Cable net structure prestress correction method and system based on multi-experiment sensitivity

Abstract

The invention discloses a cable net structure prestress correction method and system based on multi-experiment sensitivity, and relates to the technical field of structural engineering and structural health monitoring. A sensitivity matrix is approximately constructed through a finite difference method, and construction of the sensitivity matrix is completed in combination with multi-working-condition displacement data; meanwhile, a parameter-aware Tikhonov regularization method is introduced to suppress the ill-conditioned error amplification problem, and self-adaptive step length optimization is realized by adopting left-one-out cross validation (LOOCV), so that the convergence efficiency of prestress correction is effectively improved. The method is not only suitable for a pre-stress identification scene of a cable net antenna, but also can be extensively applied to multiple fields such as large-span space structures, bridge engineering and civil engineering health monitoring, and provides effective technical support for parameter identification and finite element model correction requirements related to complex coupling structures in the fields; and the method has very wide application range and practical value.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of structural engineering and structural health monitoring, and particularly relates to a prestress correction method and system for cable net structure based on multi-experiment sensitivity. BACKGROUND

[0002] In the field of design of cable net antennas, one of the core requirements is to form an approximate parabolic surface shape that meets the use requirements by applying initial prestress to each cable in the structure. The initial prestress has a dual key role in the cable net antenna: on the one hand, it is a core parameter for ensuring the geometric accuracy of the reflecting surface, directly determining the basic performance of antenna signal reception and transmission; on the other hand, it is an important basis for the structure to maintain a stable surface under the action of working load. Once the prestress deviates, it is easy to cause the reflecting surface to deform beyond the allowable range, affecting the overall function of the antenna.

[0003] However, in the whole life cycle process of the cable net antenna, from the manufacturing and assembly links to the on-orbit deployment stage, various uncontrollable factors will cause significant deviation between the actual prestress and the design value. Specifically, the deviation of the processing accuracy of the cable material, the assembly error of the cable body and the connecting parts in the manufacturing process will directly introduce inherent deviation of the initial prestress; the friction effect in the assembly and deployment process, the slow release of the residual stress in the cable body will further change the prestress distribution state; in addition, the space environment of the satellite-borne cable net antenna is special, the drastic change of temperature gradient and the long-term thermal cycle effect will cause the cable material to expand and contract, and then cause the prestress to fluctuate dynamically. The superposition of these factors will eventually cause the reflecting surface to be out of shape, and in severe cases, the antenna may not work normally.

[0004] However, the current prestress correction research on cable net structure has obvious limitations: existing technologies are mostly concentrated in the field of building space structure or bridge engineering. The cable net structure in this kind of scene usually has thick cable material, large self-weight and low vibration frequency, so the method of measuring the vibration frequency of the cable is generally used to realize the prestress correction. However, the structural characteristics of the cable net antenna are essentially different from the above-mentioned scenes, the cable material has the characteristics of lightweight, high-frequency vibration and small amplitude, and there is a lack of effective excitation conditions in the space environment, and the deployment of high-precision frequency measurement equipment is extremely difficult, which makes the traditional frequency method difficult to apply in the prestress correction of the satellite-borne cable net antenna. SUMMARY

