Static linear guided physical information neural network-based stay cable force and rigidity two-parameter identification method and system

Abstract

The invention relates to an inhaul cable force and rigidity two-parameter identification method and system of a physical information neural network based on static linear guidance, and belongs to the technical field of artificial intelligence. According to the method, the deflection and corner information of the static line shape of the inhaul cable is used as input, the characteristic deflection and the dimensionless cable force in a dimensionless and regularization standard physical system are used as output through a technical framework of a cooperative static tension Euler beam equation and a PINN, and finally, the back calculation of the cable force and the bending rigidity is achieved with high precision. According to the method, the precision and reliability of identifying the cable force and the bending rigidity of the inhaul cable can be remarkably improved; a traditional cable force recognition means is optimized, namely, local measuring points or frequency information is not depended on, fusion recognition based on global line shape and physical prior is achieved, and dependence on field sensor arrangement and manual measurement is greatly reduced; the problem that an existing method is insufficient in recognition precision under the long-distance and complex working conditions is solved, and the method has good engineering application prospects.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of artificial intelligence, in particular to the technical field of bridge cable force measurement, and relates to a cable force and stiffness double parameter identification method and system based on a static linear guide physical information neural network. BACKGROUND

[0002] Cable structure bridges are widely used in long-span bridge construction due to their reasonable structure and convenient construction. The cable is the main force-bearing component, and its stress state is directly related to the safety and durability of the bridge structure. The change of cable force directly affects the internal force distribution and linear shape of the structure, and therefore can be used as an important indicator for evaluating the health condition of the bridge. During the whole life cycle of the bridge, how to efficiently and accurately identify the cable force is always a core problem in the engineering field.

[0003] At present, the commonly used cable force identification methods mainly include the following categories: (1) direct measurement method, including measurement by a jack or pressure gauge, and measurement by installing a pressure sensor at the anchoring end. This method can directly measure the cable force, but has problems such as complex installation, potential damage risk to the anchoring section, and high cost. (2) magnetic flux method, which is susceptible to the influence of factors such as steel strand specifications, material properties, environmental temperature, and sensor magnetic circuit structure, and has insufficient measurement stability. (3) vibration method, which inversely calculates the cable force through the natural frequency of the cable, and is the most widely used method. However, this method assumes that the cable is an ideal flexible cable, while the actual cable has a certain bending stiffness, and the boundary reduction is also relatively complex, resulting in deviations between the identification model and the actual situation, thereby affecting the accuracy of cable force calculation.

[0004] In summary, the existing methods have deficiencies in applicability and accuracy. In particular, for medium and short cables, the bending stiffness and end boundary conditions have a significant impact on the dynamic characteristics and static linear shape, and traditional cable force identification methods based on vibration or simplified models are difficult to simultaneously identify the cable force and bending stiffness of the cable. In addition, cable force identification methods based on image recognition often ignore the influence of bending stiffness, resulting in limited cable force identification accuracy. SUMMARY

[0005] Therefore, the present application aims to provide a cable force and stiffness double parameter identification method and system based on a static linear guide physical information neural network, which combines photogrammetry technology and physical information neural network to achieve double parameter identification of cable force and bending stiffness of medium and short cables while considering the influence of cable end boundary conditions.

[0006] To achieve the above-mentioned purpose, the present application provides the following technical solutions: A cable force and stiffness double parameter identification method based on a static linear guide physical information neural network, which specifically includes the following steps: S1, photogrammetry of the static linear shape of the cable: the unmanned aerial vehicle is flown to a preset image acquisition position, the target cable is photographed, and static linear image data of the cable are acquired; S2, the cable length is taken as prior information, the static linear image of the cable acquired in step S1 is processed, the static linear information of the cable is extracted, and the deflection and the rotation angle information are combined to be used as PINN input; S3, the static tension Euler beam equation and its dimensionless form are derived, the physical information neural network and its composite loss function are constructed in cooperation with the dimensionless equation, and the network optimization mode and the optimal hyperparameters are configured; S4, the training of the physical information neural network is guided by the deflection, the rotation angle and the curvature information of the static deflection curve of the cable, the characteristic deflection and the dimensionless cable force are obtained, and the cable force and the bending stiffness are inversely calculated.

