Bridge pier digital twin intelligent monitoring method and system based on agent model

Abstract

The application discloses a kind of bridge pier digital twin intelligent monitoring method and system based on agent model, it is related to bridge pier state monitoring technical field.The method includes the following steps: constructing the finite element model of the bridge pier to be monitored;The intrinsic orthogonal decomposition method is used to reduce dimension and extract features to input-output data set;The agent model is constructed and trained using the Gaussian process regression method, an adaptive particle swarm optimization and a nested cross-verification strategy are used to verify the agent model during the training process, and the optimal hyperparameters are obtained;The agent model is retrained using the optimal hyperparameters, and the final bridge pier digital twin intelligent monitoring agent model is obtained.The application aims to predict and evaluate the health status of the bridge pier under various complex external conditions such as horizontal stress, scour depth, vibration, inclination and settlement with high precision, speed and visualization.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of bridge pier state monitoring, and in particular to a bridge pier digital twin intelligent monitoring method and system based on a proxy model. BACKGROUND

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

[0003] With the continuous development of bridge construction, the importance of the health state monitoring of bridge piers, as the key supporting structure of bridges, is increasingly prominent. Traditional bridge pier monitoring techniques mainly rely on finite element model analysis and on-site sensor data acquisition. However, these techniques have many limitations. First, in the modeling process, due to assumptions and simplifications in aspects such as element division, boundary condition setting, and material parameter selection, the calculated results deviate from the actual responses. Second, the traditional monitoring method is slow in the training process and has limited accuracy when dealing with high-dimensional, multi-coupling input conditions. In addition, existing techniques have insufficient model generalization capabilities and are difficult to adapt to various variable working conditions.

[0004] Under the background of the gradual rise of digital twin technology, although it has played a certain role in bridge monitoring, there are still some problems to be solved in existing technologies. For example, some technologies only achieve a simple combination of finite element simulation and visual models, lacking the ability to quantify model uncertainty. Some technologies are low in efficiency in terms of hyperparameter optimization, affecting the training speed and accuracy of the model. At the same time, existing technologies are not perfect in the setting of multi-level early warning systems, and cannot timely and accurately warn of potential risks of bridge piers.

[0005] In summary, existing technologies have problems such as insufficient model accuracy, low training efficiency, weak generalization ability, and imperfect early warning systems in bridge pier health state monitoring. Therefore, it is urgent to develop an intelligent monitoring method that can accurately, quickly, and visually predict and evaluate the health state of bridge piers to meet the high requirements of modern bridge engineering for bridge pier monitoring. SUMMARY

[0006] In view of the deficiencies of existing technologies, the present application aims to provide a bridge pier digital twin intelligent monitoring method and system based on a proxy model, which aims to accurately, quickly, and visually predict and evaluate the health state of bridge piers under various complex external working conditions such as horizontal stress, scour depth, vibration, inclination, and settlement.

[0007] In order to achieve the above-mentioned purpose, the present application is realized by the following technical solutions:

[0008] The first aspect of the present application provides a bridge pier digital twin intelligent monitoring method based on a proxy model, comprising the following steps:

[0009] A finite element model of the bridge pier to be monitored is constructed, the input data is a combination of working condition factors, the bridge pier state data calculated by the finite element model according to the working condition data is taken as the output data, and an input-output data set is obtained;

[0010] The intrinsic orthogonal decomposition method is used to reduce the dimension and extract the features of the input-output data set, and a characteristic coefficient matrix is obtained;

[0011] The Gaussian process regression method is used to construct a proxy model, the characteristic coefficient matrix is taken as the output, and the working condition factor combination is taken as the input to train the proxy model, and an adaptive particle swarm optimization and nested cross combination verification strategy is used to verify the proxy model during the training process to obtain optimal hyperparameters;

[0012] The proxy model is retrained using the optimal hyperparameters to obtain a final bridge pier digital twin intelligent monitoring proxy model, and the bridge pier digital twin intelligent monitoring proxy model is applied in a digital twin platform.

[0013] Further, the combination of working condition factors is a combination of horizontal pressure data, scour depth data, vibration data, inclination data and settlement data, and the bridge pier state data includes bridge pier stress field data, plastic strain field data and displacement field information.

[0014] Further, the specific steps of using the intrinsic orthogonal decomposition method to reduce the dimension and extract the features of the input-output data set are as follows:

[0015] The bridge pier state data is composed into a snapshot matrix, and the snapshot matrix is subjected to a separate average field processing;

[0016] The snapshot matrix after the separate average field processing is subjected to snapshot intrinsic orthogonal decomposition to obtain an eigenvalue diagonal matrix and an eigenvector matrix, and the eigenvalues are sorted;

[0017] Based on the snapshot matrix after the separate average field processing, the eigenvalue diagonal matrix and the eigenvector matrix, an orthogonal basis matrix is calculated according to the eigenvalue sorting, and a characteristic coefficient matrix is further calculated;

[0018] The orthogonal basis vector and the characteristic coefficient matrix are used to reconstruct the bridge pier state data according to the eigenvalue.

[0019] Further, the specific steps of training the proxy model with the characteristic coefficient matrix as the output and the working condition factor combination as the input are as follows:

[0020] The training set and the test set are divided according to the characteristic coefficient matrix and the working condition factor combination;

[0021] A weighted sum of a radial basis function and a Matern function is used as a kernel function;

[0022] The hyperparameters of the kernel function are iteratively optimized using a training set, and the optimal hyperparameters are obtained by testing using a test set.