[0005] In view of the problems of high coupling degree of each cable of large cable net structure, low measurement accuracy and poor identification efficiency of the traditional frequency method, the present application provides a prestress correction method and system for cable net structure based on multi-experiment sensitivity, which combines with the photogrammetry to obtain the measured displacement of the node, realizes the accurate correction of the prestress through the multi-working condition sensitivity matrix construction, the regularization optimization and the adaptive step adjustment, According to a first aspect of the embodiments of the present disclosure, a cable net structure prestress correction method based on multi-experiment sensitivity is provided, comprising the following steps: The prestress correction problem of the cable net structure is converted into an unconstrained optimization problem of minimizing the mean square error of the finite element calculation displacement and the experimentally measured displacement; The sensitivity linearization solving method is applied to the unconstrained optimization problem, and the nonlinear optimization problem is converted into a linear least square problem in each iteration through linearization iteration, so as to solve the prestress correction amount; Based on the finite element model, the finite difference method is used to construct the sensitivity matrix under multiple load conditions, the sensitivity matrices under various conditions are stacked and assembled into a multi-experiment overall sensitivity matrix, the overall error vector is assembled for the finite element calculation displacement and the experimentally measured displacement under the corresponding load conditions, and the uniqueness of the prestress correction solution is determined by judging the full rank of the overall sensitivity matrix; The parameter-aware Tikhonov regularization is introduced, a penalty term related to the initial prestress is added to the optimization objective, the overall sensitivity matrix is singular value decomposed, and the L-curve criterion is used to select the applicable regularization parameter, so as to suppress the ill-conditioned amplification and the out-of-bound update; The adaptive step size adjustment is realized through the leave-one-out cross validation (LOOCV), the optimal step size is selected based on the comprehensive score, and the prestress correction amount is obtained.

[0006] According to a second aspect of the embodiments of the present disclosure, a cable net structure prestress correction system based on multi-experiment sensitivity is provided, comprising: An optimization problem conversion module, which converts the prestress correction problem of the cable net structure into an unconstrained optimization problem of minimizing the mean square error of the finite element calculation displacement and the experimentally measured displacement; A linearization iteration solving module, which applies the sensitivity linearization solving method to the unconstrained optimization problem, and converts the nonlinear optimization problem into a linear least square problem in each iteration through linearization iteration, so as to solve the prestress correction amount; A multi-experiment sensitivity matrix assembly module, which uses the finite difference method to construct the sensitivity matrix under multiple load conditions, stacks and assembles the sensitivity matrices under various conditions into a multi-experiment overall sensitivity matrix, simultaneously assembles the overall error vector, and determines the uniqueness of the prestress correction solution by judging the full rank of the overall sensitivity matrix; A regularization optimization module, which introduces the parameter-aware Tikhonov regularization, adds a penalty term related to the initial prestress to the optimization objective, singular value decomposes the overall sensitivity matrix, and uses the L-curve criterion to select the applicable regularization parameter, so as to suppress the ill-conditioned amplification and the out-of-bound update; An adaptive step size adjustment module realizes adaptive step size adjustment through leave-one-out cross validation (LOOCV), selects an optimal step size based on a comprehensive score, and obtains a prestress correction amount.

[0007] According to a third aspect of the embodiments of the present disclosure, an electronic device is provided, which comprises a memory, a processor and a computer program stored in the memory and run on the memory, and the processor implements the prestress correction method for cable-net structure based on multi-experiment sensitivity when executing the program.

[0008] According to a fourth aspect of the embodiments of the present disclosure, a computer readable storage medium is provided, which stores a computer program, and the program is executed by a processor to implement the prestress correction method for cable-net structure based on multi-experiment sensitivity.

[0009] The above technical solutions adopted by the present application have the following advantages compared with the prior art: 1. The present application adopts the finite difference method to approximate the construction of the sensitivity matrix, without the need for complex analytical derivation, thereby reducing the calculation threshold.

[0010] 2. The present application combines displacement data of multiple experimental conditions to complete the construction of the sensitivity matrix, which can effectively expand the sensitivity information, break the near-linear correlation problem between the sensitivity matrix rows under a single condition, improve the matrix rank deficiency, and lay a data foundation for the subsequent accurate identification of prestress parameters.

[0011] 3. In view of the problem that the sensitivity matrix is prone to ill-conditioning and leads to error amplification, the present application introduces a parameter-aware Tikhonov regularization method. By increasing a penalty term related to the initial prestress in the optimization objective and determining the regularization parameter for each iteration, a targeted penalty weight is given according to the difference in initial prestress of different cables, which can avoid the out-of-bound update of cables with small initial prestress and effectively suppress the error amplification effect caused by the ill-conditioned matrix, thereby improving the stability and reliability of parameter identification.

