Bridge pier digital twinning intelligent monitoring method and system based on proxy model

Abstract

The invention discloses a bridge pier digital twinning intelligent monitoring method and system based on an agent model, and relates to the technical field of bridge pier state monitoring. The method comprises the following steps: constructing a finite element model of a to-be-monitored pier; carrying out dimension reduction and feature extraction on the input and output data set by utilizing an intrinsic orthogonal decomposition method; constructing an agent model by using a Gaussian process regression method for training, and verifying the agent model by using a verification strategy combining adaptive particle swarm optimization and nested cross combination in the training process to obtain an optimal hyper-parameter; and retraining the proxy model by using the optimal hyper-parameter to obtain a final digital twin intelligent monitoring proxy model for the bridge pier. The invention aims to carry out high-precision, rapid and visual prediction and evaluation on the health state of the bridge pier under various complex external working conditions such as horizontal stress, scouring depth, vibration, inclination and settlement.

Description

Technical Field

[0001] The present invention relates to the technical field of bridge pier status monitoring technology, and in particular to a bridge pier digital twin intelligent monitoring method and system based on an agent model. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] With the continuous development of bridge construction, the importance of health status monitoring of bridge piers, as the key supporting structures of bridges, has become increasingly prominent. Traditional bridge pier monitoring technologies mainly rely on finite element model analysis and on-site sensor data acquisition. However, these technologies have many limitations. First, during the modeling process of the finite element model, due to assumptions and simplifications in terms of unit division, boundary condition setting, and material parameter values, there is a deviation between the calculated results and the actual response. Secondly, when dealing with high-dimensional and multi-coupled input conditions, the traditional monitoring method has a slow training process and limited accuracy. In addition, the existing technology has deficiencies in model generalization capabilities and is difficult to adapt to various variable working conditions.

[0004] Despite the rise of digital twin technology, which has played a significant role in bridge monitoring, existing technologies still face challenges. For example, some technologies offer only a simple combination of finite element simulation and visualization, lacking the ability to quantify model uncertainty. Other technologies are inefficient in hyperparameter optimization, impacting model training speed and accuracy. Furthermore, existing technologies lack a robust multi-level early warning system, preventing them from providing timely and accurate warnings of potential risks to bridge piers.

[0005] In summary, existing technologies for bridge pier health monitoring suffer from issues such as insufficient model accuracy, low training efficiency, weak generalization capabilities, and imperfect early warning systems. Therefore, there is an urgent need to develop an intelligent monitoring method that can accurately, quickly, and visually predict and assess the health of bridge piers to meet the high demands of modern bridge engineering for pier monitoring. Summary of the Invention

[0006] In response to the shortcomings of the existing technology, the purpose of the present invention is to provide a digital twin intelligent monitoring method and system for bridge piers based on an agent model, which aims to perform high-precision, rapid and visual prediction and evaluation of the health status of bridge piers under various complex external working conditions such as horizontal force, scour depth, vibration, tilt, and settlement.

[0007] In order to achieve the above object, the present invention is implemented through the following technical solutions: A first aspect of the present invention provides a bridge pier digital twin intelligent monitoring method based on an agent model, comprising the following steps: Construct a finite element model of the bridge pier to be monitored, using the combination of working condition factors as input data. The finite element model calculates the bridge pier status data based on the working condition data as output data, thus obtaining an input and output data set. The eigenorthogonal decomposition method is used to reduce the dimension and extract features of the input and output data sets to obtain the characteristic coefficient matrix; The surrogate model is constructed using the Gaussian process regression method. The characteristic coefficient matrix is ​​used as output and the operating condition factor combination is used as input to train the surrogate model. During the training process, the surrogate model is verified using an adaptive particle swarm optimization and nested cross validation strategy to obtain the optimal hyperparameters. The agent model is retrained using the optimal hyperparameters to obtain the final bridge pier digital twin intelligent monitoring agent model, which is then applied in the digital twin platform.

[0008] Furthermore, the working condition factor combination is a combination of horizontal pressure data, scour depth data, vibration data, tilt data and settlement data, and the pier status data includes pier stress field data, plastic strain field data and displacement field information.

[0009] Furthermore, the specific steps of using the eigenorthogonal decomposition method to reduce the dimension and extract features of the input and output data sets are as follows: The bridge pier status data are organized into a snapshot matrix, and the snapshot matrix is ​​subjected to separation mean field processing; Perform snapshot eigenorthogonal decomposition on the snapshot matrix after separation of the mean field to obtain the eigenvalue diagonal matrix and eigenvector matrix, and sort the eigenvalues; Based on the snapshot matrix, eigenvalue diagonal matrix and eigenvector matrix after separation of the mean field, the orthogonal basis matrix is ​​calculated according to the eigenvalue sorting, and the characteristic coefficient matrix is ​​further calculated; The pier status data is reconstructed by extracting orthogonal basis vectors and characteristic coefficient matrices based on eigenvalues.

