Prestressed cable finite element model correction method and system based on artificial intelligence

Abstract

This application relates to the field of data processing technology and discloses a method and system for correcting a prestressed cable finite element model based on artificial intelligence. The method includes: establishing an initial finite element model; calculating the relative error between simulated cable force data and measured cable force data to determine the parameters to be corrected and their value range; generating a training sample set within the value range; dividing the training sample set into high-density and low-density regions based on the density function values ​​of each sample point; training random forest and Gaussian process regression respectively; obtaining the predicted cable force response value based on the comparison between the density function value of the point to be predicted and a density threshold; calculating the difference between the predicted cable force response value and the measured cable force data to obtain the particle fitness; obtaining the optimal parameter combination based on the particle fitness; and substituting this combination into the initial finite element model to obtain the corrected model parameters. This application improves the computational efficiency and accuracy of correcting the prestressed cable finite element model.

Description

Technical Field

[0001] This application relates to the field of data processing technology, and in particular to a method and system for correcting the finite element model of prestressed cable based on artificial intelligence. Background Technology

[0002] Prestressed cable structures are widely used as efficient load-bearing systems in modern long-span bridges, stadiums, and transmission towers. The accuracy of their finite element models directly affects the reliability of structural safety assessments and health monitoring. Existing finite element model correction methods mainly rely on manual trial calculations or automated searches based on optimization algorithms such as genetic algorithms and standard particle swarm optimization. By repeatedly adjusting key parameters such as elastic modulus, cross-sectional area, and prestress value, the error between the model output and measured data is gradually reduced. This type of method is feasible to a certain extent in small-scale parameter correction.

[0003] However, the above methods have significant technical shortcomings. First, each fitness evaluation requires calling the complete finite element static solver, with each calculation typically taking several minutes. When the number of optimization iterations reaches thousands or even tens of thousands, the total computation time severely restricts the timeliness of engineering applications. Second, existing methods generally use random sampling or uniform grid sampling in the initial training sample generation stage, which cannot identify regions with high model uncertainty in the parameter space. This results in sparse samples in high uncertainty regions and redundant samples in low uncertainty regions, reducing the overall prediction accuracy of subsequent surrogate models. Third, the standard particle swarm optimization algorithm uses a fixed inertia weight strategy, which has insufficient global search capability in the early stages of optimization and lacks local fine search capability in the later stages of optimization. It is prone to premature convergence to local optima in complex nonlinear regions of the parameter space. Summary of the Invention

[0004] This application provides an artificial intelligence-based method and system for correcting the finite element model of prestressed cables. It solves the problems of low computational efficiency caused by strong coupling between the optimization process and finite element solution in existing methods for correcting the finite element model of prestressed cables, imbalance in prediction of a single surrogate model in the full parameter space, and easy trapping of the optimization algorithm in local optima. It improves the computational efficiency and correction accuracy of the correction of the finite element model of prestressed cables.

[0005] Firstly, this application provides an artificial intelligence-based method for correcting the finite element model of prestressed cables, the artificial intelligence-based method for correcting the finite element model of prestressed cables comprising:

[0006] Step S1: Establish an initial finite element model based on the engineering design parameters of the prestressed cable structure, calculate the relative error between the simulated cable force data and the collected measured cable force data, and determine the parameters to be corrected and their value ranges.

[0007] Step S2: Generate a set of sample points within the range of values ​​and perform finite element calculations to obtain a training sample set;

[0008] Step S3: Divide the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set. Train a random forest on the high-density region samples and train a Gaussian process regression on the low-density region samples. Compare the density function value of the point to be predicted with a density threshold. When the density function value of the point to be predicted is not lower than the density threshold, call the prediction result of the random forest. When the density function value of the point to be predicted is lower than the density threshold, call the prediction result of the Gaussian process regression to obtain the predicted value of the force response.

[0009] Step S4: Calculate the particle fitness by subtracting the predicted cable force response value from the measured cable force data. Update the particle position based on the particle fitness to obtain the optimal parameter combination. Substitute the optimal parameter combination into the initial finite element model to perform static analysis and obtain the corrected model parameters.

[0010] Secondly, this application provides an artificial intelligence-based finite element model correction system for prestressed cables, the artificial intelligence-based finite element model correction system comprising:

[0011] The modeling module is used to establish an initial finite element model based on the engineering design parameters of the prestressed cable structure, calculate the relative error between the simulated cable force data and the collected measured cable force data, and determine the parameters to be corrected and their value ranges.

[0012] The calculation module is used to generate a set of sample points within the range of the values ​​and perform finite element calculations to obtain a training sample set;

[0013] The training module is used to divide the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set, train a random forest on the high-density region samples, train a Gaussian process regression on the low-density region samples, compare the density function value of the point to be predicted with a density threshold, and call the prediction result of the random forest when the density function value of the point to be predicted is not lower than the density threshold, and call the prediction result of the Gaussian process regression when the density function value of the point to be predicted is lower than the density threshold to obtain the predicted value of the force response.

[0014] The update module is used to calculate the particle fitness by subtracting the predicted cable force response value from the measured cable force data, update the particle position according to the particle fitness, obtain the optimal parameter combination, and substitute the optimal parameter combination into the initial finite element model to perform static analysis to obtain the corrected model parameters.