[0012] 4. The present application introduces leave-one-out cross validation (LOOCV) to realize adaptive step size optimization, selects the optimal step size by dividing the training set and validation set and calculating the comprehensive score, can dynamically adapt to the parameter changes in the iteration process, avoids the slow convergence or oscillation problem caused by fixed step size, significantly improves the convergence efficiency of prestress correction, guarantees the robustness of the correction result, and reduces the influence of accidental errors on the final result.

[0013] 5. This invention is not only applicable to the prestress identification of cable-net antennas, a core scenario, solving the problem that traditional methods are not applicable to spaceborne cable-net antennas due to cable material characteristics and space environment limitations; it can also be extended to multiple fields such as large-span spatial structures, bridge engineering, and civil engineering health monitoring, providing effective technical solutions for parameter identification and finite element model correction needs of complex coupled structures in these fields, covering diverse scenarios and having significant practical application value. Attached Figure Description

[0014] The accompanying drawings, which form part of this application, are used to provide a further understanding of this application. The illustrative embodiments of this application and their descriptions are used to explain this application and do not constitute an undue limitation of this application.

[0015] Figure 1 This is a schematic diagram of the planar cable net nodes and loading positions; Figure 2 This is a schematic diagram of the singular value spectrum; Figure 3 This is a schematic diagram of the residual norm-solution norm curve (L-curve); Figure 4 This is a curve plot of curvature-regularization parameters; Figure 5 This is a graph showing the RMS error of the surface versus the average percentage error of the prestress. Detailed Implementation

[0016] The present disclosure will be further described below with reference to the accompanying drawings and embodiments.

[0017] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0018] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0019] It should be noted that the flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of methods and systems according to various embodiments of this disclosure. It should be noted that each block in a flowchart or block diagram may represent a module, segment, or portion of code, which may include one or more executable instructions for implementing the logical functions specified in the various embodiments. It should also be noted that in some alternative implementations, the functions marked in the blocks may occur in a different order than that shown in the drawings. For example, two consecutively represented blocks may actually be executed substantially in parallel, or they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the flowcharts and / or block diagrams, and combinations of blocks in the flowcharts and / or block diagrams, may be implemented using a dedicated hardware-based system that performs the specified functions or operations, or using a combination of dedicated hardware and computer instructions.

[0020] Example 1: This embodiment provides a method for correcting the prestress of cable-net structures based on multiple experimental sensitivities, including the following steps: S1. The prestress correction problem of the cable net structure is transformed into an unconstrained optimization problem that minimizes the mean square error between the displacement calculated by finite element method and the displacement measured by experiment; Specifically, let the total number of degrees of freedom of the nodes in the cable net structure be... N The number of ropes is r The vector of prestressing parameters to be corrected is expressed as: (1) The outward load vectors in the X, Y, and Z directions at the free node are: (2) Because the cable net is a tension structure, the displacement of the cable net nodes is simultaneously affected by the prestress and external loads. Under a given prestress... and external load The displacements of the cable net nodes can be obtained through the finite element equilibrium equations: (3) in It is a stiffness matrix that includes prestress. It is the displacement vector of the corresponding node in the X, Y, and Z directions, which is affected by both prestress and external load.

