A Deep Learning-Based Calibration Method and System for Digital Twin Dynamic Models of Arch Dams

Abstract

This invention discloses a deep learning-based calibration method and system for the dynamic model of an arch dam digital twin, belonging to the field of water conservancy engineering safety management. The method includes: an offline training step, establishing an initial finite element model and training a deep learning surrogate model; a data acquisition and automatic modal identification step, using COV-SSI and HDBSCAN algorithms to automatically identify the operating modal parameters of the arch dam; a model parameter inversion step, constructing an unweighted multi-objective optimization function using the modal parameter residuals, and solving for the optimal correction parameters using a GNDO-optimized DHKELM surrogate model and the MOGNDO algorithm; and an online calibration step, updating the model and verifying its accuracy. This invention achieves efficient and accurate calibration of the arch dam dynamic model, significantly improving the automation level and computational efficiency of modal identification and parameter correction, ensuring real-time synchronization between the physical and virtual models in the digital twin system, and providing reliable technical support for arch dam condition assessment, risk warning, and life prediction.

Description

Technical Field

[0001] This invention relates to the field of water conservancy project operation safety management technology, specifically a method and system for calibrating a digital twin dynamic model of an arch dam based on deep learning. Background Technology

[0002] In the context of the deep integration of smart water conservancy and digital twin technology, digital twins provide a new technical path for the full life-cycle management of arch dams. Its core lies in achieving precise mapping and bidirectional dynamic interaction between the physical arch dam and the virtual numerical model. The mapping from the physical model to the virtual numerical model relies on a multi-source sensor network to comprehensively collect physical data such as the arch dam's geometry, material properties, vibration response, and stress state. After data fusion processing, this data is transformed into initialization and update parameters for the virtual model, constructing a high-fidelity virtual twin that is geometrically consistent, mechanically equivalent, and operating conditions synchronized. The bidirectional interaction is manifested in the virtual model outputting prediction results through simulation calculations, which in turn guide the optimization of monitoring points, the adjustment of operating parameters, and the formulation of maintenance plans for the physical arch dam, forming a closed-loop operation mechanism of "physical perception - virtual simulation - data feedback - physical control." This mechanism is also the core logic of how digital twin technology empowers the safety management and control of arch dams.

[0003] Model calibration is a core step in maintaining the accuracy of the physical-virtual mapping of an arch dam digital twin system, directly determining the reliability of the virtual model's predictions of the physical entity. Essentially, it involves dynamically correcting virtual model parameters to compensate for errors caused by initial modeling assumptions, uncertainties in material parameters, simplified boundary conditions, and time-varying structural characteristics, enabling the virtual model to track the mechanical response of the physical arch dam in real time. Without efficient and accurate calibration methods, digital twin models will struggle to adapt to the time-varying characteristics of arch dam concrete aging and load accumulation, leading to deviations between virtual simulation results and actual working conditions. This will fail to provide effective support for engineering decisions and may even pose safety risks. Therefore, developing intelligent calibration technology adapted to digital twin scenarios is a crucial prerequisite for promoting the engineering implementation of arch dam digital twin technology.

[0004] Vibration testing technology and system identification theory are constantly being updated. Finite element model updating (FEMU) based on vibration response has received widespread attention and research, and is an effective means to improve the accuracy of finite element models. In FEMU, obtaining structural modal parameters is the first step. Operational modal analysis obtains modal parameters by collecting and analyzing vibration response signals of arch dams under environmental excitation during operation. It is convenient to operate, does not affect engineering operation, and allows for continuous monitoring, providing an economical and practical solution for arch dam modal parameter identification. Among these methods, the stochastic subspace identification (SSI) method directly processes time-domain vibration data using subspace decomposition technology. It has high computational efficiency and good robustness, and is a commonly used and effective method in arch dam operational modal analysis. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of FEMU (Featured Dynamic Model) for arch dams in modal recognition and surrogate model research, and to propose a deep learning-based method and system for calibrating the digital twin dynamic model of arch dams. After training the surrogate model based on the initial finite element method (FEM) calculation, this invention employs an automatic modal identification method that combines environmental vibration data and covariance-driven stochastic subspace (COV-SSI) with hierarchical density clustering for noise data (HDBSCAN) to solve the problem of automatically and accurately identifying the modal parameters of arch dams. Furthermore, it uses a multi-output deep hybrid kernel extreme learning machine (DHKELM) improved with the generalized normal distribution algorithm (GNDO) to accurately capture the nonlinear mapping relationship between the dynamic model parameters and modal parameters of the arch dam, constructing a surrogate model to replace traditional FEM calculations. Finally, a multi-objective optimization function is constructed based on the residuals of the identified modal parameters and the FEM modal parameters of the arch dam. The optimal FEM parameters are solved using the multi-objective GNDO algorithm and applied to the intelligent calibration of the arch dam dynamic model. This not only improves the efficiency and accuracy of modal identification and parameter correction but also ensures real-time synchronization between the physical and virtual models in the digital twin system, providing reliable technical support for the arch dam digital twin to achieve core functions such as state assessment, risk warning, and life prediction.

[0006] To achieve the above objectives, the present invention adopts the following technical solution.

[0007] In a first aspect, this invention provides a deep learning-based method for calibrating a digital twin dynamic model of an arch dam, comprising the following steps: Step S1: Offline training; An initial dynamic finite element model of the arch dam was established, the coefficients to be corrected were determined, and an experimental design method was used to generate a sample set and train a deep learning surrogate model. Step S2: Data acquisition and automatic modality recognition; The vibration response data of the arch dam under environmental excitation is collected in real time. The vibration response data is processed by the covariance-driven random subspace method COV-SSI. The stability graph is clustered using the hierarchical puzzle clustering algorithm HDBSCAN to automatically remove false stability poles, thereby identifying the operating modal parameters of the arch dam. Step S3: Model parameter inversion; A multi-objective optimization function is constructed using the residuals between the identified arch dam operating modal parameters and the finite element calculation modal parameters. A GNDO-DHKELM surrogate model is constructed by optimizing the deep hybrid kernel extreme learning machine using the generalized normal distribution algorithm GNDO. The multi-objective optimization function is then solved using the multi-objective generalized normal distribution algorithm MOGNDO to obtain the optimal correction parameters. Step S4: Online calibration; The optimal correction parameters are substituted into the initial dynamic finite element model to complete the model update and accuracy verification.