[0015] The technical solution provided in this application determines the parameters to be corrected and their value range by calculating the relative error between simulated cable force data and measured cable force data. This limits the parameter search boundary to a reasonable fluctuation range of the initial value, avoiding the waste of computational resources caused by blind searching. Within the value range, a set of sample points is generated and finite element calculations are performed to obtain a training sample set. Using the accurate finite element calculation results as training data, a mapping relationship between parameter combinations and cable force response is established, providing a data foundation for the subsequent construction of a proxy model. Based on the density function values ​​of each sample point in the training sample set, the training sample set is divided into high-density region samples and low-density region samples. For high-density samples, a random forest is trained on high-density samples and a Gaussian process regression is trained on low-density samples. The random forest, through the ensemble prediction of multiple decision trees, has an efficient predictive ability in dense sample areas, while the Gaussian process regression, through the probabilistic prediction framework of the covariance kernel function, has an extrapolation ability in sparse sample areas. The two are adaptively switched based on the comparison between the density function value of the point to be predicted and the density threshold, which overcomes the inherent defect of the single surrogate model in predicting imbalance in the full parameter space. This allows the surrogate model to maintain high prediction accuracy in different regions of the parameter space and reduces the time for a single fitness evaluation from minutes to milliseconds.

[0016] The particle fitness is calculated by subtracting the predicted cable force response from the measured cable force data. The particle fitness directly quantifies the degree of deviation between the current parameter combination and the actual parameters, thereby driving the update of the particle position. This ensures that the optimization direction always converges towards the parameter region where the finite element model calculation results and the measured cable force data have a higher degree of agreement. After updating the particle position based on the particle fitness and obtaining the optimal parameter combination, the optimal parameter combination is substituted into the initial finite element model to perform static analysis. The final verification basis is the accurate finite element calculation results rather than the prediction results of the surrogate model. This eliminates the influence of the surrogate model prediction error on the correction accuracy and ensures that the output corrected model parameters have finite element level accuracy. This allows the corrected elastic modulus, cross-sectional area, and prestress value to truly reflect the actual physical properties of the prestressed cable structure, ultimately achieving a high degree of agreement between the cable force calculated by the finite element model and the cable force measured on site. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0018] Figure 1 This is a schematic diagram of an embodiment of the artificial intelligence-based finite element model correction method for prestressed cables in this application.

[0019] Figure 2 This is a schematic diagram comparing the relative errors of the prestressed cable finite element model before and after correction in the embodiments of this application. Detailed Implementation

[0020] This application provides a method and system for correcting finite element models of prestressed cables based on artificial intelligence. The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this application are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data used can be interchanged where appropriate so that the embodiments described herein can be implemented in a sequence other than that illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0021] For ease of understanding, the specific process of the embodiments of this application is described below. Please refer to [link / reference]. Figure 1 One embodiment of the artificial intelligence-based finite element model correction method for prestressed cable in this application includes:

[0022] Step S1: Establish an initial finite element model based on the engineering design parameters of the prestressed cable structure, calculate the relative error between the simulated cable force data and the collected measured cable force data, and determine the parameters to be corrected and their value ranges.

[0023] Specifically, simulated cable force data refers to the axial tensile force obtained by extracting the axial stress of each prestressed cable element and multiplying it by the corresponding cross-sectional area after performing static analysis in the ANSYS finite element model with the initial elastic modulus, initial cross-sectional area, and initial prestress as input parameters. The unit is N. Measured cable force data refers to the actual axial tensile force obtained on-site by collecting strain time history data using vibrating wire strain sensors deployed on the prestressed cable surface, measuring the cable's fundamental frequency using the impact method, and then calculating it based on string vibration theory. The range of values ​​for the parameters to be corrected is defined by the lower and upper bounds of the values ​​obtained by multiplying the initial elastic modulus, initial cross-sectional area, and initial prestress value by their respective lower and upper bound coefficients.

[0024] Step S2: Generate a set of sample points within the range of values ​​and perform finite element calculations to obtain the training sample set;

[0025] Specifically, the training sample set refers to a dataset consisting of several sets of parameter combinations generated within the range of values ​​for the parameters to be corrected. Each parameter combination is substituted into the initial finite element model to perform static analysis, and the corresponding cable force response value is extracted. The dataset is a mapping between the parameter combinations and the cable force response values. Each sample point in the training sample set contains a set of elastic modulus values, cross-sectional area values, prestress values, and corresponding cable force response values. The training sample set as a whole describes the mapping relationship between parameter combinations and cable force responses within the parameter space to be corrected.

[0026] Step S3: Divide the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set. Train a random forest on the high-density region samples and train a Gaussian process regression on the low-density region samples. Compare the density function value of the point to be predicted with the density threshold. When the density function value of the point to be predicted is not lower than the density threshold, call the prediction result of the random forest. When the density function value of the point to be predicted is lower than the density threshold, call the prediction result of the Gaussian process regression to obtain the predicted value of the force response.

[0027] Specifically, the density function value refers to the value obtained by standardizing the parameter combinations of each sample point in the training sample set, substituting the Euclidean distance between the sample points into the Gaussian kernel function, and summing all kernel function values. This value reflects the degree of clustering of samples in the local neighborhood of that sample point in the parameter space; the larger the value, the denser the surrounding samples. The density threshold is the median of the density function values ​​of all sample points, thus dividing the training sample set into two parts: sample points with density function values ​​not lower than the density threshold constitute high-density regions, and sample points with density function values ​​lower than the density threshold constitute low-density regions, with no overlap between the two. The cable force response prediction value is the cable force prediction result output by the adaptive hybrid surrogate model for the particle's current position, which is directly used for subsequent particle fitness calculations.

[0028] Step S4: Calculate the particle fitness by subtracting the predicted cable force response from the measured cable force data. Update the particle position based on the particle fitness to obtain the optimal parameter combination. Substitute the optimal parameter combination into the initial finite element model to perform static analysis and obtain the corrected model parameters.

