are saved to obtain the pre-trained hybrid neural network model. The composite loss function is composed of a weighted average of the log-mean square error and the mean absolute percentage error.

[0015] Furthermore, the enhancing features include at least one of the following: the square term of the first three vibration frequencies, the interaction term of the first three vibration frequencies, the square term of length, the combination term of stiffness and length, the combination term of density and length, the combination term of stiffness and density, and the interaction term of the first three vibration frequencies and length.

[0016] As a second aspect of this application, some embodiments of this application provide a dual-fusion neural network-based bridge cable force prediction system based on physical data, including: The data acquisition module is used to acquire the input features of the bridge cable to be predicted and perform preprocessing to obtain standardized input features; the input features include the vibration frequency, cable length, bending stiffness and linear density of the bridge cable to be predicted; Model module: Used to input standardized input features into a pre-trained hybrid neural network model to obtain standardized cable force prediction values; The hybrid neural network model includes a physical guidance path, a data-driven path, and a fusion gating module. The hybrid neural network model processes input features through the physical guidance path to generate physical prediction values; processes input features through the data-driven path to generate data-driven correction values; and dynamically fuses the physical prediction values ​​and data-driven correction values ​​through the fusion gating module to output standardized cable force prediction values.

[0017] Furthermore, the dual-fusion neural network bridge cable force prediction system based on physical data also includes an inverse standardization module, which is used to convert the standardized cable force prediction values ​​into cable force prediction values ​​with physical dimensions.

[0018] As a third aspect of this application, some embodiments of this application provide an electronic device having a computer program stored thereon, which, when executed by a processor, implements the above-described method for predicting the cable tension of a bridge using a dual-fusion neural network based on physical data.

[0019] 3. Beneficial effects Compared with the prior art, the advantages of this invention are: (1) This invention constructs a hybrid neural network architecture that integrates physical guidance and data-driven dual paths. Through the deep integration of the physical guidance path and the data-driven path, the accuracy and generalization ability of cable force prediction are improved in a coordinated manner. The physical path dynamically corrects the systematic deviation of the traditional formula based on trainable parameters, and the data path learns complex nonlinear residual errors. The two are adaptively weighted through a gating mechanism, which overcomes the systematic calculation deviation caused by the idealized assumption of boundary conditions in the traditional formula method and significantly improves the prediction accuracy under different boundary conditions. (2) By introducing trainable parameters to adaptively correct the traditional physical formula, the model can directly learn the actual influence of complex boundary conditions such as anchorage constraints and damping effects from the actual measured or simulated data of the bridge, thereby overcoming the systematic calculation deviation caused by the idealized assumption of boundary conditions in the traditional formula method and significantly improving the prediction accuracy in the actual engineering environment. (3) To address the problem of multi-order frequency noise interference in bridge cables, the modal weights are automatically allocated through the physical attention mechanism. For example, when high-order frequencies are polluted by environmental vibration, the model reduces their weights and relies on the stable prediction of low-order frequencies, thus maintaining high robustness in the noise environment of the construction site. The gating mechanism can dynamically balance the contributions of physical prediction and data-driven correction. Under normal working conditions, it relies on physical output, while under abnormal or complex working conditions, it relies on data-driven supplementation, thereby greatly improving the stability and generalization ability of the model in different bridges and different environments. (4) The model of the present invention is not a “black box”. Its physical guidance path output, the trainable parameter values ​​that converge after training, and the attention weights and gating weights provide direct basis for analyzing the model decision logic and understanding the deviation between actual boundary conditions and theoretical assumptions, which greatly enhances the transparency and credibility of the model in the high-risk application of bridge safety monitoring. Attached Figure Description

[0020] Fig. 1 The overall flowchart of the dual-fusion neural network bridge cable force prediction method based on physical data provided in the embodiments of the present invention is shown below. Fig. 2 The graph shows the comparison between the predicted cable force and the actual cable force of the hybrid neural network model provided in this embodiment of the invention on the test set. The yellow line represents the predicted cable force, the blue line represents the actual cable force, the horizontal axis represents the group number, and the vertical axis represents the corresponding cable force. Fig. 3 This is a schematic diagram of the parameter performance of the dual-fusion neural network based on physical data according to the present invention. In this diagram, RMSE is the root mean square error, which measures the average error between the predicted value and the true value. R² is the coefficient of determination, which measures the goodness of fit of the model to the data and indicates how much variance of the target variable the model explains. MAPE is the mean absolute percentage error, which measures the average percentage error between the predicted value and the true value. Detailed Implementation

[0021] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0022] like Figs. 1 to 3 As shown, the dual-fusion neural network bridge cable force prediction method based on physical data of the present invention includes the following steps: S1. Data Preparation Several sets of input features and actual cable forces of bridge cables are obtained to construct an original dataset. Feature engineering is then used to expand the input features of the original dataset to obtain an enhanced feature set. Finally, standardization is applied to the enhanced feature set to obtain a standardized dataset. The specific process is as follows: S101, Obtain Data Several sets of input features and actual cable forces of bridge cables are obtained through finite element simulation or on-site data acquisition, forming the original dataset for model training.