[0007] Further, in step S2, specifically comprising: S21, cable static linear image processing and coordinate conversion; S22, cable static linear shape based on cable length prior information; S23, extraction and data processing of cable static linear information.

[0008] Further, in step S21, the cable static linear image processing and coordinate conversion comprises: The cable static linear image acquired in step S1 is preprocessed to eliminate imaging distortion and light effects and to enhance linear boundary features; the image processing comprises distortion correction, graying, image enhancement and edge detection and the like operations, and a clear cable linear contour image is obtained.

[0009] The pixel point set of the cable static linear shape is extracted from the processed image, and is expressed as: (1) Wherein, u i and v i are the horizontal and vertical pixel positions in the image coordinate system respectively; The internal parameter matrix K and the external parameter matrix [R|t] obtained by camera calibration are used to map the pixel coordinates (u i and v i ) to the world coordinate system through the camera imaging geometric model, and the point set is obtained: (2) Wherein, Π -1 (·) represents the back projection transformation from the pixel plane to the world coordinate, x i is the coordinate of the cable in the horizontal projection direction, and y i is the corresponding vertical deflection coordinate; The discrete vertical deflection obtained from reverse photography satisfies: (3) Where w(x) i e(x) represents the actual deflection of the cable; i The systematic error (n(x)) is mainly caused by camera distortion, perspective error, calibration residuals, etc., and usually manifests as low-frequency components; i This is random noise, mainly caused by image noise, shooting shake, or pixel quantization error. It changes rapidly and can be regarded as a high-frequency component.

[0010] In subsequent fitting, high-frequency random noise will be suppressed by smoothing constraints, while low-frequency systematic errors will be further constrained by the cable length prior.

[0011] Furthermore, in step S22, the static alignment of the cable based on prior information about the cable length specifically includes: In the world coordinate system, if the static geometry of the cable is represented by a continuous function f(x;ψ), then its cable length can be calculated: (4) Where x min and x max Let L0 be the two ends of the cable; using the cable length L0 as prior information, introduce length constraints and construct the optimization problem: (5) Where, λ s To smooth out the regularized weights, λ L The first term is the data fitting residual, ensuring that the curve approximates the observed data; the second term is the smoothing constraint, suppressing high-frequency noise; the third term is the cable length prior, constraining low-frequency systematic errors. By solving the optimization problem, the static linear curve of the cable in the world coordinate system can be obtained: (6) In this process, high-frequency noise is effectively suppressed due to the smoothing constraint, and the originally slowly changing low-frequency system error is partially corrected due to the cable length constraint. Therefore, the fitted curve satisfies: (7) Among them, the residual random error ñ(x) is a low-amplitude, high-frequency component; the residual systematic error It consists of low-amplitude, low-frequency components; Taking the derivative further, we get (8) According to the properties of Fourier transform The spatial Fourier transform can be expressed as Its spectrum is concentrated in the low-frequency region |ω|≤ω0, and whose derivative can be expressed as: (9) where ω is the spatial angular frequency and j is the imaginary unit; Therefore, the two-norm of the first derivative is: (10) Residual systematic error The energy in the first derivative is reduced by and the residual random error The energy in the first derivative is also reduced; therefore, the curve After differentiation, part of the systematic error can be effectively eliminated.

[0012] Further, in step S23, the extraction of the static linear information of the cable and data processing specifically includes: The static deflection curve of the cable obtained in S22 , extract its deflection and angle information: (11) where the first derivative is the static deflection curve angle of the cable; According to the first-order Taylor expansion, the obtained deflection and angle information are processed to form the input data set of the physical information neural network: (12) where Δx = L / N, and N is the number of pixel points.