[0010] Furthermore, the specific steps for training the agent model with the characteristic coefficient matrix as output and the working condition factor combination as input are as follows: Divide the training set and test set according to the characteristic coefficient matrix and the combination of working condition factors; The weighted sum of radial basis function and Mattern function is used as kernel function; The training set is used to iteratively optimize the kernel function's hyperparameters, and the test set is used to test to obtain the optimal hyperparameters.

[0011] Furthermore, the specific steps for verifying the surrogate model using the adaptive particle swarm optimization and nested cross validation strategy during the training process are as follows: Divide the input and output data sets into several subsets as the basis for outer layer verification; In each outer layer, a non-repeated subset is selected as the outer layer validation set for the final evaluation of the model, and the remaining subsets are used as the outer layer training set for inner layer cross-validation again to search for Gaussian process regression through particle swarm optimization.

[0012] Furthermore, the specific steps of inner cross validation are: The outer training set is evenly divided into several groups for inner cross-validation. In each inner fold, a non-repeated subset is selected as the inner test set, and the remaining subsets are used as the inner training set to train the Gaussian process regression model. Use the adaptive particle swarm optimization method to optimize hyperparameters, and use the trained proxy model to calculate the root mean square error in the inner test set, record it and enter the inner next fold cross validation; Finally, all cross-validations in the inner layer are completed, and the hyperparameter combination with the smallest root mean square error is selected.

[0013] Furthermore, the digital twin platform visualizes the overall physical field of the bridge pier obtained by the digital twin intelligent monitoring agent model of the bridge pier in real time, and initiates a multi-level early warning strategy through disaster prediction.

[0014] A second aspect of the present invention provides a digital twin intelligent monitoring system for bridge piers based on an agent model, comprising: The data set acquisition module is configured to construct a finite element model of the bridge pier to be monitored, using a combination of working condition factors as input data and bridge pier status data calculated by the finite element model based on the working condition data as output data, thereby obtaining an input and output data set; The data set processing module is configured to perform dimensionality reduction and feature extraction on the input and output data sets using an eigenorthogonal decomposition method to obtain a feature coefficient matrix; The surrogate model training module is configured to construct a surrogate model using the Gaussian process regression method, with the characteristic coefficient matrix as output and the operating condition factor combination as input to train the surrogate model. During the training process, the surrogate model is verified using a validation strategy combining adaptive particle swarm optimization and nested crossover to obtain the optimal hyperparameters; The agent model application module is configured to retrain the agent model using the optimal hyperparameters to obtain the final bridge pier digital twin intelligent monitoring agent model, and apply the bridge pier digital twin intelligent monitoring agent model in the digital twin platform.

[0015] The third aspect of the present invention provides a computer-readable storage medium, which stores a computer program, and the computer program is suitable for being loaded by a processor and executing the steps in the agent model-based bridge pier digital twin intelligent monitoring method as described in the first aspect of the present invention.

[0016] A fourth aspect of the present invention provides a computer device, comprising: a processor adapted to execute a computer program; A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium. When the computer program is executed by the processor, the agent-model-based bridge pier digital twin intelligent monitoring method as described in the first aspect of the present invention is implemented.

[0017] One or more of the above technical solutions have the following beneficial effects: The present invention discloses a digital twin intelligent monitoring method and system for bridge piers based on an agent model. Through the above links, it can not only solve the problems of slow training and limited accuracy of traditional models under high-dimensional and multi-coupled input conditions, but also ensure that the selected model has good robustness under various variable working conditions. The agent model of the present invention can be connected with the bridge monitoring big data system and the digital twin platform to provide more intelligent, efficient and reliable technical means for bridge pier maintenance and structural safety assessment. In summary, the digital twin intelligent monitoring method for bridge piers based on the nested cross-validation PSO-POD-GPR agent model fully utilizes the advantages of POD in feature dimensionality reduction, the efficiency of PSO in hyperparameter search, and the advantages of GPR in uncertainty quantification and generalization performance, providing a new solution for intelligent monitoring and early warning of bridge foundation parts, which has broad application prospects and significant engineering value.

[0018] By constructing a finite element model and utilizing a combination of operating factors as input data, this method can more accurately simulate the actual state of bridge piers under actual operating conditions, providing a more realistic data basis for monitoring. Furthermore, by employing the proper orthogonal decomposition method to reduce the dimensionality of the data and extract features, this method effectively reduces the amount of data, improves computational efficiency, and extracts more representative features, further enhancing the accuracy and efficiency of monitoring.

[0019] This method uses Gaussian process regression to construct a surrogate model and employs a validation strategy combining adaptive particle swarm optimization and nested crosstalk. This allows for more accurate determination of optimal hyperparameters, resulting in better training of the surrogate model and improved accuracy in predicting bridge pier conditions. Compared to traditional single-verification methods, this optimized model training and validation approach provides a more comprehensive assessment of model performance, avoids overfitting and underfitting, and ensures the model's reliability and stability in practical applications.