[0023] Input features are parameters that describe the state and physical properties of the bridge cables, including the first three vibration frequencies of the bridge cables, cable length (L, unit: meter), bending stiffness (EI, unit: Newton-meter²), and linear density (m, unit: kilogram-meter).

[0024] The first three vibration frequencies refer to the three natural vibration frequencies with the lowest energy when the bridge cable vibrates freely, including the first frequency (f1), the second frequency (f2), and the third frequency (f3), and the unit is Hertz.

[0025] Specifically, cable length is the effective length between two anchor points of the cable, measured in meters. In this embodiment, the cable length ranges from 10 meters to 300 meters. Bending stiffness (EI) is the product of the material's elastic modulus (E) and the moment of inertia of the section (I), measured in Newton-meters (N·m²), and its value is determined by the cable type. Linear density (m) is the mass per unit length of the cable, measured in kilograms per meter, and its value is determined by the cable type.

[0026] The actual cable force (T) of the bridge cables is measured in kilonewtons (kN). In the simulation, it is a set value; in the field data, it is a measured value, which serves as the target for model learning.

[0027] In this embodiment, the finite element simulation uses the finite element analysis software ANSYS to obtain the accurate correspondence between the first three vibration frequencies of the stay cable and its actual cable force under different physical parameters and boundary conditions.

[0028] In one specific embodiment, the process of obtaining the original dataset is as follows: Traditional formula methods are prone to errors due to the idealized assumptions of boundary conditions. Therefore, in this embodiment, boundary conditions covering three typical anchorage states are set, including hinged at both ends, fixed at both ends, and hinged at one end and fixed at the other.

[0029] Under three boundary conditions, referencing industry standards (such as "Technical Conditions for Hot-Extruded Polyethylene High-Strength Steel Wire Bundle Cables for Cable Extension"), 10 commonly used cable models (such as PES(C)7-73 to PES(C)7-283, a total of 10 commonly used cable models) were selected, and their key parameters were set randomly.

[0030] For each model, the cable length (L) is randomly selected from 10 meters to 300 meters, and the actual cable force (T) is randomly selected from 50% to 100% of the design cable force range. Using ANSYS, a finite element model is built based on each set of parameters, and modal analysis is performed to obtain the corresponding first three vibration frequencies. Each simulation generates a data sample.

[0031] Each type of cable generates 2000 sets of data under three boundary conditions, forming an original dataset containing 60000 data samples of 10 types × 3 boundary conditions × 2000 sets. Each data sample in the original dataset contains 6 original features (f1, f2, f3, L, EI, m).

[0032] S102, Extended Input Features Feature engineering is performed on the input features in the original dataset to construct combined features with clear physical meaning. Each set of input features is expanded from 6 dimensions to higher dimensions, generating a more information-rich enhanced feature set. The specific process is as follows: Construct a feature engineering function (named addphysicsfeatures in this embodiment). Input each group (6 features) from the original dataset into the feature engineering function, which will expand the feature vector and output the expanded enhanced feature vector.

[0033] Specifically, feature engineering extends the input features based on the mathematical relationships between the parameters in the physics formula of cable force, constructing enhanced features, including: The squares of the first three vibration frequencies: , , ; Interaction terms of the first three vibration frequencies: , , ; Length squared term: ; Combination of stiffness and length: ; Combinations of density and length: ; Combination of stiffness and density: ; The interaction terms between the first three vibration frequencies and lengths: , , .

[0034] Each set of input features in the original dataset is concatenated with its 13 extended enhancement features in a predefined order to form several sets of 19-dimensional feature vectors, constituting an enhancement feature set with dimensions [N, 19], where N is the total number of samples in the original dataset (60000 in this embodiment).

[0035] Specifically, the splicing order in this embodiment is: f1, f2, f3, L, EI, m. , , , , , , , , , , , , .

[0036] S103, Standardization Processing This step aims to standardize the enhanced feature set and the actual cable force, converting the data into a standard normal distribution with a mean of 0 and a standard deviation of 1, eliminating the influence caused by differences in physical dimensions and numerical ranges among the features, and generating the final standardized dataset.

[0037] In this embodiment, the enhanced feature set and the actual cable force are stored and calculated in the program in the form of a two-dimensional array or matrix, where each row represents a bridge cable sample and each column represents a feature (or actual cable force).