[0023] Further, the specific steps for verifying the surrogate model during the training process using the adaptive particle swarm optimization and the nested cross-validation strategy are as follows:

[0024] The input-output data set is evenly divided into several subsets as the basis for outer validation;

[0025] In each fold of the outer layer, a non-repeating subset is selected as the outer validation set for final model evaluation, and the remaining subset is used as the outer training set for further inner cross-validation to search for a Gaussian process regression through particle swarm optimization.

[0026] Further, the specific steps for inner cross-validation are as follows:

[0027] The outer training set is evenly divided into several groups for inner cross-validation, and in each fold of the inner layer, a non-repeating subset is selected as the inner test set, and the remaining subset is used as the inner training set to train the Gaussian process regression model;

[0028] The adaptive particle swarm optimization method is used for hyperparameter optimization, and the surrogate model obtained by training is used to calculate the root mean square error in the inner test set, which is recorded and used for the next fold of inner cross-validation;

[0029] After completing all the inner cross-validation, the hyperparameter combination with the smallest root mean square error is selected.

[0030] Further, the digital twin platform visualizes the overall physical field of the bridge pier obtained by the bridge pier digital twin intelligent monitoring surrogate model in real time, and starts a multi-level early warning strategy through disaster prediction.

[0031] The second aspect of the present application provides a bridge pier digital twin intelligent monitoring system based on a surrogate model, comprising:

[0032] The data set acquisition module is configured to construct a finite element model of the bridge pier to be monitored, use the combination of working condition factors as input data, and use the bridge pier state data calculated by the finite element model according to the working condition data as output data to obtain the input-output data set.

[0033] The data set processing module is configured to use the intrinsic orthogonal decomposition method to reduce the dimension and extract the features of the input-output data set to obtain a characteristic coefficient matrix.

[0034] The agent model training module is configured to construct an agent model by using a Gaussian process regression method, train the agent model by taking a feature coefficient matrix as output and a working condition factor combination as input, verify the agent model by using a verification strategy combining adaptive particle swarm optimization and nested cross validation in the training process, and obtain optimal hyperparameters;

[0035] The agent model application module is configured to retrain the agent model by using the optimal hyperparameters, obtain a final bridge pier digital twin intelligent monitoring agent model, and apply the bridge pier digital twin intelligent monitoring agent model in a digital twin platform.

[0036] The third aspect of the present application provides a computer readable storage medium storing a computer program, and the computer program is suitable for being loaded and executed by a processor to perform the steps in the agent model-based bridge pier digital twin intelligent monitoring method according to the first aspect of the present application.

[0037] The fourth aspect of the present application provides a computer device, which comprises:

[0038] A processor suitable for executing a computer program;

[0039] A computer readable storage medium storing a computer program, and the computer program is executed by the processor to implement the agent model-based bridge pier digital twin intelligent monitoring method according to the first aspect of the present application.

[0040] The above one or more technical solutions have the following beneficial effects:

[0041] The present application discloses an agent model-based bridge pier digital twin intelligent monitoring method and system, which can not only solve the problems of slow training and limited precision of traditional models under high-dimensional and multi-coupling input conditions, but also ensure that the selected model has good robustness under various variable working condition conditions. The agent model of the present application can be connected with a bridge monitoring big data system and a digital twin platform, and provide more intelligent, efficient and reliable technical means for bridge pier maintenance and structure safety evaluation. In summary, the agent model-based bridge pier digital twin intelligent monitoring method of the present application fully utilizes the advantages of POD in feature dimension reduction, the efficiency of PSO in hyperparameter search, and the advantages of GPR in uncertainty quantification and generalization performance, provides a new solution for intelligent monitoring and early warning of bridge foundation parts, and has wide application prospect and significant engineering value.

[0042] The application can more accurately simulate the state of the bridge pier under actual working conditions by constructing a finite element model and using working condition factor combinations as input data, providing a more realistic data basis for monitoring. At the same time, the intrinsic orthogonal decomposition method is used for dimension reduction and feature extraction of the data, which can effectively reduce the data amount, improve the calculation efficiency, and extract more representative features, further improving the accuracy and efficiency of monitoring.

[0043] The application uses the Gaussian process regression method to construct the surrogate model, and adopts the adaptive particle swarm optimization and nested cross combination verification strategy, which can more accurately determine the optimal hyperparameters, so that the training effect of the surrogate model is better, thereby improving the accuracy of the model in predicting the state of the bridge pier. Compared with the traditional single verification method, this optimized model training and verification method can more comprehensively evaluate the performance of the model, avoid overfitting or underfitting phenomenon, and ensure the reliability and stability of the model in practical application.

[0044] The application applies the finally obtained bridge pier digital twin intelligent monitoring surrogate model to the digital twin platform, can realize real-time visualization of the overall physical field of the bridge pier, and enables the monitoring personnel to intuitively understand the real-time state of the bridge pier. In addition, a multi-level early warning strategy is started through disaster prediction, which can timely find potential safety hazards and take corresponding measures in advance, effectively ensuring the safety of the bridge pier.