[0020] The resulting digital twin intelligent monitoring agent model for bridge piers is applied to a digital twin platform. This model provides real-time visualization of the overall physical field of the piers, enabling monitoring personnel to intuitively understand the piers' real-time status. Furthermore, by initiating a multi-level early warning strategy through disaster prediction, potential safety hazards can be promptly identified, enabling proactive measures to effectively safeguard the piers.

[0021] Advantages of additional aspects of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without any creative work.

[0023] Figure 1 This is a flow chart of the intelligent monitoring method for bridge pier digital twins based on the agent model in the first embodiment of the present invention; Figure 2 This is a flow chart of the intrinsic orthogonal decomposition process in Example 1 of the present invention. DETAILED DESCRIPTION

[0024] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by those skilled in the art to which the present invention belongs.

[0025] It should be noted that the terms used herein are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention. As used herein, unless the context clearly indicates otherwise, the singular form is intended to include the plural form. In addition, it should be understood that when the terms "comprise" and / or "include" are used in this specification, they indicate the presence of features, steps, operations, devices, components and / or their combinations; The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0026] Example 1: The first embodiment of the present invention provides a digital twin intelligent monitoring method for bridge piers based on an agent model, such as Figure 1 As shown, the following steps are included: Step 1: Construct a finite element model of the bridge pier to be monitored, using the working condition factor combination as input data. The finite element model calculates the bridge pier status data based on the working condition data as output data to obtain the input and output data sets.

[0027] Among them, the working condition factor combination is a combination of horizontal pressure data, scour depth data, vibration data, tilt data and settlement data, and the pier status data includes pier stress field data, plastic strain field data and displacement field information.

[0028] This example uses Abaqus to build a finite element model of a bridge pier based on field measurements and design drawings, and then performs finite element numerical simulation. Latin hypercube sampling is used to extract multi-factor input data related to the pier, including combinations of working conditions such as horizontal pressure, scour depth, vibration, tilt, and settlement, as the input dataset. The finite element calculations of the finite element model yield information on the pier's stress, plastic strain, and displacement fields as the output dataset.

[0029] Step 2: Use the eigenorthogonal decomposition method to reduce the dimension and extract features of the input and output data sets to obtain the feature coefficient matrix.

[0030] For this high-dimensional input and output data set, this embodiment introduces the Proper Orthogonal Decomposition (POD) method for dimensionality reduction and feature extraction, eliminating redundant dimensions and highlighting the main features, making subsequent model training more efficient. By performing proper orthogonal decomposition on the snapshot matrix composed of the finite element output data of each node under different working conditions, the obtained characteristic coefficient matrix is ​​used as output, and the combination of factors in different working conditions is used as input to obtain the bridge pier physical field proxy model through Gaussian process regression.

[0031] like Figure 2 The specific steps are as follows: Step 2.1: Organize the bridge pier status data into a snapshot matrix and perform separated mean field processing on the snapshot matrix.

[0032] In a specific implementation, in order to obtain different modes of intrinsic orthogonal decomposition, it is necessary to first calculate samples of system behavior (the solutions at different times for dynamic problems and the equilibrium solutions under different parameter values ​​for static problems). These samples are used to form a snapshot matrix. Taking the stress field data of bridge piers as an example, this embodiment divides the grid according to the component ratio in the Abaqus finite element software, and derives the stress values ​​at all grid nodes of the multi-pile bridge pier cap under different working conditions from Abaqus to construct a matrix of size N×K, as shown in formula (1): (1).

[0033] Where N represents the number of grid nodes, K represents the number of working conditions, and S i Represents the stress value of all grid nodes under a certain working condition. In this embodiment, the data is concentrated into an S iThe sample point is called a snapshot, and the dataset It is called the snapshot matrix. The snapshot matrix is ​​separated by mean field, as shown in formula (2): (2).

[0034] Where, is the snapshot matrix after separating the mean field, i.e. the stress field snapshot matrix, The vector obtained by taking the average of the stress values ​​of all mesh nodes for all load cases.

[0035] Step 2.2: Perform snapshot eigenorthogonal decomposition on the snapshot matrix after separating the mean field to obtain the eigenvalue diagonal matrix and eigenvector matrix, and sort the eigenvalues.

[0036] In a specific implementation, different from the original intrinsic orthogonal decomposition, in order to reduce the size of the covariance matrix and further reduce the dimension, this embodiment adopts snapshot intrinsic orthogonal decomposition to obtain the covariance matrix, as shown in formula (3): (3).

[0037] Where, is the covariance matrix of size K×K.

[0038] Then, the covariance matrix is ​​decomposed by eigenvectors to obtain the eigenvalue matrix and eigenvector matrix. In order to facilitate the eigenvalue interception of orthogonal basis vectors and eigencoefficient matrices in subsequent steps, they are sorted from large to small according to the size of the eigenvalues. The corresponding index of the eigenvalue is recorded during the sorting process, and the eigenvectors are sorted synchronously, as shown in Equation (4).

[0039] (4).