[0038] Specifically, Z-score standardization is used to standardize the true tension in both the enhanced feature set and the original dataset.

[0039] First, calculate the standardized parameters: For the augmented feature set, calculate the mean of each column (i.e., each feature). and standard deviation A total of 19 means and 19 standard deviations were obtained.

[0040] For a true series of sols, calculate its mean. and standard deviation .

[0041] Then, perform the Z-score normalization transformation: Using the mean and standard deviation obtained above, Z-score normalization transformations are performed on the enhanced feature set and the actual cable force, respectively.

[0042] For each feature column in the enhanced feature set, according to the formula Perform the conversion. For the actual cable series, follow the formula... Perform the conversion. The standardized values ​​of the eigenvalues This is the standardized value of the actual cable force.

[0043] This transformation converts the data in each feature column of the augmented feature set and the true force column into a distribution with a mean of 0 and a standard deviation of 1. This eliminates the influence of different physical units and numerical ranges, prevents the gradient from being dominated by features with larger values ​​during model training, and makes the surface of the loss function more regular, which helps accelerate the convergence speed and improve the stability of model training. The augmented feature set obtained after the transformation, together with the true force, constitutes a standardized dataset for model training and validation.

[0044] S2. Constructing a hybrid neural network model This invention constructs a hybrid neural network model in the PyTorch framework and defines its complete dynamic computation logic from forward propagation to final output.

[0045] Specifically, the hybrid neural network model comprises a physical guidance path, a data-driven path, and a fusion gating module. This model adopts an architecture that integrates physical guidance and data-driven approaches. It receives a 19-dimensional standardized feature vector processed in step S1 as input, and through parallel computation and dynamic fusion via the physical guidance path and data-driven path, outputs a standardized cable force prediction value. The construction process of each module is first detailed below, and then their collaborative workflow is explained.

[0046] S201, Constructing the physical boot path The core of the physics-guided path is to generate predictions with clear physical meaning based on modified physics formulas with trainable physics parameters.

[0047] Define two trainable physical parameters: frequency scaling factor α and boundary effect correction factor β.

[0048] The frequency scaling factor α and the boundary effect correction factor β are both tensors containing three elements, corresponding to the correction factors of the first three vibration frequencies, and are denoted as α=[α1, α2, α3] and β=[β1, β2, β3], respectively.

[0049] An initialization strategy based on prior knowledge is adopted, setting the initial value of all 6 elements to the theoretical value of 1.0, and superimposing a random perturbation sampled from a normal distribution with a mean of 0 and a standard deviation of 0.05.

[0050] Therefore, the initial values ​​of all elements in the frequency scaling factor α and the boundary effect correction factor β are approximately distributed in the range of (0.85, 1.15).

[0051] Next, a physical attention module is constructed, which consists of parallel physical computing units and attention networks connected sequentially.

[0052] The hybrid neural network model receives a 19-dimensional normalized input feature vector from step S1. The physical guidance path first extracts the corresponding basic physical parameters from the first 6 dimensions of this feature vector, namely the first three vibration frequencies (f1, f2, f3), cable length (L), bending stiffness (EI), and linear density (m).

[0053] In addition, the traditional formula for calculating cable tension is expressed as: ; In the formula, It indicates the frequency order, which in physical formulas represents the mode order at which frequency is used. The cable force value calculated using the traditional cable force calculation formula.

[0054] Subsequently, the parallel physics computing unit utilizes trainable physical parameters (frequency scaling factor α and boundary effect correction factor β) and, based on fundamental physical parameters (f1, f2, f3, L, EI, m), calculates in parallel three preliminary cable force predictions corresponding to the first three vibration frequencies according to the corrected physical formula. The corrected physical formula is expressed as: ; In the formula, It indicates the frequency order, which in physical formulas represents the mode order at which frequency is used. To correct the cable force value calculated by the physical formula.

[0055] Specifically, the attention network is a small feedforward neural network with the following layer structure: a linear layer with an input dimension of 3 and an output dimension of 16, a GELU activation function, another linear layer with an input dimension of 16 and an output dimension of 3, and a softmax output layer. The attention network receives initial predictions. Output three attention weights that sum to 1. .

[0056] Based on preliminary forecast values and attention weight The physics attention module generates weighted fusion physics predictions. , represented as: .

[0057] S202, Constructing a Data-Driven Path This sub-step aims to construct a data-driven path for the hybrid neural network model. Complementing the physics-guided path, the data-driven path learns complex nonlinear relationships from the full 19-dimensional normalized input features that the physical formulas fail to describe, and outputs a data-driven corrected prediction.

[0058] Specifically, the data-driven path is implemented by a deep residual network, which consists of the following components connected in sequence: Input layer: A linear layer that maps the input dimension from 19 to 512.