[0029] Specifically, particle fitness refers to the value obtained by calculating the absolute value of the difference between the predicted cable force response corresponding to the particle's current position vector and the measured cable force data. The smaller the absolute value of the difference, the closer the parameter combination corresponding to the particle position is to the true parameters. The optimal parameter combination refers to the combination of elastic modulus, cross-sectional area, and prestress values ​​corresponding to the globally optimal position of the particle swarm after iterative convergence. After substituting this combination into the initial finite element model to perform static analysis, verification cable force data is extracted. When the relative error between the verification cable force data and the measured cable force data meets the accuracy threshold, the optimal parameter combination is the corrected model parameters.

[0030] In one specific embodiment, step S1 includes:

[0031] A three-dimensional finite element model is established based on the engineering design parameters of the prestressed cable structure. The initial elastic modulus, initial cross-sectional area, and initial prestress value are used as input parameters of the three-dimensional finite element model. Static analysis is performed, and the axial stress of each prestressed cable element is multiplied by the initial cross-sectional area to obtain the simulated cable force data.

[0032] Vibrating wire strain sensors are deployed on the surface of the prestressed cable to collect strain time history data. The fundamental frequency of the prestressed cable is measured by the impact method. Based on the strain time history data and the fundamental frequency, the axial tension of the prestressed cable is calculated inversely based on the string vibration theory to obtain the measured cable force data.

[0033] The difference between the simulated cable force data and the measured cable force data is calculated. The absolute value of the difference is divided by the measured cable force data and multiplied by 100% to obtain the relative error percentage. When the relative error percentage is greater than the preset error threshold, the initial elastic modulus, initial cross-sectional area and initial prestress value are determined as parameters to be corrected.

[0034] Multiply the parameter to be corrected by the lower limit coefficient and the upper limit coefficient respectively to obtain the lower limit and upper limit of the value of each parameter to be corrected. The interval between the lower limit and the upper limit is determined as the value range of the parameter to be corrected.

[0035] Specifically, the three-dimensional finite element model is established based on the geometric dimensions, nominal material values, and load conditions in the engineering design drawings of the prestressed cable structure. The prestressed cable is discretized using three-dimensional rod elements that only transmit axial force, and the degrees of freedom of each node include displacement in three directions. The initial elastic modulus reflects the ability of the prestressed cable material to resist elastic deformation, the initial cross-sectional area is the cross-sectional area of ​​the prestressed cable perpendicular to the axial direction, and the initial prestress value simulates the initial stress state within the cable during tensioning. These three parameters are used together as input parameters for the finite element model. After performing static analysis, the axial stress of each prestressed cable element is extracted. The axial stress represents the axial normal stress borne per unit area of ​​the element. Multiplying the axial stress by the initial cross-sectional area yields the total axial tensile force borne by the element, i.e., the simulated cable force data.

[0036] Vibrating wire strain gauges are deployed along the axial direction of the prestressed cable. Their working principle is based on the change in the vibration frequency of the internal steel wire as the cable strain changes. The strain value is calculated by measuring the frequency change, and the steady-state strain is obtained by averaging the collected strain time-history data. The impact method applies transient impact excitation to the cable using a hammer. An accelerometer collects the vibration response signal, and a fast Fourier transform is performed on the signal. The frequency corresponding to the maximum amplitude peak is extracted from the spectrum as the fundamental frequency, which is the first natural frequency of the prestressed cable vibration. According to string vibration theory, the measured cable force is obtained by multiplying the mass per unit length, the square of the straight-line distance between the two anchor points, the square of the fundamental frequency, and a constant 4. The mass per unit length is obtained by multiplying the prestressed cable material density by the initial cross-sectional area. The straight-line distance between the two anchor points is directly read from the geometric parameters in the engineering design drawings. The fundamental frequency is extracted from the spectrum after the fast Fourier transform. The final result of multiplying these four factors is the measured cable force data, representing the actual axial tension borne by the prestressed cable in its current state.

[0037] The lower limit coefficient is less than 1, and the upper limit coefficient is greater than 1. These two coefficients are determined based on the actual fluctuation range of the engineering material properties, and are set to 0.9 times and 1.1 times the initial parameter values, respectively. This means the search range for the parameters to be corrected is within ±10% of the initial values. The initial elastic modulus, initial cross-sectional area, and initial prestress value are multiplied by the lower limit coefficient to obtain the lower bound of each parameter value, and multiplied by the upper limit coefficient to obtain the upper bound of each parameter value. The intervals between the lower and upper bounds of each of the three parameters together constitute a three-dimensional parameter space to be corrected. Each point in this space corresponds to a parameter combination consisting of the elastic modulus value, cross-sectional area value, and prestress value. Subsequent sample point generation and optimization searches are all performed within this three-dimensional parameter space.

[0038] In one specific embodiment, step S2 includes:

[0039] Within the range of values, the Latin hypercube sampling method is used to generate an initial sample point set. The parameter combination of each sample point in the initial sample point set is substituted into the initial finite element model to perform static analysis and obtain the cable force response value of each sample point.

[0040] The initial random forest is trained by using the parameter combination of the initial sample point set as input and the force response value as output. A candidate sample point set is generated in the parameter space. The candidate sample point set is input into the initial random forest. Based on the prediction variance, a preset number of candidate sample points with the largest prediction variance are selected from the candidate sample point set as supplementary sample points.

[0041] Substitute the supplementary sample points into the initial finite element model to perform static analysis, obtain the cable force response values ​​corresponding to the supplementary sample points, and merge the supplementary sample points and their corresponding cable force response values ​​into the initial sample point set to obtain the training sample set.

[0042] Specifically, the Latin hypercube sampling method is a space-filling sampling method. In its implementation, the value ranges of the three parameters—elastic modulus, cross-sectional area, and prestress value—are each divided into a predetermined number of equal-width sub-intervals. A value is randomly selected from each sub-interval of each parameter dimension. The sampled values ​​of the three parameters are then randomly paired and combined to generate an initial sample point set. Each sample point in the initial sample point set contains a parameter combination of elastic modulus, cross-sectional area, and prestress value. The sample points are uniformly distributed in the three-dimensional parameter space without clustering. The parameter combination of each sample point in the initial sample point set is sequentially substituted into the initial finite element model. Following the same static analysis process as in step S1, the axial stress of each prestressed cable element is extracted and multiplied by the corresponding cross-sectional area to obtain the cable force response value of that sample point. The cable force response value represents the magnitude of the axial tension of the prestressed cable calculated by the finite element model under that parameter combination.