[0040] Where, is a K×K eigenvector matrix, is a K×K diagonal eigenvalue matrix, where the eigenvalue Arrange from largest to smallest , is the eigenvector corresponding to working condition i, the order is synchronized with the eigenvalue matrix, and i is the counting parameter of the working condition.

[0041] Step 2.3: Based on the snapshot matrix, eigenvalue diagonal matrix, and eigenvector matrix after the separated mean field, the orthogonal basis matrix is ​​calculated according to the eigenvalue sorting, and the characteristic coefficient matrix is ​​further calculated.

[0042] Step 2.3.1: Based on the snapshot matrix, eigenvalue diagonal matrix, and eigenvector matrix after the separated mean field, calculate the orthogonal basis matrix according to the eigenvalue sorting.

[0043] As shown in formula (5): (5).

[0044] Where, is an orthogonal basis matrix of size N×K, is an orthogonal basis vector, each of which represents the mechanical behavior and characteristics of each modal of the physical system. Represents the proportion of the orthogonal basis corresponding to the i-th working condition in the behavior and characteristics of the entire physical system.

[0045] Step 2.3.2: Calculate the characteristic coefficient matrix.

[0046] The corresponding characteristic coefficient is calculated by formula (6): (6).

[0047] Where, is the characteristic coefficient matrix of size K×K, Represents the characteristic coefficients of the first-order orthogonal basis vectors of the snapshots corresponding to the K working conditions. i It can be reconstructed based on the orthogonal basis vectors and their characteristic coefficients according to formula (7): (7).

[0048] Step 2.4: Reconstruct the pier status data by extracting the orthogonal basis vectors and characteristic coefficient matrix based on the eigenvalues.

[0049] Because the orthogonal basis vectors in an orthogonal basis matrix are all orthogonal and normalized, any number of orthogonal basis vectors can be used to construct a reduced-order subspace, thereby achieving model order reduction. To control the number of orthogonal basis vectors to reduce error, the energy ratio (the ratio of the first n eigenvalues ​​to the sum of all eigenvalues) is controlled, as shown in the formula. In this embodiment, 99.9% is used.

[0050] (8).

[0051] Wherein, j represents the counting parameter of the working condition.

[0052] Finally, any stress field snapshot can be reconstructed by intercepting the first n orthogonal basis vectors to achieve order reduction, which greatly reduces the amount of computation required to train the proxy model, as shown in Equation (9): (9).

[0053] Therefore, if the stress field snapshot matrix is ​​determined, the stress field snapshots at different sample points are determined, and the orthogonal basis vectors of the entire stress field snapshot matrix are also determined, then only the characteristic coefficients change when reconstructing each sample point after order reduction. Therefore, the characteristic coefficients can reflect the stress field snapshots calculated for different working conditions within a given range. Therefore, there is a mapping relationship between different finite element input working conditions and the characteristic coefficients. As shown in Equation (10), if the corresponding mapping relationship can be found, the stress field of the entire multi-pile bridge pier cap under different other working conditions can be obtained.

[0054] (10).

[0055] Where, is the mapping relationship between the finite element input conditions and characteristic coefficients, is the working condition input by finite element, For working conditions The corresponding characteristic coefficient vector. Using the surrogate model, we can infer the corresponding characteristic coefficient vector under the new finite element input condition. The physical field under the new condition can be expressed as a linear combination of POD basis functions. Next, Gaussian process regression is used to find the mapping relationship between this finite element input condition and the characteristic coefficient.

[0056] Step 3: Use the Gaussian process regression method to construct a surrogate model, use the characteristic coefficient matrix as output and the operating condition factor combination as input to train the surrogate model. During the training process, the surrogate model is verified using a validation strategy combining adaptive particle swarm optimization and nested cross-validation to obtain the optimal hyperparameters.

[0057] In a specific implementation, in order to effectively prevent overfitting, obtain unbiased evaluation indicators of the proxy model in the entire data set, and improve the generalization ability of the proxy model under unknown working conditions, this embodiment adopts the Nested Cross Validation (NCV) validation strategy of Adaptive Particle Swarm Optimization (APSO). Figure 1 As shown, the characteristic coefficient matrix obtained by intrinsic orthogonal decomposition is used as the output data set, the working condition factor combination is used as the input data set, and is evenly divided into K fold Subsets are used as the outer layer verification basis, with a total of K cycles fold times, called K fold In each outer fold, a data subset that is not repeated in the previous fold is reserved as the outer validation set for the final evaluation model; the remaining K fold-1 subset is used as the outer training set for inner K-fold cross validation again, which is used to search for the optimal hyperparameter combination of Gaussian Process Regression (GPR) model through particle swarm optimization. fold -1 subsets are evenly divided into K' subsets. Similarly, one subset that does not repeat with the previous fold is selected as the inner test set, and the remaining K'-1 subsets are used as the inner training set for Gaussian process regression. Each fold will use different training / testing partitions to train and verify the GPR model. In the process of training the GPR model, PSO is used for hyperparameter optimization. The proxy model obtained by the inner GPR-PSO training is used to calculate the root mean square error in the inner test set, record it and enter the next inner fold cross-validation, and finally complete all inner cross-validations. The hyperparameter combination with the smallest root mean square error is selected, and the Gaussian process regression proxy model is trained on the outer training set of this fold. The evaluation indicators (Root Mean Squared Error (RMSE), Coefficient of Determination (R-Square, R2), Mean Absolute Error (MAE)) are calculated on the outer validation set of this fold. After the outer layer completes K cycles, the evaluation metrics of all outer folds on the outer validation set are summarized. The average evaluation metric for each fold serves as the true unbiased evaluation metric of the Gaussian process regression surrogate model on the complete dataset, providing an objective and unbiased measure of the model's generalization ability. The hyperparameter combinations used for each outer fold on the outer validation set are statistically analyzed. If a mode exists for the hyperparameter combination, the mode hyperparameter combination is used. If no mode exists, the hyperparameter combination that yields the lowest root mean square error (RMSE) on the outer validation set is used.