[0045] The advantages of the additional aspects of the application will be partially given in the following description, partially become obvious from the following description, or be known by the practice of the application. BRIEF DESCRIPTION OF DRAWINGS

[0046] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description. Obviously, the drawings in the following description only some embodiments of the present application, and for those skilled in the art, other drawings can be obtained without creative labor on the basis of these drawings.

[0047] Figure 1 The flow chart of the bridge pier digital twin intelligent monitoring method based on the surrogate model in the embodiment one of the application is shown in the figure.

[0048] Figure 2 The intrinsic orthogonal decomposition process flow chart in the embodiment one of the application is shown in the figure. DETAILED DESCRIPTION

[0049] It should be pointed out that the following detailed description is exemplary and is intended to provide further explanation of the present application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as generally understood by those skilled in the art to which the present application belongs.

[0050] It is to be noted that the terms used herein are merely for the purpose of describing specific embodiments and are not intended to limit the exemplary embodiments according to the present application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. It will be further understood that the terms "comprise" and / or "comprising," when used in this specification, specify the presence of stated features, steps, operations, devices, components and / or combinations thereof, but do not preclude the presence or addition of one or more other features, steps, operations, devices, components and / or combinations thereof.

[0051] The technical solutions in the embodiments of the present application will be described clearly and completely in the following with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative work fall within the scope of protection of the present application.

[0052] Embodiment one

[0053] The embodiment one of the present application provides a bridge pier digital twin intelligent monitoring method based on a proxy model, as shown in the following steps. Figure 1

[0054] Step 1: A finite element model of a bridge pier to be monitored is constructed, a combination of working condition factors is taken as input data, and bridge pier state data calculated by the finite element model according to working condition data is taken as output data, so as to obtain an input-output data set.

[0055] The combination of working condition factors is a combination of horizontal pressure data, scour depth data, vibration data, inclination data and settlement data, and the bridge pier state data includes bridge pier stress field data, plastic strain field data and displacement field information.

[0056] In this embodiment, the finite element model of the bridge pier is established by abaqus through field measurement and design drawings, and finite element numerical simulation is performed thereon. Latin hypercube sampling is adopted to extract the input data set of the multiple factors related to the bridge pier, including the working condition combination of horizontal pressure, scour depth, vibration, inclination, settlement, etc.; and the bridge pier stress field, plastic strain field and displacement field information obtained by the finite element calculation of the finite element model are taken as the output data set.

[0057] Step 2: The intrinsic orthogonal decomposition method is used to reduce the dimension and extract the features of the input-output data set, so as to obtain a characteristic coefficient matrix.

[0058] ​For this high-dimensional input and output data set, the embodiment introduces the proper orthogonal decomposition (POD) method for dimension reduction and feature extraction, eliminates redundant dimensions and highlights the main features, making the subsequent model training more efficient. The snapshot matrix composed of the finite element output data of each node under different working conditions is subjected to proper orthogonal decomposition, and the obtained characteristic coefficient matrix is taken as the output. The factor combination in different working conditions is taken as the input, and the bridge pier physical field surrogate model can be obtained by Gaussian process regression.

[0059] As shown in Figure 2 , the specific steps are as follows:

[0060] Step 2.1: The bridge pier state data is composed into a snapshot matrix, and the snapshot matrix is subjected to separated average field processing.

[0061] In a specific embodiment, in order to obtain different modes of proper orthogonal decomposition, it is necessary to first calculate the samples of system behavior (solutions at different times for dynamic problems, and equilibrium solutions under different parameter values for static problems), and use these samples to form a snapshot matrix. Taking the bridge pier stress field data as an example, the embodiment divides the grid according to the component ratio in the abaqus finite element software, exports the stress values of all grid nodes of the multi-pile pier cap under different working conditions from abaqus, and constructs a matrix with a size of N×K, as shown in formula (1):

[0062] (1).

[0063] In the formula, N represents the number of grid nodes, K represents the number of working conditions, S i represents the stress values of all grid nodes under a certain working condition, and the embodiment takes one S i sample point in the data set as a snapshot, and the data set is called a snapshot matrix. The snapshot matrix is subjected to separated average field, as shown in formula (2):

[0064] (2).

[0065] In the formula, is the snapshot matrix after separated average field, i.e. the stress field snapshot matrix, is a vector obtained by averaging the sum of stress values of all grid nodes for all working conditions.

[0066] Step 2.2: The snapshot matrix after separated average field is subjected to snapshot proper orthogonal decomposition to obtain an eigenvalue diagonal matrix and an eigenvector matrix, and the eigenvalues are sorted.

[0067] In one specific embodiment, unlike the original eigenvalue decomposition, in order to reduce the size of the covariance matrix and further reduce the dimension, the embodiment takes a snapshot eigenvalue decomposition to obtain the covariance matrix, as shown in equation (3):

[0068] (3).

[0069] In the formula, is a covariance matrix of size KxK.

[0070] Then the eigenvector decomposition of the covariance matrix is performed to obtain the eigenvalue matrix and the eigenvector matrix. In order to facilitate the subsequent steps of eigenvalue truncation, the orthogonal basis vector and the characteristic coefficient matrix are sorted in descending order according to the size of the eigenvalue. The sorting process records the corresponding index of the eigenvalue, and the eigenvectors are sorted synchronously, as shown in equation (4).