[0021] Under external load conditions The displacements of the cable net nodes measured in the experiment are denoted as follows: (4) Therefore, the unconstrained optimization problem is: (5) S2. The sensitivity linearization solution method is applied to the unconstrained optimization problem. The nonlinear optimization problem is transformed into a linear least squares problem in each iteration through linear iteration in order to solve the prestress correction amount. Specifically, by introducing the small displacement assumption and based on linearized iteration, in the first... k Initial prestress of the next iteration At this point, perform a first-order Taylor expansion on the displacement: (6) in, The sensitivity matrix (Jacobi matrix) has the following elements. Indicates the first j The change of the first prestressing variable affects the first i The effect of the response; subtract both sides of equation (6) simultaneously get: (7) make: (8) in, Indicates the first k The residual between the response and the experimental response is calculated in the next iteration. Indicates the first k The prestress correction amount for the next iteration is obtained by substituting equation (8) into equation (7): (9) Furthermore, the nonlinear RMS minimization unconstrained optimization problem of equation (6) is transformed into solving a linear least squares problem in each iteration: (10) The method for solving the prestress correction in each iteration is as follows: (11) in express The Moore-Penrose pseudoinverse, i.e.: (12) S3. Based on the finite element model, the finite difference method is used to construct sensitivity matrices under multiple load conditions. The sensitivity matrices under each load condition are stacked and assembled into a multi-experimental overall sensitivity matrix. At the same time, the overall error vector is assembled from the finite element calculation displacement and experimental displacement under the corresponding load conditions. The uniqueness of the prestressed correction solution is determined by judging the full rank of the overall sensitivity matrix. Specifically, in the k-th iteration, respectively... Apply a small perturbation to each prestress variable The prestress after disturbance is obtained The response after disturbance is obtained by finite element method. Therefore, the sensitivity matrix The i-th displacement response to the i-th j The sensitivity of each prestressed element is: (13) In different n Apply load and measure under each working condition m Each free node, for each experimental condition n First, construct its sensitivity matrix. Then, the sensitivity matrices of all operating conditions are superimposed row by row to assemble the overall sensitivity matrix. The resulting overall sensitivity matrix has the following dimensions: That is, (number of measurement nodes m × number of experiments n rows) × number of parameters to be corrected. r By determining whether the overall sensitivity matrix meets the full-rank requirement, a unique solution for prestress correction is obtained; the error vector is also superimposed according to the overall sensitivity matrix method, for the n One experiment, error The residual between the displacement calculated using the finite element method and the experimental displacement is as follows: (14) The individual error vectors are superimposed into a single overall error vector. ; Furthermore, by correcting the prestress using the overall sensitivity matrix, the correction amount for the prestress is obtained as follows: (15) S4. Introduce parameter-aware Tikhonov regularization, add a penalty term related to the initial prestress to the optimization objective, perform singular value decomposition on the overall sensitivity matrix and use the L-curve criterion to select the appropriate regularization parameter to suppress ill-conditioned amplification and out-of-bounds updates. Specifically, the parameter-aware Tikhonov regularization is as follows: Constructing a regularization matrix : (16) in, It is the first i Initial prestress of the root cable, diagonal element This results in relatively large initial prestresses corresponding to smaller penalty weights, while smaller initial prestresses are given stronger penalties, and each cable is updated accordingly. Each is penalized to varying degrees based on its "maximum permissible offset": The larger the value, the greater the penalty for that amount.

[0022] Sensitivity matrix Perform singular value decomposition (SVD) to obtain the singular value spectrum and calculate the condition number. : (17) in, For the maximum singular value, It is the smallest singular value; The L-curve criterion is used to apply the regularization parameter. Select the appropriate parameter; define the residual norm. Solution norm Plot the residual norm-solution norm curve to characterize the trade-off between fitting accuracy and stability of the solution; In logarithmic coordinates, let: (18) Then curvature The formula is: (19) Will As the x-axis, Plot the curvature-regularization parameter curve using the ordinate as the vertical axis, and plot the regularization coefficient corresponding to the point of maximum curvature. As the best compromise; Finally, the prestress correction amount is solved. This is equivalent to minimizing the following objective function: (20) The prestress correction amount after regularization is: (twenty one) S5. Adaptive step size adjustment is achieved through leave-one-out cross-validation (LOOCV). The optimal step size is selected based on the comprehensive score to obtain the prestress correction amount.

