A coupling cable-strut cable force prediction method based on an improved physical information neural network

Abstract

The application discloses a kind of coupling cable rod cable force prediction methods based on improved physical information neural network, belong to cable force prediction technical field, including the following steps: derivation physical information, obtain training dataset;Physical information is integrated into loss function, and improved physical information neural network cable force prediction model is constructed by adaptive weight strategy;Through physical information and data loss double-drive optimization training neural network model, obtain mature physical information neural network cable force prediction model and save;Physical parameter is input in the cable force prediction model of physical information neural network, and cable force value is obtained.The application integrates physical information into deep learning network, realizes accurate identification in actual engineering under small sample condition, realizes the dynamic balance of physical loss and data loss, improves the stability and generalization of coupling cable rod system cable force identification model.The application is especially suitable for in the case of insufficient sample data, higher precision, and less training sample quantity is required.

Description

Technical Field

[0001] This invention belongs to the field of cable force prediction technology, and specifically relates to a method for predicting the cable force of coupled cables based on an improved physical information neural network. Background Technology

[0002] In practical engineering, there are numerous cable structures with rigid coupling, such as suspension bridge suspenders with vibration dampers, power transmission lines connected by spacers, and unbonded steel strand stay cables with hoops. Under rigid coupling, the system's vibration exhibits both independence and coupling. As a crucial load-bearing component of a bridge, the mechanical behavior of the cable affects the overall service performance of the bridge. In recent years, safety accidents caused by cable structure fractures in bridges have been frequent. Due to various error factors, the actual cable force often deviates from the design value; therefore, accurately identifying the cable force value is particularly important for bridge safety assessment.

[0003] Currently, the vibration frequency method has become the preferred method for cable force measurement due to its advantages such as simple operation, high accuracy, and low cost. Scholars both domestically and internationally have conducted a series of studies on cable force identification based on the vibration frequency method. Although these methods consider the conversion relationship between frequency and cable force and can perform cable force identification based on the vibration frequency method to a certain extent, they still have certain limitations, such as complex formula calculations, high computational costs, and insufficient identification accuracy. In recent years, with the development of computer technology, new technologies such as machine learning and deep learning have been gradually applied in the field of civil engineering, giving new impetus to cable force identification. Scholars have begun to introduce machine learning into the cable force identification of cables (i.e., cable rods), and have carried out a series of studies, mainly including BP neural networks, particle swarm optimization, and genetic algorithms. However, some shortcomings still exist. For example, well-trained models have high identification accuracy for data from the training sample source (within their own scope), but because the model requires a large amount of data, when the sample data is insufficient, the identification accuracy for data outside the training set is poor, resulting in poor performance in practical engineering applications, insufficient generalization, and difficulty in obtaining the desired identification effect.

[0004] In existing technologies, most research on deep learning networks employs the PINN method with fixed weights. However, for cable force identification in coupled cable-stayed systems, this method struggles to accommodate dynamic weight changes during training, exhibiting poor stability and a tendency to get trapped in local optima. Furthermore, the inability to accurately identify cable forces during bridge safety assessments compromises the bridge's safety performance. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the cable force of coupled cables based on an improved physical information neural network, which aims to solve the technical problems of low accuracy, insufficient model generalization, and inability to accurately identify the cable force of bridges when the model sample data is limited by existing neural networks and traditional machine learning algorithms.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0007] A method for predicting the cable force of a coupled cable rod based on an improved physical information neural network includes the following steps:

[0008] Step 1: Derive physical information and obtain the training dataset:

[0009] Based on the coupled cable-rod model, the natural frequency equation of the rigid coupled cable-rod system is obtained, and its frequency equation is solved by the moving bisection method to obtain the dataset and corresponding physical information required for training.

[0010] Step 2: Incorporate physical information into the loss function and construct an improved physical information neural network cable force prediction model through an adaptive weighting strategy;

[0011] Step 3: Using the dataset from Step 1, optimize and train the neural network model through dual-drive optimization of physical information and data loss to obtain a complete and mature physical information neural network cable force prediction model and save it.

[0012] Step 4: Input the physical parameters of the cable rod into the cable force prediction model of the physical information neural network to obtain the cable force value.