[0043] Random forest is an ensemble learning model consisting of a predetermined number of decision trees. During training, each decision tree uses a bootstrap sampling method to randomly select a subset of samples with replacement from the initial sample point set. At each node split, several features are randomly selected from three parameter features as candidates. The feature that maximizes the reduction in the variance of the node's sample force response value, along with the split threshold, is used to perform the node split. This process continues until the number of leaf node samples falls below a predetermined minimum. The predicted value of a leaf node is the arithmetic mean of the force response values ​​of all samples within that node. After training, the parameter combination of each candidate sample point in the candidate sample point set is input into all decision trees in the initial random forest for prediction. The sum of the squares of the differences between each decision tree's predicted value and its arithmetic mean is calculated and then divided by the number of decision trees to obtain the prediction variance of that candidate sample point. The prediction variance reflects the degree of uncertainty in the initial random forest's prediction of the candidate position.

[0044] The candidate sample point set is randomly generated in the three-dimensional parameter space, with a much larger number of sample points than the initial sample point set, densely covering the entire parameter space. All candidate sample points are arranged in descending order of prediction variance. A predetermined number of candidate sample points with the largest prediction variance are selected as supplementary sample points. The location with the largest prediction variance corresponds to the region with the highest uncertainty in the initial random forest prediction. Supplementing this region with precise finite element calculation results can specifically improve the prediction accuracy of the subsequent surrogate model in high-uncertainty regions. The supplementary sample points are sequentially substituted into the initial finite element model to perform static analysis. Following the same calculation process as the initial sample point set, the cable force response values ​​corresponding to each supplementary sample point are obtained. The parameter combinations and corresponding cable force response values ​​of the supplementary sample points are appended to the data records of the initial sample point set. After merging, the training sample set is obtained. Each sample point in the training sample set contains four data items: elastic modulus, cross-sectional area, prestress, and corresponding cable force response value.

[0045] In one specific embodiment, step S3, dividing the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set, includes:

[0046] Standardize the parameter combination for each sample point in the training sample set to obtain a standardized parameter vector.

[0047] The Euclidean distance between any two sample points is calculated based on the standardized parameter vector. The Euclidean distance is then substituted into the Gaussian kernel function and all kernel function values ​​are summed to obtain the density function value of each sample point.

[0048] Sort all density function values ​​in ascending order, take the median as the density threshold, classify sample points with density function values ​​not lower than the density threshold as high-density region samples, and classify sample points with density function values ​​lower than the density threshold as low-density region samples.

[0049] Specifically, standardization involves subtracting the minimum value of the corresponding parameter in the training sample set from the elastic modulus, cross-sectional area, and prestress value of each sample point in the training sample set, and then dividing by the range of the corresponding parameter's value (i.e., the difference between the upper and lower bounds). This maps all three parameter values ​​to the interval between zero and one, eliminating the influence of the different dimensions and numerical ranges of the three parameters on subsequent distance calculations. The standardized parameter vector is a three-dimensional vector composed of the above three normalized components, representing the position coordinates of the corresponding sample point in the standardized parameter space.

[0050] Euclidean distance refers to the square root of the sum of the squares of the differences between corresponding components in the standardized parameter vectors of two sample points. This value reflects the geometric distance between the two sample points in the standardized parameter space. The Gaussian kernel function is specifically formed by dividing the square of the Euclidean distance by twice the square of the bandwidth parameter, taking the negative value as the exponent, and calculating the exponential function value with the natural constant as the base. The bandwidth parameter is determined by the standard deviation and sample size of the training sample set according to the Silverman rule. For each other sample point in the training sample set (excluding the target sample point), the Euclidean distance between that point and the target sample point is calculated and substituted into the Gaussian kernel function. All kernel function values ​​are summed to obtain the density function value of the target sample point. A larger density function value indicates a denser cluster of neighboring sample points in the standardized parameter space, while a smaller density function value indicates a sparser cluster of neighboring sample points.

[0051] The density threshold refers to the median value of all density function values ​​in the training sample set, which is the value at the center of the ascending order. This method ensures that the training sample set is equally divided into two parts. The high-density region consists of a subset of sample points with density function values ​​at or above the density threshold, corresponding to a densely distributed region in the parameter space. The low-density region consists of a subset of sample points with density function values ​​below the density threshold, corresponding to a sparsely distributed region in the parameter space. The two subsets do not overlap and, when merged, restore the complete training sample set.

[0052] In one specific embodiment, step S3, training a random forest on high-density region samples and training a Gaussian process regression on low-density region samples, includes:

[0053] The parameters of high-density region samples are used as input and the force response value is used as output to train a random forest containing a preset number of decision trees. The input parameter combinations are fed into each decision tree for prediction, and the arithmetic mean of the prediction values ​​of each decision tree is calculated to obtain the prediction result of the random forest.

[0054] Using the parameter combination of low-density region samples as input and the cable response value as output, a weighted combination of radial basis function kernel and Matérn kernel is constructed as the covariance kernel function. The hyperparameters of the covariance kernel function are optimized by maximizing the log marginal likelihood function. The covariance matrix of the low-density region samples is calculated and inverted to obtain the Gaussian process regression.