[0059] Five residual block sequences: Residual block 1 and residual block 2: both have an input dimension and an output dimension of 512.

[0060] Residual block 3: Input dimension is 512, output dimension is 256.

[0061] Residual block 4: Both the input and output dimensions are 256.

[0062] Residual block 5: Input dimension is 256, output dimension is 128.

[0063] Each residual block contains: a first linear layer, a layer normalization function (LayerNorm), a GELU activation function, a dropout layer (with a dropout rate of 0.3), and a second linear layer. Residual connections are used to sum the block input with the output of the second linear layer to facilitate deep network training.

[0064] Output layer: A linear layer that maps the input dimension from 128 to 1.

[0065] The data-driven path receives complete 19-dimensional normalized input features and outputs data-driven corrected predictions. .

[0066] In a specific embodiment, the 19-dimensional standardized input features output from step S1 are fed into a deep residual network in a data-driven path for deep nonlinear feature extraction. Five sequentially connected residual blocks perform the following operations: linear transformation of the input data; application of LayerNorm to stabilize the training process; introduction of nonlinearity through the GELU activation function; random dropping of some neurons using a Dropout layer to prevent overfitting; another linear transformation; and finally, residual connection between the input of the residual block and the output calculated above to promote gradient flow and deep network training. As the data flows through the residual block sequence, its feature dimensions change along the following path: 512→512→256→256→128, thereby gradually refining and compressing information. The feature tensor (128 dimensions) processed by the deep residual network is fed into the output linear layer, which maps the 128-dimensional features to a single scalar value, i.e., a corrected prediction value. This serves as a supplement and correction to physical predictions.

[0067] S203, Constructing a converged gating module The fusion gating module is used to dynamically balance the contributions of the physical guidance path and the data-driven path.

[0068] Specifically, the fusion gating module includes a fully connected neural network. This fully connected neural network receives the physical predictions from the physical attention module and the corrected predictions from the deep residual network. Then output a dynamic gating weight. .

[0069] The layer structure of a fully connected neural network is as follows: a linear layer with an input dimension of 2 and an output dimension of 16; a GELU activation function; a linear layer with an input dimension of 16 and an output dimension of 1; and a Sigmoid activation function. The GELU activation function introduces a non-linear transformation to enhance the model's expressive power. The Sigmoid activation function compresses the final output value to the (0, 1) interval, resulting in dynamically gating weights. .

[0070] The fully connected neural network constructed in this way is the fusion gating module. The fusion gating module intelligently fuses the predicted values ​​from the physical attention module and the correction values ​​from the deep residual network to generate the final cable force prediction value.

[0071] Specifically, based on dynamic gating weights ,right Weighted fusion is performed to obtain standardized cable force prediction values, calculated using the following formula: ; To standardize cable force predictions, it combines the interpretability of physical mechanisms with the flexibility of data-driven approaches: when When the value is close to 1, it indicates that the hybrid neural network model relies more on the prediction of the physical guidance path. A value close to 0 indicates that the hybrid neural network model relies more on data-driven path predictions. This design allows the hybrid neural network model to flexibly adopt the most reliable prediction strategy when faced with samples of different characteristics, greatly enhancing its generalization ability.

[0072] The above steps complete the construction of the hybrid neural network model. This model embodies a deep integration of physical mechanisms and data-driven intelligence.

[0073] In a specific embodiment, the complete forward propagation process of the hybrid neural network model from input features to force prediction values ​​specifically performs the following sequential operations: The hybrid neural network model receives a 19-dimensional normalized input feature vector from step S1. Through the physical guidance path, it first extracts the corresponding basic physical parameters from the first 6 dimensions of the feature vector, namely the first three vibration frequencies (f1, f2, f3), cable length (L), bending stiffness (EI), and linear density (m).

[0074] Subsequently, the parallel physics computing unit uses two trainable physical parameters and, based on the corrected physics formula, calculates three preliminary prediction values ​​in parallel. Input this initial prediction into the attention network, and it outputs the corresponding attention weights. The weighted physical prediction value is calculated.

[0075] Meanwhile, the complete 19-dimensional standardized input feature vector is input into the deep residual network, and after a series of nonlinear transformations, the data-driven corrected prediction value is finally output.

[0076] The physical prediction value and the corrected prediction value are input into the fusion gating module to calculate the dynamic gating weight and the cable force prediction value.

[0077] At this point, the hybrid neural network model has completed the entire forward propagation process from input features to standardized cable force prediction values.