[0058] The specific steps are as follows: Step 3.1: Train the agent model with the characteristic coefficient matrix as output and the operating condition factor combination as input.

[0059] Step 3.1.1: Divide the training set according to the characteristic coefficient matrix and working condition factor combination k train With the test set k test .

[0060] Specifically, the input values ​​used to train the Gaussian process regression of multi-pile pier caps are shown in formula (11): (11).

[0061] Where, represents the combination matrix of working condition factors of the training set, f represents the vector composed of the size of different factors of each working condition, ktrain The number of input conditions for finite element analysis is given by equation (12): (12).

[0062] Where, represents the characteristic coefficient matrix, is n× k train Through k train The characteristic coefficient matrix after the intrinsic orthogonal decomposition of the stress field calculated by finite element under each working condition is: for k train The characteristic coefficient vector under each working condition is: for k train The nth-order eigenvalue under each working condition, where n is the number of retained orthogonal basis vectors. Each working condition vector input corresponds to a characteristic coefficient vector output. The training set and test set are normalized, where the training set and test set satisfy Equation (13): (13).

[0063] Where, is the characteristic coefficient set of the test set, is the mean of the working condition factor values ​​of the training set input data. Since the actual data usually contains a certain amount of noise, the noise satisfies the mean of zero and the variance is Gaussian distribution, yes k train dimensional identity matrix.

[0064] Step 3.1.2: Use the weighted sum of the radial basis function and the Mattern function as the kernel function.

[0065] Specifically, Input data condition factor values ​​for the training set and the working condition factor values ​​of the training set test data The covariance matrix of is also a kernel function. Here, the weighted sum of the radial basis function and the Matern function is used as the kernel function to achieve nonlinear approximation, as shown in formula (14): (14).

[0066] Where, To calculate the covariance, since the covariance calculation is complicated, the kernel function is used to approximate it. is the radial basis kernel function, is the Matern kernel function, C is the constant hyperparameter of the weighted sum of the two kernel functions, where the radial basis kernel function is shown in formula (15): (15).

[0067] Where, is the hyperparameter of the radial basis kernel function, and the Matern kernel function is shown in formula (16): (16).

[0068] Where, is the hyperparameter of the Matern kernel function. The hyperparameter is continuously optimized in the subsequent process to obtain the proxy model with the best prediction effect.

[0069] (17), (18).

[0070] In summary, the characteristic coefficient prediction function can be obtained The density function of is shown in formula (19): (19).

[0071] Where, is the characteristic coefficient prediction function The density function of .

[0072] Step 3.1.3: Use the training set to iteratively optimize the kernel function's hyperparameters, and use the test set to test and obtain the optimal hyperparameters.

[0073] Step 3.2: During the training process, the surrogate model is validated using a combination of adaptive particle swarm optimization and nested cross validation. Figure 1 As shown in Figure 3, it is divided into inner layer verification and outer layer verification, among which the adaptive particle swarm optimization method is applied to the inner layer verification.

[0074] The specific steps are as follows: Step 3.2.1: Divide the input and output data sets into several subsets as the basis for outer layer verification.

[0075] Step 3.2.2: In each outer layer fold, select a non-repeated subset as the outer layer validation set for the final evaluation of the model, and the remaining subsets are used as the outer layer training set for inner layer cross-validation again to search for Gaussian process regression through particle swarm optimization.

[0076] The specific steps of inner cross validation are: The outer training set is evenly divided into several groups for inner cross-validation. In each inner fold, a non-repeated subset is selected as the inner test set, and the remaining subsets are used as the inner training set to train the Gaussian process regression model. An adaptive particle swarm optimization method is used to optimize hyperparameters, and the root mean square error (RMSE) of the trained proxy model is calculated in the inner test set, recorded, and entered into the inner next-fold cross-validation.

[0077] The specific steps of adaptive particle swarm optimization hyperparameter optimization are: In a specific embodiment, the hyperparameters of the Gaussian process regression proxy model of this embodiment are Four,fivefold grid search is used, and the ranges of hyperparameters are defined as shown in Table 1: Table 1. Hyperparameter optimization range .