[0008] Specifically, the data acquisition and automatic modality recognition in step S2 are as follows: Step S21: Process the vibration response data using the covariance-driven random subspace method COV-SSI, construct the Toeplitz matrix, and perform singular value decomposition. First, construct the Hankel matrix and then calculate the covariance matrix of the output data. : ; In the above formula, Let s represent the vector composed of vibration response data at time k, where k = 1, 2, ..., s, and s is the number of data points. for The transpose of ; m is the number of measurement points; n is the modal order; From the covariance matrix Constructing the Toeplitz matrix : ; In the above formula, i is the number of columns in the matrix; j is the number of rows in the matrix; Perform singular value decomposition on the Toeplitz matrix: ; In the above formula, U and V are orthogonal matrices; It is the transpose of V; A submatrix consisting of left singular vectors with non-zero singular values; A submatrix consisting of left singular vectors with zero singular values; A submatrix consisting of right singular vectors with non-zero singular values; A submatrix consisting of right singular vectors with zero singular values; It is a diagonal matrix. ; Represents a diagonal matrix The main diagonal element is a non-zero element. , Represents non-zero singular values. The number of non-zero singular values; The observable matrix Γ of the system is expressed as: ; In the above formula, express The square root matrix; The system matrix A is then represented as: ; In the above formula, Representing an observable matrix The former Moore-Penrose pseudoinverse of the submatrix formed by rows; Describing the observable matrix Γ Arrive at the The submatrix formed; Observable matrix Half of the row dimension; This indicates a Moore-Penrose pseudo-inverse; Perform eigenvalue decomposition on system matrix A: ; In the above formula, This represents a matrix composed of eigenvectors; For including eigenvalues a diagonal matrix; express The inverse matrix; The system's modal parameters are calculated based on the eigenvalues ​​and eigenvectors of the identified system matrix: ; ; In the above formula, Represents characteristic frequencies; To indicate the sampling time interval for data acquisition; Indicates the damping ratio; Indicates taking the complex number The real part; Indicates modal parameters; An eigenvector representing the eigenvalues ​​corresponding to the system matrix; Step S22: Automatically determine the system order and generate a stability graph using singular entropy increments; The order of the vibration system under noise-free conditions In actual testing, the signal is affected by noise. Number of non-zero singular values ​​in ,at this time It can be represented as a combination of the system's vibration information and the singular values ​​corresponding to the noise. : ; In the above formula, In the presence of noise The number of non-zero singular values ​​in the array; because The magnitudes of the diagonal elements correspond to the vibrational information content of the system. To distinguish between singular values ​​caused by noise and singular value components caused by the system's own vibration, the singular entropy increment theory is introduced to automatically determine the system order. Singular entropy is defined as : ; In the above formula, The singular entropy represents the first... The singular entropy increment at position is calculated using the following formula: ; In the above formula, After the singular value decomposition of the Toeplitz matrix, sorted in descending order, the first... Singular values ​​of order; For all singular values ​​sorted in descending order, For traversal index; When the decreasing trend of the singular entropy increment stabilizes, it indicates that the characteristic information contained in the signal is complete, and the corresponding singular spectrum order is the order of the vibration system. structural modal order for , Indicates rounding down; Based on the determined system order, set the maximum order of the stability graph. , The system matrix at multiple orders is decomposed into eigenvalues ​​to obtain candidate mode parameters of each order. Based on the obtained candidate mode parameters of each order, a stability graph is generated. Step S23: The hierarchical puzzle clustering algorithm HDBSCAN is used to calculate the modal distance of the stable points, perform cluster analysis, and automatically remove the poles in the clusters with fewer than the preset threshold as false stable poles, and use the average value of the clustering results of the remaining stable points as the identified running modal parameters. Step S231: Spatial transformation of data points; For modal parameter data, first calculate the modal distance between data points: ; In the above formula, Representing data points and Modal distance between them; , Representing data points respectively , modal frequencies; , These represent the modal shape vectors of the data points; , They represent , transpose; Represents the modal shape vector , The modal confidence criterion between them is expressed as: ; right To perform a spatial transformation, first define the maximum nearest neighbor number of the sample points. And calculate the mutual reachability distance: ; In the above formula, Representing data points and The mutual reachability distance between them; This is an identifier subscript for the distance metric, used to distinguish it from other distance definitions; Indicates the distance from the current point to its i-th position. The original distance between the nearest points; Step S232: Construct the minimum spanning tree; Using the data points in the dataset as vertices, and the edge weight between any two vertices being the mutual reachability distance between the two vertices, the Prim algorithm is used to construct the minimum spanning tree. Step S233: Construct a clustering hierarchy; Sort the edges in the minimum spanning tree in ascending order by weight, and merge the subgraphs containing the two points corresponding to each edge to obtain a clustering tree with a multi-level structure. Step S234: Compress the clustering hierarchy; Traverse the clustering tree from top to bottom. When splitting a node, if the sample size of one of the two sub-clusters is less than a preset threshold, then the sub-cluster is removed to obtain a simplified clustering tree. Step S235: Extract stable clusters; Traverse the clustering tree from bottom to top and calculate the stability of each node: ; In the above formula, S is the stability metric of the node; Represents sample points Because it is the reciprocal of the weight of the disconnected edge when the split leaves the node; This represents the reciprocal of the weight of the broken edge when a node is split into two child nodes; If the stability of the parent node is lower than the sum of the stability of its child nodes, then update the stability of the parent node to the sum of the stability of its child nodes; otherwise, mark the parent node as an independent cluster and prune its child nodes; after traversing to the root node, the set of independent clusters obtained is the stable cluster. Extremes in clusters with fewer than a preset threshold of stable points are removed as spurious stable extremes, and the average value of the clustering results of the remaining stable points is used as the final identified operating mode parameter.

[0009] Specifically, the content of constructing the multi-objective optimization function in step S3 is as follows: Based on the calculated and identified natural frequencies of the arch dam model, and the modal guarantee criterion (MAC) value of the calculated and identified mode shapes, a multi-objective function without weighting coefficients is constructed: ; ; In the above formula, X is a material parameter vector. , These are the lower and upper bound vectors of the material parameter vector, respectively; The objective function is constructed based on the calculation and identification of frequencies and mode shapes using an arch dam model; Calculate and identify frequency residuals for arch dam models; Modal mode residuals for calculation and identification of arch dam model; N m The maximum modal order; These are the p-th calculated and identified arch dam modal frequencies; These are the p-th order calculated and identified mode shapes of the arch dam measuring points; As a modal guarantee criterion, , express The transpose of .

[0010] Specifically, step S3, which involves using the Generalized Normal Distribution Algorithm (GNDO) to optimize the Deep Hybrid Kernel Extreme Learning Machine (DHKELM) and constructing the GNDO-DHKELM surrogate model, includes: Step S311: Construct a deep network structure by cascading multiple extreme learning machines based on the idea of ​​autoencoders, thereby extracting input features in layers; The autoencoder extreme learning machine (ELM-AE) randomly generates the input weights and bias parameters of the hidden layer, and then the output vector of the hidden layer... Represented as: ; In the above formula, This is the input matrix for the autoencoder extreme learning machine ELM-AE; The input parameter weight vector; These are bias parameters; For activation functions; This is the index for hidden layer nodes. , This represents the number of hidden layer nodes. The output of the autoencoder extreme learning machine ELM-AE is represented as follows: β; In the above formula, β is the hidden layer output weight vector, β=[β1, β2, …, β L H(x) is the output weight matrix; The problem of solving the autoencoder extreme learning machine (ELM-AE) can be expressed as minimizing the error between the model output and the actual output: ; In the above formula, Y is the output matrix of the training set; According to the theory of generalized inverse matrices, the solution is obtained. : ; In the above formula, Let H be the generalized inverse matrix; for The transpose of ; C is the regularization parameter; I is the identity matrix; Using kernel function matrix Replace the random matrix in the autoencoder extreme learning machine ELM-AE After feature mapping, the output of the Kernel Extreme Learning Machine (KELM) is represented as follows: ; In the above formula, For kernel function, For the Nth sample input vector in the training set, The total number of training samples in the training set; This is the penalty coefficient; The kernel function matrix For a hybrid kernel function that combines polynomial kernel functions and radial basis kernel functions: ; In the above formula, These are weighting coefficients; For polynomial kernel functions, , Two input samples respectively , eigenvectors; It is a radial basis kernel function; ; In the above formula, For constant terms; The power of the polynomial; It is an exponential function; This represents the Euclidean distance between two vectors. Scale factor; Step S312: Construct a deep extreme learning machine (DELM) by cascading multiple ELM-AEs. Each ELM-AE is used as a layer, and the hidden layer output of the previous ELM-AE is used as the input of the next ELM-AE. At the top layer or a specified output layer of the deep network structure, the learned features are input into the extreme learning machine HKELM with hybrid kernels for regression prediction, thus constructing a deep hybrid kernel extreme learning machine (DHKELM).