[0013] Furthermore, step 1 includes the following:

[0014] Step 11: Taking a double-cable-stayed system as an example, the natural frequency equation of a single rigidly coupled cable-stayed system is as follows:

[0015]

[0016] In the formula, T1 is the cable force of the first cable, T2 is the cable force of the second cable, a1 and a2 are the relevant parameters for solving, and l 11 l 12 l 21 l 22 Let be the length of the cable rod in each subsystem.

[0017] Step 12: The natural frequency of the single rigidly coupled double cable-stayed system is calculated using the moving bisection method;

[0018] Step 13, the steps for obtaining the dataset are as follows:

[0019] Select the cable type, and determine the cable linear density, length, and coupling position of the cable;

[0020] Under normal operating conditions, 300 sets of samples with cable force between 800-1400KN were randomly generated, with cable force non-uniformity set to 5%, 8%, and 10%; 270 sets were used for training, divided into training set and validation set in an 8:2 ratio; the remaining 30 sets were used as test set.

[0021] Under boundary conditions, an additional 15 sets of samples with cable forces between 400-600KN and 1600-1800KN were randomly generated as test sets, for a total of 315 sets of cable rod sample data;

[0022] The frequencies of the cables and rods were all solved using the moving bisection method.

[0023] Furthermore, in step 12, the moving bisection method comprises the following steps:

[0024] 1) Initialize parameters, define the objective function F(x), set the initial interval [a,b], step size t=0.1; error precision ε=1×10 -6 The search proceeds iteratively from left to right;

[0025] 2) Determine if there is a root in the interval. If the two sides of the function have opposite signs, it means that there is a solution in the interval.

[0026] 3) Gradually narrow down the interval; if a root is found, determine if the intermediate value is close to 0.

[0027] If yes, record this value; if no, continuously narrow the interval until the middle value is close to 0.

[0028] 4) Algorithm update interval; if there is no root, advance the left and right intervals by one step, and repeat steps 2) and 3) above until all frequencies are found;

[0029] 5) Select the first five frequencies, and the algorithm terminates.

[0030] Furthermore, step 2 includes the following:

[0031] (1) For a rigidly coupled cable-stayed system, incorporating physical information constraints means incorporating information about boundary conditions, continuity requirements, or vertical force requirements at the coupling points into the loss function of the neural network. The expression for the loss function based on physical information is as follows:

[0032]

[0033] In the formula, For the weights of the data loss items, Weights for physical loss terms;

[0034] w represents the connection weights between neurons; b represents the bias value; Ldata For data loss; L phy For physical loss;

[0035] (2) The adaptive weight strategy uses the loss variance as an effective measure of prediction uncertainty. A large variance indicates that the prediction is unstable and the uncertainty is high; a small variance indicates that the prediction is stable and the uncertainty is low.

[0036] Taking data loss as an example, the uncertainty of data loss is quantified as follows:

[0037]

[0038] In the formula, Indicates the variance of data loss. Let E represent the data loss, and E represent the expected value.

[0039] To improve the stability of weight allocation, the exponentially weighted moving average method is introduced into the estimated loss variance, along with a time-varying decay factor. Taking data loss as an example, the loss variance is:

[0040]

[0041] In the formula, Let L be the decay factor in round t, E represent the expected value, and L represent the decay factor in round t. data,t This is represented as data loss; The variance of the data from the previous time step;

[0042] Attenuation factor The following adjustments will be made dynamically during training:

[0043]

[0044] In the formula, The initial decay factor, The final decay factor is T, the maximum number of training rounds is T, and the decay node parameter is P.

[0045] In adaptive weight optimization training, the weight allocation method is as follows:

[0046]

[0047] In the formula and The standard deviation of data loss and material loss. For data loss, This is a physical loss.

[0048] Furthermore, in step 21, the expression for the data-driven loss function is:

[0049] In the formula, N is the number of training samples, and is the actual value of the sample. This is a predicted value;

[0050] By employing a numerically driven approach, a suitable optimization strategy is selected to minimize the loss function, and the optimal weighting coefficients and biases are found, so that the predicted values ​​and actual values ​​approach each other infinitely.

