A cable force identification and uncertainty quantification method based on multi-sensor information fusion and BNN

Abstract

The present application relates to the technical field of cable force identification, and in particular to a cable force identification and uncertainty quantification method based on multi-sensor information fusion and BNN. The non-contact measurement of the vibration signal of the cable can be effectively realized by the millimeter wave radar device, the accuracy and reliability of the self-vibration frequency identification of the cable are improved, the weight and bias parameters of the BNN are assumed to be random variables subject to Gaussian distribution, the posterior distribution of the network hyperparameters is optimized and solved by using the approximate Gaussian inference algorithm, and the complexity of the network training is significantly reduced. The measured cable parameters and self-vibration frequency are input into the trained BNN model, the high-precision prediction of the cable force can be realized, and the uncertainty of the cable force identification caused by boundary conditions and other factors can be quantified.

Description

Technical Field

[0001] This invention relates to the field of cable force recognition technology, specifically to a cable force recognition and uncertainty quantification method based on multi-sensor information fusion and BNN. Background Technology

[0002] As the core load-bearing component of cable-stayed bridges, the mechanical state of cables is a key indicator for assessing structural damage and identifying potential risks. Therefore, accurate monitoring of cable forces is crucial for the long-term operational safety of cable-stayed bridges.

[0003] To accurately identify the stress state of cables, common cable force measurement methods include the frequency method, pressure sensor method, and magnetic flux method. Among these, the frequency method has become the most widely used cable force identification method due to its advantages such as high measurement accuracy, low cost, and reusability. Its principle is to identify cable force by establishing a mapping relationship between cable force and cable vibration frequency.

[0004] To address the frequency-based identification of cable forces, scholars both domestically and internationally have undertaken a series of optimizations to the methods. For example, based on the vibration differential equations of stay cables, calculation formulas for cable-stayed bridge force models considering bending stiffness have been proposed. For stay cables with complex boundary conditions, a real-time prediction method for stay bridge cable forces based on gated recurrent unit neural networks (GRNNs) for processing time-series data has been proposed, enabling real-time prediction of stay cable forces during the operational period. Alternatively, a precise cable force identification method has been proposed by combining modal shape functions and modal frequencies, and rigorous mathematical derivation has proven that stay cables can be equivalent to multiple simply supported beams to eliminate the influence of complex boundary conditions.

[0005] Existing technologies also propose a cable force recognition method based on machine vision and generalized regression neural networks. By simulating cables with complex boundary conditions through rotational constraint stiffness, the results show that this method can effectively improve the accuracy of cable force recognition.

[0006] In the above studies, cable force was identified as a fixed value. However, in actual engineering, due to the effects of variable loads such as wind and vehicles, cable force is usually not a fixed value. Therefore, it is necessary to further explore the problem of cable force identification under the influence of uncertain factors and improve the accuracy of cable force analysis and identification. Summary of the Invention

[0007] To address the aforementioned shortcomings of existing technologies, this invention provides a cable force identification and uncertainty quantification method based on multi-sensor information fusion and BNN, which can effectively solve the problem of cable force identification being affected by neglecting the action of variable loads in existing technologies.

[0008] To achieve the above objectives, the present invention provides the following technical solution: This invention provides a cable force identification and uncertainty quantification method based on multi-sensor information fusion and BNN, which includes at least: cable natural frequency identification: using millimeter-wave radar to measure the vibration displacement of the cable, calculating the time history data of the cable vibration displacement based on the phase difference of the radar echo at different times, and performing spectrum analysis on the vibration displacement time history data to obtain at least the first few natural frequencies of the cable. A tripod is securely placed on the bridge deck as a support base, with an adjustable high-precision gimbal mounted on top. A millimeter-wave radar is fixed to the upper part of the gimbal, while an accelerometer is rigidly mounted on the side of the gimbal, ensuring its sensitive axis is strictly aligned with the radar's measurement line of sight. During measurement, the millimeter-wave radar transmits signals, and based on the echo phase difference, the relative vibration displacement time history of the stay cables, including interference from tripod and bridge deck vibrations, is obtained. Simultaneously, an accelerometer mounted on the middle gimbal synchronously collects the vibration acceleration time history of the tripod and gimbal system along this line of sight. Environmental vibration interference is eliminated through data fusion. Specifically, the millimeter-wave radar uses the tripod and gimbal system as the measurement reference; the measured relative vibration displacement time history of the stay cables includes environmental disturbances such as bridge deck vibration, wind vibration, and traffic flow vibration. The system interference displacement caused by motion cannot directly reflect the true vibration state of the stay cable. However, the accelerometer is rigidly mounted on the side of the gimbal, and its sensitive axis is strictly aligned with the radar measurement line of sight. It can simultaneously collect the vibration acceleration time history of the tripod and gimbal system in this line of sight. By performing two integration operations on this acceleration time history, the interference displacement time history of the system itself can be obtained, achieving accurate matching of the interference signal. During data fusion, the interference displacement obtained by the accelerometer integration is used as the benchmark. The interference displacement time history measured by the millimeter-wave radar is subtracted from the interference-containing relative displacement time history, thereby eliminating environmental and system vibration interference and reconstructing the true vibration displacement time history of the stay cable relative to the fixed reference frame of the bridge deck. Finally, the reconstructed displacement time history data is subjected to spectrum analysis to accurately extract at least the first few orders of the natural frequencies of the stay cable. Training sample construction: A cable force recognition sample dataset is constructed based on the cable length, linear density and natural frequency, where the sample output is the corresponding cable force value; Bayesian neural network construction: A cable force identification sample dataset is constructed based on the cable length, linear density, and natural frequency, where the sample output is the corresponding cable force value; Using the length, linear density, and natural frequency of the stay cables as input variables and the cable force as the output variable, a Bayesian neural network model is constructed, and the network weight parameters and bias parameters are modeled as random variables. Posterior distribution of network parameters: Based on the approximate Gaussian inference algorithm, the posterior distribution of the weight parameters and bias parameters of the Bayesian neural network is estimated to obtain the mean and covariance information of the network parameters; Cable force identification and uncertainty quantification: The input parameters of the cable to be tested are input into the trained Bayesian neural network, and the cable force prediction result and its corresponding uncertainty interval are output to realize cable force identification and uncertainty quantification.