[0055] Specifically, the random forest consists of a predetermined number of decision trees. It uses parameter combinations (elastic modulus, cross-sectional area, and prestress) from high-density region samples as input features and the corresponding cable force response value as the output target for training. During training, each decision tree uses a bootstrap sampling method to randomly select samples with replacement from the high-density region samples, forming its own training subset. At each node split, several features are randomly selected as candidates from the three parameter features. The feature that maximizes the reduction in the variance of the cable force response value of the node samples, along with the splitting threshold, is selected to perform the node split. This process continues until the number of leaf node samples falls below a predetermined minimum. The predicted value of a leaf node is the arithmetic mean of the cable force response values ​​of all samples within that node. For any input parameter combination, it is fed into all decision trees in the random forest for prediction. Each decision tree, based on the comparison between the input parameter combination and the node splitting condition, propagates the prediction down the tree structure to the corresponding leaf node. The predicted value of that leaf node is taken as the prediction result of that decision tree. The arithmetic mean of the prediction results of all decision trees is calculated to obtain the prediction result of the random forest.

[0056] Gaussian process regression is trained using parameter combinations from low-density region samples as input and force response values ​​as output. The covariance kernel function is constructed using a weighted combination of radial basis function kernels and Matérn kernels. The radial basis function kernel calculates the exponential function value by dividing the square of the Euclidean distance between the two input parameter combinations by twice the square of the length scale parameter, taking the negative value as the exponent, and then multiplying it by the signal variance. The Matérn kernel introduces an additional polynomial correction term on the basis of the radial basis function kernel to enhance the fitting ability to non-smooth functions. The two are linearly combined through weighted coefficients to obtain the covariance kernel function. The hyperparameter set includes three parameters: signal variance, length scale, and weighting coefficients. The log-marginal likelihood function is composed of the logarithmic term of the determinant of the covariance matrix of the low-density region samples and the quadratic term of the force response vector after inverse transformation of the covariance matrix. By maximizing the log-marginal likelihood function, the above three hyperparameters are optimized. After obtaining the optimal combination of hyperparameters, the kernel function values ​​between each pair of all parameter combinations of the low-density region samples are calculated to form the covariance matrix. The covariance matrix is ​​inverted and stored to obtain the Gaussian process regression.

[0057] In one specific embodiment, step S3 involves comparing the density function value of the point to be predicted with a density threshold to obtain the predicted cable force response value, including:

[0058] Standardize the parameter combination of the point to be predicted to obtain the standardized parameter vector of the point to be predicted. Substitute the Euclidean distance between the standardized parameter vector of the point to be predicted and the standardized parameter vectors of each sample point in the training sample set into the Gaussian kernel function and sum them to obtain the density function value of the point to be predicted.

[0059] When the density function value of the point to be predicted is not lower than the density threshold, the parameter combination of the point to be predicted is input into the random forest, and the arithmetic mean of the predicted values ​​of each decision tree is calculated to obtain the predicted value of the force response.

[0060] When the density function value of the point to be predicted is lower than the density threshold, the covariance vector between the point to be predicted and the parameter combinations of the low-density region sample is calculated. The covariance vector is multiplied by the inverse of the covariance matrix and the cable force response value of the low-density region sample to obtain the cable force response prediction value.

[0061] Specifically, the standardized parameter vector of the point to be predicted is obtained using the same standardization method as the sample points in the training sample set. This involves subtracting the minimum value of the corresponding parameter in the training sample set from the elastic modulus, cross-sectional area, and prestress values ​​of the point to be predicted, and then dividing by the range of the corresponding parameter values, mapping the result to the interval between zero and one. The density function value of the point to be predicted is obtained by calculating the Euclidean distance between the standardized parameter vector of the point to be predicted and the standardized parameter vectors of all sample points in the training sample set, substituting each Euclidean distance into a Gaussian kernel function, and summing all kernel function values. This density function value is calculated in the same way as the density function values ​​of each sample point in the training sample set, and therefore is directly comparable to the density threshold.

[0062] When the density function value of the point to be predicted is not lower than the density threshold, the point is determined to be located in a high-density region of the parameter space. The parameter combination of the point to be predicted is then fed into all decision trees in the random forest for prediction. Each decision tree, based on the comparison result between the input parameter combination and the node splitting condition, propagates downwards along the tree structure to the corresponding leaf node and takes the predicted value of that leaf node. The arithmetic mean of the predicted values ​​of all decision trees is calculated to obtain the cable force response prediction value. When the density function value of the point to be predicted is lower than the density threshold, the point is determined to be located in a low-density region of the parameter space. The covariance vector is a vector formed by sequentially arranging the kernel function values ​​between the standardized parameter vector of the point to be predicted and the standardized parameter vector of each sample point in the low-density region. The dimension of this vector is equal to the number of samples in the low-density region. The covariance vector is transposed, multiplied by the inverse of the covariance matrix, and then multiplied by the cable force response value vector of the low-density region sample to finally obtain the cable force response prediction value.

[0063] In one specific embodiment, step S4 includes:

[0064] Within the range of values, the position vector and velocity vector of the particle swarm are randomly initialized. The position vector of each particle is input into the prediction algorithm corresponding to the predicted cable force response value. The absolute value of the difference between the predicted cable force value and the measured cable force data is calculated to obtain the particle fitness. The individual optimal position and the global optimal position of each particle are recorded.

[0065] The adaptive inertia weight is calculated based on the ratio of the current global optimal fitness to the initial global optimal fitness. The adaptive inertia weight, the individual optimal position, and the global optimal position are substituted into the velocity update formula to obtain the new position vector.

[0066] When the improvement of the global optimal fitness within a consecutive preset number of iterations is less than the stagnation threshold, a chaotic sequence is generated by the Logistic chaotic mapping. The position vector of the preset proportion of particles with the worst fitness is perturbed according to the chaotic sequence, the particle fitness and optimal position are updated, and the optimal parameter combination is output after iteration until convergence.