[0078] S3, Model Training Based on the hybrid neural network model constructed in step S2, this step executes the model training process to optimize all trainable parameters in the hybrid neural network model (including trainable physical parameters, as well as the neural network weights of the physical guidance path and the data-driven path), resulting in a final hybrid neural network model capable of accurately predicting bridge cable forces. The model training process includes: dividing the standardized dataset into training and validation sets; defining the parameter update algorithm and learning rate adjustment rules; formulating a composite loss function to guide the direction of parameter optimization; iteratively executing parameter optimization; and automatically selecting the best model through an early stopping mechanism. The specific process is as follows: S301. Preparing Training Data and Splitting the Dataset Obtain the standardized dataset generated in step S1, which includes: a matrix of dimension [N, 19] containing the standardized 19-dimensional features of all samples; and a standardized target set: a vector of dimension [N, 1] containing the standardized true cable forces of all samples.

[0079] The standardized dataset is randomly divided into two mutually exclusive subsets: a training set and a validation set. The training set contains 80% of the total samples and is used directly in the forward and backward propagation of the model to update all trainable parameters of the hybrid neural network model. The validation set contains the remaining 20% ​​of the samples. The samples in the validation set are not used for parameter updates but are only used to calculate the validation loss after each training epoch to monitor the model's generalization ability and provide a basis for early stopping mechanisms.

[0080] Specifically, the standardization process for partitioning the dataset must ensure randomness to guarantee that both subsets represent the overall distribution of the data. Simultaneously, it must ensure that the samples in the training and validation sets are mutually exclusive, meaning that any sample can only belong to one of the sets.

[0081] More specifically, by setting a fixed random number seed, we ensure that the same training and validation sets are obtained in each experiment, thus guaranteeing the reproducibility of the experimental process.

[0082] This step yields training and validation sets that can be directly used for model training.

[0083] S302, Configuration Optimization Strategy This step configures the core optimization strategy for model training, including the parameter update algorithm and learning rate adjustment rules. Its input is all trainable parameters of the hybrid neural network model constructed in step S2, and its output is the configured optimizer and learning rate scheduler instances. The specific configuration process is as follows: Configuration optimizer: This invention selects the AdamW optimizer as the core algorithm for parameter updates. As an improved version of the Adam optimizer, the AdamW optimizer can handle weight decay more effectively. By decoupling weight decay from gradient updates, it helps to prevent model overfitting more effectively.

[0084] Specifically, the initial learning rate of the AdamW optimizer is set to 1×10. -4 This is used to control the initial step size for parameter updates. The weight decay of the AdamW optimizer is set to 1×10. -5 As a regularization method, it prevents overfitting by penalizing large weights.

[0085] In one specific embodiment, the configured AdamW optimizer is associated with all trainable parameters of the hybrid neural network model in the code implementation.

[0086] To further improve training performance, this invention employs a learning rate scheduler to dynamically adjust the learning rate. Within a preset training period, the learning rate scheduler smoothly decays the learning rate from its initial value to a minimum value following the curve of a cosine function. This strategy allows for faster convergence using a larger learning rate in the early stages of training, while automatically employing a smaller learning rate in the later stages to help the model fine-tune around the optimal solution, avoiding oscillations.

[0087] Specifically, this embodiment uses a cosine annealing scheduler (CosineAnnealingLR) to dynamically adjust the learning rate.

[0088] In one specific embodiment, the scheduling parameters include a period and a learning rate range. The period is set to complete the learning rate adjustment within 100 training epochs. The learning rate range is set to increase the learning rate from an initial 1×10⁻⁶ within 100 training epochs. -4 Smooth decay to a minimum of 1×10 -6 This allows for faster convergence during the initial training phase, while a smaller learning rate is used later in the training phase to help fine-tune the hybrid neural network model.

[0089] S303, Define the composite loss function Construct a composite loss function to accurately measure the error between the predicted and actual values ​​of the hybrid neural network model, which will serve as the basis for the optimizer to update the model parameters in step S302.

[0090] To achieve high-precision and stable cable force prediction, this invention does not employ a single loss function, but instead designs a composite loss function (CompositeLoss) to comprehensively address the specific challenges in cable force prediction tasks. This composite loss function consists of two parts: log-mean squared error (RMSE)... ) and Mean Absolute Percentage Error (MAPE). Its design is based on the following two core considerations: The model is responsible for stabilizing the numerical scale, as cable force values ​​can span large orders of magnitude (e.g., from thousands to tens of thousands of Newtons). Directly using the mean squared error (MSE) would allow the training process to be dominated by a few extremely large error samples. Taking the logarithm of both the predicted and true values ​​before calculating the MSE effectively compresses the dynamic range of the numerical values, making the loss function stable and sensitive to cable force values ​​of varying magnitudes. MAPE is responsible for optimizing relative accuracy, as cable force prediction is more concerned with the percentage of error relative to the true value. MAPE directly calculates the average percentage error, ensuring that model optimization focuses on improving the relative accuracy of predictions, which is more meaningful than absolute error in practical engineering.