[0023] Specifically, using the Leave-One-Out-of-One Cross-Validation (LOOCV) concept from machine learning, for each candidate step size... Evaluation is performed on both the "training set" and the "validation set". Let there be a total of... n Group of experimental data, including n-1 Group 1 is used as the training set, the 1st group n The group serves as the validation set; for each candidate step size On the training set, the RMS error is calculated for all free nodes and the average is taken; on the validation set, only the RMS error of the free nodes on the upper surface is calculated, prioritizing the accuracy of the nodes on the upper reflecting surface. Finally, the sum of the average training set RMS error and twice the validation set RMS error is used as the comprehensive score. (twenty two) Choose the one that minimizes the score The value serves as the step size for this iteration.

[0024] Example 2: This embodiment provides a cable-net structure prestress correction system based on multiple experimental sensitivities, including: The optimization problem transformation module transforms the prestress correction problem of the cable net structure into an unconstrained optimization problem that minimizes the mean square error between the displacement calculated by finite element method and the displacement measured by experiment. The linearized iterative solution module applies the sensitivity linearization solution method to the unconstrained optimization problem. Through linear iteration, the nonlinear optimization problem is transformed into a linear least squares problem in each iteration to solve for the prestress correction amount. The multi-experiment sensitivity matrix assembly module uses the finite difference method to construct sensitivity matrices under multiple load conditions, and then assembles the sensitivity matrices under each condition into a multi-experiment overall sensitivity matrix by superimposing them row by row. At the same time, it assembles the overall error vector accordingly, and determines the uniqueness of the prestress correction solution by judging the full rank of the overall sensitivity matrix. The regularization optimization module introduces parameter-aware Tikhonov regularization, adds a penalty term related to the initial prestress to the optimization objective, performs singular value decomposition on the overall sensitivity matrix, and uses the L-curve criterion to select applicable regularization parameters to suppress ill-conditioned amplification and out-of-bounds updates. The adaptive step size adjustment module achieves adaptive step size adjustment through leave-one-out cross-validation (LOOCV), selects the optimal step size based on the comprehensive score, and obtains the prestress correction amount.

[0025] The above modules can be deployed on the same device or distributed devices; the division of modules is only a functional logic description and does not limit the specific physical boundaries or implementation order.

[0026] Example 3: An electronic device includes a memory, a processor, and a computer program stored in the memory and running thereon. When the processor executes the program, it implements the aforementioned method for correcting the prestress of a cable-net structure based on multiple experimental sensitivities, comprising: The problem of prestress correction for cable net structures is transformed into an unconstrained optimization problem that minimizes the mean square error between the displacement calculated by finite element method and the displacement measured by experiment. The sensitivity linearization solution method is applied to the unconstrained optimization problem. The nonlinear optimization problem is transformed into a linear least squares problem in each iteration through linear iteration in order to solve the prestress correction amount. The finite difference method is used to construct sensitivity matrices under multiple load conditions. The sensitivity matrices under each condition are stacked row by row to form a multi-experimental overall sensitivity matrix. At the same time, the overall error vector is assembled accordingly. The uniqueness of the prestress correction solution is determined by judging the full rank of the overall sensitivity matrix. We introduce parameter-aware Tikhonov regularization, add a penalty term related to the initial prestress to the optimization objective, perform singular value decomposition on the overall sensitivity matrix, and use the L-curve criterion to select the appropriate regularization parameter to suppress ill-conditioned amplification and out-of-bounds updates. Adaptive step size adjustment is achieved by using leave-one-out cross-validation (LOOCV). The optimal step size is selected based on the comprehensive score to obtain the prestress correction amount.

[0027] The hardware can be one of a server, personal computer, workstation, industrial controller, edge computing device, or mobile terminal; the processor can be a general-purpose CPU, GPU, NPU, FPGA, or a combination thereof; the memory can be RAM, ROM, flash memory, or disk array. The device can interact with local / remote data storage (acquiring observation data and outputting inversion results) through a communication interface. The above hardware configuration does not constitute a limitation of the present invention.

[0028] Example 4: A computer-readable storage medium having a computer program stored thereon, which, when run on a processor of an electronic device, causes the program to perform the method described in Embodiment 1; the storage medium may be a disk, optical disk, flash memory, solid-state drive, read-only memory, random access memory, or any combination of the above media.