[0067] The optimal parameter combination is substituted into the initial finite element model to perform static analysis. The relative error between the verification cable force data and the measured cable force data is calculated to obtain the verification error. When the verification error is greater than the accuracy threshold, the optimal parameter combination is added to the training sample set in a weighted manner, and incremental updates are performed on the random forest and Gaussian process regression. Particle swarm optimization is re-executed until the verification error does not exceed the accuracy threshold, and the corrected model parameters are output.

[0068] Specifically, the particle swarm consists of a predetermined number of particles. Each particle's position vector contains three components corresponding to the elastic modulus, cross-sectional area, and prestress value, respectively. Each component is randomly generated in a uniform distribution within the range of the corresponding parameter values. The velocity vector also contains three components, each randomly generated within the range of negative to positive maximum velocity, with the maximum velocity being 20% ​​of the corresponding parameter value range. The position vectors of each particle are input into the corresponding prediction algorithm according to the density judgment process in step S3 to obtain the predicted cable force value. The absolute value of the difference between the predicted cable force value and the measured cable force data is taken to obtain the particle fitness. The smaller the fitness value, the closer the parameter combination corresponding to the particle position is to the true parameters. The individual optimal position refers to the position vector corresponding to the particle with the minimum fitness in all executed iterations. The global optimal position refers to the position vector with the minimum fitness among all individual optimal positions of all particles. The global optimal fitness is the fitness value corresponding to the global optimal position.

[0069] The adaptive inertia weight is obtained by multiplying the minimum inertia weight by the difference between the maximum and minimum inertia weights, and then multiplying by an exponential function. The exponent of the exponential function is the negative decay coefficient multiplied by the nonlinear exponential power of the current global optimal fitness divided by the initial global optimal fitness. The ratio of the current global optimal fitness to the initial global optimal fitness reflects the optimization progress. When the ratio is close to 1, the inertia weight approaches its maximum value; when the ratio is much less than 1, the inertia weight approaches its minimum value. The velocity update formula consists of three terms: the first term is the adaptive inertia weight multiplied by the current velocity vector, reflecting the particle's current motion inertia; the second term is the first learning factor multiplied by the first random number multiplied by the difference between the individual's optimal position and the current position vector, reflecting the particle's tendency to move closer to its historical optimal position; the third term is the second learning factor multiplied by the second random number multiplied by the difference between the global optimal position and the current position vector, reflecting the particle's tendency to move closer to the global optimal position. The sum of these three terms yields the new velocity vector. The sum of the current position vector and the new velocity vector yields the new position vector. Components of the new position vector that exceed the range of values ​​are corrected to their corresponding boundary values.

[0070] The recursive formula for the Logistic chaotic mapping is: the chaotic variable at the next time step equals the chaotic parameter multiplied by the current chaotic variable, then multiplied by one minus the current chaotic variable. A chaotic parameter of 4.0 is used to put the system in a completely chaotic state. The initial chaotic variable is randomly selected within the range of 0.1 to 0.9. A chaotic sequence of equal length to the number of particles is generated through recursive calculation. This chaotic sequence traverses the range from zero to one and exhibits pseudo-randomness. All particles are arranged in descending order of fitness. A preset proportion of particles with the worst fitness is selected. For each selected particle's position vector, a perturbation intensity coefficient multiplied by the corresponding parameter range multiplied by the chaotic sequence value minus 0.5 is added to each component of the position vector to obtain the perturbed position vector. Components of the perturbed position vector that exceed the range are corrected to their corresponding boundary values. The weighted supplementation method refers to using the optimal parameter combination and the corresponding validation force data as new sample points, and repeatedly adding them to the training sample set with a preset multiple of the weight of ordinary samples. The incremental update of random forest is achieved by recalculating the sample mean and sample number of the leaf node to which the new sample point belongs in a weighted manner. The incremental update of Gaussian process regression is achieved by performing incremental correction on the inverse of the covariance matrix through the Woodbury matrix identity, avoiding the need to recalculate the inverse of the complete covariance matrix.

[0071] Figure 2 This is a schematic diagram comparing the relative errors of the prestressed cable finite element model before and after correction in the embodiments of this application. Figure 2 This diagram illustrates the comparison of relative errors before and after correction of the prestressed cable finite element model in this application embodiment. The horizontal axis represents the prestressed cable number, and the vertical axis represents the percentage of relative error. The relative error curve before correction is obtained by dividing the absolute value of the difference between the simulated cable force data and the measured cable force data of each prestressed cable by the measured cable force data and multiplying by 100%. The values ​​range from 4.14% to 5.53%, all exceeding the accuracy threshold of 1%. The relative error curve after correction is obtained by performing the same calculation on the verification cable force data obtained by substituting the optimal parameter combination into the initial finite element model and performing static analysis, and the values ​​range from 0.10% to 0.22%, all below the accuracy threshold of 1%. This verifies the effectiveness of the improved particle swarm optimization algorithm combined with the online incremental learning mechanism described in this application in the correction of the prestressed cable finite element model.

[0072] The above describes the artificial intelligence-based finite element model correction method for prestressed cables in the embodiments of this application. The following describes the artificial intelligence-based finite element model correction system for prestressed cables in the embodiments of this application. One embodiment of the artificial intelligence-based finite element model correction system for prestressed cables in the embodiments of this application includes:

[0073] The modeling module is used to establish an initial finite element model based on the engineering design parameters of the prestressed cable structure, calculate the relative error between the simulated cable force data and the collected measured cable force data, and determine the parameters to be corrected and their value ranges.