[0071] (4).

[0072] In the formula, is an eigenvector matrix of size KxK, is a diagonal eigenvalue matrix of size KxK, where the eigenvalues are arranged in descending order , is the eigenvector corresponding to the working condition i, and the order is synchronized with the eigenvalue matrix. i is the count parameter of the working condition.

[0073] Step 2.3: Based on the snapshot matrix after separating the average field, the eigenvalue diagonal matrix and the eigenvector matrix, the orthogonal basis matrix is calculated according to the eigenvalue sorting, and the characteristic coefficient matrix is further calculated.

[0074] Step 2.3.1: Based on the snapshot matrix after separating the average field, the eigenvalue diagonal matrix and the eigenvector matrix, the orthogonal basis matrix is calculated according to the eigenvalue sorting.

[0075] As shown in equation (5):

[0076] (5).

[0077] In the formula, is an orthogonal basis matrix of size NxK, is an orthogonal basis vector, each orthogonal basis vector represents the mechanical behavior and characteristics of each mode of the physical system, and the eigenvalue represents the proportion of the behavior and characteristics of the orthogonal basis corresponding to the i-th working condition in the entire physical system.

[0078] Step 2.3.2: Calculate the characteristic coefficient matrix.

[0079] The corresponding characteristic coefficient is calculated by equation (6):

[0080] (6).

[0081] wherein, is the eigenvalue matrix of size KxK, represents the eigenvalue of the first order orthogonal basis vector corresponding to the K snapshots of stress. Stress snapshot S i The orthogonal basis vector and its eigenvalue can be reconstructed according to formula (7) based on the orthogonal basis vector and its eigenvalue:

[0082] (7).

[0083] Step 2.4: According to the eigenvalue, the orthogonal basis vector and the eigenvalue matrix are used to reconstruct the pier state data.

[0084] Since the orthogonal basis vectors in the orthogonal basis matrix are orthogonal and normalized, any number of orthogonal basis vectors can be used to construct a reduced order subspace, thereby achieving the purpose of model reduction. In order to control the number of orthogonal basis vectors to reduce the error, the energy ratio, i.e. the proportion of the first n eigenvalues to the sum of all eigenvalues, is controlled, as shown in the formula. In this embodiment, 99.9% is taken.

[0085] (8).

[0086] wherein, j represents the count parameter of the working condition.

[0087] Finally, by intercepting the first n orthogonal basis vectors, any stress field snapshot can be reconstructed to achieve reduction, greatly reducing the amount of calculation required for training the proxy model, as shown in formula (9):

[0088] (9).

[0089] Therefore, if the stress field snapshot of different sample points is determined for a certain stress field snapshot matrix, the orthogonal basis vector of the entire stress field snapshot matrix is also determined, and only the eigenvalue changes when reconstructing each sample point after reduction. Therefore, the eigenvalue can reflect the stress field snapshot calculated for different working conditions within a given range, and therefore there is a mapping relationship between different finite element input working conditions and eigenvalues. As shown in formula (10), if the corresponding mapping relationship can be found, the stress field of the entire multi-pile pier pile cap under different other working conditions can be obtained.

[0090] (10).

[0091] wherein, is the mapping relationship between the finite element input working condition and the eigenvalue, is the working condition input by the finite element, is the working condition The corresponding characteristic coefficient vector can be inferred using the surrogate model, and the physical field under the new finite element input condition can be expressed as a linear combination of the POD basis functions. Next, Gaussian process regression is used to find the mapping relationship between the finite element input condition and the characteristic coefficient.

[0092] Step 3: Construct a surrogate model using the Gaussian process regression method, with the characteristic coefficient matrix as the output and the working condition factor combination as the input to train the surrogate model. During the training process, the adaptive particle swarm optimization and nested cross-validation verification strategy are used to verify the surrogate model, and the optimal hyperparameters are obtained.

[0093] In a specific embodiment, in order to effectively prevent overfitting, obtain the unbiased evaluation index of the surrogate model in the full data set, and improve the generalization ability of the surrogate model under unknown working conditions, this embodiment adopts the nested cross-validation (NCV) verification strategy of adaptive particle swarm optimization (APSO). As shown in Figure 1 The characteristic coefficient matrix obtained by eigenvalue orthogonal decomposition is used as the output data set, and the working condition factor combination is used as the input data set. The data set is divided into K fold subsets as the outer validation basis, and a total of K fold times of circulation, called K fold folds, in each outer fold, one data subset that is not repeated in the previous fold is left as the outer validation set for final model evaluation; the remaining K fold -1 subset is used as the outer training set to perform K`-fold cross-validation again, in order to search for the optimal hyperparameter combination of the Gaussian process regression (GPR) model through particle swarm optimization. In the inner cross-validation process, K fold-1 subset of the outer training set is divided into K' subsets, and 1 subset that is not repeated in 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 uses different training / test division to train and validate the GPR model. In the process of training the GPR model, PSO is used for hyperparameter optimization. The root mean square error of the proxy model trained by the inner GPR-PSO in the inner test set is calculated, recorded and entered into the next cross-validation fold. Finally, all cross-validation in the inner layer is completed, and the hyperparameter combination with the smallest root mean square error is selected. The Gaussian process regression proxy model is trained on the outer training set in this fold, and the evaluation indicators (root mean squared error (RMSE), R-square (R2), mean absolute error (MAE)) are calculated on the outer validation set. After K cycles of the outer layer, the evaluation indicators of all outer folds on the outer validation set are summarized, and the average evaluation indicators of each fold cycle are used as the unbiased evaluation indicators of the Gaussian process regression proxy model on the complete dataset. The objective and unbiased measure of the model generalization ability can be obtained. The hyperparameter combination used for evaluation on the outer validation set of each outer fold is statistically analyzed. If there is a mode, the hyperparameter combination of the mode is used. If there is no mode, the hyperparameter combination with the smallest root mean square error obtained by evaluating on the outer validation set is used.