[0029] Application example: A prestress identification experiment was conducted using a planar cable net containing 17 cables from a certain umbrella-shaped antenna as the research object. The initial prestress obtained by the cable net shape finding was used as the initial value of the correction process. A random perturbation of 0.8-1.2 times was applied to the initial prestress, and the prestress obtained after the perturbation was used as the "true value of prestress" for this experiment to verify the accuracy of the correction algorithm.

[0030] The experiment employed the aforementioned sensitivity correction method based on multiple experiments for prestress correction. The specific loading and measurement scheme is as follows: -1N loads in the X, Y, and Z directions were applied at nodes 2, 3, 4, 5, and 6 of the cable net, respectively. Simultaneously, using simulated photogrammetry, displacement measurements were performed on the upper and lower free nodes of the cable net (nodes 2, 3, 4, 5, 6, 9, 10, 11, 12, and 13), collecting displacement response data for these nodes in the X, Y, and Z directions. Details of the node distribution and loading positions of the cable net can be found in [reference needed]. Figure 1 .

[0031] Constructing the sensitivity matrix Singular value decomposition (SVD) yields the singular value spectrum, as shown below. Figure 2 As shown, the condition number is calculated as follows: The singular value spectrum obtained after singular value decomposition of the constructed sensitivity matrix exhibits a rapid decay characteristic. This characteristic indicates that the sensitivity matrix has strong ill-conditioning and is prone to noise amplification. Therefore, the Tikhonov regularization method is adopted to suppress the noise amplification effect by adding a penalty term related to the initial prestress to the optimization objective, thereby obtaining a robust prestress correction solution.

[0032] Selecting regularization parameters using the L-curve criterion Plot the residual norm-solution norm curve (L-curve) as follows: Figure 3 As shown, the curvature-regularization parameter curve is further plotted as follows. Figure 4 As shown.

[0033] Using the L-curve criterion and curvature analysis method described above, the optimal regularization coefficient is determined to be: It is 8.310×10 −11 .

[0034] Obtaining the optimal regularization coefficient Then, in each iteration, the regularized prestress correction amount is obtained using the overall sensitivity matrix and the overall error vector. Then, the optimal step size for this iteration is selected using the leave-one-out method. .

[0035] The convergence of the prestress correction RMS error and the prestress average error based on the multi-experiment sensitivity algorithm is as follows: Figure 5 As shown, after 5 iterations, the average error was reduced from 11.04% to 0.36%, a decrease of 96.73%. The prestress correction algorithm based on multi-experiment sensitivity has high recognition accuracy.

[0036] Those skilled in the art will understand that the modules or steps described above can be implemented using general-purpose computer devices. Optionally, they can be implemented using computer-executable program code, which can then be stored in a storage device for execution by a computer device. Alternatively, they can be fabricated as separate integrated circuit modules, or multiple modules or steps can be fabricated as a single integrated circuit module. This disclosure is not limited to any particular combination of hardware and software.

[0037] The above description is merely a preferred embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application should be included within the protection scope of this application.

[0038] While the specific embodiments of this disclosure have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of this disclosure. Those skilled in the art should understand that various modifications or variations that can be made by those skilled in the art without creative effort based on the technical solutions of this disclosure are still within the scope of protection of this disclosure.