[0074] The calculation module is used to generate a set of sample points within the range of the values ​​and perform finite element calculations to obtain a training sample set;

[0075] The training module is used to divide the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set, train a random forest on the high-density region samples, train a Gaussian process regression on the low-density region samples, compare the density function value of the point to be predicted with a density threshold, and call the prediction result of the random forest when the density function value of the point to be predicted is not lower than the density threshold, and call the prediction result of the Gaussian process regression when the density function value of the point to be predicted is lower than the density threshold to obtain the predicted value of the force response.

[0076] The update module is used to calculate the particle fitness by subtracting the predicted cable force response value from the measured cable force data, update the particle position according to the particle fitness, obtain the optimal parameter combination, and substitute the optimal parameter combination into the initial finite element model to perform static analysis to obtain the corrected model parameters.

[0077] 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 do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for correcting the finite element model of prestressed cable based on artificial intelligence, characterized in that, The method includes: Step S1: Establish an initial finite element model based on the engineering design parameters of the prestressed cable structure, calculate the relative error between the simulated cable force data and the collected measured cable force data, and determine the parameters to be corrected and their value ranges. Step S2: Generate a set of sample points within the range of values ​​and perform finite element calculations to obtain a training sample set; Step S3: Divide the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set. Train a random forest on the high-density region samples and train a Gaussian process regression on the low-density region samples. Compare the density function value of the point to be predicted with a density threshold. When the density function value of the point to be predicted is not lower than the density threshold, call the prediction result of the random forest. When the density function value of the point to be predicted is lower than the density threshold, call the prediction result of the Gaussian process regression to obtain the predicted value of the force response. Step S4: Calculate the particle fitness by subtracting the predicted cable force response value from the measured cable force data. Update the particle position based on the particle fitness to obtain the optimal parameter combination. Substitute the optimal parameter combination into the initial finite element model to perform static analysis and obtain the corrected model parameters.

2. The method for correcting the finite element model of prestressed cable based on artificial intelligence according to claim 1, characterized in that, Step S1 includes: A three-dimensional finite element model is established based on the engineering design parameters of the prestressed cable structure. The initial elastic modulus, initial cross-sectional area, and initial prestress value are used as input parameters of the three-dimensional finite element model. Static analysis is performed, and the axial stress of each prestressed cable element is multiplied by the initial cross-sectional area to obtain the simulated cable force data. Vibrating wire strain sensors are deployed on the surface of the prestressed cable to collect strain time history data. The fundamental frequency of the prestressed cable is measured by the impact method. Based on the strain time history data and the fundamental frequency, the axial tension of the prestressed cable is calculated inversely based on the string vibration theory to obtain the measured cable force data. The difference between the simulated cable force data and the measured cable force data is calculated. The absolute value of the difference is divided by the measured cable force data and multiplied by 100% to obtain the relative error percentage. When the relative error percentage is greater than a preset error threshold, the initial elastic modulus, the initial cross-sectional area and the initial prestress value are determined as parameters to be corrected. The parameters to be corrected are multiplied by a lower limit coefficient and an upper limit coefficient respectively to obtain the lower bound and upper bound of each parameter to be corrected. The interval between the lower bound and the upper bound is determined as the range of values ​​of the parameter to be corrected.

3. The method for correcting the finite element model of prestressed cable based on artificial intelligence according to claim 1, characterized in that, Step S2 includes: Within the specified range, an initial sample point set is generated using the Latin hypercube sampling method. The parameter combination of each sample point in the initial sample point set is substituted into the initial finite element model to perform static analysis, thereby obtaining the cable force response value of each sample point. The initial random forest is trained by taking the parameter combination of the initial sample point set as input and the cable response value as output. A candidate sample point set is generated in the parameter space. The candidate sample point set is input into the initial random forest. Based on the prediction variance, a preset number of candidate sample points with the largest prediction variance are selected from the candidate sample point set as supplementary sample points. The supplementary sample points are substituted into the initial finite element model to perform static analysis, and the cable force response values ​​corresponding to the supplementary sample points are obtained. The supplementary sample points and the corresponding cable force response values ​​are then merged into the initial sample point set to obtain the training sample set.

4. The method for correcting the finite element model of prestressed cable based on artificial intelligence according to claim 1, characterized in that, In step S3, the training sample set is divided into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set, including: The parameter combination of each sample point in the training sample set is standardized to obtain a standardized parameter vector. The Euclidean distance between any two sample points is calculated based on the standardized parameter vector. The Euclidean distance is then substituted into the Gaussian kernel function, and all kernel function values ​​are summed to obtain the density function value of each sample point. All density function values ​​are sorted in ascending order, and the median is taken as the density threshold. Sample points with density function values ​​not lower than the density threshold are classified as high-density region samples, and sample points with density function values ​​lower than the density threshold are classified as low-density region samples.

5. The method for correcting the finite element model of prestressed cable based on artificial intelligence according to claim 4, characterized in that, In step S3, training a random forest on the high-density region samples and training a Gaussian process regression on the low-density region samples includes: The parameters of the high-density region samples are used as input and the force response value is used as output to train a random forest containing a preset number of decision trees. The input parameter combinations are fed into each decision tree for prediction, and the arithmetic mean of the prediction values ​​of each decision tree is calculated to obtain the prediction result of the random forest. Using the parameter combination of the low-density region samples as input and the cable response value as output, a weighted combination of the radial basis function kernel and the Matérn kernel is constructed as the covariance kernel function. The hyperparameters of the covariance kernel function are optimized by maximizing the log marginal likelihood function. The covariance matrix of the low-density region samples is calculated and inverted to obtain the Gaussian process regression.

