Coupling cable-strut cable force prediction method based on improved physical information neural network

Abstract

The invention discloses a coupling cable-strut cable force prediction method based on an improved physical information neural network, and belongs to the technical field of cable force prediction, and the method comprises the following steps: deducing physical information, and obtaining a training data set; integrating the physical information into a loss function, and constructing an improved physical information neural network cable force prediction model through an adaptive weight strategy; a neural network model is trained through physical information and data loss dual-drive optimization, and a mature cable force prediction model of a physical information neural network is obtained and stored; and inputting physical parameters into the cable force prediction model of the physical information neural network to obtain a cable force value. According to the method, physical information is integrated into a deep learning network, accurate recognition in actual engineering under the condition of small samples is achieved, dynamic balance of physical loss and data loss is achieved, and the stability and generalization of a cable force recognition model of the coupling cable-strut system are improved. The method is especially suitable for the condition that sample data is insufficient, the precision is higher, and the number of needed training samples is smaller.

Description

Technical Field

[0001] The present invention belongs to the technical field of cable force prediction, and in particular relates to a coupled cable rod cable force prediction method based on an improved physical information neural network. Background Art

[0002] In practical engineering, numerous cable structures with rigid coupling exist, such as suspension bridge hangers with vibration dampers, transmission lines connected by spacers, and unbonded steel strand cables with hoop clamps. Due to rigid coupling, the system's vibrations exhibit both independent and coupled characteristics. As critical load-bearing components of bridges, the mechanical behavior of cables impacts the overall performance of the bridge. In recent years, safety incidents caused by cable fractures in bridges have become commonplace. Due to various error factors, actual cable forces often deviate from the designed values. Therefore, accurately identifying cable forces is crucial for bridge safety assessments.

[0003] Currently, the vibration frequency method has become the preferred method for cable force measurement due to its simplicity, high accuracy, and low cost. Domestic and international researchers have conducted a series of studies on cable force identification based on the vibration frequency method. While these methods consider the frequency-cable force conversion relationship and can, to a certain extent, identify cable forces based on the vibration frequency method, they still have certain limitations, such as complex formulas, high computational costs, and insufficient identification accuracy. In recent years, with the advancement of computer technology, new technologies such as machine learning and deep learning have been gradually applied in civil engineering, providing new impetus for cable force identification. Researchers have begun to introduce machine learning to cable force identification in cables (i.e., rods), conducting a series of studies, primarily using BP neural networks, particle swarm optimization algorithms, and genetic algorithms. However, some limitations remain. For example, while a trained model has high recognition accuracy for data within its own training sample set, due to its high data requirements, recognition accuracy for data outside the training set is poor when insufficient sample data is available. This results in poor performance in practical engineering applications, insufficient generalization, and difficulty achieving the desired recognition results.

[0004] Existing research on deep learning networks mostly uses the fixed-weight PINN method. However, for identifying cable forces in coupled cable-strut systems, this method struggles with the dynamic weight changes during training, suffers from poor stability, and is prone to falling into local optimal solutions. This inability to accurately identify cable forces during bridge safety assessments can hinder bridge safety performance. Summary of the Invention

[0005] The purpose of the present invention is to provide a coupled cable-rod tension prediction method based on an improved physical information neural network, aiming to solve the technical problems in the existing technology of neural networks and traditional machine learning algorithms, such as low accuracy, insufficient model generalization, and inability to accurately identify bridge cable tension when the model sample data is limited.

[0006] To achieve the above object, the technical solutions adopted by the present invention are as follows:

[0007] A coupled cable-rod force prediction method based on an improved physical information neural network comprises the following steps:

[0008] Step 1: Derive physical information and obtain training data sets:

[0009] Based on the coupled cable-strut model, the natural frequency equation of the rigid coupled cable-strut system is obtained, and its frequency equation is solved by the moving bisection method to obtain the data set 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 weight strategy;

[0011] Step 3: Using the data set in step 1, the neural network model is trained through dual-driven 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, the step 1 includes the following:

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

[0015]

[0016] Where T1 is the cable force of the first cable rod, T2 is the cable force of the second cable rod, a1 and a2 are the relevant parameters to be solved, and l 11 、l 12 、l 21 、l 22 is the cable length of each subsystem.