[0011] Furthermore, the multi-objective optimization function is solved using the MOGNDO multi-objective generalized normal distribution algorithm in step S3, as detailed below: Step S321: Initialize the population and establish an external archive for storing non-dominated solutions; Let the population size be The maximum number of iterations is The archive capacity is Balance factor ; An initial population is randomly generated within the feasible region of the optimization parameters, and each individual in the population represents a set of hyperparameter combinations: ; In the above formula, Indicates the first in the initial population Individual position vectors , The number of parameters to be optimized; The random numbers are uniformly distributed. ; , These represent the upper and lower bound vectors of the optimization parameters, respectively. For each individual DHKELM is constructed using its hyperparameter combination, and the prediction error of DHKELM on the validation set is calculated as the initial fitness value: ; In the above formula, Indicates the first in the initial population The initial fitness value of each individual, The number of parameters output by DHKELM; and They represent the first DHKELM predicted values ​​and actual sample values ​​for each output parameter; The individual with the lowest fitness value in the current population is identified as the optimal individual, and the position of the optimal individual in the current population is recorded. Calculate the average position of all individuals in the current population. : ; In the above formula, Population size; For the first The individual in the first Position vector under the next iteration; For each individual Generate random numbers , Introducing a balance factor Switching between local and global development behaviors for individuals: ; In the above formula, Indicates the first The individual in the first The trajectory vector under the next iteration; Indicates the first The generalized average position of an individual ; Indicates the first The generalized standard deviation of an individual. ; As a penalty factor; It is a random number. ; , All are random numbers that follow a standard normal distribution; , All are trajectory vectors; ; ; In the above formula, , , The values ​​are randomly selected and the range is within... Integers that are not equal to each other; Will As candidate solutions, a DHKELM model is constructed using combinations of hyperparameters from the candidate solutions, and the fitness value is calculated. Based on the selection mechanism, a better solution will be introduced into the next generation of the population. : ; Step S322: In each iteration, the solutions are layered according to the non-dominated relationship based on the elite non-dominated sorting, and non-dominated layering is performed according to the objective superiority, while retaining the historical high-quality elite solutions, so as to realize the superiority sorting and hierarchical division of multi-objective solutions. Step S323: After the iteration is completed, output the Pareto optimal solution set. Since the solutions in the Pareto optimal solution set are not mutually exclusive and their quality cannot be directly determined, the inflection point strategy is adopted to screen the optimal solution. By calculating the local bending angle of each discrete point of the Pareto front, the feature inflection point with the largest bending angle on the curve is selected. This inflection point is located at the most significant turning point of the front and can achieve the best trade-off between multiple objectives. The corresponding parameter combination is determined as the final optimal correction parameter.

[0012] Specifically, the online calibration in step S4 also includes: connecting the calibrated finite element model to the online monitoring system to achieve real-time linkage between the digital twin model and the physical structure, and establishing a dynamic update mechanism for model parameters. When the deviation of the monitoring data exceeds the preset threshold, the system automatically backtracks to the model parameter inversion step for recalibration.

[0013] On the other hand, this invention also provides a deep learning-based digital twin dynamic model calibration system for arch dams, used to implement the above method. The system includes: Offline training module; used to establish an initial dynamic finite element model, generate a sample set, and train a deep learning proxy model. Online data acquisition and modal identification module; used to acquire arch dam vibration response data in real time, and automatically identify the operating modal parameters of the arch dam based on the covariance-driven random subspace method COV-SSI and the hierarchical puzzle clustering algorithm HDBSCAN. Model parameter inversion module; used to construct a multi-objective optimization function from the residuals of the identified arch dam operating modal parameters and the finite element calculated modal parameters, and to solve for the optimal model correction parameters based on the deep hybrid kernel extreme learning machine DHKELM surrogate model optimized by the generalized normal distribution algorithm GNDO and the multi-objective generalized normal distribution algorithm MOGNDO. The online calibration module is used to substitute the optimal correction parameters into the initial model, complete the model update and accuracy verification, and connect to the online monitoring system.

[0014] Specifically, the online data acquisition and modality recognition module includes: Sensor units are deployed at key locations on the dam crest and cap beam of the arch dam to collect vibration response data. The signal preprocessing unit is used to filter and denoise the raw vibration response data; The automatic identification unit is used to execute the covariance-driven random subspace method COV-SSI, the order determination based on singular entropy increment, the hierarchical mystery clustering algorithm HDBSCAN, and to automatically output the natural frequency, damping ratio, and mode shape of the arch dam.

[0015] Compared with the prior art, the present invention has the following beneficial effects: 1. The method of this invention combines the covariance-driven random subspace method COV-SSI with the hierarchical density clustering HDBSCAN for noisy data, realizing the automatic identification of vibration modal parameters of arch dam environment. It effectively solves the problems of traditional modal analysis relying on manual interpretation and being susceptible to noise interference. It can robustly and accurately extract real modal parameters such as natural frequency, mode shape and damping ratio from noisy signals, providing a reliable measured data basis for model correction.

[0016] 2. The method of this invention uses a multi-output deep hybrid kernel extreme learning machine (DHKELM) improved by generalized normal distribution optimization (GNDO) to construct a surrogate model, accurately capturing the nonlinear mapping relationship between finite element model parameters and modal parameters. The deep learning surrogate model replaces the traditional time-consuming finite element calculation, which greatly improves the computational efficiency of response prediction and parameter inversion, and meets the timeliness requirements of real-time online calibration of digital twin systems.

[0017] 3. The method of this invention is based on the residuals of the identified modal parameters and the modal parameters calculated by finite element method to construct a multi-objective optimization function, and uses the multi-objective generalized normal distribution optimization GNDO algorithm to search for the optimal correction parameters. This achieves synchronous and accurate calibration of multiple parameters such as elastic modulus and boundary conditions, effectively compensating for errors caused by initial modeling assumption deviations, material parameter uncertainties and time-varying structural characteristics, enabling the virtual model to track the mechanical response law of the physical arch dam in real time.

[0018] 4. The system of this invention adopts a working mode that combines offline training and online calibration. The surrogate model is trained in the offline stage, and the parameters are automatically optimized and the model is updated in the online stage based on the measured data. The closed-loop mechanism formed can ensure that the digital twin model is synchronized with the physical arch dam. The updated model can be directly used for online monitoring and safety assessment, which improves the engineering practicality of the arch dam digital twin system. Attached Figure Description

[0019] Figure 1 This is a framework diagram of the intelligent calibration method and system for the dynamic model of arch dams of the present invention.

[0020] Figure 2 This is a flowchart of the automatic modal recognition method (COV-SSI+HDBSCAN) of the present invention.

[0021] Figure 3This is a schematic diagram of spatial transformation in the HDBSCAN algorithm of this invention (schematic diagram of mutual reachability distance calculation).

[0022] Figure 4 This is a detailed flowchart of the intelligent calibration method for the dynamic model of arch dams (including surrogate model and multi-objective optimization) of the present invention.

[0023] Figure 5 This is a schematic diagram of the network structure of the Deep Hybrid Kernel Extreme Learning Machine (DHKELM) of the present invention.