[0013] Further, in step S3, specifically includes: S31: Construction of the static tension Euler beam model The static tension Euler beam equation sTEB of formula (13): the length of the cable is L, under the action of gravity, it bears the cable force H, and its deflection w is controlled by the following equation: (13) where EI is the bending stiffness, and q is the weight per unit length of the cable; considering the influence of the boundary conditions of the cable end, the boundary conditions are defined as: (14) where k r is the rotational stiffness at the boundary; S32: Construction of the standard physical system Define the dimensionless parameter as formula (15): (15) where ξ is the dimensionless spatial axial coordinate, m is the characteristic deflection, n is the dimensionless cable force, and ω is the dimensionless deflection; the operator operation is performed according to equation (16): (16) The obtained cable control equation and its simplified form are equation (17) and equation (18), respectively (17) (18) At this time, the mapping relationship between the equation and the actual engineering scene is established by inversely deducing equation (16) and equation (17); finally, a dimensionless, normalized standard physical system suitable for PINN solving is constructed to avoid multi-scale effects, as shown in equation (19): (19) Similarly, the boundary conditions are scaled into the standard physical system, and the dimensionless rotational stiffness is defined as: (20) The corresponding boundary condition integrated into the PINN is represented as: (21) S33: Construction of the positive problem composite loss function After completing steps S31 and S32, the standard physical system, i.e., equation (18) and (21), is solved under the cable end boundary condition; a neural network with trainable parameters η is constructed, and its output is defined as to approximate the solution ω(x); on the region Ω, define the parameterized solution w(x) as: (22) and specify the boundary conditions: (23) After using a set of configuration points in the domain and a set of configuration points on the boundary, the positive problem composite loss function is defined as: (24) where k f and k b are weights and satisfy the following definition: (25) S34: Construction of the inverse problem composite loss function To solve the inverse problem of sTEB, the cable static linear information obtained in step S2 is used as additional measurement information to guide the PINN to solve the inverse problem, i.e., if the parameters in equation (25) are unknown, while at a set of configuration points with additional measurements on w, the inverse problem composite loss function is defined as: (26) where k m is the weight, the cable static linear observation loss from photogrammetry is: (27) where g(x i ) is the local correction of the first-order Taylor expansion of the observation w(x i ), as shown in equation (12); this loss function incorporates both the observation value and its local variation trend by introducing a local first-order derivative correction at the observation point, so that the network prediction not only fits the observation value itself, but also follows the function variation law near the observation point; compared with separately adding a corner loss term, this method utilizes the first-order derivative information without introducing additional weight parameters, thus simplifying the loss function design. Since the relative error of the first-order derivative is usually smaller than the deflection itself due to the image preprocessing of the static linear curve, introducing it into the loss function is equivalent to introducing a set of high-precision data to enhance the PINN's constraint on the local trend near the observation point. In addition, the local first-order correction can smooth the high-frequency disturbance in the observation data and suppress the influence of noise on the loss function and network prediction, thus improving the stability and physical consistency of the inverse problem solution.

[0014] S35: Optimization of network structure and hyperparameters For the sTEB equation, equation (26) is the composite loss function composed of the control equation loss , the boundary loss , and the observation loss If the constructed PINN can accurately solve the forward and inverse problems of sTEB, it means that the gradients of each independent loss function and its composite loss function tend to zero, which also means that the predicted values at each point in the backpropagation calculation of the PINN tend to the true values; thus, solving the forward and inverse problems of the sTEB equation is converted to optimizing the composite loss function, and the automatic differentiation technique is used to encapsulate the basic physical processes of steps S31, S32, S33, and S34; the goal is to calculate the neural network parameters η* by minimizing the loss functions in equations (24) and (26); where the hyperparameters are set as the control equation loss weight k f , the boundary loss weight k b , the observation loss weight k m , the geometric domain configuration points , the boundary training points , and the additional observation points , learning rate lr, number of neurons nn, number of network layers nl; the optimization process is set to the optimizer Adam, the activation function is Sin, and the initialization strategy is Xavier; the test index is set to the L2 norm.