[0078] For the problem of minimizing a function with four hyperparameters, the qth particle in the Gth generation is , the G generation population is recorded as , where NP is the number of individuals in the population. Construct the particle fitness function: (20).

[0079] in, (twenty one).

[0080] Therefore, the optimization problem can be expressed as follows: (twenty two), (twenty three).

[0081] in, is the particle fitness function, is the optimization function, that is, finding the maximum fitness value among the particles in the current iteration number, and are the lower and upper limits of the particle's d-th dimension hyperparameters, i.e. 、 、 、 The lower and upper bounds of , D represents the total dimension. Four-dimensional search space Defined in area The specific steps are as follows: 1) Initialization operation. Generate initial individuals , q = 1, 2, …, NP and the velocity vector , q = 1, 2,…, NP. Determine the upper and lower bounds of the inertia weight and , the upper and lower bounds of the two acceleration constants (i.e. and ) and the maximum number of iterations Gmax. Then set the current generation G = 0.

[0082] 2) For each individual , q = 1, 2, …, NP, perform steps 3 to 4 to generate the next generation of population.

[0083] 3) Velocity and particle update operations. The velocity of each individual is generated as follows: (twenty four).

[0084] Where rand1 and rand2 are uniform random numbers in the range [0, 1]; is the best previous position of the qth particle; and In the entire group In the best position. 、 They are 、 The weight of Determined by the following formula: (25).

[0085] Where, , are the maximum and minimum values ​​of the inertia weight respectively, G represents the number of current evolution iterations, is the maximum number of evolutionary iterations, , They are respectively the optimal particle fitness value of the current generation and the average fitness value of the particles of the current generation. That is: (26), (27).

[0086] 、 Calculated by the following formulas: (28), (29).

[0087] Where e is a constant.

[0088] For each , generate a trial individual as follows: (30).

[0089] 4) Yes and The following updates have been made: (31), (32).

[0090] 5) G = G + 1 Predicted distribution: The distribution of the predicted value can be obtained as shown in formula (33): (33).

[0091] Where, is the mean function, as shown in formula (34), is the covariance function, as shown in formula (35), is the input data vector set of the test set, is the input data vector set of the training set, Is the output data vector set of the training set. Input test set , the posterior mean is: (34).

[0092] The forecast covariance is: (35).

[0093] Finally, we get the predicted density: (36).

[0094] 6) Error analysis: In order to evaluate the accuracy of the proxy model, five error metrics are considered: mean squared error (MSE), mean absolute error (MAE), mean absolute percentage error (MAPE), root mean squared error (RMSE), and coefficient of determination (R-Square, R2). Equation (37) shows the mean absolute percentage error (MAPE), relative error (R2). .

[0095] (37).

[0096] Where, Calculate the physical quantity values ​​of the mesh nodes for the finite element, The physical quantity value predicted by the proxy model for the same grid node under the same working condition.

[0097] Formula (38) is the mean square error MSE: (38).

[0098] Where, formula (39) is the mean absolute error MAE: (39).

[0099] Formula (40) is the root mean square error RMSE: (40).

[0100] Where, is the average value of the physical quantities of all mesh nodes calculated by the finite element under the i-th working condition, is the average value of the physical quantities predicted by the Gaussian process proxy model at all grid nodes under the i-th working condition. is the number of working conditions involved in the error analysis.

[0101] Since this embodiment uses the characteristic coefficient matrix of POD as the output of Gaussian process regression, as a multi-output regression problem, each working condition input corresponds to multiple characteristic coefficients. This embodiment takes the average of the fitting degree of each output dimension, so the overall determination coefficient is used. , as shown in formula (41): (41).

[0102] Where, is the coefficient of determination for each test set sample point Take the mean, is the number of samples in the test set, n is the number of dimensions retained, is the jth test set sample , is the true feature coefficient of the i-th dimension of the j-th test set, is the predicted feature coefficient of the i-th dimension of the j-th test set, is the mean of all true feature coefficients of the j-th test set.

[0103] Finally, all cross-validations in the inner layer are completed, and the hyperparameter combination with the smallest root mean square error is selected.

[0104] Step 4: Retrain the agent model using the optimal hyperparameters to obtain the final bridge pier digital twin intelligent monitoring agent model, and apply the bridge pier digital twin intelligent monitoring agent model in the digital twin platform.

[0105] In this embodiment, the digital twin platform visualizes the overall physical field of the bridge pier obtained by the digital twin intelligent monitoring agent model of the bridge pier in real time, and activates a multi-level early warning strategy through disaster prediction.