[0009] Furthermore, millimeter-wave radar obtains the vibration displacement of the cable-stayed bridge by measuring the phase change of the radar echo signal. The displacement calculation relationship satisfies the following: the displacement change of the cable-stayed bridge is calculated by the functional relationship between the radar operating wavelength and the phase difference between the previous and next times.

[0010] Furthermore, the method for calculating the displacement change of the stay cable is as follows: Select a certain moment as the benchmark Based on the difference between the phase of the radar image at subsequent times and the reference phase, the displacement change of the observation point is calculated. : in, Let R be the radar operating wavelength, h be the straight-line distance between the radar wave emission point and the observation point, and h be the radar incident angle. The phase difference between the two observations is expressed as: ; in, For the observation point to undergo downward deformation, =R / h is the projection of the cable displacement onto the radar wave transmission path.

[0011] The inference process of a Bayesian neural network is described by a feedforward neural network, which includes an input layer, a hidden layer, and an output layer.

[0012] By using a linear combination of Gaussian random variables, we obtain Z The mean vector, variance matrix, and covariance matrix of .

[0013] Furthermore, in the forward propagation of the BNN, assuming that the network weights and bias parameters both follow a Gaussian distribution, when the activation function is a linear rectified function, the distribution of the network parameters is expressed as: ; and Let represent the expected value vector and covariance matrix of parameter θ, respectively, where θ contains the weights and biases of all hidden layers in the BNN; Given the Gaussian prior, the joint probability distribution of the parameters and the observed samples is as follows: ; in, and These are the expected value vector and covariance matrix of the observed samples, respectively. =cov(Y,θ); When the observed sample Y is known, the conditional distribution of the parameters is as follows: 。

[0014] Furthermore, an RTS smoother is used to recursively solve for the hidden layer neurons. The solution process for each hidden layer neuron is as follows: ; Furthermore, the recursive solution process for the hyperparameters of the network model is as follows: Furthermore, it also includes: judging the prediction performance of the network after training based on the error index of the theoretical cable force and the model predicted cable force of the test sample.

[0015] The technical solution provided by this invention has the following advantages compared with the known prior art: (1) Combining the good penetration performance of radar waves into the cable covering medium, the millimeter-wave radar device can effectively realize non-contact measurement of the cable vibration signal, which improves the accuracy and reliability of cable natural frequency identification. (2) Assuming that the weights and bias parameters of BNN are random variables that follow a Gaussian distribution, the posterior distribution of the network hyperparameters can be optimized by using an approximate Gaussian inference algorithm, which can significantly reduce the complexity of network training. (3) By inputting the measured cable parameters and natural frequency into the trained BNN model, high-precision prediction of cable force can be achieved, and the uncertainty of cable force identification caused by boundary conditions and other factors can be quantified. Attached Figure Description

[0016] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the accompanying drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are merely some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without any creative effort.

[0017] Figure 1 This is a flowchart of the cable force test of the present invention.

[0018] Figure 2 This is a basic architecture diagram of the feedforward neural network of the present invention.

[0019] Figure 3 This is a diagram illustrating the Gaussian approximation theory in the BNN network propagation of this invention.

[0020] Figure 4 This is a flowchart of the cable force recognition based on BNN-AGI of the present invention.

[0021] Figure 5a This is the first-order mode shape diagram of the present invention.

[0022] Figure 5b This is the second-order mode shape diagram of the present invention.

[0023] Figure 5c This is the third-order mode shape diagram of the present invention.

[0024] Figure 6 The cable frequency of the present invention and Relationship diagram.

[0025] Figure 7a This is a diagram showing the different numbers of neurons in this invention.

[0026] Figure 7b This is a diagram showing different numbers of hidden layers in this invention.

[0027] Figure 8a This is the posterior distribution diagram of the cable force C1 of the present invention.

[0028] Figure 8b This is the posterior distribution diagram of the cable force C2 of the present invention.

[0029] Figure 8c This is the posterior distribution diagram of the cable force C3 of the present invention.

[0030] Figure 8d This is the posterior distribution diagram of the cable force C4 of the present invention.

[0031] Figure 9 This is a bridge layout diagram for the present invention.

[0032] Figure 10 This is a diagram showing the tensioning and monitoring of stay cables during bridge construction according to the present invention.

[0033] Figure 11a This is a diagram showing the initial tensioning condition of the cable DS3 of the present invention.

[0034] Figure 11b These are two working condition diagrams for the DS3 cable of the present invention.

[0035] Figure 12a This is a diagram showing the initial tensioning condition of the cable DS3 of the present invention.

[0036] Figure 12b These are two working condition diagrams for the DS3 cable of the present invention. Detailed Implementation

[0037] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0038] As the core load-bearing component of cable-stayed bridges, the mechanical state of cables is a key indicator for assessing structural damage and identifying potential risks. Therefore, accurate monitoring of cable forces is crucial for the long-term operational safety of cable-stayed bridges.

[0039] To accurately identify the stress state of cables, common cable force measurement methods include the frequency method, pressure sensor method, and magnetic flux method. Among these, the frequency method has become the most widely used cable force identification method due to its advantages such as high measurement accuracy, low cost, and reusability. Its principle is to identify cable force by establishing a mapping relationship between cable force and cable vibration frequency.

[0040] In current research, cable force is identified as a fixed value. However, in actual engineering, due to the effects of variable loads such as wind and vehicles, cable force is usually not a fixed value. Further research is needed on the identification of cable force under the influence of uncertain factors.

[0041] To address the uncertainty in cable force recognition, some scholars have introduced Bayesian theory into the field of cable force recognition, using the posterior probability density function to explicitly model the parameter uncertainty.

[0042] For example: The modal parameters of the cable are automatically identified by combining the Bayesian FFT algorithm and a lightweight frequency band automatic selection network.

[0043] Based on Bayesian theory, analytical expressions for identifying uncertainties in cable force and bending stiffness are derived. The physical vibration model of the cable is embedded into the Bayesian framework to achieve uncertainty identification of cable force and bending stiffness.

[0044] By using Bayesian inference to identify the uncertainty of boundary conditions, and by constructing a cable force model through an artificial neural network to output the probability distribution of cable force, the uncertainty of cable boundary conditions and cable force is quantified.