[0015] Further, in step S4, the following specific steps are specifically included: S41: embedding the static tension Euler beam equation into the physical information neural network The static tension Euler beam equation established in step S3 is embedded into the neural network training framework, specifically including: first, obtaining the static linear information w, w' and w" of the cable by photogrammetry technology; second, determining the variables x, w, w' and w" in the solution scheme, the unknown parameters H and EI to be identified, and the known parameters q and L; third, converting the variables and parameters into dimensionless forms in the standard physical system:,, and ; fourth, determining the boundary conditions; fifth, generating configuration points and integrating the static linear observation points of the cable: geometric domain configuration points , boundary configuration points and additional static linear observation points ; sixth, establishing a neural network model for sTEB, obtaining the high-order derivatives of the output through automatic differentiation technology, and substituting the obtained results into the composite loss function, so that the network meets the physical equation constraint, boundary condition constraint and observation data constraint during the training process.

[0016] S42: double parameter identification of cable force and bending stiffness The neural network parameters are iteratively updated by the back propagation and gradient descent method, and the unknown parameters n and m to be identified are simultaneously updated; during the training process, it is judged whether the preset maximum number of iterations is reached, and the physical information neural network is continuously guided to converge by the composite loss function during the iteration process; when the network converges to the optimal model in the sense of L2 norm, the characteristic deflection m and the dimensionless cable force n are output, and the cable force H and the bending stiffness EI of the cable are calculated according to formula (15).

[0017] The application also provides a cable force and stiffness double parameter identification system based on a static linear guided physical information neural network.

[0018] The application has the following advantages: The method can significantly improve the accuracy and reliability of cable force and bending stiffness identification; the traditional cable force identification method is optimized, that is, it is not dependent on local measurement points or frequency information, but is based on the fusion identification of global linear and physical priori, greatly reducing the dependence on on-site sensor layout and manual measurement; the problem of insufficient identification accuracy in long distance and complex working conditions of existing methods is solved, and has good engineering application prospect.

[0019] Additional advantages, objects, and features of the application will be apparent to those skilled in the art upon examination of the following specification. It is intended to be covered by the following claims. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to make the objectives, technical solutions and advantages of the present application clearer, the preferred embodiments of the present application will be described in detail below with reference to the accompanying drawings, in which: Figure 1 A flow chart of the method of the present application; Figure 2 The identification results of Scheme A in the examples; Figure 3 The identification results of Scheme B in the examples. DETAILED DESCRIPTION

[0021] The technical solutions of the present application will be described in detail below with reference to the accompanying drawings.

[0022] The present application provides a cable force and stiffness double parameter identification method based on static linear guide physical information neural network, which uses the deflection and angle information of the static linear cable as input, cooperates the static tension Euler beam equation and PINN technical framework, outputs the characteristic deflection in dimensionless and normalized standard physical system and dimensionless cable force, and finally realizes the inverse calculation of cable force and bending stiffness with high precision. Figure 1 A flow chart of the method of the present application.

[0023] In order to verify the improvement effect of the added angle information on the cable parameter identification accuracy, the test cable shown in Table 1 is selected as an example object, and the cable force and bending stiffness are identified by using two kinds of input forms respectively: Scheme A: only use the deflection information of the cable linear form obtained by photogrammetry as the PINN input; Scheme B: use the deflection and angle information of the cable linear form as the PINN input.

[0024] The model structures and physical constraints of the two schemes are consistent, and only differ in the input data types.

[0025] Table 1 Test cable parameters The identification results are shown in Figure 2 and Figure 3 Figure 2 The identification results of Scheme A, the identified cable force is 1163.91 N, the error is 3.01%, and the bending stiffness is 188.48 N·m 2 ​, the error is -27.79%; Figure 3 The identified cable force is 1180.77 N, the error is 1.6%, and the bending stiffness is 167.19 N·m 2 , the error is -13.35%. From the above identification results, it can be seen that after further introducing the angle of the cable static linear form based on the deflection information, the identification accuracy of the cable force and the bending stiffness is significantly improved. Specifically, the cable force identification error is reduced from 3.01% to 1.60%, and the bending stiffness identification error is reduced from to . The angle of the linear form as an important geometric quantity reflecting the local deformation trend of the cable, has a lower dependence on the absolute coordinate accuracy than the deflection, which can effectively reduce the influence of the deflection measurement error caused by pixel quantization, perspective distortion and other factors in photogrammetry, thereby improving the description ability of the model to the static form, and significantly enhancing the identifiability of the double-parameter coupling identification problem.