6. The artificial intelligence-based finite element model correction method for prestressed cables according to claim 5, characterized in that, In step S3, the density function value of the point to be predicted is compared with the density threshold to obtain the cable force response prediction value, including: Standardize the parameter combination of the point to be predicted to obtain the standardized parameter vector of the point to be predicted. Substitute the Euclidean distance between the standardized parameter vector of the point to be predicted and the standardized parameter vectors of each sample point in the training sample set into the Gaussian kernel function and sum them to obtain the density function value of the point to be predicted. When the density function value of the point to be predicted is not lower than the density threshold, the parameter combination of the point to be predicted is input into the random forest, and the arithmetic mean of the predicted values ​​of each decision tree is calculated to obtain the predicted value of the force response. When the density function value of the point to be predicted is lower than the density threshold, the covariance vector between the point to be predicted and each parameter combination of the low-density region sample is calculated. The covariance vector is multiplied by the inverse of the covariance matrix and the cable force response value of the low-density region sample to obtain the cable force response prediction value.

7. The method for correcting the finite element model of prestressed cable based on artificial intelligence according to claim 1, characterized in that, Step S4 includes: Within the specified value range, the position vector and velocity vector of the particle swarm are randomly initialized. The position vector of each particle is input into the prediction algorithm corresponding to the predicted cable force response value. The absolute value of the difference between the predicted cable force value and the measured cable force data is calculated to obtain the particle fitness. The individual optimal position and global optimal position of each particle are recorded. The adaptive inertia weight is calculated based on the ratio of the current global optimal fitness to the initial global optimal fitness. The adaptive inertia weight, the individual optimal position, and the global optimal position are substituted into the velocity update formula to obtain the new position vector. When the improvement of the global optimal fitness within a consecutive preset number of iterations is less than the stagnation threshold, a chaotic sequence is generated by the Logistic chaotic mapping. The position vector of the preset proportion of particles with the worst fitness is perturbed according to the chaotic sequence, the particle fitness and optimal position are updated, and the optimal parameter combination is output after iteration until convergence. The optimal parameter combination is substituted into the initial finite element model to perform static analysis. The relative error between the verification cable force data and the measured cable force data is calculated to obtain the verification error. When the verification error is greater than the accuracy threshold, the optimal parameter combination is added to the training sample set in a weighted manner, and incremental updates are performed on the random forest and the Gaussian process regression. Particle swarm optimization is re-executed until the verification error does not exceed the accuracy threshold, and the corrected model parameters are output.

8. A prestressed cable finite element model correction system based on artificial intelligence, characterized in that, For implementing the AI-based prestressed cable finite element model correction method as described in any one of claims 1-7, the AI-based prestressed cable finite element model correction system comprises: The modeling module is used to establish an initial finite element model based on the engineering design parameters of the prestressed cable structure, calculate the relative error between the simulated cable force data and the collected measured cable force data, and determine the parameters to be corrected and their value ranges. The calculation module is used to generate a set of sample points within the range of the values ​​and perform finite element calculations to obtain a training sample set; The training module is used to divide the training sample set into high-density region samples and low-density region samples according to the density function values ​​of each sample point in the training sample set, train a random forest on the high-density region samples, train a Gaussian process regression on the low-density region samples, compare the density function value of the point to be predicted with a density threshold, and call the prediction result of the random forest when the density function value of the point to be predicted is not lower than the density threshold, and call the prediction result of the Gaussian process regression when the density function value of the point to be predicted is lower than the density threshold to obtain the predicted value of the force response. The update module is used to calculate the particle fitness by subtracting the predicted cable force response value from the measured cable force data, update the particle position according to the particle fitness, obtain the optimal parameter combination, and substitute the optimal parameter combination into the initial finite element model to perform static analysis to obtain the corrected model parameters.

9. The system according to claim 8, characterized in that, An initial finite element model is established based on the engineering design parameters of the prestressed cable structure. The relative error between the simulated cable force data and the collected measured cable force data is calculated to determine the parameters to be corrected and their value ranges, including: A three-dimensional finite element model is established based on the engineering design parameters of the prestressed cable structure. The initial elastic modulus, initial cross-sectional area, and initial prestress value are used as input parameters of the three-dimensional finite element model. Static analysis is performed, and the axial stress of each prestressed cable element is multiplied by the initial cross-sectional area to obtain the simulated cable force data. Vibrating wire strain sensors are deployed on the surface of the prestressed cable to collect strain time history data. The fundamental frequency of the prestressed cable is measured by the impact method. Based on the strain time history data and the fundamental frequency, the axial tension of the prestressed cable is calculated inversely based on the string vibration theory to obtain the measured cable force data. The difference between the simulated cable force data and the measured cable force data is calculated. The absolute value of the difference is divided by the measured cable force data and multiplied by 100% to obtain the relative error percentage. When the relative error percentage is greater than a preset error threshold, the initial elastic modulus, the initial cross-sectional area and the initial prestress value are determined as parameters to be corrected. The parameters to be corrected are multiplied by a lower limit coefficient and an upper limit coefficient respectively to obtain the lower bound and upper bound of each parameter to be corrected. The interval between the lower bound and the upper bound is determined as the range of values ​​of the parameter to be corrected.

10. The system according to claim 8, characterized in that, A set of sample points is generated within the range of the given values, and finite element analysis is performed to obtain a training sample set, including: Within the specified range, an initial sample point set is generated using the Latin hypercube sampling method. The parameter combination of each sample point in the initial sample point set is substituted into the initial finite element model to perform static analysis, thereby obtaining the cable force response value of each sample point. The initial random forest is trained by taking the parameter combination of the initial sample point set as input and the cable response value as output. A candidate sample point set is generated in the parameter space. The candidate sample point set is input into the initial random forest. Based on the prediction variance, a preset number of candidate sample points with the largest prediction variance are selected from the candidate sample point set as supplementary sample points. The supplementary sample points are substituted into the initial finite element model to perform static analysis, and the cable force response values ​​corresponding to the supplementary sample points are obtained. The supplementary sample points and the corresponding cable force response values ​​are then merged into the initial sample point set to obtain the training sample set.

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