[0045] A dynamic monitoring method for cable vibration frequency based on a Bayesian inference model combined with the Metropolis-Hastings (MH) sampling algorithm is proposed to adaptively identify cable stress damage in bridges.

[0046] In probability-based structural parameter and operational status prediction, BNN combines the advantages of traditional neural networks and Bayesian methods. While improving the computational efficiency of the model, it can capture the uncertainty in the data or model and quantify the uncertainty by solving the posterior distribution.

[0047] To improve the reliability of cable force identification results under complex boundary conditions, this paper constructs a method for cable force identification and uncertainty quantification under complex boundary conditions based on a Bus-Neural Network (BNN). A BNN model is constructed with cable natural frequencies, geometric and physical parameters as inputs and cable force as output. Then, the AGI algorithm is used to optimize the posterior distribution of the network hyperparameters. Finally, leveraging the advantages of millimeter-wave radar technology in cable natural frequency testing, rapid identification and uncertainty quantification of cable forces in stay cables are achieved.

[0048] To enhance the reliability of cable force identification results under complex boundary conditions, a method for cable force identification and uncertainty quantification based on Bayesian neural network (BNN) and Approximate Gaussian Inference (AGI) is proposed.

[0049] First, the dynamic displacement response of the cable-stayed bridge is acquired using millimeter-wave radar, and its natural frequency is identified. Then, a BNN model is constructed with the cable's natural frequency, geometric and physical parameters as inputs and the cable force as the output. The training sample set of the network is obtained through random sampling and finite element analysis. Finally, using the training samples as inputs, the AGI algorithm is used to optimize the posterior distribution of the hyperparameters of the network model.

[0050] Since this algorithm eliminates the need for backpropagation and performs analytical Gaussian inference on network parameters using the Gaussian assumption, it significantly improves the optimization efficiency of the BNN model. After network optimization, the measured cable parameters are used as input to the BNN model. Leveraging the randomness of the posterior distribution of the network parameters, the identification and uncertainty quantification of the cable forces are achieved. To verify the feasibility and accuracy of the method, numerical simulations are performed on a single cable, and the reliability of the method is further validated through field experiments on cable stays.

[0051] The research results show that the BNN model optimized based on the AGI algorithm can significantly improve the reliability of the cable force identification results and quantify the uncertainty caused by factors such as boundary condition errors.

[0052] The present invention will be further described below with reference to embodiments.

[0053] Example 1 (see Figure 1-1 2): A method for cable force identification and uncertainty quantification based on multi-sensor information fusion and BNN, comprising at least: Step 1: Identification of the natural frequency of the stay cable based on millimeter-wave radar S1.1) Cable force identification based on frequency method includes the following steps: For a cable tensioned at both ends, neglecting the effect of its own sag, the differential equation of the cable's vibration can be expressed by the following equation 1: In the formula: EI represents the bending stiffness of the cable, T is the cable force; m is the mass per unit length of the cable; y(x,t) represents the vertical displacement of each point on the cable at time t.

[0054] The boundary conditions for the long cables in a cable-stayed bridge can be considered as hinged at both ends. In this case, the solution to Equation 1 is given in Equation 2: Furthermore, for stay cables with a large slenderness ratio, the influence of bending stiffness EI can be neglected. At this point, the classical cable force model based on tensioned chord theory is obtained, Equation 3: in, f n It is the first n First natural frequency, n It is the vibration order ( n =1 corresponds to the fundamental frequency. n =2 corresponds to the first harmonic frequency, and so on.

[0055] In practical engineering, the actual boundary conditions of cables differ significantly from the idealized hinged assumption, typically exhibiting a complex elastic boundary state: the cable possesses a certain rotational capacity under stress, but this capacity is not unconstrained; rather, it is limited by the boundary rotational stiffness. Therefore, by modifying Equation 3, we can obtain the cable force formula under elastic constraints, namely Equation 4: in, , For elastic stiffness parameters, It is a dimensionless parameter that combines the bending stiffness of the cable with the cable force and the cable length, reflecting the relative influence of the cable bending effect on vibration.

[0056] S1.2) Cable vibration displacement measurement and frequency identification based on millimeter-wave radar, including the following steps: Compared to traditional contact vibration testing methods, millimeter-wave radar can perform multi-point and multi-angle measurements on stay cables according to calculation requirements, which is highly efficient and reduces the influence of cable end dampers. In addition, millimeter-wave radar has excellent penetration capabilities, enabling it to directly measure the vibration characteristics of cables through coverings, with high measurement accuracy, especially advantageous for short cable vibration testing. Its working principle is as follows: Figure 1 As shown, by Figure 1 As shown, a certain moment is selected as the reference. The displacement change of the observation point can be calculated based on the difference between the phase of the radar image at subsequent times and the reference phase. As shown in equation 5: in, For radar operating wavelength, Represents any measurement time t s The phase value of the radar receiving the cable echo changes in real time with the cable vibration; the greater the cable displacement, the greater the phase difference. When using millimeter-wave radar to measure the vibration displacement of the cable, assume the straight-line distance between the radar wave emission point and the observation point is R, the elevation difference is h, and the radar incident angle is... Then the phase difference between the two observations can be expressed as (Equation 6): in, For the observation point to undergo downward deformation, =R / h is the projection of the cable displacement onto the radar wave propagation path. The radar echo phase at the second observation time is the real-time phase value measured by the radar at the same observation point after the cable experiences a slight vibration. This indicates the radar echo phase at the moment of the first observation.

[0057] Because of its short operating wavelength and high phase measurement accuracy, the radar can achieve a vibration displacement measurement accuracy of 0.01 mm for cable-stayed bridges. After acquiring the vibration displacement data of the cable-stayed bridge using millimeter-wave radar, a fast Fourier transform can be used to identify the frequency of the cable-stayed bridge. The testing procedure is as follows: Figure 1 As shown.