[0024] Figure 6 This is a flowchart illustrating the construction process of the GNDO-optimized DHKELM (GNDO-DHKELM) of this invention.

[0025] Figure 7 This is a schematic diagram of non-dominated sorting in the multi-objective optimization of this invention.

[0026] Figure 8 This is a diagram showing the vibration test and sensor arrangement of the arch dam prototype in a specific embodiment of the present invention.

[0027] Figure 9 The image shows the prototype vibration response time history curve collected in a specific embodiment of the present invention.

[0028] Figure 10 This is a schematic diagram illustrating the determination of the system order based on the singular entropy increment in a specific embodiment of the present invention.

[0029] Figure 11 The following is a comparison of the stable graphs of automatic modality recognition in specific embodiments of the present invention: (a) stable graph without clustering, (b) stable graph after HDBSCAN clustering.

[0030] Figure 12 The above are the three-mode vibration diagrams of the arch dam identified in a specific embodiment of the present invention.

[0031] Figure 13 This is a dynamic finite element model of an arch dam established in a specific embodiment of the present invention.

[0032] Figure 14 The following is a diagram showing the prediction effect of the GNDO-DHKELM surrogate model on the first three natural frequencies in a specific embodiment of the present invention: (a) first modal frequency, (b) second modal frequency, and (c) third modal frequency.

[0033] Figure 15 Radar charts comparing the performance of different surrogate models (BP neural network, KELM, GNDO-DHKELM) in specific embodiments of the present invention: (a) natural frequency prediction performance, (b) mode shape coefficient prediction performance at typical measurement point S5.

[0034] Figure 16 This is the Pareto optimal solution set obtained by solving the MOGNDO algorithm in a specific embodiment of the present invention.

[0035] Figure 17 This refers to the Modal Assurance Criterion (MAC) value between the calculated modal and the measured modal after model calibration in a specific embodiment of the present invention.

[0036] Figure 18 The following are the three modal shapes of the arch dam calculated after model calibration in a specific embodiment of the present invention: (a) first modal shape, (b) second modal shape, and (c) third modal shape. Detailed Implementation

[0037] To facilitate understanding and implementation of the present invention by those skilled in the art, the various steps of the method proposed in this invention are described in detail below. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention. Furthermore, it should be understood that after reading the teachings of this invention, those skilled in the art can make various modifications or alterations to the invention, and these equivalent forms also fall within the scope defined by the appended claims.

[0038] Example 1 like Figure 1 As shown, this invention presents a deep learning-based method for calibrating a digital twin dynamic model of an arch dam, comprising the following steps: Step S1: Offline training; An initial dynamic finite element model of the arch dam was established, the coefficients to be corrected were determined, and an experimental design method was used to generate a sample set and train a deep learning surrogate model. Step S2: Data acquisition and automatic modality recognition; The vibration response data of the arch dam under environmental excitation is collected in real time. The vibration response data is processed by the covariance-driven random subspace method COV-SSI. The stability graph is clustered using the hierarchical puzzle clustering algorithm HDBSCAN to automatically remove false stability poles, thereby identifying the operating modal parameters of the arch dam. Step S3: Model parameter inversion; like Figure 4 As shown, a multi-objective optimization function is constructed using the residuals between the identified arch dam operating modal parameters and the finite element calculated modal parameters. The GNDO-DHKELM surrogate model is constructed by optimizing the deep hybrid kernel extreme learning machine using the generalized normal distribution algorithm GNDO. The multi-objective optimization function is then solved using the multi-objective generalized normal distribution algorithm MOGNDO to obtain the optimal correction parameters. Step S4: Online calibration; The optimal correction parameters are substituted into the initial dynamic finite element model to complete the model update and accuracy verification.

[0039] Specifically, such as Figure 2 As shown, the data acquisition and automatic modality recognition in step S2 are as follows: Step S21: Process the vibration response data using the covariance-driven random subspace method COV-SSI, construct the Toeplitz matrix, and perform singular value decomposition. First, construct the Hankel matrix and then calculate the covariance matrix of the output data. : ; In the above formula, Let s represent the vector composed of vibration response data at time k, where k = 1, 2, ..., s, and s is the number of data points. for The transpose of ; m is the number of measurement points; n is the modal order; From the covariance matrix Constructing the Toeplitz matrix : ; In the above formula, i is the number of columns in the matrix; j is the number of rows in the matrix; Perform singular value decomposition on the Toeplitz matrix: ; In the above formula, U and V are orthogonal matrices; It is the transpose of V; A submatrix consisting of left singular vectors with non-zero singular values; A submatrix consisting of left singular vectors with zero singular values; A submatrix consisting of right singular vectors with non-zero singular values; A submatrix consisting of right singular vectors with zero singular values; It is a diagonal matrix. ; Represents a diagonal matrix The main diagonal element is a non-zero element. , Represents non-zero singular values. The number of non-zero singular values; The observable matrix Γ of the system is expressed as: ; In the above formula, express The square root matrix; The system matrix A is then represented as: ; In the above formula, Representing an observable matrix The former Moore-Penrose pseudoinverse of the submatrix formed by rows; Describing the observable matrix Γ Arrive at the The submatrix formed; Observable matrix Half of the row dimension; This indicates a Moore-Penrose pseudo-inverse; Perform eigenvalue decomposition on system matrix A: ; In the above formula, This represents a matrix composed of eigenvectors; For including eigenvalues a diagonal matrix; express The inverse matrix; The system's modal parameters are calculated based on the eigenvalues ​​and eigenvectors of the identified system matrix: ; ; In the above formula, Represents characteristic frequencies; To indicate the sampling time interval for data acquisition; Indicates the damping ratio; Indicates taking the complex number The real part; Indicates modal parameters; An eigenvector representing the eigenvalues ​​corresponding to the system matrix; Step S22: Automatically determine the system order and generate a stability graph using singular entropy increments; The order of the vibration system under noise-free conditions In actual testing, the signal is affected by noise. Number of non-zero singular values ​​in ,at this time It can be represented as a combination of the system's vibration information and the singular values ​​corresponding to the noise. : ; In the above formula, In the presence of noise The number of non-zero singular values ​​in the array; because The magnitudes of the diagonal elements correspond to the vibrational information content of the system. To distinguish between singular values ​​caused by noise and singular value components caused by the system's own vibration, the singular entropy increment theory is introduced to automatically determine the system order. Singular entropy is defined as : ; In the above formula, The singular entropy represents the first... The singular entropy increment at position is calculated using the following formula: ; In the above formula, After the singular value decomposition of the Toeplitz matrix, sorted in descending order, the first... Singular values ​​of order; For all singular values ​​sorted in descending order, For traversal index; When the decreasing trend of the singular entropy increment stabilizes, it indicates that the characteristic information contained in the signal is complete, and the corresponding singular spectrum order is the order of the vibration system. structural modal order for , Indicates rounding down; Based on the determined system order, set the maximum order of the stability graph. , The system matrix at multiple orders is decomposed into eigenvalues ​​to obtain candidate mode parameters of each order. Based on the obtained candidate mode parameters of each order, a stability graph is generated. Step S23: The hierarchical puzzle clustering algorithm HDBSCAN is used to calculate the modal distance of the stable points, perform cluster analysis, and automatically remove the poles in the clusters with fewer than the preset threshold as false stable poles, and use the average value of the clustering results of the remaining stable points as the identified running modal parameters. Step S231: Spatial transformation of data points; like Figure 3 As shown, for modal parameter data, the modal distance between data points is first calculated: ; In the above formula, Representing data points and Modal distance between them; , Representing data points respectively , modal frequencies; , These represent the modal shape vectors of the data points; , They represent , transpose; Represents the modal shape vector , The modal confidence criterion between them is expressed as: ; right To perform a spatial transformation, first define the maximum nearest neighbor number of the sample points. And calculate the mutual reachability distance: ; In the above formula, Representing data points and The mutual reachability distance between them; This is an identifier subscript for the distance metric, used to distinguish it from other distance definitions; Indicates the distance from the current point to its i-th position. The original distance between the nearest points; Step S232: Construct the minimum spanning tree; Using the data points in the dataset as vertices, and the edge weight between any two vertices being the mutual reachability distance between the two vertices, the Prim algorithm is used to construct the minimum spanning tree. Step S233: Construct a clustering hierarchy; Sort the edges in the minimum spanning tree in ascending order by weight, and merge the subgraphs containing the two points corresponding to each edge to obtain a clustering tree with a multi-level structure. Step S234: Compress the clustering hierarchy; Traverse the clustering tree from top to bottom. When splitting a node, if the sample size of one of the two sub-clusters is less than a preset threshold, then the sub-cluster is removed to obtain a simplified clustering tree. Step S235: Extract stable clusters; Traverse the clustering tree from bottom to top and calculate the stability of each node: ; In the above formula, S is the stability metric of the node; Represents sample points Because it is the reciprocal of the weight of the disconnected edge when the split leaves the node; This represents the reciprocal of the weight of the broken edge when a node is split into two child nodes; If the stability of the parent node is lower than the sum of the stability of its child nodes, then update the stability of the parent node to the sum of the stability of its child nodes; otherwise, mark the parent node as an independent cluster and prune its child nodes; after traversing to the root node, the set of independent clusters obtained is the stable cluster. Extremes in clusters with fewer than a preset threshold of stable points are removed as spurious stable extremes, and the average value of the clustering results of the remaining stable points is used as the final identified operating mode parameter.