[0094] The specific steps are as follows:

[0095] Step 3.1: Train the proxy model with the characteristic coefficient matrix as the output and the working condition factor combination as the input.

[0096] Step 3.1.1: Divide the training set according to the characteristic coefficient matrix and the working condition factor combination k train and the test set k test .

[0097] Specifically, the input values for training the Gaussian process regression of the multi-pile pier pile cap are as shown in formula (11):

[0098] (11).

[0099] In the formula, represents the working condition factor combination matrix of the training set, and f represents the vector composed of the size of each working condition factor, k train The number of input working conditions of finite element analysis is

[0100] (12).

[0101] In the formula, Represents the characteristic coefficient matrix, For size n× k train through k train The eigenvalue matrix of the stress field after eigenorthogonal decomposition in finite element analysis under various working conditions. for k train The feature coefficient vector under each working condition for k train The nth order eigenvalues ​​under each working condition, where n is the number of orthogonal basis vectors retained. Each input working condition vector corresponds to an output feature coefficient vector. The training and test sets are standardized, where the training and test sets satisfy equation (13):

[0102] (13).

[0103] In the formula, The set of feature coefficients for the test set. The input data for the training set represents the mean of the operating condition factor values. Since actual data typically contains some noise, the noise must have a mean of zero and a variance of... Gaussian distribution, yes k train 3D identity matrix.

[0104] Step 3.1.2: Use the weighted sum of radial basis functions and Matrn functions as the kernel function.

[0105] Specifically, Input data for the training set: working condition factor values and training set test data working condition factor values The covariance matrix is ​​also the kernel function. Here, the weighted sum of the radial basis functions and the Matern function is used as the kernel function to achieve nonlinear approximation, as shown in equation (14):

[0106] (14).

[0107] In the formula, To calculate the covariance, a kernel function is used as an approximation due to the complexity of covariance calculation. For radial basis kernel functions, Let C be the Matern kernel function, and C be a weighted constant hyperparameter of the two kernel functions, where the radial basis kernel function is shown in equation (15):

[0108] (15).

[0109] wherein, is a hyperparameter of the radial basis function, and the Matern kernel function is shown in equation (16):

[0110] (16).

[0111] wherein, is a hyperparameter of the Matern kernel function. The hyperparameter is continuously optimized in the subsequent process to obtain the best prediction effect of the surrogate model.

[0112] (17),

[0113] (18).

[0114] In summary, the characteristic coefficient prediction function is obtained, and the density function is shown in equation (19):

[0115] (19).

[0116] wherein, is the density function of the characteristic coefficient prediction function .

[0117] Step 3.1.3: The hyperparameters of the kernel function are iteratively optimized using the training set, and the test set is used for testing to obtain the optimal hyperparameters.

[0118] Step 3.2: In the training process, the adaptive particle swarm optimization and nested cross-validation strategy are used to verify the surrogate model. The nested cross-validation strategy is shown in Figure 1 , which is divided into inner and outer validation, and the adaptive particle swarm optimization method is applied to the inner validation.

[0119] The specific steps are as follows:

[0120] Step 3.2.1: The input and output data sets are evenly divided into several subsets as the basis for outer validation.

[0121] Step 3.2.2: In each fold of the outer layer, a non-repeated subset is selected as the outer validation set for final model evaluation, and the remaining subset is used as the outer training set for inner cross-validation to search for Gaussian process regression through particle swarm optimization.

[0122] The specific steps of the inner cross-validation are as follows:

[0123] The step outer layer training set is divided into several groups for inner layer cross validation. In each inner layer fold, a non-repeated subset is selected as the inner layer test set, and the remaining subset is used as the inner layer training set to train the Gaussian process regression model.

[0124] The adaptive particle swarm optimization method is used for hyperparameter optimization, and the root mean square error in the inner layer test set is calculated using the trained surrogate model, which is recorded and used in the next cross validation fold.

[0125] The specific steps of adaptive particle swarm optimization hyperparameter optimization are as follows:

[0126] In a specific embodiment, the hyperparameters of the Gaussian process regression surrogate model of the present embodiment are four, and five-fold grid search is used, and the range of hyperparameters is defined as shown in Table 1:

[0127] Table 1. Hyperparameter optimization range

[0128] .

[0129] For the function problem with four hyperparameters, the Gth generation qth particle is represented by , and the Gth generation population is represented by , where NP is the number of individuals in the population. The particle fitness function is constructed as follows:

[0130] (20).

[0131] where

[0132] (21).

[0133] Therefore, the optimization problem can be expressed as follows:

[0134] (22),

[0135] (23).