[0058] Step 2: Force Identification and Uncertainty Quantification Based on Bayesian Neural Network (BNN) S2.1) Bayesian Neural Network (BNN), including the following steps: Traditional neural networks typically output deterministic point estimates, making it difficult to effectively assess the confidence or uncertainty of their predictions. BNNs, however, employ probabilistic modeling, treating the weight coefficients W and biases b in the network as random variables controlled by probability distributions, thereby quantifying the uncertainty in the model's predictions. This embodiment will describe the inference process of a BNN using a feedforward neural network. The basic architecture of a multi-hidden-layer feedforward neural network is as follows: Figure 2 As shown. By Figure 2 As we know, a feedforward neural network typically includes an input layer, a hidden layer, and an output layer. Assuming... j Layer neurons, weights, and bias parameters are respectively 、 and Then the weighted input of layer (j+1) enter It can be expressed as (Equation 7): , in, It is the linear output of the nth neuron in the (j+1)th layer. This represents the connection weight between the k-th neuron in the j-th layer and the i-th neuron in the (j+1)-th layer. The activation output value of the k-th neuron in the j-th layer is the final output of the neuron after performing a linear weighted summation, bias compensation, and nonlinear mapping of the activation function on the input signal. It reflects the extraction result of the input features by the neuron. It is the bias value of the i-th neuron in the (j+1)-th layer. Its function is to compensate for the intercept of the linear transformation and prevent the model from only fitting functions that pass through the origin.

[0059] Introducing matrices and Then, equation 7 above can be written as equation 8 below:

[0060] in, The linear pre-output (before activation) of the (j+1)th layer neuron is the final result we want to obtain, which is then transformed by ReLU. . The artificially introduced weight-activation value integration matrix serves to integrate the weight matrix... With activation output The product result is adapted for dimension and linearly mapped to simplify the writing. The weight matrix of the j-th layer With activation output vector The vectorized expansion result (converting the result of matrix multiplication from two dimensions into a one-dimensional column vector) is Input. The artificially introduced bias term integration matrix serves to adjust the biased random vector. Perform a linear mapping so that its dimension is the same as the linear mapping. , They are consistent and satisfy the rules of addition.

[0061] By using a linear combination of Gaussian random variables, we can obtain Z mean vector variance matrix Covariance Matrix They are respectively: Formula 9: Formula 10: Formula 11: In the formula, θ = (W, B); Random vector The mean vector, It is the vectorized result of the product of the weight and the activation value. Biased random vector The mean vector (in BNN) It follows a Gaussian distribution. E: Mathematical expectation (mean), which is the average of a random variable or vector, and is one of the core parameters describing the Gaussian distribution. The covariance matrix of the result of "weights × activation values". T: transpose, e.g. that is The transpose of the matrix ensures dimension matching for matrix multiplication (e.g., a 15×225 matrix can only be multiplied by a 225×15 matrix). : The covariance matrix of the bias vector, describing the dispersion of the neuron's bias values. cov: covariance, for example... It is a description The correlation. : The vectorized result of the weight matrix of the j-th layer × the activation output vector; It is a column vector, where the superscript (j) indicates that it belongs to the j-th layer of the network, and is used to compute the linear pre-output of neurons in the (j+1)-th layer. . The covariance matrix of (the vectorized result of weights × activation values) and θ.

[0062] The activation function is locally linearized to reduce computational cost (Equation 12): ,formula: (Z) For the sake of mathematical simplicity, g(Z) is replaced by a tangent line to replace the curve of the original function. : is the activation output vector of the (j+1)th layer neuron in a Bayesian neural network (BNN).

[0063] The above formula can be further expressed as (Formula 13):

[0064] in, Jacobian matrix: the activation function at the mean point The derivative matrix at point .

[0065] : The mean vector (obtained by Equation 9).

[0066] in J It is a Jacobian matrix, which can be defined as (Equation 14):

[0067] The diagonal matrix construction operator "flattens" the input column vector onto the diagonal of the matrix, with all off-diagonal elements set to 0. It is the gradient operator, and its complete form is: , which represents the gradient (derivative) of the activation function g(z) with respect to the variable z.

[0068] Similarly, through linear combinations of Gaussian random variables, A mean vector variance matrix Covariance Matrix They are represented as follows: Formula 15:

[0069] Formula 16:

[0070] in, : Linear pre-output of the (j+1)th layer; The covariance matrix (obtained from Equation 10). var( right Operators for finding the covariance matrix. : The diagonal Jacobian matrix of the activation function at the mean point (defined by Equation 14) represents the linearized slope matrix. Linear pre-output of layer j+1 The covariance matrix with parameter θ (obtained by Equation 11).

[0071] Formula 17:

[0072] Once the BNN model is built, it can be trained using a training sample set to obtain the optimized network weights and bias parameters. However, accurately obtaining the posterior distribution of BNN model parameters is often difficult, especially for complex network structures. Therefore, approximate inference algorithms are needed to obtain the posterior distribution of network parameters. Commonly used posterior inference algorithms include expectation propagation, variational inference, and Laplace approximation. These posterior estimation methods transform the parameter inference problem into a gradient-based optimization process, which may lead to potential overfitting and low continuous learning efficiency. Furthermore, Monte Carlo Dropout provides another approach for estimating the posterior distribution of network weights by randomly dropping neurons to approximate the posterior distribution of model parameters. However, this method is limited by its inability to provide analytical expressions for network weights and biases. Therefore, this paper proposes to use the AGI algorithm to optimize and solve for the posterior distribution of network parameters. Since this algorithm does not require backpropagation and performs analytical Gaussian inference of network parameters using the Gaussian assumption, it can significantly improve the training efficiency of the BNN model.

[0073] 2.2) Solving the posterior distribution of BNN hyperparameters based on Approximate Gaussian Inference (AGI) In the forward propagation of a BNN, it is assumed that the weights and bias parameters of the network follow a Gaussian distribution. When the activation function is a linear rectified function (ReLU), the output of each layer can be approximated as a Gaussian distribution under the Gaussian prior assumption. The forward propagation process of the network is shown in Figure 3. At this time, the distribution of the network parameters can be expressed as (Equation 18): In equation (18), and Let represent the expected value vector and covariance matrix of the model parameters θ, respectively, where θ contains the weights and biases of all hidden layers in the BNN. The prior probability distribution of the model parameter θ represents our prior knowledge of the parameter values ​​before observing the data. N represents a multivariate Gaussian distribution.

[0074] Given the Gaussian prior, the joint probability distribution of the parameters and the observed samples is shown in the equation.