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

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

[0019] Select the cable rod model, determine the cable rod linear density, length and cable rod coupling position;

[0020] Under normal working conditions, 300 groups of samples with cable tensions between 800 and 1400 kN were randomly generated, with cable tension unevenness set to 5%, 8%, and 10%. 270 groups were used for training and divided into training and validation sets in an 8:2 ratio. The remaining 30 groups were used as test sets.

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

[0022] The cable rod frequencies are all solved by the moving bisection method.

[0023] Furthermore, in step 12, the steps of the moving dichotomy are as follows:

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

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

[0026] 3) Gradually narrow the interval, and if there is a root, determine whether the middle value is close to 0;

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

[0028] 4) The algorithm updates the interval; if there is no root, the left and right intervals are each moved forward one step, and the above steps 2) and 3) are repeated until all frequencies are found;

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

[0030] Furthermore, the step 2 includes the following:

[0031] (1) For the rigid coupled cable-rod system, incorporating physical information constraints means incorporating information on boundary conditions, continuity requirements, or vertical force requirements at the coupling point into the loss function of the neural network. The loss function expression based on physical information is:

[0032]

[0033] Where, is the weight of the data loss term, is the weight of the physical loss item;

[0034] w is the connection weight between neurons; b is the bias value; Ldata For data loss; L phy For physical losses;

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

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

[0037]

[0038] Where, represents the data loss variance, represents data loss, and E represents expectation;

[0039] In order to improve the stability of weight distribution, the exponentially weighted moving average method is introduced into the estimated loss variance, and a time-varying attenuation factor is introduced. Taking data loss as an example, the loss variance is:

[0040]

[0041] Where, is the decay factor of the tth round, E represents the expectation, L data,t Represented as data loss; is the data loss variance at the previous moment;

[0042] Attenuation Factor Dynamic adjustments during training are as follows:

[0043]

[0044] Where, is the initial attenuation factor, is the final attenuation factor, T is the maximum training round, and P is the attenuation node parameter;

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

[0046]

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

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

[0049] Where N is the number of training samples, is the actual value of the sample, is the predicted value;

[0050] Using a numerically driven approach, we select an appropriate optimization strategy to minimize the loss function and find the optimal weighting coefficient and bias, so that the predicted value and the actual value are infinitely close.

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

[0052]

[0053]

[0054] Where M is the mass per unit length of the cable member; l is the unit length of the cable member; f is the frequency equation, f1 and f2 are the input frequencies, T1' is the predicted cable force value of the first cable member, and T2' is the predicted cable force value of the second cable member; N is the number of samples; a1 and a2 are solution-related parameters; 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] Where, is the data loss weight, is the physical loss weight.

[0058] Furthermore, in step 3, a complete cable force prediction model integrating physical information neural network is constructed based on the physical information of adaptive weights and data-driven weight distribution method, with the cable length, linear density, first-order frequency and second-order frequency of the cable rod as input and the cable force as output;

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

[0060]

[0061] Where: Output value for the neural network; is the connection weight 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 rod include linear density, cable length, cable force, frequency and order.

[0063] Furthermore, it also includes step 5, evaluating the intelligent recognition effect of the cable force.

[0064] Compared with the prior art, the present invention has the following technical advances:

[0065] The present invention embeds physical information into a neural network model, obtains data samples through numerical calculation methods, uses linear density, length, frequency, and order as feature inputs, and cable tension as feature output; uses the variance of the loss function as an uncertainty quantification indicator, and uses an adaptive physical information and data-driven weight distribution method to place the data samples into a physical information neural network cable tension identification model for training, thereby constructing a mature physical information neural network cable tension identification model, thereby enabling cable tension to be identified by directly inputting cable length, linear density, first-order frequency, and second-order frequency. By integrating physical information into the deep learning network, the present invention can reduce the model's demand for data, achieve accurate identification in actual engineering projects with small sample sizes, achieve a dynamic balance between physical loss and data loss, and improve the stability and generalization of the coupled system cable tension identification model. The present invention is particularly suitable for situations where sample data is insufficient, has higher accuracy, stronger generalization, requires fewer training samples, has high practical engineering value, and is of great significance to the construction and safety status assessment of bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0066] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0067] In the attached figure:

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

[0069] Figure 2 Schematic diagram of a multi-rigid coupled cable-rod model in an embodiment of the present invention;

[0070] Figure 3 This is a flow chart of the moving bisection calculation method used in an embodiment of the present invention;

[0071] Figure 4 Schematic diagram of the working principle of neurons in an embodiment of the present invention;

