Structural Damage Identification Method Based on Digital Twin and Feature Migration
By constructing a damage recognition model for bridge structures based on digital twins and feature migration methods, the problems of high cost of data acquisition, reduced accuracy and high computing resource requirements in traditional methods are solved, and efficient and accurate bridge structure damage recognition is achieved.
Patent Information
- Application Number
- CN202411234132.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2024-09-04
- Publication Date
- 2025-06-03
- Estimated Expiration
- 2044-09-04
AI Technical Summary
Traditional bridge structure damage detection methods have problems such as low detection accuracy, low efficiency, insufficient data and high computing resource requirements, making it difficult to achieve efficient and accurate damage identification.
Using a structural damage recognition method based on digital twins and feature migration, the source domain and target domain data sets are constructed, and the data is mapped to the public feature space using migration component analysis, and a damage recognition model is constructed to achieve online damage recognition.
Reliance on a large amount of actual annotated data is reduced, the accuracy and robustness of the model is improved, the computing resource requirements are reduced, and efficient and accurate identification of bridge structure damage is achieved.
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Figure CN119027741B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of structural damage identification, and particularly relates to a structural damage identification method, device, storage medium and product based on digital twin and feature transfer. Background Art
[0002] Existing structural health monitoring technologies mainly rely on the collection and analysis of sensor data, and structural damage is identified through vibration signals, strain data, etc. However, traditional methods usually require a large amount of labeled data for training, with high data acquisition costs and unstable data quality, and are easily affected by environmental noise. With the rapid development of digital twin technology, a new method for structural health monitoring is provided by constructing a virtual digital model to simulate and monitor the state of a physical structure. At the same time, transfer learning, as a machine learning technology, can utilize the knowledge of a trained model to quickly adapt to and optimize a new task, thereby reducing the dependence on a large amount of labeled data and improving the generalization ability and accuracy of the model.
[0003] As an important part of transportation infrastructure, the health status of bridges is directly related to public safety and economic development. With the increase in the service life of bridges, problems such as material aging and fatigue damage gradually emerge, and efficient and accurate damage detection of bridge structures has become a technical problem to be solved urgently. At present, traditional bridge structure damage detection methods mainly rely on manual inspections and simple monitoring devices, and these methods have the following deficiencies:
[0004] (1) Low detection accuracy: Manual inspections are easily limited by the experience and subjective judgment of inspectors, resulting in missed detections and misjudgments;
[0005] (2) Low efficiency: Manual inspections take a long time and it is difficult to achieve real-time monitoring and rapid response to bridge structures;
[0006] (3) Insufficient data: Traditional methods are difficult to obtain sufficient damage sample data, which affects the training effect and accuracy of the detection model;
[0007] (4) High computational resource requirements: The establishment and simulation calculation of finite element models require a large amount of professional knowledge and computational resources, increasing the complexity and cost of the detection system. Summary of the Invention
[0008] The purpose of the present invention is to provide a structural damage identification method based on digital twin and feature transfer, so as to solve at least one of the problems of high cost of collecting damage sample data, reduced accuracy due to insufficient damage sample data, and high computational resource requirements for obtaining sample data using finite element models in traditional methods.
[0009] The present invention solves the above technical problems through the following technical solutions: A structural damage identification method based on digital twin and feature migration, including:
[0010] Construct a source domain dataset and a target domain dataset; wherein, each sample in the source domain dataset includes the first time-frequency image of the structure and its damage type, and each sample in the target domain dataset includes the second time-frequency image of the structure and its damage type. Both the first time-frequency image and the second time-frequency image are converted from the acceleration response signal of the structure; the source domain dataset is constructed by using the digital twin model of the structure;
[0011] Extract features from each of the first time-frequency images to obtain first feature vectors; combine all the first feature vectors to obtain a first feature matrix; extract features from each of the second time-frequency images to obtain second feature vectors; combine all the second feature vectors to obtain a second feature matrix;
[0012] Stitch the first feature matrix and the second feature matrix to obtain a joint feature matrix;
[0013] Perform transfer component analysis on the joint feature matrix to obtain the source domain feature vectors and target domain feature vectors in the common feature space;
[0014] Construct a damage identification model, and perform supervised training on the damage identification model by using the source domain feature vectors and the damage types in the source domain dataset;
[0015] Perform unsupervised training on the damage identification model after supervised training by using the target domain feature vectors;
[0016] Perform performance evaluation on the damage identification model after unsupervised training by using the target domain feature vectors and the damage types in the target domain dataset to obtain a target recognition model.