[0075] Formula 19: Wherein, P( The probability that network weight bias θ and cable force data Y occur simultaneously; The transpose of the matrix, and These are the expected value vector and covariance matrix of the observed samples, respectively. = cov(Y,θ). When the observed sample Y is known, the conditional distribution of the parameters is shown in Equation 20.

[0076] P Conditional probability density: Given the cable force Y, find the probability of the network parameter θ. Conditional mean, the most likely average value of parameter θ after training; Conditional covariance: the magnitude of uncertainty in parameter θ after training.

[0077] The conditional mean vector and the oblique variance matrix in Equation 20 can be further expressed as: Equation 21: Equation 22: in, The average value of the initial parameters of the network at the beginning; The degree of correlation between cable force data and network parameters; : The inverse matrix of data covariance; the smaller the data noise, the larger the weight; Y: Measured cable force value; The uncertainty (dispersion) of the model parameter θ after combining the measured value of cable force Y.

[0078] To achieve recursive parameter solving, this embodiment uses an RTS smoother to recursively solve for the hidden layer neurons. The solution process for each hidden layer neuron is shown in Equations 23-26. Specifically: Equation 23: Among them, P Conditional probability density, given the force data Y, the probability distribution of the hidden layer neurons Z; The optimal average value of neurons in the j-th hidden layer; Conditional covariance, the magnitude of uncertainty in neurons of the j-th hidden layer.

[0079] Formula 24:

[0080] in, most Ultimately, the more accurate average value of hidden layer j is obtained. : The mean of the j-th layer before correction (prior), the initial mean before correction; : The strength / weight of the correction.

[0081] Formula 25: in, The corrected covariance of the j-th layer (posterior), representing the final uncertainty of the current layer; : The covariance of the j-th layer before correction (prior), the original uncertainty of the current layer; : Covariance before the next layer correction, and the original uncertainty of the next layer.

[0082] Equation 26: in, The covariance of parameter θ with the next layer neuron Z, and the degree of correlation between the parameter and the next layer neuron.

[0083] Similarly, the recursive solution process for the hyperparameters of the network model is shown in Equations 27-30: Equation 27: in, : The posterior mean of parameter θ, the final optimal average value of the parameters after training.

[0084] Equation 28: in, : The posterior mean of parameter θ, the final optimal average value of the parameters after training; The prior mean of parameter θ, the initial average value of the parameter; Gain matrix, representing the strength and weight of the correction; : Posterior mean of neurons in the next layer, the accurate value of the next layer after correction; The initial value of the next layer that has not been corrected.

[0085] Equation 29:

[0086] in, The posterior covariance of parameter θ represents the final uncertainty of the parameter given the observed data. : The prior covariance of parameter θ, the initial uncertainty of the parameter.

[0087] Formula 30:

[0088] In the above equations, since both the hidden layer neurons and the hyperparameter matrix are diagonal matrices, the computational complexity of the model when using the AGI algorithm to solve for the above parameters is only Ω(n), where n represents the number of hyperparameters. During hyperparameter estimation, the hyperparameters optimized in the previous iteration will serve as prior information for the hyperparameters in the current step. When the marginal likelihood (DV) of the test dataset reaches its maximum, the iteration process terminates, and the optimized hyperparameter vector is shown in Equation 31. After the BNN hyperparameters are corrected, the corrected BNN can be used to predict the cable force under the new input parameters, and Equation 31 becomes: in argmax: The variable that takes the maximum value, finding the value that maximizes the integral. ; : The set of hyperparameters, the sum of the empirical mean and the prior covariance; f( Likelihood function, given input data When the network parameter θ is used, output cable force data. The probability measures how well the model fits the cable force data; The parameter prior distribution, the parameter θ follows a hyperparameter. Distribution; : Input data set, used to predict cable forces.

[0089] 2.3) Identification of cable forces and quantification of uncertainties in stay cables Key parameters affecting the identification of cable tension include: Cable length l, linear density m, bending stiffness EI, cable natural frequency (i=1,2,…, ); When the slenderness ratio of the cable is large, the influence of bending stiffness on the calculation results can be ignored. Therefore, this embodiment uses cable length l, linear density m, and the first k natural frequencies as parameters. As input and cable force T as output, a cable force prediction model based on a BNN is constructed. Then, based on the network training samples and the AGI algorithm, the network weights and bias parameters of the initial BNN model are optimized. Through multiple iterations of optimization, the random distribution of the network hyperparameters is obtained. Furthermore, the trained BNN model is used to identify the cable force and quantify its uncertainty. The cable force identification process based on BNN is as follows: Figure 4 As shown.

[0090] To evaluate the predictive performance of BNN, this study intends to use an error index. The prediction error of the quantified network model is defined by the error index shown in Equation 32: In the formula, The measured cable force value of the i-th sample. The BNN model predicts the cable force value for the i-th sample. represents the mean cable force of the test samples; represents the theoretical cable force and the model-predicted cable force of the test samples, respectively; r represents the number of test samples. The smaller the calculated error index value, the better the prediction performance of the trained network.

[0091] Step 3: Numerical Simulation 3.1) Simulation and Parameter Analysis of Cable-Stayed Cable Element This embodiment conducts numerical simulation on a 4m long cable and establishes a finite element model of the cable element using finite element software.

[0092] The cable was simulated using Beam3 elements with a cross-sectional diameter of 6 mm. The elastic modulus and linear density of the cable were assumed to be as follows: The initial cable force T0 was 800 kN, and the cable was subjected to a stress of 0.15 kg / m and the initial stress method was used to simulate the cable force application process. The cable ends were subjected to hinged constraints.

[0093] By performing modal analysis, the first three bending modes of the cable were obtained, as shown in 5(a)-(c).

[0094] As shown in Figure 5, when the cable ends are hinged, the first three natural frequencies of the cable are 9.172 Hz, 18.614 Hz, and 28.572 Hz, respectively. However, in practical engineering applications, the constraint conditions at the cable anchorage end are often very complex and not ideal hinged or fixed forms. Inappropriate boundary simulation may cause errors in cable force identification.

[0095] Therefore, to investigate the influence of the rotational stiffness of the cable anchorage end on frequency identification, the cable finite element model described in this embodiment is used as the basic structure, and different rotational constraint stiffnesses are investigated. Modal analysis was performed on the cable, and the first three natural frequencies of the cable were obtained as follows: Figure 6 As shown.