[0136] where is the particle fitness function, is the optimization function, i.e. finding the maximum fitness value in the current iteration number of particles, and are the lower and upper limits of the dth dimension of the particle hyperparameter, i.e. , , , lower and upper limits of the total dimension D. The four-dimensional search space is defined in the region The detailed steps are as follows:

[0137] 1) Initialization operation. Generating initial individuals , q = 1, 2, …, NP and velocity vectors , q = 1, 2, …, NP. Determine the upper and lower bounds of the inertia weight and , the upper and lower bounds of two acceleration constants (i.e. and ) and the maximum number of iterations Gmax. Then set the current generation G = 0.

[0138] 2) For each individual , q = 1, 2, …, NP, perform steps 3 to 4 to generate the population of the next generation.

[0139] 3) Velocity and particle update operation. The velocity of each individual is generated as follows:

[0140] (24).

[0141] In the formula, rand1 and rand2 are uniform random numbers with values in the range [0, 1]; is the best previous position of the qth particle; and is the position that is best in the entire population . , are the weights of , respectively. Among them, the weight is determined by the following formula:

[0142] (25).

[0143] In the formula, , are the maximum and minimum values of the inertia weight respectively, G represents the current evolution iteration number, is the maximum evolution iteration number, , are the fitness value of the optimal particle of the current generation and the average value of the fitness values of the particles of the current generation respectively. Namely:

[0144] (26),

[0145] (27).

[0146] , are calculated by the following formula respectively:

[0147] (28),

[0148] (29).

[0149] where e is a constant e.

[0150] For each , a trial individual is generated as follows:

[0151] (30).

[0152] 4) The and are updated as follows:

[0153] (31),

[0154] (32).

[0155] 5) G = G + 1

[0156] The predictive distribution:

[0157] The predictive distribution of the value can be obtained as follows:

[0158] (33).

[0159] where is the mean function given by is the covariance function given by 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. The input test set , the posterior mean is:

[0160] (34).

[0161] The predictive covariance is:

[0162] (35).

[0163] Finally, the predictive density is:

[0164] (36).

[0165] 6) Error analysis:

[0166] To evaluate the accuracy of the surrogate model, five error metrics are considered: Mean Squared Error (MSE), Mean Absolute Error (MAE), Mean Absolute Percent Error (MAPE), and Root Mean Squared Error (RMSE), and the coefficient of determination (R-Square, R2). The Mean Absolute Percent Error MAPE is shown in equation (37), and the relative error .

[0167] (37).

[0168] wherein, is the physical quantity value of the finite element calculation grid node, is the physical quantity value predicted by the surrogate model for the same grid node under the same working condition.

[0169] The Mean Squared Error MSE is shown in equation (38):

[0170] (38).

[0171] wherein, the Mean Absolute Error MAE is shown in equation (39):

[0172] (39).

[0173] The Root Mean Squared Error RMSE is shown in equation (40):

[0174] (40).

[0175] wherein, is the average value of the physical quantity of all grid nodes calculated by the finite element under the i-th working condition, is the average value of the physical quantity predicted by the Gaussian process surrogate model at all grid nodes under the i-th working condition. is the number of working conditions participating in the error analysis calculation.

[0176] Since the characteristic coefficient matrix of the POD is used as the output of the Gaussian process regression in the present embodiment, as a multi-output regression problem, each working condition input corresponds to multiple characteristic coefficients. The present embodiment adopts mean value of the fitting degree of each output dimension, so the overall coefficient of determination is shown in equation (41):

[0177] (41).

[0178] wherein, R2 is the coefficient of determination for each test set sample point taking the mean, n is the number of samples in the test set, and d is the retained dimension, R2 is the coefficient of determination for each test set sample point , R2 is the coefficient of determination for each test set sample point R2 is the coefficient of determination for each test set sample point R2 is the coefficient of determination for each test set sample point

[0179] Finally, all cross-validations in the inner layer are completed, and the hyperparameter combination with the smallest root mean square error is selected.

[0180] Step 4: retrain the surrogate model using the optimal hyperparameters to obtain the final pier digital twin intelligent monitoring surrogate model, and apply the pier digital twin intelligent monitoring surrogate model in the digital twin platform.

[0181] In this embodiment, the digital twin platform performs real-time visualization on the overall physical field of the pier obtained by the pier digital twin intelligent monitoring surrogate model, and starts a multi-level early warning strategy through disaster prediction.

[0182] Specifically, after obtaining the optimal hyperparameters, the GPR surrogate model can be retrained based on the complete data set data, thereby constructing the final "pier digital twin intelligent monitoring surrogate model" that can be put into actual use. In the application stage, only the real-time collected pier operating state parameters (such as horizontal pressure, on-site measured inclination angle, scour depth change, vibration, settlement, etc.) need to be input into this surrogate model to obtain the characteristic coefficient vector, and by predicting the linear combination of the characteristic coefficient vector and the orthogonal basis vector of the snapshot matrix obtained by the previous eigenvalue orthogonal decomposition, the stress field and displacement field prediction results of the pier at the present or future time can be quickly obtained.

[0183] This Gaussian process regression surrogate model has good uncertainty quantification capability and can provide effective basis for the evaluation of the pier structure health degree and safety margin; combined with the digital twin platform, the overall or local stress and deformation of the pier can be visualized in real time, and potential risks and abnormal situations can be timely alarmed and preventive maintenance.