[0026] In addition, the double-parameter identification of cable force and bending stiffness of the 5 real cable stays shown in Table 2 is carried out, and the comparative test of Table 3 shows that among the test results of the 5 real cable stays, the present application shows significant multi-parameter identification ability. The maximum error of cable force identification is 6.28%, and the minimum error is 0.63%; the maximum error of bending stiffness identification is -8.09%, and the minimum error is -0.23%. It is particularly noteworthy that the present application method ignores the influence of the cable end boundary condition on the model when performing cable force and bending stiffness inversion, which is particularly important because the end boundary condition of the real cable stay is usually unknown, and the model uses the standard boundary condition, and the boundary condition defined in the model remains consistent in all tests. This makes the method of the present application still be able to provide stable and high-precision identification results without relying on the actual boundary condition, further verifying its application potential and robustness in practical engineering.

[0027] Table 2 5 real cable stay parameters Table 3 Double-parameter identification results of cable force and bending stiffness of 5 real cable stays The comprehensive results show that: thanks to the cable force and stiffness double parameter identification method of the physical information neural network based on the static linear guide proposed in the application. In the photogrammetry of the static linear of the cable, the length of the cable is taken as prior information and measurement constraint equation, and high-precision static linear information of the cable is obtained; under the guidance of high-precision static linear, combined with the introduction of the rotation angle information, the cable force and bending stiffness parameters can be stably and accurately inverted in the case of ignoring the actual cable end boundary condition, thereby avoiding the influence caused by the uncertainty of the boundary condition, and further verifying the robustness and application potential in the actual engineering.

[0028] In summary, the specific advantages of the present scheme are as follows: 1 High-precision static linear information acquisition: by taking the length of the cable as prior information and constructing a measurement constraint equation, the application effectively acquires high-precision static linear information of the cable, significantly improving the reliability and accuracy of the data.

[0029] 2 Boundary condition independence: the PINN solving method based on the static linear guide can effectively ignore the influence of the cable end boundary condition on the model, so that even in the case of unknown boundary conditions, the cable force and bending stiffness can still be accurately identified, especially suitable for the case of actual short cable.

[0030] 3 Effective fusion of rotation angle information: through first-order Taylor expansion, the rotation angle information of the observation point is combined with the deflection data, and a new loss function is constructed, which not only improves the convergence performance of PINN, but also further enhances the accuracy of cable force and bending stiffness identification, overcoming the challenge of multi-scale effect.

[0031] Finally, it should be pointed out that the above examples are only used to illustrate the technical solutions of the present application and are not limiting, although the present application has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that the technical solutions of the present application can be modified without departing from the purpose and scope of the present technical solutions, and all should be covered in the scope of the claims of the present application.

Claims

1. A method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network, characterized in that: The method specifically includes the following steps: S1. Photogrammetry of the static alignment of the cable: Use a drone to fly to the preset image acquisition position, take pictures of the target cable, and obtain static alignment image data of the cable; S2. Using the cable length as prior information, process the static alignment image of the cable obtained in step S1 to extract the static alignment information of the cable, and combine the deflection and rotation information as PINN input. S3. Derive the static tensioned Euler beam equation and its dimensionless form, construct a physical information neural network and its composite loss function in conjunction with the dimensionless equation, and configure the network optimization method and optimal hyperparameters. S4. By using the deflection, rotation angle, and curvature information of the static deflection curve of the cable to guide the training of the physical information neural network, the characteristic deflection and dimensionless cable force are obtained, and the cable force and bending stiffness are calculated inversely.

2. The method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network according to claim 1, characterized in that: Step S2 specifically includes: S21. Static linear image processing and coordinate transformation of cable; S22. Static cable alignment based on prior information about cable length; S23. Extraction and data processing of static cable alignment information.