[0040] Specifically, the content of constructing the multi-objective optimization function in step S3 is as follows: Based on the calculated and identified natural frequencies of the arch dam model, and the modal guarantee criterion (MAC) value of the calculated and identified mode shapes, a multi-objective function without weighting coefficients is constructed: ; ; In the above formula, X is a material parameter vector. , These are the lower and upper bound vectors of the material parameter vector, respectively; The objective function is constructed based on the calculation and identification of frequencies and mode shapes using an arch dam model; Calculate and identify frequency residuals for arch dam models; Modal mode residuals for calculation and identification of arch dam model; N m The maximum modal order; These are the p-th calculated and identified arch dam modal frequencies; These are the p-th order calculated and identified mode shapes of the arch dam measuring points; As a modal guarantee criterion, , express The transpose of .

[0041] Specifically, such as Figure 5 As shown, step S3, which involves using the Generalized Normal Distribution Algorithm (GNDO) to optimize the Deep Hybrid Kernel Extreme Learning Machine (DHKELM) and constructing the GNDO-DHKELM surrogate model, includes: Step S311: Construct a deep network structure by cascading multiple extreme learning machines based on the idea of ​​autoencoders, thereby extracting input features in layers; The autoencoder extreme learning machine (ELM-AE) randomly generates the input weights and bias parameters of the hidden layer, and then the output vector of the hidden layer... Represented as: ; In the above formula, This is the input matrix for the autoencoder extreme learning machine ELM-AE; The input parameter weight vector; These are bias parameters; For activation functions; This is the index for hidden layer nodes. , This represents the number of hidden layer nodes. The output of the autoencoder extreme learning machine ELM-AE is represented as follows: β; In the above formula, β is the hidden layer output weight vector, β=[β1, β2, …, β L H(x) is the output weight matrix; The problem of solving the autoencoder extreme learning machine (ELM-AE) can be expressed as minimizing the error between the model output and the actual output: ; In the above formula, Y is the output matrix of the training set; According to the theory of generalized inverse matrices, the solution is obtained. : ; In the above formula, Let H be the generalized inverse matrix; for The transpose of ; C is the regularization parameter; I is the identity matrix; Using kernel function matrix Replace the random matrix in the autoencoder extreme learning machine ELM-AE After feature mapping, the output of the Kernel Extreme Learning Machine (KELM) is represented as follows: ; In the above formula, For kernel function, For the Nth sample input vector in the training set, The total number of training samples in the training set; This is the penalty coefficient; The kernel function matrix For a hybrid kernel function that combines polynomial kernel functions and radial basis kernel functions: ; In the above formula, These are weighting coefficients; For polynomial kernel functions, , Two input samples respectively , eigenvectors; It is a radial basis kernel function; ; In the above formula, For constant terms; The power of the polynomial; It is an exponential function; This represents the Euclidean distance between two vectors. Scale factor; Step S312: Construct a deep extreme learning machine (DELM) by cascading multiple ELM-AEs. Each ELM-AE is used as a layer, and the hidden layer output of the previous ELM-AE is used as the input of the next ELM-AE. At the top layer or a specified output layer of the deep network structure, the learned features are input into the extreme learning machine HKELM with hybrid kernels for regression prediction, thus constructing a deep hybrid kernel extreme learning machine (DHKELM).

[0042] Furthermore, such as Figure 6 As shown, the multi-objective optimization function is solved using the MOGNDO multi-objective generalized normal distribution algorithm in step S3, and the specific content is as follows: Step S321: Initialize the population and establish an external archive for storing non-dominated solutions; Let the population size be The maximum number of iterations is The archive capacity is Balance factor ; An initial population is randomly generated within the feasible region of the optimization parameters, and each individual in the population represents a set of hyperparameter combinations: ; In the above formula, Indicates the first in the initial population Individual position vectors , The number of parameters to be optimized; The random numbers are uniformly distributed. ; , These represent the upper and lower bound vectors of the optimization parameters, respectively. For each individual DHKELM is constructed using its hyperparameter combination, and the prediction error of DHKELM on the validation set is calculated as the initial fitness value: ; In the above formula, Indicates the first in the initial population The initial fitness value of each individual, The number of parameters output by DHKELM; and They represent the first DHKELM predicted values ​​and actual sample values ​​for each output parameter; The individual with the lowest fitness value in the current population is identified as the optimal individual, and the position of the optimal individual in the current population is recorded. Calculate the average position of all individuals in the current population. : ; In the above formula, Population size; For the first The individual in the first Position vector under the next iteration; For each individual Generate random numbers , Introducing a balance factor Switching between local and global development behaviors for individuals: ; In the above formula, Indicates the first The individual in the first The trajectory vector under the next iteration; Indicates the first The generalized average position of an individual ; Indicates the first The generalized standard deviation of an individual. ; As a penalty factor; It is a random number. ; , All are random numbers that follow a standard normal distribution; , All are trajectory vectors; ; ; In the above formula, , , The values ​​are randomly selected and the range is within... Integers that are not equal to each other; Will As candidate solutions, a DHKELM model is constructed using combinations of hyperparameters from the candidate solutions, and the fitness value is calculated. Based on the selection mechanism, a better solution will be introduced into the next generation of the population. : ; Step S322: In each iteration, the solutions are layered according to the non-dominated relationship based on the elite non-dominated sorting, and non-dominated layering is performed according to the objective superiority, while retaining the historical high-quality elite solutions, so as to realize the superiority sorting and hierarchical division of multi-objective solutions. Step S323, as follows Figure 7 As shown, after the iteration is completed, the Pareto optimal solution set is output, and the point with the largest bending angle on the Pareto front curve is determined as the optimal solution according to the inflection point strategy, which is used as the final optimal correction parameter.