[0051] The expression for the physics-driven loss function is:

[0052]

[0053]

[0054] In the formula, M is the mass per unit length of the cable rod; l is the unit length of the cable rod; f is the frequency equation, f1 and f2 are the input frequencies, T1' is the predicted cable force value of the first cable rod, and T2' is the predicted cable force value of the second cable rod; N is the number of samples; a1 and a2 are the relevant parameters for solving; when the predicted cable force satisfies the physical constraints, the physical loss approaches zero.

[0055] The loss function of the neural network model driven by both physical information and data is:

[0056]

[0057] In the formula, To reduce data loss weights, This represents the weight of physical loss.

[0058] Furthermore, in step 3, the cable length, linear density, first-order frequency, and second-order frequency of the cable rod are used as inputs, and the cable force is used as the output. Based on the physical information and data-driven weight allocation method with adaptive weights, a complete cable force prediction model that integrates physical information neural networks is constructed.

[0059] The relationship between the input and output of a physical information neural network is as follows:

[0060]

[0061] In the formula: The output value of the neural network; The connection weights are the connection weights between the i-th neuron in the previous layer and the j-th neuron in this layer. is the bias value; f is the activation function.

[0062] Furthermore, in step 4, the physical parameters of the cable include linear density, cable length, cable force, frequency, and order.

[0063] Furthermore, step 5, evaluating the effectiveness of the Soli intelligent recognition system, is also included.

[0064] The technological advancements achieved by this invention compared to existing technologies are as follows:

[0065] This invention embeds physical information into a neural network model, acquiring data samples through numerical calculations. Line density, length, frequency, and order are used as feature inputs, while cable force is used as the feature output. The variance of the loss function is used as an uncertainty quantification index. Through an adaptive physical information and data-driven weight allocation method, the data samples are fed into the physical information neural network cable force recognition model for training, constructing a mature physical information neural network cable force recognition model. This allows for the identification of cable force simply by directly inputting cable length, line density, first-order frequency, and second-order frequency. By integrating physical information into a deep learning network, this invention reduces the model's data requirements, achieving accurate identification in practical engineering scenarios with small sample sizes. It achieves a dynamic balance between physical and data losses, improving the stability and generalization of the coupled system cable force recognition model. This invention is particularly suitable for situations with insufficient sample data, offering higher accuracy, stronger generalization, and requiring fewer training samples. It has high practical engineering value and is of significant importance for assessing the construction and safety status of bridges. Attached Figure Description

[0066] The accompanying drawings are provided to further illustrate the invention and form part of the specification. They are used together with the embodiments of the invention to explain the invention and do not constitute a limitation thereof.

[0067] In the attached diagram:

[0068] Figure 1 A flowchart of a coupled cable force prediction method based on an improved physical information neural network provided in an embodiment of the present invention;

[0069] Figure 2 This is a schematic diagram of a multi-rigidly coupled cable-stayed rod model in an embodiment of the present invention;

[0070] Figure 3 This is a flowchart of the moving bisection method used in the embodiments of the present invention;

[0071] Figure 4 This is a schematic diagram illustrating the working principle of neurons in an embodiment of the present invention;

[0072] Figure 5 This is a diagram of the cable force recognition architecture of the physical information neural network coupled cable-stayed system in an embodiment of the present invention;

[0073] Figure 6 This is a diagram illustrating the cable force recognition effect of the first cable rod in an embodiment of the present invention.

[0074] Figure 7 This is a diagram illustrating the cable force recognition effect of the second cable rod in an embodiment of the present invention. Detailed Implementation

[0075] The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described again in some embodiments. The embodiments of the present invention will now be described with reference to the accompanying drawings.

[0076] This invention provides a method for predicting the cable force of coupled cable rods based on an improved physical information neural network, the process of which is as follows: Figure 1 As shown, it includes the following steps:

[0077] Step 1: Calculate the physical information and obtain the training dataset:

[0078] Based on the boundary conditions, continuity requirements, and balance of vertical forces at the coupling point of the coupled cable-stayed system model, the natural frequency equation of the rigid coupled cable-stayed system is obtained. The frequency equation is then solved using the bisection method to obtain the dataset required for training.