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

[0073] Figure 6 This is a diagram showing the cable force identification effect of the first cable rod in an embodiment of the present invention;

[0074] Figure 7 This is a diagram showing the cable force identification effect of the second cable rod in an embodiment of the present invention. DETAILED DESCRIPTION

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

[0076] The present invention provides a coupled cable-rod force prediction method based on an improved physical information neural network, the process is as follows: Figure 1 As shown, the following steps are included:

[0077] Step 1: Calculate physical information and obtain training data sets:

[0078] Based on the boundary conditions, continuity requirements, and vertical force balance of the coupled cable-strut model, the natural frequency equation of the rigid coupled cable-strut system is obtained. The frequency equation is solved using the bisection method to obtain the data set required for training.

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

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

[0081] The present invention takes a double cable rod as an example. The differential equation of the lateral vibration of a single cable rod under tension is:

[0082] (1)

[0083] Where 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] Formula (1) can be solved by separation of variables method, assuming that the solution of the equation is in the form of:

[0085] (2)

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

[0087] (3)

[0088] (4)

[0089] Where A, B, C, and D are all constants, and the coefficients .

[0090] Substituting (3) and (4) above into formula (2), the vibration equation solutions of each subsystem can be obtained as follows:

[0091] (5)

[0092] Where 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-rod model shown in the figure, the frequency equation of the free vibration of the system 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 both ends of the cable are consolidated, the displacement of the cable ends is 0, that is:

[0096] (6)

[0097] There are 2n equations in total.

[0098] 2) Continuity requirements:

[0099] The displacements of the same cable rod 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 requirement: 5

[0104] The vertical component of the cable strand at the coupling position should meet the equilibrium force requirements. 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 get 2nm equations, which can be written into 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] After derivation and solution, the natural frequency equation of the single rigid coupled double cable-rod system (n=2, m=2) is:

[0114] (13)

[0115] When the number of cables is 3, the natural frequency equation of the rigid coupled double cable-rod system (n=2, m=3) is:

[0116] (14)

[0117] By analogy, when the number of cables is n, the natural frequency equation of the rigid coupled cable-rod system is as follows:

[0118] (15)

[0119] Where n is the number of cables; i is the cable number, ranging from 1 to n; j is the subsystem number, ranging from 1 to m. The cable length of each subsystem is l ij (i represents the cable rod number, j represents the subsystem number), a i is the relevant solution coefficient, T i For the cable rod force.

[0120] When the number of cables n=1, it can also be degenerated into the natural vibration equation under the non-coupled condition.

[0121] In order to solve the natural frequency of the single rigid coupled double cable-rod system (n=2, m=2), the moving bisection method is used to perform numerical solution.

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

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

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

[0125] 3) Gradually narrow the interval, and if there is a root, determine whether the middle value is close to 0;

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

[0127] 4) The algorithm updates the interval; if there is no root, the left and right intervals are each moved forward one step, and the above steps 2) and 3) are repeated 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 rod model, determine the cable rod linear density, length and cable rod coupling position;

[0131] Under normal working conditions, 300 groups of samples with cable tensions between 800 and 1400 kN were randomly generated, with cable tension unevenness set to 5%, 8%, and 10%. 270 groups were used for training and divided into training and validation sets in an 8:2 ratio. The remaining 30 groups were used as test sets.

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

[0133] The cable rod frequencies are all solved by the moving bisection method.

[0134] In this example, three cable members, PES-7-55, PES-7-61, and PES-7-73, widely used in bridge engineering, were selected. The cable member coupling position was L / 10 from the left end. The linear densities m of the three cable members were 16.6 kg / m, 18.4 kg / m, and 22 kg / m, respectively. 300 sets of samples were randomly generated, with cable member forces T1 and T2 ranging from 800 to 1400 kN. Three different cable member nonuniformities were set, 5%, 8%, and 10%. 270 of these sets served as the training set, and the remaining 30 as the test set. Fifteen sets of samples, each with forces between 400 and 600 kN and 1600 and 1800 kN, were randomly selected as the test set to demonstrate the generalization performance of the model. A total of 315 sets of cable member parameter parameters were generated. Lengths were randomly selected between 5 and 25 meters. The frequency was numerically solved using a Python binary search program.