[0043] Specifically, the online calibration in step S4 also includes: connecting the calibrated finite element model to the online monitoring system to achieve real-time linkage between the digital twin model and the physical structure, and establishing a dynamic update mechanism for model parameters. When the deviation of the monitoring data exceeds the preset threshold, the system automatically backtracks to the model parameter inversion step for recalibration.

[0044] Example 2 Based on Example 1, this invention also provides a deep learning-based digital twin dynamic model calibration system for arch dams, used to implement the method described in Example 1. The system includes: Offline training module; used to establish an initial dynamic finite element model, generate a sample set, and train a deep learning proxy model. Online data acquisition and modal identification module; used to acquire arch dam vibration response data in real time, and automatically identify the operating modal parameters of the arch dam based on the covariance-driven random subspace method COV-SSI and the hierarchical puzzle clustering algorithm HDBSCAN. Model parameter inversion module; used to construct a multi-objective optimization function from the residuals of the identified arch dam operating modal parameters and the finite element calculated modal parameters, and to solve for the optimal model correction parameters based on the deep hybrid kernel extreme learning machine DHKELM surrogate model optimized by the generalized normal distribution algorithm GNDO and the multi-objective generalized normal distribution algorithm MOGNDO. The online calibration module is used to substitute the optimal correction parameters into the initial model, complete the model update and accuracy verification, and connect to the online monitoring system.

[0045] Specifically, the online data acquisition and modality recognition module includes: Sensor units are deployed at key locations on the dam crest and cap beam of the arch dam to collect vibration response data. The signal preprocessing unit is used to filter and denoise the raw vibration response data; The automatic identification unit is used to execute the covariance-driven random subspace method COV-SSI, the order determination based on singular entropy increment, the hierarchical mystery clustering algorithm HDBSCAN, and to automatically output the natural frequency, damping ratio, and mode shape of the arch dam.

[0046] The technical effects of the present invention will be further illustrated by the following practical engineering examples.

[0047] 1. Engineering Background and Vibration Testing A prototype test of discharge-excited vibration was conducted on a high arch dam, such as... Figure 8As shown, radial displacement sensors were installed at the dam crest (measuring points S1-S7) and capping beam (measuring points S8-S11) of the prototype dam body for vibration testing. The sensors used were DP-type low-frequency dynamic displacement sensors, and data was collected using a DASP system with a sampling frequency of 200Hz. Figure 9 The image shows the vibration response time history curves of the arch dam measuring points.

[0048] 2. Modal Analysis of Arch Dam Engineering Operation Using the vibration responses from 11 measuring points collected during the prototype test of the arch dam as input, the proposed automatic modal analysis method was employed to determine the modal order of the arch dam model system, such as... Figure 10 As shown, when the singular spectrum order i reaches 7, the increase in singular entropy decreases and tends to stabilize, indicating that the system order N s The order is 7, further leading to the conclusion that the order of the real system is N. t =3.

[0049] Then the maximum order N of the stability graph is... max Set to 3N s That is, 21, resulting in the following: Figure 11 The stability diagram shown in (a) is as follows: Figure 11 As shown in (b), the HDBSCAN algorithm is further used to perform cluster analysis on the stable graph and remove discrete points. Figure 11 As shown in (b) of the diagram, the discrete spurious modal points in the stability plot are significantly eliminated. The final identified arch dam model structure frequencies and damping parameters are shown in Table 1 below. The proposed automatic modal identification method and the EFDD method show good consistency in their identification results. Finally, as... Figure 12 As shown, the first three mode shapes of the arch dam model structure were extracted. Figure 12 (a) in the text corresponds to the first-order mode shape. Figure 12 (b) in the text corresponds to the second mode shape. Figure 12 (c) in the equation corresponds to the third-order mode shape.

[0050] Table 1. Modal parameters of arch dams ; 3. Construction of GNDO-DHKELM proxy model like Figure 13As shown, a finite element model of the arch dam-foundation was established based on the design data of the project. The foundation elements were simulated as a massless elastic foundation, with normal constraints around the foundation and fixed constraints at the bottom. The number of elements for the dam foundation and the dam body were 6,553 and 3,433, respectively, with 8,017 and 4,201 nodes. The effect of the water body was applied as an additional mass using the finite element method and calculated using a modified Westergaard formula. According to the design partitioning of the arch dam model, it was divided into two regions: the dam body and the dam foundation. Density and dynamic elastic modulus (selected as material parameters to be updated in the model, with corresponding value ranges shown in Table 2 below) were also considered.

[0051] Table 2. Range of values ​​for arch dam material parameters ; 500 sets of material parameter samples were randomly generated using the LHS method, and then the dataset was calculated based on the FEM model. A GNDO-DHKELM surrogate model was then established. The optimal DHKELM hyperparameters were obtained by optimizing the DHKELM model using GNDO: N J =[2,96,100], C=0.002, M=0.001, =0.4429. Subsequently, a DHKELM surrogate model was constructed based on the optimal parameters, and the fitting effect was verified. In the training set, the structural intrinsic frequencies predicted by the GNDO-DHKELM surrogate model are in high agreement with the actual values, such as... Figure 14 As shown, the correlation coefficient between the predicted and actual values ​​on the test set reaches 0.9999. This indicates that the constructed GNDO-DHKELM surrogate model can effectively capture the highly nonlinear mapping relationship between material parameters and modal parameters. Figure 15 As shown, the GNDO-DHKELM model significantly outperforms the BP neural network and KELM model in terms of prediction accuracy of modal frequencies and typical measurement point mode shape coefficients, demonstrating higher prediction accuracy and generalization ability. This indicates that the proposed GNDO-DHKELM surrogate model can more effectively fit the nonlinear relationship between arch dam material parameters and modal parameters.

[0052] 4. Multi-objective optimization, calibration, and verification of the dynamic model of the arch dam like Figure 16 As shown, the mathematical model of the finite element model of the arch dam dynamic proposed in the technical solution section is calibrated using MOGDNO to obtain the Pareto optimal solution set. Then, the Knee point in the Pareto optimal solution set is selected as the optimal solution. The corresponding identification results of the dynamic material parameters of the optimal arch dam model are shown in Table 3 below.

[0053] Table 3. Updated values ​​of arch dam material parameters ; like Figure 17 As shown in Table 4, the FEM of the arch dam is corrected based on the material parameter values ​​obtained from the inversion. Then, the modal parameters calculated by the corrected FEM are compared with the corresponding measured values. The errors between the calculated first four natural frequencies and the measured values ​​are all less than 4%. Figure 18 As shown, the first three modes of the FEM of the arch dam were further calculated. The MAC values ​​between the measured mode and the calculated mode both exceeded 0.96, showing good consistency and verifying the effectiveness of the proposed method for actual arch dam projects.

[0054] Table 4. Comparison of Natural Frequencies ; 5. Engineering Applications of Online Monitoring Systems for Arch Dams After verifying the model's accuracy, the calibrated finite element model is integrated into the arch dam's online monitoring system, enabling real-time linkage between the digital twin model and the physical structure. Based on real-time vibration data, the model can rapidly update the structural dynamic response prediction results, providing reliable digital support for dynamic early warning, damage identification, and long-term health status assessment of the dam. Simultaneously, a dynamic parameter update mechanism is established. If subsequent monitoring data shows significant deviations, the model can be quickly reverted to the correction stage for parameter recalibration, ensuring the model's applicability and accuracy throughout the arch dam's entire lifecycle and providing continuous technical support for engineering operation and maintenance decisions.