3. The method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network according to claim 2, characterized in that: In step S21, the static linear image processing and coordinate transformation of the cable includes: The static linear image of the cable obtained in step S1 is preprocessed to eliminate imaging distortion and illumination effects, and to enhance the linear boundary features. The pixel set of the static line shape of the cable is extracted from the processed image and represented as: (1) Among them, u i ,v i These represent the horizontal and vertical pixel positions in the image coordinate system, respectively. Using the intrinsic parameter matrix K and extrinsic parameter matrix [R|t] obtained from camera calibration, the pixel coordinates (u) are determined through the camera imaging geometry model. i ,v i Mapping to the world coordinate system yields a point set: (2) Among them, Π -1 (·) represents the back projection transformation from the pixel plane to world coordinates, x i Let y be the coordinates of the cable in the horizontal projection direction. i These are the corresponding vertical deflection coordinates; The discrete vertical deflection obtained from reverse photography satisfies: (3) Where w(x) i e(x) represents the actual deflection of the cable; i ) represents systematic error.

4. The method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network according to claim 3, characterized in that: In step S22, the static alignment of the cable based on prior information about the cable length specifically includes: In the world coordinate system, if the static geometry of the cable is represented by a continuous function f(x;ψ), then its cable length can be calculated: (4) Where x min and x max Let L0 be the two ends of the cable; using the cable length L0 as prior information, introduce length constraints and construct the optimization problem: (5) Where, λ s To smooth out the regularized weights, λ L The first term is the data fitting residual, ensuring that the curve approximates the observed data; the second term is the smoothing constraint, suppressing high-frequency noise; the third term is the cable length prior, constraining low-frequency systematic errors. By solving the optimization problem, the static linear curve of the cable in the world coordinate system can be obtained: (6) In this process, high-frequency noise is effectively suppressed due to the smoothing constraint, and the originally slowly changing low-frequency system error is partially corrected due to the cable length constraint. Therefore, the fitted curve satisfies: (7) Among them, the residual random error ñ(x) is a low-amplitude, high-frequency component; the residual systematic error It consists of low-amplitude, low-frequency components; Taking the derivative further, we get (8) According to the properties of Fourier transform The spatial Fourier transform can be expressed as Its spectrum is concentrated in the low-frequency region |ω|≤ω0, and Its derivative can be expressed as: (9) Where ω is the spatial angular frequency and j is the imaginary unit; Therefore, the second norm of the first derivative is expressed as: (10) Residual systematic error Energy in the first derivative And reduction; similarly, residual random error The energy in the first derivative also shrinks; therefore, the curve After differentiation, some systematic errors can be effectively eliminated.

5. The method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network according to claim 4, characterized in that: In step S23, the extraction and data processing of the static alignment information of the cable specifically includes: Static deflection curve of the cable obtained from S22 Extract its deflection and rotation information: (11) The first derivative is the angle of the static deflection curve of the cable; Based on the first-order Taylor expansion, the obtained deflection and rotation angle information is processed to form the input dataset for the physical information neural network: (12) Where Δx = L / N, and N is the number of pixels.