[0079] Step 11, the derivation process of the physical equation is as follows:

[0080] Figure 2 The diagram shows a cable-stayed system consisting of n independently anchored steel strands of length L, a multi-rigidly coupled cable-stayed system; the cable forces in each cable are T1…T n The cables are connected by lightweight rigid couplings, and each cable is divided into m subsystems. The length of the cable in each subsystem is l. j (j is the subsystem number), and each subsystem establishes an xoy coordinate system with the origin. In the figure, x n,m and y n,m These represent the x-coordinate and y-coordinate of the nth cable rod in the mth subsystem, respectively.

[0081] Taking a double-cable rod as an example, the differential equation for the lateral vibration of a single cable rod under tension is as follows:

[0082] (1)

[0083] In the formula, v(x,t) is the lateral displacement of the cable rod; x is the coordinate along the axis of the cable rod; t is the vibration time; T is the tension of the cable rod; and m is the mass per unit length of the cable rod.

[0084] Equation (1) can be solved using the method of separation of variables. Let the solution of the equation be in the form of:

[0085] (2)

[0086] Solving equation (2) by separating the variables yields:

[0087] (3)

[0088] (4)

[0089] In the formula, A, B, C, and D are all constants, and their coefficients are... .

[0090] Substituting (3) and (4) into equation (2), we can obtain the following forms of the vibration equations for each subsystem:

[0091] (5)

[0092] In the formula, i represents the cable rod number, ranging from 1 to n; j represents the subsystem number, ranging from 1 to m.

[0093] for Figure 2 For the multi-rigid coupled cable-stayed model shown, the frequency equation of the system's free vibration can be determined by solving the boundary conditions, continuity requirements, and equilibrium conditions of the vertical forces at the coupling points using the mathematical software Mathematica.

[0094] 1) Boundary conditions:

[0095] Since the two ends of the cable are fixed, the displacement of the cable strand ends is 0, that is:

[0096] (6)

[0097] There are 2n equations in total.

[0098] 2) Continuity requirement:

[0099] The displacements of the same cable member at the coupling point are equal, that is:

[0100] (7)

[0101] (8)

[0102] (r=1,2...n-1; s=1,2...m-1), there are a total of (2n-1)×(m-1) equations.

[0103] 3) Vertical balance force requirements: (referring to point 5)

[0104] The vertical component of the cable strand at the coupling point should satisfy the requirement of balanced forces. That is:

[0105] (9)

[0106] (r=1,2...n-1; s=1,2...m-1), there are a total of (m-1) equations.

[0107] From the above, we can obtain 2nm equations. These equations can be written in matrix form:

[0108] (10)

[0109] K is a 2nm × 2nm coefficient matrix, and X is a 2nm × 1 column vector of undetermined coefficients.

[0110] (11)

[0111] If equation (11) has a solution, then the determinant of the coefficient matrix is ​​zero, that is:

[0112] (12)

[0113] Through derivation and solution, the natural frequency equation of a single rigidly coupled double-cable-stayed system (n=2, m=2) is:

[0114] (13)

[0115] When the number of cable members is 3, the natural frequency equation of the rigidly coupled two-cable system (n=2, m=3) is:

[0116] (14)

[0117] By analogy, when the number of cable members is n, the natural frequency equation of the rigidly coupled cable system is as follows:

[0118] (15)

[0119] In the formula, n represents the number of cable struts; i represents the cable strut number, ranging from 1 to n; j represents the subsystem number, ranging from 1 to m. The length of the cable strut in each subsystem is l. ij (i represents the cable rod number, j represents the subsystem number), a i For the relevant solution coefficients, T i The force on the cable rod.

[0120] When the number of cable rods n=1, it can also degenerate into the natural vibration equation under the uncoupled condition.

[0121] To solve for the natural frequencies of a single rigidly coupled double cable-stayed system (n=2, m=2), a numerical solution is obtained using the moving bisection method.

[0122] Step 12: The natural frequencies of the single rigidly coupled double cable-stayed system (n=2, m=2) are calculated using the moving bisection method, as follows: Figure 3 As shown, the specific steps are as follows:

[0123] 1) Initialize parameters, define the objective function F(x), set the initial interval [a,b], step size t=0.1; error precision ε=1×10 -6 The search is performed iteratively from left to right;

[0124] 2) Determine if there is a root in the interval. If the two sides of the function have opposite signs, it means that there is a solution in the interval.

[0125] 3) Gradually narrow down the interval; if a root is found, determine if the intermediate value is close to 0.