[0017] Further, constructing the source domain dataset by using the digital twin model of the structure includes:
[0018] Step A1: Construct a parametric finite element model of the structure;
[0019] Step A2: Perform dynamic analysis on the parametric finite element model and export the Inp file;
[0020] Step A3: Use a Python script to open the Inp file and parse the element sets and their material properties in the Inp file;
[0021] Step A4: Modify the material properties of the element sets according to different damage types of the structure to update the material properties at different damage positions and obtain Inp files of different damage types;
[0022] Step A5: Use the subprocess module to perform ABAQUS simulation calculations on Inp files of different damage types to obtain ODB result files of different damage types;
[0023] Step A6: Use a Python script to open the ODB result files of different damage types, and extract the acceleration response signals of the structural nodes from the ODB result files of different damage types to obtain the acceleration response signals under different damage types;
[0024] Step A7: Convert the acceleration response signals under different damage types into images to obtain the first time-frequency images under different damage types;
[0025] Step A8: Construct a source domain dataset based on the first time-frequency images under different damage types.
[0026] Furthermore, using the spectral Markov transfer field to convert the acceleration response signal of the structure into the first time-frequency image or the second time-frequency image, including:
[0027] Calculate the spectral signal of the acceleration response signal, and the calculation formula is:
[0028]
[0029] where s(k) represents the k-th component in the spectral signal, x(i) represents the value of the i-th sampling point in the acceleration response signal, n represents the number of sampling points of the acceleration response signal, abs() represents the modulus function, and j represents the imaginary unit;
[0030] Normalize each component in the spectral signal to obtain the normalized components of the spectral signal;
[0031] Uniformly divide the value range of the amplitude set to obtain Q subintervals; where the amplitude set includes the amplitudes of all normalized components of the spectral signal;
[0032] Map each amplitude in the amplitude set to a subinterval; where the specific mapping formula is:
[0033]
[0034] where A k represents the k-th amplitude in the amplitude set, q j represents the j-th subinterval, argmin j represents finding the j that makes the function reach the minimum value;
[0035] Generate a spectral Markov transfer field matrix according to the probability of each amplitude transferring from the current subinterval to other subintervals;
[0036] Convert the spectral Markov transition field matrix into a two-dimensional image to obtain a first time-frequency image or a second time-frequency image.
[0037] Furthermore, use a pre-trained convolutional neural network model to extract features from the first time-frequency image and the second time-frequency image; wherein, the pre-trained convolutional neural network model does not include a fully connected layer.
[0038] Furthermore, perform transfer component analysis on the joint feature matrix, including:
[0039] Construct a joint Gaussian kernel matrix according to the joint feature matrix, and the specific formula is:
[0040]
[0041] where k ij represents the element in the i-th row and j-th column of the joint Gaussian kernel matrix; x i , x j represent two feature vectors in the joint feature matrix; σ represents the bandwidth of the Gaussian kernel function;
[0042] Construct a joint centered kernel matrix according to the joint Gaussian kernel matrix, and the specific formula is:
[0043]
[0044] where K c represents the joint centered kernel matrix; K represents the joint Gaussian kernel matrix; H represents the centering matrix; I and 1 both represent all-ones matrices; n s represents the number of samples in the source domain dataset, and n t represents the number of samples in the target domain dataset;
[0045] Construct a maximum mean discrepancy matrix, and the maximum mean discrepancy matrix is expressed as:
[0046]
[0047] where M represents the maximum mean discrepancy matrix; 1 a×b represents an all-ones matrix of size a×b;
[0048] Construct an objective function according to the joint centered kernel matrix and the maximum mean discrepancy matrix; wherein, the expression of the objective function is:
[0049]
[0050] where A represents the projection matrix, the superscript T represents the transpose, λ represents the regularization parameter, and tr() represents the trace of the matrix; It means to solve for the optimal projection matrix to minimize the distribution difference between the source domain and the target domain in the common feature space;
[0051] Solve the objective function to obtain the projection matrix;
[0052] Construct the first centralized kernel matrix according to the first feature matrix and the joint feature matrix, and obtain the source domain feature vectors based on the first centralized kernel matrix and the projection matrix;
[0053] Construct the second centralized kernel matrix according to the second feature matrix and the joint feature matrix, and obtain the target domain feature vectors based on the second centralized kernel matrix and the projection matrix.
[0054] Furthermore, solving the objective function using generalized eigenvalue decomposition includes:
[0055] Convert the objective function into a generalized eigenvalue problem:
[0056] (K c MK c +λK c )A=K c AΛ;
[0057] where, Λ represents the eigenvalue diagonal matrix, and the eigenvalue diagonal matrix contains the first k smallest eigenvalues;
[0058] Select the eigenvectors corresponding to the smallest eigenvalues as the column vectors of the projection matrix to obtain the projection matrix.