[0106] Specifically, after obtaining the optimal hyperparameters, the present invention can retrain the GPR proxy model based on the complete data set, thereby constructing a "bridge pier digital twin intelligent monitoring proxy model" that can ultimately be put into practical use. During the application phase, simply input the real-time collected bridge pier operating state parameters (such as horizontal pressure, on-site measured tilt angle, scour depth changes, vibration, settlement, etc.) into this proxy model to obtain the characteristic coefficient vector. By predicting the linear combination of the characteristic coefficient vector and the orthogonal basis vectors of the snapshot matrix obtained by the previous intrinsic orthogonal decomposition, the stress and displacement field prediction results of the bridge pier at the current or future time can be quickly obtained. This Gaussian process regression proxy model has good uncertainty quantification capabilities and can provide an effective basis for evaluating the health and safety margin of bridge pier structures. Combined with the digital twin platform, it can visualize the overall or local stress and deformation of the bridge piers in real time, and promptly issue alarms and preventive maintenance for potential risks and abnormal situations.

[0107] This embodiment's digital twin platform integrates monitoring, visualization, prediction, and alerting. Data such as horizontal pressure, vibration, tilt, settlement, and scour depth transmitted by field instruments can be visualized on the digital twin platform. By feeding real-time data transmitted from the field into a proxy model, the overall physical field of the bridge pier can be visualized in real time using the Python library PyVista. When a bridge pier encounters a disaster such as a flood, earthquake, or debris flow, the proxy model can be loaded into a structural failure condition based on the type of disaster. This automatically predicts the physical field of the pier under the most severe instability and damage conditions, identifies the type and area of ​​instability, and promptly notifies professionals to reinforce and repair the relevant areas. A multi-level early warning strategy is also implemented. A third-level alert is initiated if any of the pier top displacement, strain, plastic strain, settlement, or tilt indicators reaches 80% of the ultimate limit; a second-level alert is initiated if any of these indicators reaches 90% of the ultimate limit; and a first-level alert is initiated if any of these indicators reaches 100% of the ultimate limit.

[0108] Example 2: A second embodiment of the present invention provides a digital twin intelligent monitoring system for bridge piers based on an agent model, comprising: The data set acquisition module is configured to construct a finite element model of the bridge pier to be monitored, using a combination of working condition factors as input data and bridge pier status data calculated by the finite element model based on the working condition data as output data, thereby obtaining an input and output data set; The data set processing module is configured to perform dimensionality reduction and feature extraction on the input and output data sets using an eigenorthogonal decomposition method to obtain a feature coefficient matrix; The surrogate model training module is configured to construct a surrogate model using the Gaussian process regression method, with the characteristic coefficient matrix as output and the operating condition factor combination as input to train the surrogate model. During the training process, the surrogate model is verified using a validation strategy combining adaptive particle swarm optimization and nested crossover to obtain the optimal hyperparameters; The agent model application module is configured to retrain the agent model using the optimal hyperparameters to obtain the final bridge pier digital twin intelligent monitoring agent model, and apply the bridge pier digital twin intelligent monitoring agent model in the digital twin platform.

[0109] Example 3: Embodiment 3 of the present invention provides a computer-readable storage medium, which stores a computer program. The computer program is suitable for being loaded by a processor and executing the steps in the agent model-based bridge pier digital twin intelligent monitoring method as described in Embodiment 1 of the present invention.

[0110] Example 4: A fourth embodiment of the present invention provides a computer device, comprising: a processor adapted to execute a computer program; A computer-readable storage medium, wherein a computer program is stored in the computer-readable storage medium. When the computer program is executed by the processor, the steps of the intelligent monitoring method for digital twins of bridge piers based on the agent model as described in the first embodiment of the present invention are implemented.

[0111] The steps involved in the above embodiments 2, 3 and 4 correspond to those in the method embodiment 1. For the specific implementation methods, please refer to the relevant description part of the embodiment 1.

[0112] Those skilled in the art will appreciate that the units and algorithmic steps of each example described in conjunction with the embodiments disclosed in this application can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are performed in hardware or software depends on the specific application and design constraints of the technical solution. Professional technical personnel may use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application. In the above embodiments, all or part of the embodiments can be implemented using software, hardware, firmware, or any combination thereof. When implemented using software, all or part of the embodiments can be implemented in the form of a computer program product. A computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, all or part of the processes or functions according to the embodiments of the present application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted via a computer-readable storage medium. The computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, optical fiber, digital line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that can be accessed by a computer, or a data processing device such as a server or data center that integrates one or more available media. Available media can be magnetic media (e.g., floppy disks, hard disks, tapes), optical media (e.g., DVDs), or semiconductor media (e.g., solid-state drives (SSDs)). The above description is merely a specific embodiment of the present application, but the scope of protection of the present application is not limited thereto. Any technical object of a person skilled in the art that can be easily conceived of within the technical scope disclosed in this application should be included in the scope of protection of the present application. Therefore, the scope of protection of the present application should be based on the scope of protection of the claims.