[0055] The above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A deep learning-based calibration method for an arch dam digital twin dynamic model, characterized in that, Includes the following steps: Step S1: Offline training; An initial dynamic finite element model of the arch dam was established, the coefficients to be corrected were determined, and an experimental design method was used to generate a sample set and train a deep learning surrogate model. Step S2: Data acquisition and automatic modality recognition; The vibration response data of the arch dam under environmental excitation is collected in real time. The vibration response data is processed by the covariance-driven random subspace method COV-SSI. The stability graph is clustered using the hierarchical puzzle clustering algorithm HDBSCAN to automatically remove false stability poles, thereby identifying the operating modal parameters of the arch dam. Step S3: Model parameter inversion; A multi-objective optimization function is constructed using the residuals between the identified arch dam operating modal parameters and the finite element calculation modal parameters. A GNDO-DHKELM surrogate model is constructed by optimizing the deep hybrid kernel extreme learning machine using the generalized normal distribution algorithm GNDO. The multi-objective optimization function is then solved using the multi-objective generalized normal distribution algorithm MOGNDO to obtain the optimal correction parameters. Step S4: Online calibration; The optimal correction parameters are substituted into the initial dynamic finite element model to complete the model update and accuracy verification.

2. The method of claim 1, wherein the method is characterized by, The specific details of data acquisition and automatic modality recognition in step S2 are as follows: Step S21: Process the vibration response data using the covariance-driven random subspace method COV-SSI, construct the Toeplitz matrix, and perform singular value decomposition. First, construct the Hankel matrix and then calculate the covariance matrix of the output data. : ； In the above formula, Let s represent the vector composed of vibration response data at time k, where k = 1, 2, ..., s, and s is the number of data points. for The transpose of ; m is the number of measurement points; n is the modal order; From the covariance matrix Constructing the Toeplitz matrix : ； In the above formula, i is the number of columns in the matrix; j is the number of rows in the matrix; Perform singular value decomposition on the Toeplitz matrix: ； In the above formula, U and V are orthogonal matrices; It is the transpose of V; A submatrix consisting of left singular vectors with non-zero singular values; A submatrix consisting of left singular vectors with zero singular values; A submatrix consisting of right singular vectors with non-zero singular values; A submatrix consisting of right singular vectors with zero singular values; It is a diagonal matrix. ; Represents a diagonal matrix The main diagonal element is a non-zero element. , Represents non-zero singular values. The number of non-zero singular values; The observable matrix Γ of the system is expressed as: ； In the above formula, express The square root matrix; The system matrix A is then represented as: ； In the above formula, Representing an observable matrix The former Moore-Penrose pseudoinverse of the submatrix formed by rows; Describing the observable matrix Γ Arrive at the The submatrix formed; Observable matrix Half of the row dimension; This indicates a Moore-Penrose pseudo-inverse; Perform eigenvalue decomposition on system matrix A: ； In the above formula, This represents a matrix composed of eigenvectors; For including eigenvalues a diagonal matrix; express The inverse matrix; The system's modal parameters are calculated based on the eigenvalues ​​and eigenvectors of the identified system matrix: ； ； In the above formula, Represents characteristic frequencies; To indicate the sampling time interval for data acquisition; Indicates the damping ratio; Indicates taking the complex number The real part; Indicates modal parameters; An eigenvector representing the eigenvalues ​​corresponding to the system matrix; Step S22: Automatically determine the system order and generate a stability graph using singular entropy increments; The order of the vibration system under noise-free conditions In actual testing, the signal is affected by noise. Number of non-zero singular values ​​in ,at this time It can be represented as a combination of the system's vibration information and the singular values ​​corresponding to the noise. : ； In the above formula, In the presence of noise The number of non-zero singular values ​​in the array; because The magnitudes of the diagonal elements correspond to the vibrational information content of the system. To distinguish between singular values ​​caused by noise and singular value components caused by the system's own vibration, the singular entropy increment theory is introduced to automatically determine the system order. Singular entropy is defined as : ； In the above formula, The singular entropy represents the first... The singular entropy increment at position is calculated using the following formula: ； In the above formula, After the singular value decomposition of the Toeplitz matrix, sorted in descending order, the first... Singular values ​​of order; For all singular values ​​sorted in descending order, For traversal index; When the decreasing trend of the singular entropy increment stabilizes, it indicates that the characteristic information contained in the signal is complete, and the corresponding singular spectrum order is the order of the vibration system. structural modal order for , Indicates rounding down; Based on the determined system order, set the maximum order of the stability graph. , The system matrix at multiple orders is decomposed into eigenvalues ​​to obtain candidate mode parameters of each order. Based on the obtained candidate mode parameters of each order, a stability graph is generated. Step S23: The hierarchical puzzle clustering algorithm HDBSCAN is used to calculate the modal distance of the stable points, perform cluster analysis, and automatically remove the poles in the clusters with fewer than the preset threshold as false stable poles, and use the average value of the clustering results of the remaining stable points as the identified running modal parameters. Step S231: Spatial transformation of data points; For modal parameter data, first calculate the modal distance between data points: ； In the above formula, Representing data points and Modal distance between them; , Representing data points respectively , modal frequencies; , These represent the modal shape vectors of the data points; , They represent , transpose; Represents the modal shape vector , The modal confidence criterion between them is expressed as: ; right To perform a spatial transformation, first define the maximum nearest neighbor number of the sample points. And calculate the mutual reachability distance: ； In the above formula, Representing data points and The mutual reachability distance between them; This is an identifier subscript for the distance metric, used to distinguish it from other distance definitions; Indicates the distance from the current point to its i-th position. The original distance between the nearest points; Step S232: Construct the minimum spanning tree; Using the data points in the dataset as vertices, and the edge weight between any two vertices being the mutual reachability distance between the two vertices, the Prim algorithm is used to construct the minimum spanning tree. Step S233: Construct a clustering hierarchy; Sort the edges in the minimum spanning tree in ascending order by weight, and merge the subgraphs containing the two points corresponding to each edge to obtain a clustering tree with a multi-level structure. Step S234: Compress the clustering hierarchy; Traverse the clustering tree from top to bottom. When splitting a node, if the sample size of one of the two sub-clusters is less than a preset threshold, then the sub-cluster is removed to obtain a simplified clustering tree. Step S235: Extract stable clusters; Traverse the clustering tree from bottom to top and calculate the stability of each node: ； In the above formula, S is the stability metric of the node; Represents sample points Because it is the reciprocal of the weight of the disconnected edge when the split leaves the node; This represents the reciprocal of the weight of the broken edge when a node is split into two child nodes; If the stability of the parent node is lower than the sum of the stability of its child nodes, then update the stability of the parent node to the sum of the stability of its child nodes; otherwise, mark the parent node as an independent cluster and prune its child nodes. After traversing to the root node, the set of independent clusters obtained is the stable cluster; Extremes in clusters with fewer than a preset threshold of stable points are removed as spurious stable extremes, and the average value of the clustering results of the remaining stable points is used as the final identified operating mode parameter.