[0091] The logarithmic mean square error ( The final composite loss function is formed by combining the mean absolute percentage error (MAPE) and the mean absolute percentage error (MAPE) with certain weights, and its calculation formula is as follows: ; in, These are the weights of the MAPE loss, in this embodiment. Set it to 0.7. This is the scalar loss value.

[0092] Log-mean square error ( First, take the logarithm of the predicted value and the true value, and then calculate the mean square error. This can stably handle the huge differences in cable force values ​​that may exist, and avoid the training being dominated by a few extremely large error samples.

[0093] Mean Absolute Percentage Error (MAPE) calculates the average percentage of error relative to the true value, and can directly optimize the relative accuracy of predictions.

[0094] The scalar loss value calculated according to the above formula will be used as the direct target for parameter optimization during model training. The optimizer in step S302 will minimize this loss value to drive the update of the hybrid neural network model parameters.

[0095] S304, Execution Training After completing data preparation, configuration optimization, and defining the composite loss function, this step uses iterative optimization to bring the hybrid neural network model to its optimal state.

[0096] The training process is an iterative optimization process targeting the training set. Each complete traversal of the entire training set is called a training epoch. Each training epoch includes the following steps: (1) Batch traversal: The training set is divided into multiple batches. For each batch, the batch data is input into the hybrid neural network model, and forward propagation is performed to calculate the standardized cable force prediction value. Then, the composite loss value for that batch is calculated using the composite loss function. The training set is randomly shuffled and divided into multiple fixed-size batches. For each batch, the data of the current batch is input into the model, and the forward propagation process of step S205 is performed to obtain the standardized cable force prediction value. The error between the model's predicted value and the true label of the batch data is calculated using the composite loss function defined in step S303 to obtain the loss value for the current batch.

[0097] (2) Backpropagation and parameter update: After all batches have been processed in a training cycle, the cosine annealing scheduler configured in S302 is invoked to reduce the learning rate used in the next training cycle according to a preset strategy.

[0098] The AdamW optimizer first zeroes the gradients of all trainable parameters in the hybrid neural network model, and then automatically calculates the gradient of the loss function with respect to each trainable parameter using the backpropagation algorithm. Finally, the AdamW optimizer updates all trainable parameters based on the calculated gradients.

[0099] The learning rate scheduler adjusts the learning rate for the next iteration according to a preset strategy.

[0100] (3) Periodic verification and evaluation: At the end of the current training cycle, the hybrid neural network model performs forward propagation on the validation set that was not involved in parameter updates, and calculates the validation set loss.

[0101] Specifically, this invention employs an early stopping mechanism to prevent overfitting. The early stopping mechanism is a monitoring process for the validation set, executed after each training cycle, used to prevent model overfitting and automatically select the best model.

[0102] Specifically, the current validation set loss is compared with the historical lowest validation set loss: if the current loss is lower than the historical lowest loss, the model performance is considered to have improved. In this case, all parameters of the current model are saved as the current optimal model state, and the "patience counter" is reset. Otherwise, the patience counter is incremented by 1.

[0103] More specifically, the termination decision is made by checking whether the patience counter has reached a preset patience value, which is set to 250 in this embodiment. If the validation set loss does not decrease after 250 consecutive training cycles, it is determined that the model has been sufficiently trained and further training will not improve performance, and the training process is terminated immediately.

[0104] After training is terminated, a fully trained hybrid neural network model is obtained, which contains the optimal set of trainable parameters.

[0105] By repeating this step cyclically, the model that performs best on the validation set is finally obtained, and this model can then be used for actual bridge cable force prediction tasks.

[0106] In one specific embodiment, a trained hybrid neural network model is loaded, and the bridge cable parameters (first-order frequency, second-order frequency, third-order frequency, cable length, bending stiffness, and linear density) are input into the hybrid neural network model, outputting standardized cable force prediction values. Finally, the output is inversely normalized using the previously saved normalizer to obtain the final cable force prediction values ​​with physical units. To verify the final performance of the invention, the trained model is used to predict the test set reserved in step S301 (containing 3500 sets of samples not involved in training), and the overall performance index is calculated. Fig. 3As shown, the test results demonstrate that the prediction results of the method of the present invention are in high agreement with the true values. Its key performance indicators include: root mean square error (RMSE) of 56.1075N, coefficient of determination (R²) as high as 0.997823, and mean absolute percentage error (MAPE) as low as 1.0466%. These results fully demonstrate that the method of the present invention has extremely high prediction accuracy and reliability.