[0096] Depend on Figure 6 It can be seen that when the value is 100, its first three frequencies are equal to the theoretical values ​​of the hinged boundary conditions: 9.172 Hz, 18.614 Hz, and 28.572 Hz; then, with the rotational constraint stiffness... As the value increases, the natural frequency of the cable generally shows a trend of first increasing and then stabilizing; when When the value is greater than 10⁶, the first three frequencies of the cable approach the theoretical values ​​under the consolidated boundary condition, which are 9.793 Hz, 19.871 Hz, and 30.504 Hz, respectively. Compared with the hinged boundary condition, the changes in the first three frequencies of the cable are 6.77%, 6.75%, and 6.76%, respectively. Based on the above analysis results, different boundary condition forms have a certain influence on the natural frequency of the cable. If the influence of the boundary conditions is ignored, it may cause the cable force identification results to deviate from the true values. Therefore, in order to ensure the reliability of the cable force identification results, it is necessary to further consider the influence of the randomness of the boundary conditions on the cable force identification results and quantify the uncertainty of the cable force identification results.

[0097] In the generation of training samples for the BNN model, the parameter values ​​of the cable unit are shown in Table 1. Furthermore, in this study, since millimeter-wave radar obtains the natural frequencies of the cable unit by measuring the micro-vibration signals of the cable, and displacement response often has low-frequency characteristics compared to acceleration signals, the first three natural frequencies of the cable unit are selected for cable force identification. Then, based on the hyper-Latin cube sampling algorithm, 1000 sets of parameter sample combinations for the cable model are randomly generated, and modal analysis is further performed to obtain the cable frequency information under each parameter combination. Based on the above analysis, the parameters are obtained... For input, sol This is the output training sample set. Based on the generated training sample set, the AGI algorithm can be used to further optimize the hyperparameters of the initial BNN model.

[0098] Table 1. Range of values ​​for cable parameters 3.2) BNN Hyperparameter Optimization and Cable Force Prediction Based on AGI Algorithm In the initial BNN model construction, in order to explore the relationship between the number of hidden layer neurons, the number of layers and the model prediction accuracy, this embodiment identifies the optimal network model architecture from the two perspectives of model prediction accuracy and computational efficiency.

[0099] Using the training sample set generated in step 3.1 as input, we study the prediction accuracy and computational efficiency of the BNN model under different numbers of hidden layers and different numbers of network nodes.

[0100] The number of hidden layers in the initial network was set to 2 to investigate the impact of different network node numbers on the model's prediction results. During network training, 1000 training datasets were divided into training and test sets at a 9:1 ratio. The number of epochs during training was set to 20. The mean of the initial weights and biases of the BNN was set to 0.3, and the standard deviation of each parameter was uniformly set to 0.5. Then, the network hyperparameters were optimized for six different scenarios with 5, 10, 15, 20, 25, and 30 hidden layer nodes.

[0101] To perform network training under the above conditions, the computing device used was an Intel(R) Core(TM) i7-10700 (2.90GHz) CPU with 16GB of memory. The BNN prediction results obtained under each condition are shown in Figure 7(a).

[0102] As shown in Figure 7, when the number of hidden layers is 2, as the number of neurons increases, the test set... The calculation results show a trend of first decreasing and then stabilizing. Among them, the prediction error reaches its minimum when the number of hidden layer nodes is 15, with a minimum prediction error of 1.85%.

[0103] Furthermore, as the number of neurons increases, the network training time also increases. For the six scenarios mentioned above, the training time to complete a single epoch increases from 6.94s to 7.98s. Specifically, when the number of nodes is 15, the training time to complete a single epoch is 7.13s. Therefore, in this study, the optimal number of neurons for the BNN model is set to 15.

[0104] Similarly, this embodiment further studies the prediction performance of BNN under different hidden layer conditions. The number of hidden layer neurons is set to 15, and then the network prediction performance under the conditions of 1 to 5 hidden layers is studied. Based on the training set and the AGI algorithm, the network prediction results under each condition are shown in Figure 7(b).

[0105] As shown in Figure 7(b), with the increase of the number of hidden layers, the calculated value of the network prediction error Er shows a trend of first decreasing rapidly and then gradually stabilizing.

[0106] Specifically, when the number of hidden layers increased from 1 to 2, the network prediction error decreased from 3.74% to 1.85%; subsequently, as the number of hidden layers in the BNN increased, the network prediction error eventually decreased to 1.71%.

[0107] However, as shown in Figure 7(b) regarding network optimization time, when the number of hidden layers increases to 5, the training time for a single epoch is 13.75s, which is 92.84% longer than when there are 2 hidden layers. Meanwhile, the prediction error of the trained network on the test set only decreases by 0.54%.

[0108] Meanwhile, setting too many hidden layers may cause BNN to overfit, thus reducing the network's generalization ability. Therefore, considering both the prediction accuracy and optimization efficiency of the BNN model, the optimal number of hidden layers is set to 2.

[0109] Further construct a system based on cable length l, linear density m, elastic modulus E, cable cross-sectional diameter d, and rotational constraint stiffness. and the first three natural frequencies of the cable ( , , A cable force prediction model for cable stays with ) as input and cable force T as output.

[0110] Then, based on the training data generated in step 3.1, the posterior distribution of the hyperparameters of the prediction model is optimized by executing the AGI algorithm. Substituting the optimized hyperparameters into the BNN model enables cable force prediction based on the BNN.

[0111] To verify the reliability of the cable prediction model, four sets of cables were selected as test objects, and the cable parameters are set as shown in Table 2.

[0112] Meanwhile, considering the modal testing errors present in actual engineering, a random error of ±2% is added to the modal analysis results of the finite element model. Then, the obtained four sets of cable parameters are input into the trained BNN model to predict the cable force. However, due to the parameters... This parameter is often difficult to obtain in actual cable tension tests, therefore it is uniformly set to... Then, based on the trained BNN model, cable force prediction under unknown boundary parameters was achieved, and the prediction results are shown in Table 2. Additionally, based on the cable force prediction results in Table 2, 5000 sets of posterior cable force samples were randomly generated, as shown in Figure 8. Table 2 shows that the trained BNN model can accurately predict cable force values ​​under different combinations of cable parameters. The largest cable force prediction error occurred in group 4, at 5.58%. The main reasons for the large prediction error in this group include: In the parameter settings of this cable element, the rotational constraint stiffness is set to... The boundary conditions are approximately hinged, similar to the BNN model. The assumed values ​​deviate significantly; The 2% modal testing bias was considered, which further increased the prediction error. The posterior distribution of the predicted cable force is shown in Figure 8. The comparison with the theoretical value shows that, despite the unknown boundary parameters and the presence of testing errors, the BNN-based prediction model can still reliably provide the predicted cable force.