[0184] The digital twin platform of the embodiment combines monitoring, visualization, prediction, and alarm. The data such as horizontal pressure, vibration, inclination, settlement, and scour depth transmitted by the field instrument can be visualized on the digital twin platform. Real-time input transmitted from the field is input to the surrogate model, and the overall physical field of the pier is visualized in real time by using the pyvista library in python. When the pier encounters disasters such as floods, earthquakes, and mudslides, the pier surrogate model can be loaded to the structural failure working condition according to the disaster form, the physical field of the pier under the most serious instability and damage state is automatically predicted, the instability form and area of the pier are judged, and professional personnel are notified in time to reinforce and repair the corresponding part. A multi-level warning strategy is set, if any index of pier top displacement, strain, plastic strain, settlement, and inclination reaches 80% of the limit state, a third-level alarm is initiated, if any index of pier top displacement, strain, plastic strain, settlement, and inclination reaches 90% of the limit state, a second-level alarm is initiated, and if any index of pier top displacement, strain, plastic strain, settlement, and inclination reaches 100% of the limit state, a first-level alarm is initiated.

[0185] Embodiment two:

[0186] The embodiment two of the present application provides a pier digital twin intelligent monitoring system based on a surrogate model, comprising:

[0187] The data set acquisition module is configured to construct a finite element model of a to-be-monitored pier, to take a working condition factor combination as input data, to take pier state data calculated by the finite element model according to working condition data as output data, to obtain an input-output data set;

[0188] The data set processing module is configured to perform dimension reduction and feature extraction on the input-output data set by using an intrinsic orthogonal decomposition method, to obtain a feature coefficient matrix;

[0189] The surrogate model training module is configured to construct a surrogate model by using a Gaussian process regression method, to take the feature coefficient matrix as output, to take the working condition factor combination as input to train the surrogate model, to verify the surrogate model by using a verification strategy combining adaptive particle swarm optimization and nested cross in the training process, and to obtain optimal hyperparameters;

[0190] The surrogate model application module is configured to retrain the surrogate model by using the optimal hyperparameters, to obtain a final pier digital twin intelligent monitoring surrogate model, and to apply the pier digital twin intelligent monitoring surrogate model in a digital twin platform.

[0191] Embodiment three:

[0192] The embodiment three of the present application provides a computer readable storage medium, the computer readable storage medium stores a computer program, the computer program is suitable for being loaded and executed by a processor to execute steps in the bridge pier digital twin intelligent monitoring method based on an agent model as described in the embodiment one of the present application.

[0193] Embodiment four:

[0194] The embodiment four of the present application provides a computer device, the device comprises:

[0195] A processor is suitable for executing a computer program.

[0196] A computer readable storage medium, the computer readable storage medium stores a computer program, when the computer program is executed by the processor, the steps in the bridge pier digital twin intelligent monitoring method based on an agent model as described in the embodiment one of the present application are realized.

[0197] The steps and methods in the above embodiment two, three and four correspond to the embodiment one, and the specific implementation can refer to the related description part of the embodiment one.

[0198] The units and algorithm steps of each example described in combination with the embodiments disclosed in the present application can be realized by electronic hardware or a combination of computer software and electronic hardware. Whether the functions are realized by hardware or software depends on the specific application and design constraints of the technical solution. The professional technical object can use different methods to realize the described functions for each specific application, but such implementation should not be considered beyond the scope of the present application.

[0199] In the above embodiments, all or part of the embodiments can be implemented by software, hardware, firmware or any combination thereof. When implemented by software, all or part of the embodiments can be implemented in the form of a computer program product. The 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 or transmitted by 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 through a wired (for example, coaxial cable, optical fiber, digital line (DSL)) or wireless (for example, infrared, wireless, microwave, etc.) manner. 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, data center, etc. integrated with one or more available media. The available media can be a magnetic medium (for example, floppy disk, hard disk, magnetic tape), an optical medium (for example, DVD), or a semiconductor medium (for example, solid state disk (SSD)) and the like.

[0200] The above description is only a specific implementation of the present application, but the protection scope of the present application is not limited thereto. Any person skilled in the art can easily think of changes or replacements within the technical scope disclosed in the present application, which should be covered within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the protection scope of the claims.

Claims

1. A bridge pier digital twin intelligent monitoring method based on a proxy model, characterized in that, The method comprises the following steps: A finite element model of a bridge pier to be monitored is constructed, working condition factor combinations are taken as input data, and bridge pier state data calculated by the finite element model according to the working condition data are taken as output data, so that an input-output data set is obtained; Eigenvalue orthogonal decomposition is used to reduce the dimension and extract features of the input-output data set, and a characteristic coefficient matrix is obtained; A Gaussian process regression method is used to construct a surrogate model, the characteristic coefficient matrix is taken as output, and the working condition factor combinations are taken as input to train the surrogate model, and an adaptive particle swarm optimization and nested cross-validation strategy is used to verify the surrogate model during the training process, so that optimal hyperparameters are obtained, wherein the adaptive particle swarm optimization and nested cross-validation strategy is used to verify the surrogate model during the training process, and the specific steps are as follows: The input-output data set is evenly divided into several subsets as the basis for outer validation; In each fold of the outer layer, a non-repeating subset is selected as the outer validation set for final model evaluation, and the remaining subset is used as the outer training set for further inner cross-validation to search for a Gaussian process regression through particle swarm optimization; The specific steps of the inner cross-validation are as follows: The outer training set is evenly divided into several groups for inner cross-validation, in each fold of the inner layer, a non-repeating subset is selected as the inner test set, and the remaining subset is used as the inner training set to train the Gaussian process regression model; An adaptive particle swarm optimization method is used to optimize the hyperparameters, and the surrogate model trained is used to calculate the root mean square error in the inner test set, which is recorded and used in the next fold of the inner cross-validation; After all the inner cross-validations are completed, the hyperparameter combination with the smallest root mean square error is selected; The surrogate model is retrained using the optimal hyperparameters, and a final bridge pier digital twin intelligent monitoring surrogate model is obtained, which is applied to a digital twin platform.