[0059] Furthermore, the recognition method further includes:
[0060] Obtain the real-time acceleration response signal of the structure, and convert the real-time acceleration response signal into a time-frequency image;
[0061] Use the target recognition model to perform online damage recognition on the time-frequency image.
[0062] Based on the same concept, the present invention also provides an electronic device, including a memory, a processor, and a computer program / instructions stored on the memory, and the processor executes the computer program / instructions to implement the structure damage recognition method as described above.
[0063] Based on the same concept, the present invention also provides a computer-readable storage medium, on which a computer program / instructions is stored, and when the computer program / instructions is executed by a processor, the structure damage recognition method as described above is implemented.
[0064] Based on the same concept, the present invention also provides a computer program product, including a computer program / instructions, and when the computer program / instructions is executed by a processor, the structure damage recognition method as described above is implemented.
[0065] Beneficial effects
[0066] Compared with the prior art, the advantages of the present invention are as follows:
[0067] The present invention uses digital twin technology to generate a large number of acceleration response signals under different damage types, and then constructs a source domain dataset, reducing the dependence on a large amount of actual labeled data, ensuring the accuracy of the model, and solving the problems of high cost of collecting damage sample data, reduction of model accuracy due to insufficient damage sample data, and high demand for computing resources for obtaining sample data using finite element models.
[0068] Through feature transfer component analysis, a large amount of source domain data and limited target domain data are mapped to a common feature space, minimizing the distribution difference between the source domain features and target domain features in the common feature space, effectively improving the adaptability and performance of the recognition model in new tasks, enhancing the accuracy and robustness of the model, and being particularly suitable for scenarios with limited target domain data. Brief description of the drawings
[0069] In order to more clearly illustrate the technical solutions of the present invention, the drawings required for the description of the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only one embodiment of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.
[0070] Figure 1 is the flowchart of the structural damage identification method in the embodiment of the present invention;
[0071] Figure 2 is the digital twin model of the bridge structure generated from the Inp file in the embodiment of the present invention;
[0072] Figure 3 is a partial acceleration response signal of the bridge structure extracted from the ODB result file in the embodiment of the present invention;
[0073] Figure 4 is the acceleration response signal obtained from the on-site test model of the bridge structure in the embodiment of the present invention;
[0074] Figure 5 is the comparison of modal parameters of the on-site test model and digital twin model of the bridge structure at different orders in the embodiment of the present invention; among them, from left to right are the first order, second order, and third order;
[0075] Figure 6 is the frequency domain signal of the on-site test model of the bridge structure in the embodiment of the present invention;
[0076] Figure 7 is the frequency domain signal of different digital twin models in the embodiment of the present invention;
[0077] Figure 8 It is a schematic diagram of the process of converting the acceleration response signal into a two-dimensional time-frequency image in the embodiment of the present invention;
[0078] Figure 9 It is a two-dimensional time-frequency image obtained by using the spectral Markov transfer field in the embodiment of the present invention;
[0079] Figure 10 It is a visualization diagram of the damage recognition result of the target recognition model for the first time-frequency image in the embodiment of the present invention;
[0080] Figure 11 It is a visualization diagram of the damage recognition result of the second time-frequency image without using the TCA method in the embodiment of the present invention;
[0081] Figure 12 It is a visualization diagram of the damage recognition result of the second time-frequency image by the method of the present invention in the embodiment of the present invention;
[0082] Figure 13 It is the recognition accuracy of 8 damage categories on the target domain dataset without using TCA and using TCA in the embodiment of the present invention;
[0083] Figure 14 It is the damage recognition confusion matrix of the method of the present invention on the target domain dataset in the embodiment of the present invention. Detailed implementation manners
[0084] Next, in combination with the accompanying drawings in the embodiments of the present invention, the technical solutions in the present invention will be clearly and completely described. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. Based on the embodiments in the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.
[0085] Next, the technical solutions of the present application will be described in detail with specific embodiments. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be repeated in some embodiments.
[0086] Embodiment 1
[0087] As Figure 1 shown, a structural damage recognition method based on digital twin and feature transfer provided by the embodiment of the present invention includes the following steps:
[0088] Step 1: Construct a source domain dataset and a target domain dataset.
[0089] Each sample in the source domain dataset includes the first time-frequency image of the structure and its damage type, and each sample in the target domain dataset includes the second time-frequency image of the structure and its damage type. Both the first time-frequency image and the second time-frequency image are obtained by converting the acceleration response signal of the structure.