[0113] Table 2. Cable force prediction results based on BNN Step 4: Experimental Verification 4.1) Project Overview To further verify the reliability and applicability of the method proposed in this embodiment, this study takes the main bridge project of the Yinghe Grand Bridge of the Fuhuai Railway under construction as the research background and conducts research on cable force identification and uncertainty quantification during the construction of the main span steel box girder of the cable-stayed bridge.

[0114] The main bridge of Yinghe Grand Bridge adopts a high-low tower double cable-stayed bridge structure with a span arrangement of (31+73+230+114+40)m. It is a semi-floating system. The overall layout of the main bridge is shown in Figure 8.

[0115] The main beam above the navigation channel adopts a steel-concrete composite beam structure, while the remaining beam segments are prestressed concrete box girder structures. The main bridge towers adopt an H-shaped vase tower design, with tower heights of 83.4m and 115.1m respectively.

[0116] The lower tower has 18 pairs of stay cables, and the higher tower has 24 pairs. The cable spacing on the steel-concrete composite beam is 10.5m, and on the concrete beam it is 8.0m. The cable moment on the tower ranges from 1.8 to 4.5m. The stay cables are arranged in a fan shape longitudinally, with cable lengths ranging from 40.91m to 146.01m. The cables are epoxy-coated parallel wire cables with a tensile strength of 1770MPa, a parallel wire diameter of 7mm, and an elastic modulus of 2.05×10⁵MPa. During the cantilever assembly of the main beam, each stay cable was tensioned twice, once after the beam segment welding and once after the concrete pouring. The stay cables were tensioned at the tower end using a tower-end tensioning technique, with four jacks used for synchronous symmetrical tensioning. After tensioning under each condition, the cable force was synchronously checked using jack pressure gauge readings, vibration testing, and millimeter-wave radar. On-site test photos are shown below. Figure 10 As shown.

[0117] Two stay cables were selected from both the low tower side and the high tower side for the study. The design parameters of the selected stay cables are shown in Table 3.

[0118] Based on the design parameters, finite element models of the four stay cables were established, and 1000 sets of training samples were randomly generated for model training. After obtaining the training sample sets for each tension condition of the stay cables, a cable prediction model based on a BNN was further established. Then, combined with the cable training data, the hyperparameters of the BNN model under each tension condition were iteratively optimized using the AGI algorithm to obtain the optimized hyperparameters. Similar to numerical simulation, in network training, the 1000 sets of training data were divided into training and test sets in a 9:1 ratio, the number of epochs was set to 20, the mean of the initial weights and bias terms of the BNN was set to 0.3, and the standard deviation of each parameter was uniformly set to 0.5. After the network model optimization is completed, the measured cable parameters and modal test results can be input into the prediction model to achieve rapid prediction of the stay cable force.

[0119] Table 3 Design parameters for cable stays 4.2) Cable force identification and uncertainty quantification based on BNN under different tensioning conditions In order to identify the cable force under the tensioning condition of the Yinghe Grand Bridge, the micro-vibration signal of the cable was non-contactly measured using millimeter-wave radar equipment during the tensioning period. The sampling frequency was set to 100Hz. The typical time-lapse curves of the DS3 cable under the single-tension and double-tension conditions are shown in Figures 11(a)~(b).

[0120] The obtained displacement-time history curves were further subjected to fast Fourier transform, and the obtained spectrum analysis results are shown in Figures 12(a)~(b).

[0121] As shown in Figure 12, the first three natural frequencies of the DS3 stay cable after one tensioning cycle are 1.114Hz, 2.204Hz, and 3.305Hz, respectively, and the natural frequencies after two tensioning cycles increase to 2.069Hz, 4.133Hz, and 6.184Hz, respectively. Similarly, the first three natural frequencies of the four stay cables under various tensioning conditions, obtained based on millimeter-wave radar, are shown in Table 4.

[0122] Meanwhile, a contact-type cable force gauge was used to verify the natural frequency of the cable, such as... Figure 10 As shown, the test results are basically consistent with those of the millimeter-wave radar. Furthermore, in actual construction, data from on-site anchor point coordinate positioning and cable weighing showed that the length deviation of the four stay cables was between 0.15% and 0.3%, and the linear density deviation was between 1.8% and 2.1%.

[0123] The measured cable parameters and natural frequencies were input into the optimized BNN model, and the predicted cable force results are shown in Table 4. Considering the tensioning error of the cable, the tension value of the hydraulic jack was used as the measured cable force value under each working condition in this study. By comparing with the BNN predicted values, it can be seen that the maximum deviation between the average predicted cable force and the measured cable force value is only 4.21%, and the measured values ​​are all within the 95% confidence interval of the predicted values.

[0124] Therefore, based on the above analysis results, the cable force prediction model proposed in this paper can accurately identify the cable force of the cable and quantify the identification uncertainty caused by factors such as the cable and its boundary condition parameters.

[0125] Table 4. Cable force prediction results under different working conditions In summary, to address the challenge of cable force identification under complex boundary conditions, a method for cable force identification and uncertainty quantification based on multi-sensor information fusion and BNN (Browser Neural Network) is proposed. This method constructs a BNN-based cable force prediction model and utilizes a non-contact method based on millimeter-wave radar to obtain the natural frequencies of the cables, thereby achieving accurate cable force prediction. Based on numerical simulation and actual bridge cable force test results, the following conclusions are drawn: (1) Combining the good penetration performance of radar waves into the cable covering medium, the millimeter-wave radar device can effectively realize non-contact measurement of the cable vibration signal, which improves the accuracy and reliability of cable natural frequency identification. (2) Assuming that the weights and bias parameters of BNN are random variables that follow a Gaussian distribution, the posterior distribution of the network hyperparameters can be optimized by using an approximate Gaussian inference algorithm, which can significantly reduce the complexity of network training. (3) By inputting the measured cable parameters and natural frequency into the trained BNN model, high-precision prediction of cable force can be achieved, and the uncertainty of cable force identification caused by boundary conditions and other factors can be quantified.