6. The method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network according to claim 5, characterized in that: Step S3 specifically includes: S31: Construction of a Static Tensioned Euler Beam Model The static tensioned Euler beam equation sTEB, as shown in equation (13), is as follows: The cable length is L, and under its own weight, it bears a cable force H. Its deflection w is controlled by the following equation: (13) Where EI is the bending stiffness, and q is the weight per unit length of the cable; considering the influence of the cable end boundary conditions, the boundary conditions are defined as follows: (14) Where, k r The rotational stiffness at the boundary; S32: Construction of Standard Physical Systems Define the dimensionless parameter as Equation (15): (15) Where ξ is the dimensionless spatial axial coordinate, m is the characteristic deflection, n is the dimensionless cable force, and ω is the dimensionless deflection; the operator operation is performed according to equation (16): (16) The obtained cable control equations and their simplified forms are equations (17) and (18), respectively. (17) (18) At this point, by deriving equations (16) and (17) in reverse, a mapping relationship between the equations and the actual engineering scenario is established; finally, a dimensionless, regularized standard physical system that avoids multi-scale effects and is suitable for PINN solutions is constructed, as shown in equation (19): (19) Similarly, scaling the boundary conditions to a standard physical system, the dimensionless rotational stiffness is defined as: (20) The corresponding boundary conditions for integration into PINN are expressed as follows: (21) S33: Construction of the composite loss function for the positive problem After completing steps S31 and S32, considering the cable end boundary conditions, solve the standard physical system, i.e., equations (18) and (21); construct a neural network with trainable parameter η, and define its output as... To approximate the solution ω(x); define on the region Ω The parameterized solution w(x) is: (22) And specify boundary conditions: (23) Use a set of configuration points within the domain. and use a set of configuration points on the boundary. Then, the composite loss function for the forward problem is defined as: (24) Where, k f and k b Let be the weights, and satisfy the following definition: (25) S34: Construction of the composite loss function for the inverse problem To solve the inverse problem of sTEB, the static alignment information of the cable obtained in step S2 is used as additional measurement information to guide PINN in solving the inverse problem, that is, if the parameters in equation (25) Unknown, but in a set of configuration points If there are additional measurements on w, then the inverse problem composite loss function is defined as follows: (26) Where, k m As a weight, the observation loss of the cable static linearity obtained from photogrammetry. for: (27) Wherein, g(x) i See equation (12), which represents the observed value w(x) i The first-order Taylor expansion local correction is used; this loss function incorporates the observation value and its local change trend into the constraint by introducing a local first-order derivative correction at the observation point, so that the network prediction not only fits the observation value itself, but also follows the function change law near the observation point. S35: Optimization of Network Structure and Hyperparameters For the sTEB equation, equation (26) is the composite loss function, derived from the loss of the governing equation. Boundary loss Observation loss If the constructed PINN can accurately solve the forward and inverse problems of sTEB, it means that the gradients of each independent loss function and its composite loss function are... The value tends to zero, which is also considered as the predicted value of each point in the backpropagation calculation of PINN tending to the true value; thus, the problem of solving the forward and inverse problems of the sTEB equation is transformed into optimizing the composite loss function, and the basic physical process of steps S31, S32, S33, and S34 is encapsulated using automatic differentiation technology; the goal is to calculate the neural network parameter η* by minimizing the loss function in equations (24) and (26); where the hyperparameter is set as the loss weight k of the control equation. f Boundary loss weight k b Observation loss weight k m Geometric domain configuration points Boundary training points Additional observation points The learning rate is lr, the number of neurons is nnn, and the number of network layers is nl; the optimization process is set as the optimizer Adam, the activation function Sin, and the initialization policy Xavier; the test metric is set as the L2 norm.

7. The method for identifying the dual parameters of cable force and stiffness based on a statically guided physical information neural network according to claim 6, characterized in that: Step S4 specifically includes the following steps: S41: Static tensioned Euler beam equations embedded in a physical information neural network The static tensioned Euler beam equation established in step S3 is embedded into a neural network training framework, specifically including: First, obtaining the static alignment information w, w', and w" of the cable using photogrammetry; Second, determining the variables x, w, w', and w" in the solution scheme, the unknown parameters H and EI to be identified, and the known parameters q and L; Third, converting each variable and parameter into dimensionless forms ξ, ω, m, and n in a standard physical system; Fourth, determining the boundary conditions; Fifth, generating placement points and integrating the static alignment observation points of the cable: geometric domain placement points. Boundary configuration points and additional static linear observation points Step 6: Build a neural network model for sTEB, obtain the higher-order derivative of the output through automatic differentiation, and substitute the result into the composite loss function so that the network can simultaneously satisfy the physical equation constraints, boundary condition constraints and observation data constraints during the training process. 8.S42: Two-parameter identification of cable force and bending stiffness With the goal of minimizing the composite loss function, the neural network parameters are iteratively updated using backpropagation and gradient descent methods, while the unknown parameters n and m to be identified are updated simultaneously. During training, it is determined whether the preset maximum number of iterations has been reached, and the physical information neural network is continuously guided to converge using a composite loss function during the iteration process; When the network converges to the optimal model in the L2 norm sense, it outputs the characteristic deflection m and the dimensionless cable force n, and calculates the cable force H and bending stiffness EI of the cable according to Equation (15).

9. A dual-parameter identification system for cable force and stiffness based on a statically guided physical information neural network, characterized in that: The system employs the method described in any one of claims 1 to 7.

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