Claims

1. A method for correcting prestress in cable-net structures based on multiple experimental sensitivities, characterized in that, Includes the following steps: The problem of prestress correction for cable net structures is transformed into an unconstrained optimization problem that minimizes the mean square error between the displacement calculated by finite element method and the displacement measured by experiment. The sensitivity linearization solution method is applied to the unconstrained optimization problem. The nonlinear optimization problem is transformed into a linear least squares problem in each iteration through linear iteration in order to solve the prestress correction amount. Based on the finite element model, the finite difference method is used to construct sensitivity matrices under multiple load conditions. The sensitivity matrices under each load condition are then stacked row by row to form a multi-experimental overall sensitivity matrix. At the same time, the overall error vector is assembled from the finite element calculated displacement and experimental displacement under the corresponding load conditions. The uniqueness of the prestressed correction solution is determined by judging the full rank of the overall sensitivity matrix. We introduce parameter-aware Tikhonov regularization, add a penalty term related to the initial prestress to the optimization objective, perform singular value decomposition on the overall sensitivity matrix, and use the L-curve criterion to select the appropriate regularization parameter to suppress ill-conditioned amplification and out-of-bounds updates. Adaptive step size adjustment is achieved by using leave-one-out cross-validation (LOOCV). The optimal step size is selected based on the comprehensive score to obtain the prestress correction amount.

2. The method for correcting prestress in cable-net structures based on multiple experimental sensitivities according to claim 1, characterized in that, The prestress correction problem of the cable net structure is transformed into an unconstrained optimization problem that minimizes the mean square error between the displacement calculated by finite element analysis and the displacement measured in experiments. Specifically: Let the total number of degrees of freedom of the nodes in the cable net structure be . N The number of ropes is r The vector of prestressing parameters to be corrected is expressed as: (1) The outward load vectors in the X, Y, and Z directions at the free node are: (2) Given prestress and external load Below, the nodal displacements of the cable net are obtained through the finite element equilibrium equations: (3) in It is a stiffness matrix that includes prestress. It is the displacement vector of the corresponding node in the X, Y, and Z directions, which is affected by both prestress and external load. Under external load conditions The displacements of the cable net nodes measured in the experiment are denoted as follows: (4) Therefore, the unconstrained optimization problem is: (5)。 3. The method for correcting prestress in cable-net structures based on multiple experimental sensitivities according to claim 1, characterized in that, The nonlinear optimization problem is transformed into a linear least squares problem in each iteration through linear iteration. Specifically, based on linear iteration, in the th... k Initial prestress of the next iteration At this point, perform a first-order Taylor expansion on the displacement: (6) in, The sensitivity matrix has the following elements. Indicates the first j The change of the first prestressing variable affects the first i The effect of the response; subtract both sides of equation (6) simultaneously get: (7) make: (8) in, Indicates the first k The residual between the response and the experimental response is calculated in the next iteration. Indicates the first k The prestress correction amount for the next iteration is obtained by substituting equation (8) into equation (7): (9) The nonlinear RMS minimization unconstrained optimization problem in equation (6) is transformed into solving a linear least squares problem in each iteration: (10) The method for solving the prestress correction in each iteration is as follows: (11) in express The Moore-Penrose pseudoinverse, i.e.: (12)。 4. The method for correcting prestress in cable-net structures based on multiple experimental sensitivities according to claim 1, characterized in that, The sensitivity matrices under each working condition are stacked row-wise to form a multi-experimental overall sensitivity matrix. Simultaneously, the overall error vector is assembled, and the uniqueness of the prestressed correction solution is determined by judging the full rank of the overall sensitivity matrix columns. Specifically: In the k-th iteration, the initial prestress was respectively... A perturbation is applied to each prestress variable. The prestress after disturbance is obtained The response after disturbance is obtained by finite element method. Therefore, the sensitivity matrix The i-th displacement response to the i-th j The sensitivity of each prestressed element is: (13) In different n Apply load and measure under each working condition m Each free node, for each experimental condition n First, construct its sensitivity matrix. Then, the sensitivity matrices of all operating conditions are superimposed row by row to assemble the overall sensitivity matrix. ; The resulting overall sensitivity matrix has the following dimensions: That is, (number of measurement nodes m × number of experiments n rows) × number of parameters to be corrected. r By determining whether the overall sensitivity matrix meets the full-rank requirement, a unique solution for prestress correction is obtained; the error vector is also superimposed according to the overall sensitivity matrix method, for the n One experiment, error The residual between the displacement calculated using the finite element method and the experimental displacement is as follows: (14) The individual error vectors are superimposed into a single overall error vector. ; By correcting the prestress using the overall sensitivity matrix, the correction amount for the prestress is obtained as follows: (15)。 5. The method for correcting prestress in cable-net structures based on multiple experimental sensitivities according to claim 1, characterized in that, The parameter-aware Tikhonov regularization is: Constructing a regularization matrix : (16) in, It is the first i Initial prestress of the root cable.