[0126] If yes, record this value; if no, continuously narrow the interval until the middle value is close to 0.

[0127] 4) Algorithm update interval; if there is no root, advance the left and right intervals by one step, and repeat steps 2) and 3) above until all frequencies are found;

[0128] 5) Select the first five frequencies, and the algorithm terminates.

[0129] Step 13, the steps for obtaining the dataset are as follows:

[0130] Select the cable type, and determine the cable linear density, length, and coupling position of the cable;

[0131] Under normal operating conditions, 300 sets of samples with cable force between 800-1400KN were randomly generated, with cable force non-uniformity set to 5%, 8%, and 10%; 270 sets were used for training, divided into training set and validation set in an 8:2 ratio; the remaining 30 sets were used as test set.

[0132] Under boundary conditions, an additional 15 sets of samples with cable forces between 400-600KN and 1600-1800KN were randomly generated as test sets, for a total of 315 sets of cable rod sample data;

[0133] The frequencies of the cables and rods were all solved using the moving bisection method.

[0134] In this embodiment of the invention, three cable-stayed rod models—PES-7-55, PES-7-61, and PES-7-73—widely used in bridge engineering are selected. The coupling position of the cable-stayed rod is L / 10 from the left end. The linear densities (m) of the three models are 16.6 kg / m, 18.4 kg / m, and 22 kg / m, respectively. 300 sets of samples with cable forces T1 and T2 between 800-1400 kN are randomly generated, with three sample sets having cable force non-uniformity of 5%, 8%, and 10%. 270 sets are used as the training set, and the remaining 30 sets are used as the test set. Then, 15 sets of samples with cable forces between 400-600 kN and 1600-1800 kN are randomly selected as test sets to demonstrate the generalization performance of the model. A total of 315 sets of cable-stayed rod sample parameters are generated. The lengths are randomly selected between 5-25 m. The frequency is numerically solved using a bisection method program written in Python.

[0135] This invention utilizes the PyTorch deep learning development platform. Before training the PINN network model, the optimal hyperparameters are selected through multiple adjustments. The model is optimized using cosine annealing and a restart method, with an initial learning rate α set. max =0.0015, minimum learning rate α min = 0.0005, minimum cycle length T0 = 1000, initial restart cycle is 1000, and the learning rate is reset to α after each cycle is completed. max Furthermore, the period length increases in multiples of 2. Regarding the selection of hidden layers and neurons, since the research objective is to study training under small sample sizes, selecting too many layers can easily lead to model overfitting. Therefore, relatively few hidden layers and neurons were selected, with 3 hidden layers and each layer consisting of 64 neurons.

[0136] During training, the model is divided into batches of 32 data points. After each batch of model training iterations, the variance of the prediction error is calculated and used as the loss weights for the updated PINN model to ensure convergence. The model iterations are set to 7000 epochs. The tanh activation function and the AdamW optimizer are selected.

[0137] Step 2: Incorporate physical information into the loss function and construct an improved physical information neural network cable force prediction model through an adaptive weighting strategy;

[0138] (1) For a rigidly coupled cable-stayed system, incorporating physical information constraints means incorporating information about boundary conditions, continuity requirements, or vertical force requirements at the coupling points into the loss function of the neural network. The expression for the loss function based on physical information is as follows:

[0139] (16)

[0140] In the formula, For the weights of the data loss items, Weights for physical loss terms;

[0141] w represents the connection weights between neurons; b represents the bias value; L data For data loss; L phy For physical loss;

[0142] 1) In the backpropagation process of a neural network, optimizing the loss function is a crucial step. Typically, the expression for a data-driven loss function is: (17)

[0143] In the formula, N is the number of training samples. The actual value of the sample. This is a predicted value;

[0144] By employing a numerically driven approach, a suitable optimization strategy is selected to minimize the loss function, and the optimal weighting coefficients and biases are found, so that the predicted values ​​and actual values ​​approach each other infinitely.