[0135] The present invention adopts the Pytorch deep learning development platform. Before the PINN network model starts training, the optimal hyperparameters are selected after multiple debugging. The model is optimized by cosine annealing heating restart, and the initial learning rate α is set. max =0.0015, minimum learning rate α min = 0.0005, the minimum cycle length T0 = 1000, the initial restart cycle is 1000, and the learning rate is reset to α after each cycle. max , and the cycle length increases in multiples of 2. Regarding the selection of hidden layers and neurons. Since the research goal is to train with a small sample size, too many layers can easily lead to model overfitting. Therefore, a relatively small number of hidden layers and neurons are selected. The hidden layer is set to 3, and each layer of the network consists of 64 neurons.

[0136] During training, data is divided into batches of 32 groups. After one batch of model training iterations, the variance of the prediction error is calculated as the loss weight for the updated PINN model to ensure convergence. The model iteration count is set to 7000. The tanh function is selected as the activation function, and the AdamW optimizer is selected as the optimizer.

[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 weight strategy;

[0138] (1) For the rigid coupled cable-rod system, incorporating physical information constraints means incorporating information on boundary conditions, continuity requirements, or vertical force requirements at the coupling point into the loss function of the neural network. The loss function expression based on physical information is:

[0139] (16)

[0140] Where, is the weight of the data loss term, is the weight of the physical loss item;

[0141] w is the connection weight between neurons; b is the bias value; L data For data loss; L phy For physical losses;

[0142] 1) In the process of backpropagation of neural networks, reducing the loss function through optimization strategy is a key step. Usually, the expression of the data-driven loss function is: (17)

[0143] Formula, N is the number of training samples, is the actual value of the sample, is the predicted value;

[0144] Using a numerically driven approach, we select an appropriate optimization strategy to minimize the loss function and find the optimal weighting coefficient and bias, so that the predicted value and the actual value are infinitely close.

[0145] 2) For the rigid coupled cable-strut system, incorporating physical information constraints means incorporating boundary conditions, continuity requirements, vertical force requirements at the coupling point, and other information into the neural network loss function. From the derivation in Chapter 1, we can see that the final integration is a function. The expression of the physics-driven loss function is:

[0146] (18)

[0147] (19)

[0148] Where M is the mass per unit length of the cable member; l is the unit length of the cable member; f is the frequency equation, f1 and f2 are the input frequencies, T1' is the predicted cable tension value of the first cable member, and T2' is the predicted cable tension value of the second cable member; N is the number of samples; a1 and a2 are the relevant parameters for the solution.

[0149] In order to balance the weights of physical information and data information and improve their stability and accuracy, the present invention applies the weighting concept to the training process of the physical information neural network. The loss function of the neural network model driven by both physical information and data is shown in the above formula (16).

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

[0151] Aiming at the vibration characteristics of rigid coupled cable rods, the present invention proposes an adaptive weight strategy based on the EWMA (exponentially weighted average) idea to cope with the complex dynamic characteristics in the cable force identification process.

[0152] Different from the fixed weights in traditional PINN, the weight distribution 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] Where, represents the data loss variance, represents data loss, and E represents expectation;

[0155] To improve the stability of weight distribution, the exponential weighted moving average (EWMA) method is introduced to estimate the loss variance, and a time-varying decay factor is introduced. Taking data loss as an example, the loss variance is:

[0156] (21)

[0157] wherein, is the decay factor of the t-th round, E represents the expectation, and L data,t represents the data loss of the t-th round, is the data loss variance of the last moment;

[0158] The decay factor is dynamically adjusted as follows:

[0159] (22)

[0160] wherein, is the initial decay factor, is the final decay factor, T is the maximum training round, and P is the decay node parameter;

[0161] In the optimization training of the physical information neural network, the ideal weight distribution should consider the uncertainty of each target to improve the prediction stability and robustness. In the adaptive weight optimization training, the weight distribution method is as follows:

[0162] (23)

[0163] wherein, and are the standard deviations of the data loss and the material loss, is the data loss, is the physical loss.

[0164] The core idea of this method is: the larger the variance, the higher the uncertainty, and the smaller the weight; the smaller the variance, the lower the uncertainty, and the larger the weight. To prevent the variance from being too small and causing unstable weight calculation, the model will increase the weight of the target with high certainty and reduce the weight of the target with high uncertainty, thereby improving the overall performance. To ensure reasonable distribution of weights, the present application normalizes the weights, and the final overall loss function is shown in formula (9).