3. The method for calibrating a deep learning-based digital twin dynamic model of an arch dam according to claim 2, characterized in that, The specific details of constructing the multi-objective optimization function in step S3 are as follows: Based on the calculated and identified natural frequencies of the arch dam model, and the modal guarantee criterion (MAC) value of the calculated and identified mode shapes, a multi-objective function without weighting coefficients is constructed: ； ； In the above formula, X is a material parameter vector. , These are the lower and upper bound vectors of the material parameter vector, respectively; The objective function is constructed based on the calculation and identification of frequencies and mode shapes using an arch dam model; Calculate and identify frequency residuals for arch dam models; Modal mode residuals for calculation and identification of arch dam model; N m The maximum modal order; These are the p-th calculated and identified arch dam modal frequencies; These are the p-th order calculated and identified mode shapes of the arch dam measuring points; As a modal guarantee criterion, , express The transpose of .

4. The method for calibrating a deep learning-based digital twin dynamic model of an arch dam according to claim 3, characterized in that, Step S3, which describes using the Generalized Normal Distribution Algorithm (GNDO) to optimize the Deep Hybrid Kernel Extreme Learning Machine (DHKELM) and constructing the GNDO-DHKELM surrogate model, specifically includes: Step S311: Construct a deep network structure by cascading multiple extreme learning machines based on the idea of ​​autoencoders, thereby extracting input features in layers; The autoencoder extreme learning machine (ELM-AE) randomly generates the input weights and bias parameters of the hidden layer, and then the output vector of the hidden layer... Represented as: ； In the above formula, This is the input matrix for the autoencoder extreme learning machine ELM-AE; The input parameter weight vector; These are bias parameters; For activation functions; This is the index for hidden layer nodes. , This represents the number of hidden layer nodes. The output of the autoencoder extreme learning machine ELM-AE is represented as follows: β； In the above formula, β is an implicit layer output weight vector, β = [β1, β2, …, β L ]; H(x) is an output weight matrix; The problem of solving the autoencoder extreme learning machine (ELM-AE) can be expressed as minimizing the error between the model output and the actual output: ； In the above formula, Y is the output matrix of the training set; According to the theory of generalized inverse matrices, the solution is obtained. : ； In the above formula, Let H be the generalized inverse matrix; for The transpose of ; C is the regularization parameter; I is the identity matrix; Using kernel function matrix Replace the random matrix in the autoencoder extreme learning machine ELM-AE After feature mapping, the output of the Kernel Extreme Learning Machine (KELM) is represented as follows: ； In the above formula, For kernel function, For the Nth sample input vector in the training set, The total number of training samples in the training set; This is the penalty coefficient; The kernel function matrix For a hybrid kernel function that combines polynomial kernel functions and radial basis kernel functions: ； In the above formula, These are weighting coefficients; For polynomial kernel functions, , Two input samples respectively , eigenvectors; It is a radial basis kernel function; ； In the above formula, For constant terms; The power of the polynomial; It is an exponential function; This represents the Euclidean distance between two vectors. Scale factor; Step S312: Construct a deep extreme learning machine (DELM) by cascading multiple ELM-AEs. Each ELM-AE is used as a layer, and the hidden layer output of the previous ELM-AE is used as the input of the next ELM-AE. At the top layer or a specified output layer of the deep network structure, the learned features are input into the extreme learning machine HKELM with hybrid kernels for regression prediction, thus constructing a deep hybrid kernel extreme learning machine (DHKELM).

5. The method for calibrating a digital twin dynamic model of an arch dam based on deep learning according to claim 4, characterized in that, The multi-objective optimization function is solved using the MOGNDO (Multi-Objective Generalized Normal Distribution) algorithm in step S3, as detailed below: Step S321: Initialize the population and establish an external archive for storing non-dominated solutions; Let the population size be The maximum number of iterations is The archive capacity is Balance factor ; An initial population is randomly generated within the feasible region of the optimization parameters, and each individual in the population represents a set of hyperparameter combinations: ； In the above formula, Indicates the first in the initial population Individual position vectors , The number of parameters to be optimized; The random numbers are uniformly distributed. ; , These represent the upper and lower bound vectors of the optimization parameters, respectively. For each individual DHKELM is constructed using its hyperparameter combination, and the prediction error of DHKELM on the validation set is calculated as the initial fitness value: ； In the above formula, Indicates the first in the initial population The initial fitness value of each individual, The number of parameters output by DHKELM; and They represent the first DHKELM predicted values ​​and actual sample values ​​for each output parameter; The individual with the lowest fitness value in the current population is identified as the optimal individual, and the position of the optimal individual in the current population is recorded. Calculate the average position of all individuals in the current population. : ； In the above formula, Population size; For the first The individual in the first Position vector under the next iteration; For each individual Generate random numbers , Introducing a balance factor Switching between local and global development behaviors for individuals: ； In the above formula, Indicates the first The individual in the first The trajectory vector under the next iteration; Indicates the first The generalized average position of an individual ; Indicates the first The generalized standard deviation of an individual. ; As a penalty factor; It is a random number. ; , All are random numbers that follow a standard normal distribution; , All are trajectory vectors; ； ； In the above formula, , , The values ​​are randomly selected and the range is within... Integers that are not equal to each other; Will As candidate solutions, a DHKELM model is constructed using combinations of hyperparameters from these candidate solutions. Based on a selection mechanism, better solutions are introduced into the next generation of the population. : ； Step S322: In each iteration, the solutions are layered according to the non-dominated relationship based on the elite non-dominated sorting, and non-dominated layering is performed according to the objective superiority, while retaining the historical high-quality elite solutions, so as to realize the superiority sorting and hierarchical division of multi-objective solutions. Step S323: After the iteration is completed, output the Pareto optimal solution set, and determine the point with the largest bending angle on the Pareto front curve as the optimal solution according to the inflection point strategy, which is used as the final optimal correction parameter.

6. The method for calibrating a deep learning-based digital twin dynamic model of an arch dam according to claim 5, characterized in that, The online calibration in step S4 also includes: connecting the calibrated finite element model to the online monitoring system to realize real-time linkage between the digital twin model and the physical structure, and establishing a dynamic update mechanism for model parameters. When the deviation of the monitoring data exceeds the preset threshold, it automatically backtracks to the model parameter inversion step for recalibration.

7. A deep learning-based digital twin dynamic model calibration system for arch dams, used to implement the method described in any one of claims 1-6, characterized in that the system... include: Offline training module; Used to establish an initial dynamic finite element model, generate a sample set, and train a deep learning proxy model; Online data acquisition and modal recognition module; It is used to collect vibration response data of arch dams in real time, and automatically identify the operating modal parameters of arch dams based on the covariance-driven random subspace method COV-SSI and the hierarchical puzzle clustering algorithm HDBSCAN. Model parameter inversion module; This is used to construct a multi-objective optimization function based on the residuals of the identified arch dam operating modal parameters and the finite element calculated modal parameters, and to solve for the optimal model correction parameters based on the deep hybrid kernel extreme learning machine DHKELM surrogate model optimized by the generalized normal distribution algorithm GNDO and the multi-objective generalized normal distribution algorithm MOGNDO. The online calibration module is used to substitute the optimal correction parameters into the initial model, complete the model update and accuracy verification, and connect to the online monitoring system.

8. The deep learning-based digital twin dynamic model calibration system for arch dams according to claim 7, characterized in that, The online data acquisition and modality recognition module includes: Sensor units are deployed at key locations on the dam crest and cap beam of the arch dam to collect vibration response data. The signal preprocessing unit is used to filter and denoise the raw vibration response data; The automatic identification unit is used to execute the covariance-driven random subspace method COV-SSI, the order determination based on singular entropy increment, the hierarchical mystery clustering algorithm HDBSCAN, and to automatically output the natural frequency, damping ratio, and mode shape of the arch dam.

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