[0126] Furthermore, if the aforementioned function is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, or the part that contributes to the prior art, or a part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0127] The logic and / or steps represented in the flowchart or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing logical functions, and can be embodied in any computer-readable medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (such as a computer-based system, a processor-including system, or other system that can fetch and execute instructions from, an instruction execution system, apparatus, or device). For the purposes of this specification, "computer-readable medium" can be any means that can contain, store, communicate, propagate, or transmit programs for use by, or in conjunction with, an instruction execution system, apparatus, or device.

[0128] More specific examples of computer-readable media (a non-exhaustive list) include: electrical connections (electronic devices) having one or more wires, portable computer disk drives (magnetic devices), random access memory (RAM), read-only memory (ROM), erasable and editable read-only memory (EPROM or flash memory), fiber optic devices, and portable optical disc read-only memory (CDROM). Furthermore, computer-readable media can even be paper or other suitable media on which the program can be printed, because the program can be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting, or otherwise processing as necessary, and then stored in computer memory.

[0129] Furthermore, in order to provide a concise description of exemplary embodiments, not all features of actual embodiments (i.e., those features that are not relevant to the best mode of carrying out the invention as currently considered, or those features that are not relevant to implementing the invention) may be omitted.

[0130] It should be understood that numerous specific implementation decisions can be made during the development of any practical implementation, such as in any engineering or design project. Such development efforts may be complex and time-consuming, but for those skilled in the art who benefit from this disclosure, the development effort will be a routine work of design, manufacturing, and production without requiring much experimentation.

[0131] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions will not cause the essence of the corresponding technical solutions to deviate from the protection scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for cable force recognition and uncertainty quantification based on multi-sensor information fusion and BNN, characterized in that, include: Natural frequency identification of cable stays: The vibration displacement of the cable stays is measured by millimeter-wave radar. The vibration displacement time history data of the cable stays is calculated based on the phase difference of the radar echo at different times. The vibration displacement time history data is then subjected to spectrum analysis to obtain at least the first few natural frequencies of the cable stays. Training sample construction: A cable force recognition sample dataset is constructed based on the cable length, linear density and natural frequency, where the sample output is the corresponding cable force value; Bayesian Neural Network Construction: A cable force identification sample dataset is constructed based on the cable length, linear density, and natural frequency, where the sample output is the corresponding cable force value; wherein, the cable length, linear density, and natural frequency are used as input variables, and the cable force is used as the output variable to construct a Bayesian neural network model, and the network weight parameters and bias parameters are modeled as random variables; Posterior distribution of network parameters: Based on the approximate Gaussian inference algorithm, the posterior distribution of the weight parameters and bias parameters of the Bayesian neural network is estimated to obtain the mean and covariance information of the network parameters; Cable force identification and uncertainty quantification: The input parameters of the cable to be tested are input into the trained Bayesian neural network, and the cable force prediction result and its corresponding uncertainty interval are output to realize cable force identification and uncertainty quantification.

2. The cable force recognition and uncertainty quantification method based on multi-sensor information fusion and BNN according to claim 1, characterized in that, The millimeter-wave radar obtains the vibration displacement of the cable-stayed bridge by measuring the phase change of the radar echo signal. The displacement calculation relationship satisfies the following: the displacement change of the cable-stayed bridge is calculated by the functional relationship between the radar operating wavelength and the phase difference between the previous and next times.

3. The method for cable force recognition and uncertainty quantification based on multi-sensor information fusion and BNN according to claim 2, characterized in that, The method for calculating the displacement change of the stay cable is as follows: Select a certain moment as the reference Based on the difference between the phase of the radar image at subsequent times and the reference phase, the displacement change of the observation point is calculated. : ； in, Let R be the radar operating wavelength, h be the straight-line distance between the radar wave emission point and the observation point, and h be the radar incident angle. The phase difference between the two observations is expressed as: ； in, For the observation point to undergo downward deformation, =R / h is the projection of the cable displacement onto the radar wave transmission path.

4. The method for cable force identification and uncertainty quantification based on BNN according to claim 1, characterized in that, The inference process of a Bayesian neural network is described by a feedforward neural network, which includes an input layer, a hidden layer, and an output layer.

5. The cable force recognition and uncertainty quantification method based on multi-sensor information fusion and BNN according to claim 4, characterized in that, By using a linear combination of Gaussian random variables, we obtain Z The mean vector, variance matrix, and covariance matrix of .

6. The method for cable force recognition and uncertainty quantification based on multi-sensor information fusion and BNN according to claim 1, characterized in that, In the forward propagation of a BNN, assuming that the network weights and bias parameters both follow a Gaussian distribution, when the activation function is a linear rectified function, the distribution of the network parameters is expressed as: ； and Let represent the expected value vector and covariance matrix of parameter θ, respectively, where θ contains the weights and biases of all hidden layers in the BNN; Given the Gaussian prior, the joint probability distribution of the parameters and the observed samples is as follows: ； in, and These are the expected value vector and covariance matrix of the observed samples, respectively. = cov(Y,θ); When the observed sample Y is known, the conditional distribution of the parameters is as follows: 。 7. The method for cable force recognition and uncertainty quantification based on multi-sensor information fusion and BNN according to claim 6, characterized in that, The hidden layer neurons are solved recursively using an RTS smoother. The solution process for each hidden layer neuron is as follows: 。 8. The method for cable force recognition and uncertainty quantification based on multi-sensor information fusion and BNN according to claim 7, characterized in that, The recursive solution process for the hyperparameters of the network model is as follows: 。 9. The method for cable force recognition and uncertainty quantification based on multi-sensor information fusion and BNN according to claim 1, characterized in that, Also includes: The prediction performance of the network after training is judged based on the error index of the theoretical cable force and the model predicted cable force of the test sample.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, characterized in that, When the processor executes the program, it implements the steps of the method as described in any one of claims 1-9.

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