[0165] The architecture of the above-mentioned physical information neural network coupled with the cable force intelligent identification of the cable-strut system is shown in Figure 5 .

[0166] Step 3: Use the data in step 1 to provide data-driven, optimize the neural network model through physical information and data loss double-driven, obtain a complete and mature physical information neural network cable force prediction model, and save it.

[0167] Compared with 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. In the case of insufficient sample data, they can greatly improve training accuracy and generalization performance.

[0168] Taking the cable length, linear density, first-order frequency, and second-order frequency of the cable rod as input and the cable force as output, a complete cable force prediction model integrating physical information neural network with adaptive weights and data-driven weight distribution method is constructed. The physical information neural network can learn and capture a large number of characteristic relationships between inputs and outputs. In theory, it can approximate any nonlinear fitting function. The relationship between its input and output is as follows:

[0169] (twenty four)

[0170] Where: is the output value of the neural network; is the connection weight 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 shown.

[0172] Step 4: Input the cable rod's linear density, cable length, frequency, and order into the physical information neural network 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 ​​are obtained. A fusion physical information neural network prediction model is constructed based on adaptive weighted physical information and a data-driven weight allocation method. Simulation data obtained through numerical solution methods is trained on the improved physical information neural network prediction model, resulting in a complete and mature model that is 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-rod system.

[0174] The trained model was used to identify the cable force on the test set. The results showed that the cable force identification error of the model on the test set was at a low level and the evaluation index was relatively good. Figure 6 、 7The results show that the mean square error (MSE) between the identified and actual cable tension values ​​for T1 is 11.99, the mean absolute error (MAE) is 8.18, the mean absolute percentage error (MAPE) is 0.92%, and the coefficient of determination is 0.9988. The mean square error (MSE) between the identified and actual cable tension values ​​for T2 is 18.44, the MAE is 10.79, the MAPE is 1.18%, and the coefficient of determination is 0.9977. This demonstrates that the model identification results achieve high accuracy and can effectively meet engineering needs even with limited datasets.

[0175] Some recognition results of the boom are shown in the following table:

[0176]

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

[0178] In summary, the present invention embeds regular physical information into the neural network model, obtains data samples through numerical calculation methods, uses line density, length, frequency, and order as feature inputs, and cable tension as feature output. Using the variance of the loss function as an uncertainty quantification indicator, an adaptive physical information and data-driven weight distribution method is proposed; and the data samples are placed in the physical information neural network cable tension identification model for training, to construct a mature physical information neural network cable tension identification model, so that the cable tension can be identified by directly inputting cable length, line density, first-order frequency, and second-order frequency. By integrating physical information into the deep learning network, it not only follows the mapping relationship based on data samples, but also follows the laws of physical information. Compared with traditional neural network models, when sample data is insufficient, it has higher accuracy, stronger generalization, and requires fewer training samples. It has high 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 aforementioned embodiments, those skilled in the art will be able to modify the technical solutions described in the aforementioned embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention shall be included within the scope of protection of the claims of the present invention.

Claims

1. A coupled cable-rod force prediction method based on an improved physical information neural network, characterized in that: The following steps are involved: Step 1: Derive physical information and obtain training data sets: Based on the coupled cable-strut model, the natural frequency equation of the rigid coupled cable-strut system is obtained, and its frequency equation is solved by the moving bisection method to obtain the data set and corresponding physical information required for training; Step 2: Incorporate the physical information derived in step 1 into the loss function and construct an improved physical information neural network cable force prediction model through an adaptive weight strategy; Step 3: Using the data set in step 1, the neural network model is trained through dual-driven optimization of physical information and data loss to obtain a complete and mature physical information neural network cable force prediction model and save it; 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.

2. The coupled cable-rod force prediction method based on an improved physical information neural network according to claim 1, characterized in that: The step 1 includes the following contents: Step 11: Taking the double cable rod as an example, the natural frequency equation of the single rigid coupled double cable rod system is as follows: ； Where T1 is the cable force of the first cable rod, T2 is the cable force of the second cable rod, a1 and a2 are the relevant parameters to be solved, and l 11 、l 12 、l 21 、l 22 is the cable length of each subsystem; Step 12: The natural frequency of the single rigid coupled double cable-rod system is calculated using the moving bisection method; Step 13: The steps for obtaining the dataset are as follows: Select the cable rod model, determine the cable rod linear density, length and cable rod coupling position; Under normal working conditions, 300 groups of samples with cable tensions between 800 and 1400 kN were randomly generated, with cable tension unevenness set to 5%, 8%, and 10%. 270 groups were used for training and divided into training and validation sets in an 8:2 ratio. The remaining 30 groups were used as test sets. Under the boundary conditions, 15 additional groups of samples with cable forces between 400-600KN and 1600-1800KN were randomly generated as test sets, totaling 315 groups of cable rod sample data; The cable rod frequencies are all solved by the moving bisection method.