[0107] In one specific embodiment, the dual-fusion neural network bridge cable force prediction system based on physical data includes a data acquisition module, a model module, and an inverse standardization module.

[0108] The data acquisition module is used to acquire the input features of the bridge cable to be predicted and to preprocess them to obtain standardized input features. The input features include the vibration frequency, cable length, bending stiffness and linear density of the bridge cable to be predicted.

[0109] The model module is used to input standardized input features into a pre-trained hybrid neural network model to obtain standardized cable force prediction values.

[0110] The inverse standardization module is used to convert standardized cable force predictions into cable force predictions with physical dimensions.

[0111] Specifically, the hybrid neural network model includes a physical guidance path, a data-driven path, and a fusion gating module. The hybrid neural network model processes input features through the physical guidance path to generate physical prediction values; processes input features through the data-driven path to generate data-driven correction values; and dynamically fuses the physical prediction values ​​and data-driven correction values ​​through the fusion gating module to output standardized cable force prediction values.

[0112] Example 1 This embodiment aims to fully demonstrate the entire forward propagation process of a trained hybrid neural network model for cable force prediction using a specific bridge cable sample, intuitively showcasing the working logic of the present invention's method that integrates physical mechanisms with data-driven approaches. The example uses a sample that was not used in training, with the following physical parameters: first-order frequency f1: 2.15; second-order frequency f2: 4.31; third-order frequency f3: 6.48; cable length L: 80.5; bending stiffness EI: 15000; linear density m: 35.2.

[0113] According to the process defined in steps S102 and S103 of the present invention, the above input parameters are processed as follows: Feature engineering: The `add_physics_features` function is called to generate 13 enhanced features, such as F1. 2 =2.15 2=4.6225; f1·f2=2.15·4.31=9.2665; L²=80.5²=6480.25; EI / L²=15000 / 6480.25≈2.3147...and so on, generating a total of 13 new features.

[0114] Feature merging and standardization: The 6 original features and 13 new features are merged into a 19-dimensional vector, and then standardized using the scaler_X saved from the training phase. The mean of the corresponding feature column is subtracted from each feature value and then divided by the standard deviation to obtain the final 19-dimensional standardized input tensor x_input, which serves as the final input to the neural network.

[0115] The x_input is input into the trained EnhancedTensionNet model, which performs computations according to the process defined in S205. The core fusion process is as follows: Physics-guided path calculation: The model extracts physical parameters from x_input, uses the optimal parameters obtained during training, and calculates three preliminary prediction values ​​in parallel according to the correction formula: ; ; ; These three calculation results form a tensor physics_out of shape [1, 3].

[0116] The attention network calculates weights [w1, w2, w3] = [0.15, 0.42, 0.43] based on three preliminary predictions, and then performs weighted fusion to obtain the physical prediction value. =3410.5.

[0117] Data-driven path computation: A complete 19-dimensional tensor x_input parallel input deep residual network, after nonlinear transformation, outputs data-driven corrected predictions. =3620.2.

[0118] The x_input (dimension [1, 19]) first passes through an input linear layer, where its dimension is mapped to [1, 512]. It then undergoes layer normalization, GELU activation, and Dropout (with a dropout rate of 0.3) to prepare for entering the residual block. The data sequentially undergoes a deep nonlinear feature transformation through five residual blocks. After five residual blocks, the resulting feature tensor (dimension [1, 128]) is finally passed through an output linear layer, mapping it to a single scalar value. This value is the cable force correction value output by the data-driven path. .

[0119] Fusion Gating Decision: The fusion gating module receives... and Calculate the dynamic gating weights =0.6.

[0120] The final prediction is obtained by weighting the gating weights: =0.6×3410.5+0.4×3620.2=3490.8.

[0121] Standardized predictions from the model output The actual cable force normalizer scaler_y saved during the training phase is used for denormalization to restore the predicted cable force value of 3500.8 kN with physical dimensions.

[0122] The invention and its embodiments have been described above illustratively. This description is not restrictive, and the invention can be implemented in other specific forms without departing from its spirit or essential characteristics. The accompanying drawings are only one embodiment of the invention, and the actual structure is not limited thereto. No reference numerals in the claims should limit the scope of the claims. Therefore, if a person skilled in the art is inspired by this description and designs a similar structure and embodiment without departing from the spirit of the invention, such design should fall within the scope of protection of this patent. Furthermore, the word "comprising" does not exclude other elements or steps, and the word "a" preceding an element does not exclude the inclusion of "a plurality" of that element. Multiple elements stated in the product claims may also be implemented by a single element through software or hardware. The terms "first," "second," etc., are used to indicate names and do not indicate any specific order.