[0145] 2) For rigidly coupled cable-stayed systems, incorporating physical information constraints means integrating boundary conditions, continuity requirements, and vertical force requirements at the coupling points into the loss function of the neural network. As shown in the derivation in Chapter 1, this is ultimately fused into a single function. Therefore, the expression for the physics-driven loss function can be obtained as follows:

[0146] (18)

[0147] (19)

[0148] In the formula, M is the mass per unit length of the cable rod; l is the unit length of the cable rod; f is the frequency equation, f1 and f2 are the input frequencies, T1' is the predicted cable force value of the first cable rod, and T2' is the predicted cable force value of the second cable rod; N is the number of samples; a1 and a2 are the relevant parameters to be solved.

[0149] To balance the weights of physical information and data information and improve their stability and accuracy, this invention applies the weighting concept to the training process of the physical information neural network, resulting in a loss function for the neural network model driven by both physical information and data, as shown in equation (16) above.

[0150] (2) The adaptive weight strategy uses the loss variance as an effective measure of prediction uncertainty. A large variance indicates that the prediction is unstable and the uncertainty is high; a small variance indicates that the prediction is stable and the uncertainty is low.

[0151] In response to the vibration characteristics of rigidly coupled cables, this invention proposes an adaptive weighting strategy based on the EWMA (Exponential Weighted Average) concept to address the complex dynamic characteristics in the cable force identification process.

[0152] Unlike the fixed weights in traditional PINN, the weight allocation in this study is related to the stability of the prediction error. Taking data loss as an example, the uncertainty of data loss is quantified as follows:

[0153] (20)

[0154] In the formula, Indicates the variance of data loss. Let E represent the data loss, and E represent the expected value.

[0155] To improve the stability of weight allocation, the Exponentially Weighted Moving Average (EWMA) method is introduced into the estimated loss variance, along with a time-varying decay factor. Taking data loss as an example, the loss variance is:

[0156] (twenty one)

[0157] In the formula, Let E be the decay factor in round t, and L be the expected value. data,t Let be the data loss in round t. The variance of the data from the previous time step;

[0158] Attenuation factor The following adjustments will be made dynamically during training:

[0159] (twenty two)

[0160] In the formula, The initial decay factor, The final decay factor is T, the maximum number of training rounds is T, and the decay node parameter is P.

[0161] In the optimization training of physical information neural networks, the ideal weight allocation should consider the uncertainties of each objective to improve prediction stability and robustness. In adaptive weight optimization training, the weight allocation method is as follows:

[0162] (twenty three)

[0163] In the formula, and The standard deviation of data loss and material loss. For data loss, This is a physical loss.

[0164] The core idea of ​​this method is: the larger the variance, the higher the uncertainty, and the smaller the weight should be; the smaller the variance, the lower the uncertainty, and the larger the weight should be. To prevent the variance from being too small, which would lead to unstable weight calculation, the model will increase the weight of targets with high certainty and reduce the weight of targets with high uncertainty, thereby improving the overall performance. To ensure the reasonable allocation of weights, this invention normalizes the weights, and the final overall loss function is shown in equation (9) above.

[0165] The architecture of the above-mentioned physical information neural network coupled cable-stayed system for intelligent cable force recognition is as follows: Figure 5 As shown.

[0166] Step 3: Using the data from Step 1 to provide data-driven optimization, the neural network model is trained through dual-drive optimization using physical information and data loss, resulting in a complete and mature physical information neural network cable force prediction model, which is then saved.

[0167] Compared to traditional numerically driven neural network systems, physical information neural networks not only follow the mapping relationship based on data samples, but also follow the laws of physical information. When sample data is insufficient, they can significantly improve training accuracy and generalization performance.

[0168] Using the cable length, linear density, first-order frequency, and second-order frequency of the cable rod as inputs, and cable force as the output, a complete cable force prediction model integrating physical information neural networks is constructed based on an adaptive weighting method driven by physical information and data. The physical information neural network can learn and capture a large number of feature relationships between inputs and outputs, and theoretically can approximate any nonlinear fitting function. The relationship between its inputs and outputs is as follows:

[0169] (twenty four)

[0170] In the formula: This is the output value of the neural network; The connection weights are the connection weights between the i-th neuron in the previous layer and the j-th neuron in this layer. is the bias value; f is the activation function.

[0171] How neurons work Figure 4 As shown.