3. The method for predicting the coupling cable force based on an improved physical information neural network according to claim 2, characterized in that: In step 12, the steps of the moving dichotomy are as follows: 1) Initialize the parameters, define the objective function F(x), set the initial interval [a, b], step size t=0.1; error accuracy ε=1×10 -6 , iterative search from left to right; 2) Determine whether there is a root in the interval. If the two sides of the function have different signs, it means that there is a solution in the interval; 3) Gradually narrow the interval, and if there is a root, determine whether the middle value is close to 0; If yes, record this value; if no, continue to narrow the interval until the middle value is close to 0; 4) The algorithm updates the interval; if there is no root, the left and right intervals are each moved forward one step, and the above steps 2) and 3) are repeated until all frequencies are found; 5) Select the first five frequencies and the algorithm terminates.

4. The method for predicting the coupling cable force based on an improved physical information neural network according to claim 3, characterized in that: In the step 2, Includes the following: (1) For the rigid coupled cable-rod system, incorporating physical information constraints means incorporating information on boundary conditions, continuity requirements, or vertical force requirements at the coupling point into the loss function of the neural network. The loss function expression based on physical information is: ; Where, is the weight of the data loss term, is the weight of the physical loss item; w is the connection weight between neurons; b is the bias value; L data For data loss; L phy For physical losses; (2) The adaptive weight strategy uses loss variance as an effective measure of prediction uncertainty. A large variance indicates unstable prediction and high uncertainty; a small variance indicates stable prediction and low uncertainty. Taking data loss as an example, the uncertainty of data loss is quantified as follows: ; Where, represents the data loss variance, and E represents the expectation; In order to improve the stability of weight distribution, the exponentially weighted moving average method is introduced into the estimated loss variance, and a time-varying attenuation factor is introduced. Taking data loss as an example, the loss variance is: ; Where, is the decay factor of the tth round; E represents the expectation, L data,t Denotes the data loss in round t; D data,t-1 is the data loss variance at the previous moment; Attenuation Factor Dynamic adjustments during training are as follows: ; Where, is the initial attenuation factor, is the final attenuation factor, T is the maximum training round, and P is the attenuation node parameter; In adaptive weight optimization training, the weight distribution method is as follows: ; Where, and is the standard deviation of data loss and physical loss, For data loss, For physical loss.

5. The method for predicting the coupling cable force based on the improved physical information neural network according to claim 4 is characterized in that In step 21, the expression of the data-driven loss function is: ； Where N is the number of training samples, is the actual value of the sample, is the predicted value; Using a numerically driven approach, we select an appropriate optimization strategy to minimize the loss function and find the optimal weighting coefficient and bias, so that the predicted value and the actual value are infinitely close. The expression of the loss function driven by physical information is: ； ； Where 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 tension value of the first cable rod, and T2' is the predicted cable tension value of the second cable rod; N is the number of samples; a1 and a2 are the relevant parameters to be solved; The loss function of the neural network model driven by both physical information and data is: ； Where, is the data loss weight, is the physical loss weight.

6. The coupled cable-rod force prediction method based on an improved physical information neural network according to claim 5, characterized in that: In step 3, a complete cable force prediction model integrating physical information neural network is constructed based on the physical information of adaptive weights and a data-driven weight allocation method, with the cable length, linear density, first-order frequency, and second-order frequency of the cable rod as input and the cable force as output; The relationship between the input and output of the physical information neural network is as follows: ； Where: Output value for the neural network; is the connection weight 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.

7. The coupled cable-strut force prediction method based on an improved physical information neural network according to claim 6, characterized in that: In step 4, the physical parameters of the cable rod include linear density, cable length, cable force, frequency and order.

8. The coupled cable-strut force prediction method based on an improved physical information neural network according to claim 7, characterized in that: The method further includes step 5 of evaluating the recognition effect of the cable force.

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