Claims

1. A method for predicting bridge cable forces based on a dual-fusion neural network using physical data, comprising the following steps: The input features of the bridge cable to be predicted are obtained, including the vibration frequency, cable length, bending stiffness and linear density of the bridge cable to be predicted. The input features are preprocessed to obtain standardized input features; The standardized input features are input into a pre-trained hybrid neural network model to obtain standardized cable force prediction values; The hybrid neural network model includes a physical guidance path, a data-driven path, and a fusion gating module. The hybrid neural network model processes the input features through the physical guidance path to generate physical prediction values; and processes the input features through the data-driven path to generate data-driven correction values. The standardized cable force prediction value is output by dynamically fusing the physical prediction value and the data-driven correction value through the fusion gating module.

2. The method for predicting bridge cable force based on physical data using a dual-fusion neural network according to claim 1, characterized in that, The physical guidance path includes parallel physical computing units and an attention network; The parallel physical computing unit, based on the first three vibration frequencies, cable length, bending stiffness and linear density, combined with trainable physical parameters, calculates the preliminary cable force prediction values ​​corresponding to the first three frequencies in parallel according to the modified physical formula. The attention network performs weighted fusion of the preliminary cable force prediction values ​​to generate the physical prediction values.

3. The method for predicting bridge cable force based on physical data using a dual-fusion neural network according to claim 1, characterized in that, The physical guidance path is configured to generate the physical prediction value based on a modifiable physical formula, which is expressed as: ； In the formula, f is the vibration frequency. For frequency order, To correct the cable force value calculated by the physical formula, α and β are both trainable physical parameters, EI is the bending stiffness, L is the cable length, and m is the linear density.

4. The method for predicting bridge cable force based on physical data using a dual-fusion neural network according to claim 1, characterized in that, The data-driven path uses a deep residual network to process the input features; the deep residual network includes several sequentially connected residual blocks, and the output feature dimension of the residual blocks gradually decreases along the network propagation direction.

5. The method for predicting bridge cable forces based on physical data using a dual-fusion neural network according to claim 1, characterized in that, The fusion gating module includes a fully connected neural network and a Sigmoid function; The fusion gating module calculates a dynamic gating weight between 0 and 1 using a fully connected neural network and a sigmoid activation function, and obtains the standardized cable force prediction value based on the following formula: ； in, The physical prediction value, The data-driven correction value, To standardize the predicted cable force, For dynamic gating weights.

6. The method for predicting bridge cable force based on physical data using a dual-fusion neural network according to claim 1, characterized in that, The pre-trained hybrid neural network model is obtained through the following training steps: Several sets of bridge cable input features and actual cable forces are obtained, and feature engineering is used to construct enhanced features based on the input features; The enhanced features and the actual cable force are preprocessed to obtain standardized input features and standardized actual cable force, forming a standardized dataset; the standardized dataset is then divided into a training set and a validation set. Initialize the parameters of the hybrid neural network model, including the physical guidance path, the data-driven path, and the trainable parameters in the fusion gating module; The parameters of the model are iteratively updated on the training set with the composite loss function as the optimization objective, and the model performance is monitored on the validation set. When the model performance no longer improves within multiple consecutive training cycles, training is terminated and the optimal model parameters are saved to obtain the pre-trained hybrid neural network model. The composite loss function is composed of a weighted average of logarithmic mean square error and mean absolute percentage error.

7. The method for predicting bridge cable forces based on physical data using a dual-fusion neural network according to claim 6, characterized in that, The enhancement features include at least one of the following: the square term of the first three vibration frequencies, the interaction term of the first three vibration frequencies, the square term of length, the combination term of stiffness and length, the combination term of density and length, the combination term of stiffness and density, and the interaction term of the first three vibration frequencies and length.

8. A dual-fusion neural network-based bridge cable force prediction system based on physical data, characterized in that, include: The data acquisition module is used to acquire the input features of the bridge cable to be predicted and preprocess them to obtain standardized input features; the input features include the vibration frequency, cable length, bending stiffness and linear density of the bridge cable to be predicted. Model module: used to input the standardized input features into a pre-trained hybrid neural network model to obtain standardized cable force prediction values; The hybrid neural network model includes a physical guidance path, a data-driven path, and a fusion gating module. The hybrid neural network model processes the input features through the physical guidance path to generate physical prediction values; and processes the input features through the data-driven path to generate data-driven correction values. The standardized cable force prediction value is output by dynamically fusing the physical prediction value and the data-driven correction value through the fusion gating module.

9. The dual-fusion neural network bridge cable force prediction system based on physical data according to claim 8, characterized in that, It also includes an inverse standardization module, used to convert the standardized cable force prediction value into a cable force prediction value with physical dimensions.

10. An electronic device having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the dual-fusion neural network bridge cable force prediction method based on physical data as described in any one of claims 1 to 7.

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