2. The agent model based bridge pier digital twin intelligent monitoring method of claim 1, wherein, The working condition factor combinations are combinations of horizontal pressure data, scour depth data, vibration data, inclination data and settlement data, and the bridge pier state data includes bridge pier stress field data, plastic strain field data and displacement field information.

3. The agent model based bridge pier digital twin intelligent monitoring method of claim 1, wherein, The specific steps of using the eigenvalue orthogonal decomposition method to reduce the dimension and extract features of the input-output data set are as follows: The bridge pier state data is composed into a snapshot matrix, and the snapshot matrix is subjected to a separate average field processing; The snapshot matrix after the separate average field processing is subjected to snapshot eigenvalue orthogonal decomposition to obtain an eigenvalue diagonal matrix and an eigenvector matrix, and the eigenvalues are sorted; Based on the snapshot matrix after the separate average field processing, the eigenvalue diagonal matrix and the eigenvector matrix, an orthogonal basis matrix is calculated according to the eigenvalue sorting, and a characteristic coefficient matrix is further calculated; The orthogonal basis vectors and the characteristic coefficient matrix are used to reconstruct the bridge pier state data according to the eigenvalue cutting.

4. The agent model based bridge pier digital twin intelligent monitoring method of claim 1, wherein, The specific steps of training the surrogate model with the characteristic coefficient matrix as output and the working condition factor combinations as input are as follows: The training set and the test set are divided according to the characteristic coefficient matrix and the working condition factor combinations; A weighted sum of a radial basis function and a Matern function is used as a kernel function; The hyperparameters of the kernel function are iteratively optimized using the training set, and the test set is used for testing to obtain optimal hyperparameters.

5. The agent model based bridge pier digital twin intelligent monitoring method of claim 1, wherein, The digital twin platform realizes real-time visualization of the overall physical field of the pier obtained by the pier digital twin intelligent monitoring agent model, and starts a multi-level early warning strategy through disaster prediction. 6.A bridge pier digital twin intelligent monitoring system based on a proxy model, characterized in that, The method comprises the following steps: a dataset obtaining module configured to construct a finite element model of a bridge pier to be monitored, to obtain an input-output dataset by taking a combination of working condition factors as input data and taking pier state data calculated by the finite element model according to the working condition data as output data; a dataset processing module configured to perform dimension reduction and feature extraction on the input-output dataset by using an intrinsic orthogonal decomposition method to obtain a feature coefficient matrix; an agent model training module configured to construct an agent model by using a Gaussian process regression method, to train the agent model by taking the feature coefficient matrix as output and the combination of working condition factors as input, and to verify the agent model by using a verification strategy combining adaptive particle swarm optimization and nested cross validation during the training process to obtain optimal hyperparameters, wherein the specific steps of verifying the agent model by using the verification strategy combining adaptive particle swarm optimization and nested cross validation during the training process are as follows: the input-output dataset is evenly divided into a plurality of subsets as an outer validation basis; in each outer fold, a non-repeated subset is selected as an outer validation set for final model evaluation, and the remaining subset is used as an outer training set for inner cross-validation to search for a Gaussian process regression by particle swarm optimization; the specific steps of inner cross-validation are as follows: the outer training set is evenly divided into a plurality of groups for inner cross-validation, in each inner fold, a non-repeated subset is selected as an inner test set, and the remaining subset is used as an inner training set to train a Gaussian process regression model; an adaptive particle swarm optimization method is used to optimize hyperparameters, and the agent model trained is used to calculate root mean square errors in the inner test set, which are recorded and used in the next inner cross-validation fold; after completing all inner cross-validation, the hyperparameter combination with the smallest root mean square error is selected; an agent model application module configured to retrain the agent model by using the optimal hyperparameters to obtain a final pier digital twin intelligent monitoring agent model, and to apply the pier digital twin intelligent monitoring agent model in a digital twin platform.

7. A computer-readable storage medium, characterized in that, The computer readable storage medium stores a computer program, and the computer program is adapted to be loaded and executed by the processor to implement the agent model-based pier digital twin intelligent monitoring method according to any one of claims 1-5.

8. A computer device, characterized in that: a processor adapted to execute a computer program; a computer readable storage medium, wherein the computer readable storage medium stores a computer program, and the computer program is executed by the processor to implement the agent model-based pier digital twin intelligent monitoring method according to any one of claims 1-5.

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