[0172] Step 4: Input the linear density, length, frequency, and order of the cable into the physical information neural network's cable force prediction model. Using cable length L, linear density m, first-order frequency f1, and second-order frequency f2 as inputs, and cable forces T1 and T2 as outputs, the cable force values ​​can be obtained. Based on an adaptive weighting physical information and data-driven weight allocation method, a fused physical information neural network prediction model is constructed. Simulation data obtained through numerical solutions is fed into the improved physical information neural network prediction model for training, resulting in a complete and mature model, which is then saved.

[0173] Step 5: Evaluate the cable force identification effect. When identifying cable forces, the collected parameters such as cable length, linear density, first-order frequency, and second-order frequency are directly input into a mature physical information neural network cable force prediction model to directly obtain the cable force value of the coupled cable system.

[0174] The trained model was used to identify cable forces on a test set. The results showed that the model's cable force identification error was at a low level on the test set, and the evaluation metrics were relatively good. The cable force identification performance of slings 1 and 2 in this embodiment is as follows: Figure 6 , 7 As shown, the results indicate that for T1, the mean squared error between the identified and actual cable force values ​​is 11.99, the mean absolute error is 8.18, the mean absolute percentage error is 0.92%, and the coefficient of determination is 0.9988. For T2, the mean squared error between the identified and actual cable force values ​​is 18.44, the mean absolute error is 10.79, the mean absolute percentage error is 1.18%, and the coefficient of determination is 0.9977. It can be seen that the model's recognition results achieve high accuracy and can well meet the practical needs of engineering projects even with limited datasets.

[0175] The partial identification results of the boom are shown in the table below:

[0176]

[0177] As can be seen from the table above, most of the data within the training set range are within 0.5%, and most of the data outside the training set range are within 3%, which can well reflect its generalization ability and effectively prove that its recognition accuracy is high and has high practical engineering application value.

[0178] In summary, this invention embeds regular physical information into a neural network model, obtains data samples through numerical calculation methods, and uses line density, length, frequency, and order as feature inputs, while cable force is used as the feature output. Using the variance of the loss function as an uncertainty quantification index, an adaptive physical information and data-driven weight allocation method is proposed. The data samples are then fed into a physical information neural network cable force recognition model for training, constructing a mature physical information neural network cable force recognition model. This allows for the identification of cable force simply by directly inputting cable length, line density, first-order frequency, and second-order frequency. By integrating physical information into a deep learning network, it not only follows the mapping relationship based on data samples but also adheres to the laws of physical information. Compared to traditional neural network models, it achieves higher accuracy, stronger generalization, and requires fewer training samples when sample data is insufficient. It has significant practical engineering value.

[0179] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are 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 scope of protection of the claims of the present invention.

Claims

1. A coupling cable-strut cable force prediction method based on an improved physical information neural network, characterized by, The method comprises the following steps: Step 1, deriving physical information, obtaining a training data set: Based on the coupled cable-strut model, the natural frequency equation of the rigidly coupled cable-strut system is obtained, and the frequency equation is solved by the moving bisection method to obtain the data set required for training and the corresponding physical information; Step 2, the physical information derived in step 1 is integrated into the loss function, and an improved physical information neural network cable force prediction model is constructed through an adaptive weight strategy; The method comprises the following contents: (1) for the rigidly coupled cable-strut system, the integration of the physical information constraint is to integrate the information of the boundary condition, the continuity requirement or the vertical force requirement at the coupling into the loss function of the neural network, and the loss function expression based on the physical information and the data double driving is obtained as: (2) the adaptive weight strategy uses loss variance as an effective measure of prediction uncertainty, and a large variance indicates that the prediction is unstable and the uncertainty is high; a small variance indicates that the prediction is stable and the uncertainty is low; ； wherein is a data loss term weight, is a physical loss term weight; w is a connection weight between neurons; b is a bias value; L data Data loss; L phy Physical loss; The uncertainty quantification of data loss is as follows: In order to improve the stability of weight allocation, the exponential weighted moving average method is introduced into the estimation of loss variance, a time-varying decay factor is introduced, and the loss variance is: ； wherein denotes the variance of the data loss, E denotes the expectation; In the adaptive weight optimization training, the weight allocation method is as follows: ； wherein is the decay factor for the tth round; E is expressed as the expectation, L data,t is expressed as the data loss for the tth round; is the data loss variance for the previous time instant; Attenuation factor Adjust dynamically with training as follows: ； wherein is an initial decay factor, is a final decay factor, T is the maximum number of training rounds, and P is a decay node parameter; Step 3, the data set in step 1 is used to optimize and train the neural network model through the physical information and data loss double driving, and a complete and mature physical information neural network cable force prediction model is obtained and saved; ； wherein and is the standard deviation of data loss and physical loss, is the data loss, is the physical loss; Step 4, input the physical parameters of the cable-strut into the physical information neural network cable force prediction model, and the cable force value can be obtained. The step 1 comprises the following contents:

2. The coupled cable-strut cable force prediction method based on the improved physical information neural network according to claim 1, characterized in that: Step 11, the natural frequency equation of the single rigidly coupled double cable-strut system is as follows: Step 12, the natural frequency of the single rigidly coupled double cable-strut system is calculated by the moving bisection method; the steps of the moving bisection method are as follows: ; wherein T1 is the cable force of the first cable-strut, T2 is the cable force of the second cable-strut, a1 and a2 are the relevant parameters to be solved, l 11 , l 12 , l 21 , l 22 is the length of the cable-strut of each subsystem; 2) determine whether there is a root in the interval, if the signs of the function on both sides are different, it means that there is a solution in the interval; 1), initialization parameters, define the objective function F(x), set the initial interval [a, b], step t=0.1; error precision ε=1×10 -6 , the iteration is searched from left to right; 3) gradually narrow the interval, if there is a root, determine whether the middle value is close to 0; If yes, record the value; if no, continuously narrow the interval until the middle value is close to 0; 4) update the interval; if there is no root, move the left and right intervals forward by one step respectively, and repeat steps 2) and 3) until all frequencies are found; 5) select the first five frequencies, and the algorithm terminates; Step 13, the data set acquisition steps are as follows: Select the cable-strut model, determine the linear density, length and cable-strut coupling position of the cable-strut; Under normal working conditions, 300 groups of samples with cable-strut cable force between 800-1400KN are randomly generated, the cable force non-uniformity is set to 5%, 8% and 10%; 270 groups are used for training, and the training set and the validation set are divided according to the ratio of 8:2; the remaining 30 groups are used as the test set; Under boundary conditions, 15 groups of samples with cable force between 400-600KN and 1600-1800KN are additionally randomly generated as the test set, totaling 315 groups of cable-strut sample data; The cable-strut frequency is solved by the moving bisection method. In step 2, the expression of the loss function based on data driving is:

3. The method of claim 2, wherein the method is characterized by: ​ ； In the formula, N is the number of training samples, y i is the actual value of the sample, is the predicted value; The numerical driving method is adopted, a suitable optimization strategy is selected to minimize the loss function, and optimal weighting coefficients and biases are found, so that the predicted value and the actual value are infinitely close to each other; The expression of the loss function based on the physical information driving is as follows: ； ； In the formula, M is the unit length mass of the cable rod; l is the unit length of the cable-strut; f is the frequency equation, f 1 , f 2 is the input frequency, T1' is the predicted cable force value of the first cable-strut, T2' is the predicted cable force value of the second cable-strut; N is the number of samples; a1, a2 are the solving parameters; The loss function of the neural network model driven by physical information and data is obtained as follows: ； In the formula, is a data loss weight, is a physical loss weight.

4. The coupled cable-strut cable force prediction method based on improved physical information neural network according to claim 3, characterized in that, In the step 3, the cable length, linear density, first-order frequency and second-order frequency of the cable rod are taken as inputs, the cable force is taken as output, the physical information and data driving weight distribution method based on adaptive weight is adopted, and a complete cable force prediction model fusing the physical information neural network is constructed. The relationship between the input and output of the physical information neural network is as follows: ； wherein: is the output value of the neural network; is the connection weight of the i-th neuron of the previous layer and the j-th neuron of the layer, is the bias value; and f is the activation function.

5. The coupled cable-strut cable force prediction method based on improved physical information neural network according to claim 4, characterized in that: In the step 4, the physical parameters of the cable rod include the linear density, cable length, cable force, frequency and order.

6. The coupled cable-strut cable force prediction method based on improved physical information neural network according to claim 5, characterized in that: The step 5, evaluating the identification effect of the cable force, is further included.

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