6. The method for correcting the prestress of a cable-net structure based on multiple experimental sensitivities according to claim 5, characterized in that, The method for performing singular value decomposition on the overall sensitivity matrix and selecting the appropriate regularization parameter using the L-curve criterion is as follows: Sensitivity matrix Perform singular value decomposition to obtain the singular value spectrum and calculate the condition number. : (17) in, For the maximum singular value, It is the smallest singular value; The L-curve criterion is used to regularize the parameters. Select the appropriate parameter; define the residual norm. Solution norm Plot the residual norm-solution norm curve to characterize the trade-off between fitting accuracy and stability of the solution; In logarithmic coordinates, let: (18) Then curvature The formula is: (19) Will As the x-axis, Plot the curvature-regularization parameter curve using the ordinate as the vertical axis, and plot the regularization coefficient corresponding to the point of maximum curvature. As the best compromise; Finally, the prestress correction amount is solved. This is equivalent to minimizing the following objective function: (20) The prestress correction amount after regularization is: (21)。 7. The method for correcting prestress in cable-net structures based on multiple experimental sensitivities according to claim 1, characterized in that, Adaptive step size adjustment is achieved through leave-one-out cross-validation (LOOCV). The optimal step size is selected based on the comprehensive score, and the prestress correction is obtained, specifically as follows: Assume there is a total n Group of experimental data, including n-1 Group 1 is used as the training set, the first group n The group serves as the validation set; for each candidate step size On the training set, the RMS error is calculated for all free nodes and averaged. On the validation set, only the RMS error of the top surface free nodes is calculated. The final score is the sum of the average training set RMS error and twice the validation set RMS error. (22) Choose the one that minimizes the score The value serves as the step size for this iteration.

8. A cable-net structure prestress correction system based on multiple experimental sensitivities, characterized in that, include: The optimization problem transformation module transforms the prestress correction problem of the cable net structure into an unconstrained optimization problem that minimizes the mean square error between the displacement calculated by finite element method and the displacement measured by experiment. The linearized iterative solution module applies the sensitivity linearization solution method to the unconstrained optimization problem. Through linear iteration, the nonlinear optimization problem is transformed into a linear least squares problem in each iteration to solve for the prestress correction amount. The multi-experiment sensitivity matrix assembly module uses the finite difference method to construct sensitivity matrices under multiple load conditions, and then assembles the sensitivity matrices under each condition into a multi-experiment overall sensitivity matrix by superimposing them row by row. At the same time, it assembles the overall error vector accordingly, and determines the uniqueness of the prestress correction solution by judging the full rank of the overall sensitivity matrix. The regularization optimization module introduces parameter-aware Tikhonov regularization, adds a penalty term related to the initial prestress to the optimization objective, performs singular value decomposition on the overall sensitivity matrix, and uses the L-curve criterion to select applicable regularization parameters to suppress ill-conditioned amplification and out-of-bounds updates. The adaptive step size adjustment module achieves adaptive step size adjustment through leave-one-out cross-validation (LOOCV), selects the optimal step size based on the comprehensive score, and obtains the prestress correction amount.

9. An electronic device, comprising a memory, a processor, and a computer program stored in the memory and running thereon, characterized in that, When the processor executes the program, it implements the cable net structure prestress correction method based on multiple experimental sensitivities as described in any one of claims 1-7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When executed by a processor, the program implements the prestress correction method for cable net structures based on multiple experimental sensitivities as described in any one of claims 1-7.

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