Claims

1. A digital twin intelligent monitoring method for bridge piers based on an agent model, characterized in that: The following steps are involved: Construct a finite element model of the bridge pier to be monitored, using the combination of working condition factors as input data. The finite element model calculates the bridge pier status data based on the working condition data as output data, thus obtaining an input and output data set. The eigenorthogonal decomposition method is used to reduce the dimension and extract features of the input and output data sets to obtain the characteristic coefficient matrix; The surrogate model is constructed using the Gaussian process regression method. The characteristic coefficient matrix is ​​used as output and the operating condition factor combination is used as input to train the surrogate model. During the training process, the surrogate model is verified using an adaptive particle swarm optimization and nested cross validation strategy to obtain the optimal hyperparameters. The agent model is retrained using the optimal hyperparameters to obtain the final bridge pier digital twin intelligent monitoring agent model, which is then applied in the digital twin platform.

2. The agent-based digital twin intelligent monitoring method for bridge piers according to claim 1, characterized in that: The working condition factor combination is a combination of horizontal pressure data, scour depth data, vibration data, tilt data and settlement data. The pier status data includes pier stress field data, plastic strain field data and displacement field information.

3. The agent-based bridge pier digital twin intelligent monitoring method according to claim 1, characterized in that: The specific steps of using the eigenorthogonal decomposition method to reduce the dimension and extract features of the input and output data sets are as follows: The bridge pier status data are organized into a snapshot matrix, and the snapshot matrix is ​​subjected to separation mean field processing; Perform snapshot eigenorthogonal decomposition on the snapshot matrix after separation of the mean field to obtain the eigenvalue diagonal matrix and eigenvector matrix, and sort the eigenvalues; Based on the snapshot matrix, eigenvalue diagonal matrix and eigenvector matrix after separation of the mean field, the orthogonal basis matrix is ​​calculated according to the eigenvalue sorting, and the characteristic coefficient matrix is ​​further calculated; The pier status data is reconstructed by extracting orthogonal basis vectors and characteristic coefficient matrices based on eigenvalues.

4. The agent-based bridge pier digital twin intelligent monitoring method according to claim 1, characterized in that: The specific steps for training the agent model with the characteristic coefficient matrix as output and the working condition factor combination as input are as follows: Divide the training set and test set according to the characteristic coefficient matrix and the combination of working condition factors; The weighted sum of radial basis function and Mattern function is used as kernel function; The training set is used to iteratively optimize the kernel function's hyperparameters, and the test set is used to test to obtain the optimal hyperparameters.

5. The agent-based digital twin intelligent monitoring method for bridge piers according to claim 1, characterized in that: The specific steps for verifying the surrogate model using the adaptive particle swarm optimization and nested cross validation strategy during training are as follows: Divide the input and output data sets into several subsets as the basis for outer layer verification; In each outer layer, a non-repeated subset is selected as the outer layer validation set for the final evaluation of the model, and the remaining subsets are used as the outer layer training set for inner layer cross-validation again to search for Gaussian process regression through particle swarm optimization.

6. The agent-based digital twin intelligent monitoring method for bridge piers according to claim 5, characterized in that: The specific steps of inner cross validation are: The outer training set is evenly divided into several groups for inner cross-validation. In each inner fold, a non-repeated subset is selected as the inner test set, and the remaining subsets are used as the inner training set to train the Gaussian process regression model. Use the adaptive particle swarm optimization method to optimize hyperparameters, and use the trained proxy model to calculate the root mean square error in the inner test set, record it and enter the inner next fold cross validation; Finally, all cross-validations in the inner layer are completed, and the hyperparameter combination with the smallest root mean square error is selected.

7. The agent-based bridge pier digital twin intelligent monitoring method according to claim 1, characterized in that: The digital twin platform visualizes the overall physical field of the bridge pier obtained by the digital twin intelligent monitoring agent model of the bridge pier in real time, and initiates a multi-level early warning strategy through disaster prediction.

8. A digital twin intelligent monitoring system for bridge piers based on an agent model, characterized in that: include: The data set acquisition module is configured to construct a finite element model of the bridge pier to be monitored, using a combination of working condition factors as input data and bridge pier status data calculated by the finite element model based on the working condition data as output data, thereby obtaining an input and output data set; The data set processing module is configured to perform dimensionality reduction and feature extraction on the input and output data sets using an eigenorthogonal decomposition method to obtain a feature coefficient matrix; The surrogate model training module is configured to construct a surrogate model using the Gaussian process regression method, with the characteristic coefficient matrix as output and the operating condition factor combination as input to train the surrogate model. During the training process, the surrogate model is verified using a validation strategy combining adaptive particle swarm optimization and nested crossover to obtain the optimal hyperparameters; The agent model application module is configured to retrain the agent model using the optimal hyperparameters to obtain the final bridge pier digital twin intelligent monitoring agent model, and apply the bridge pier digital twin intelligent monitoring agent model in the digital twin platform.

9. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a computer program, which is suitable for being loaded by a processor and executing the agent-model-based bridge pier digital twin intelligent monitoring method according to any one of claims 1 to 7.

10. A computer device, characterized in that: a processor adapted to execute a computer program; A computer-readable storage medium having a computer program stored therein, wherein when the computer program is executed by the processor, the method for intelligent monitoring of bridge pier digital twins based on an agent model as described in any one of claims 1 to 7 is implemented.

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