[0090] To solve the problems of high cost of collecting damaged sample data, reduced model accuracy due to insufficient damaged sample data, and high computational resource requirements for obtaining sample data using finite element models, the present invention uses digital twin technology to generate a large number of structural damage samples. In a specific embodiment of the present invention, a digital twin model of the structure is used to construct the source domain dataset, including:
[0091] Step A1: Construct a parametric finite element model of the structure.
[0092] In this embodiment, the specific construction steps of the parametric finite element model of the structure are as follows:
[0093] Step A1.1: According to the geometric dimensions of the structure, use the ABAQUS finite element simulation platform to construct a finite element model of the structure;
[0094] Step A1.2: Perform mesh division on the finite element model, and apply loads and boundary conditions to simulate the working state of the structure in the actual environment; in this embodiment, the mesh size is 0.1 m to ensure accurate details;
[0095] Step A1.3: Define the components in different regions of the finite element model after mesh division as element sets, and set appropriate material properties for each element set to generate a parametric finite element model.
[0096] In this embodiment, the material properties include elastic modulus, density, and Poisson's ratio. Taking a bridge structure as an example, the elastic modulus is set to 2.1×10 5 N / mm 2 、the density is set to 7.9×10 -6 kg / mm 3 、and the Poisson's ratio is set to 0.3.
[0097] Step A2: Define the node set for field variable output, perform dynamic implicit analysis on the parametric finite element model, and export the Inp file.
[0098] In this embodiment, the field variable output is the vertical acceleration response signal. The nodes of the field variable output are consistent with the positions of the acceleration sensors of the actual structure. The Inp file contains material parameters, dimensional parameters, boundary conditions, loads, etc. Based on the Inp file obtained by using finite element technology, digital twin technology is used to automatically model a large number of numerical models similar to the structural model (including the test structural model and the real structure), and then perform automatic simulation calculations to provide reasonable and sufficient training samples.
[0099] Step A3: Use a Python script (or Python software) to open the Inp file and parse the element sets and their material properties in the Inp file.
[0100] The Python code to open the Inp file and read its content is: with open('model.inp','r')as file: content = file.read()
[0101] Step A4: Modify the material properties of the element set according to the damage type of the structure to update the material properties at the damage location and obtain the Inp file of this damage type (i.e., the updated Inp file).
[0102] Taking the bridge structure as an example, Figure 2 It shows the finite element model of the bridge structure to the digital twin model generated using the Inp file. According to the damage type of the structure, search for the damage locations (i.e., element sets) that need to be updated and the corresponding material properties, set the material properties of this damage location, and realize the material update at the damage location to ensure the synchronization of the digital twin model and the physical structure. The specific Python code is: content = content.replace(old_material, new_material)
[0103] Step A5: Use the subprocess module to perform ABAQUS simulation calculations on the updated Inp file to obtain the ODB result file.
[0104] The subprocess module in the Python programming language is used to run commands in the command line environment of the operating system to control the execution of external programs. In this embodiment, the subprocess module is used to execute the commands of the ABAQUS simulation software on the updated Inp file to perform finite element simulation calculations on the updated Inp file and obtain the ODB result file. The ODB result file includes the acceleration response signal under the damage type. The specific Python code is: subprocess.run(['abaqus', 'job=new_model', 'interactive'])
[0105] Step A6: After the simulation calculation is completed, use a Python script to open the ODB result file and extract the acceleration response signals of the structural nodes from the ODB result file.
[0106] After the simulation calculation is completed, use the Python API of ABAQUS to automatically read the generated ODB result file, select the node set with predefined field variable output, extract the acceleration response signals, and write the extracted acceleration response signals into a CSV file to complete the automatic data extraction. For example, select the truss node set with predefined field variable output and extract the acceleration response signals of the truss node set. Figure 3 Part of the acceleration response signals extracted from the ODB result file is shown. The specific Python code is as follows:
[0107] odb = visualization.openOdb('model.odb')
[0108] extract_acceleration_data('model.odb', 'Truss-NodeS')
[0109] Step A7: For different damage types, repeat Steps A3 to A6 to obtain the acceleration response signals under different damage types.
[0110] For different damage types, automatically update the material properties and generate Inp files for different damage types. The specific Python code is: new_inp_file = update_inp_file('model.inp', material_changes)
[0111] Use a Python script to automatically submit the ABAQUS simulation calculations of Inp files for different damage types by calling the subprocess module; run the ABAQUS simulation calculations in the background, process multiple simulation tasks in parallel, and capture the output logs to monitor the calculation progress and results, improving the efficiency of the automated modeling process.
[0112] Integrate the acceleration response signals under different damage types into a large data set to facilitate the construction of the source domain data set. The specific code is as follows:
[0113] combined_data.to_csv('combined_data.csv', index = False)
[0114] The present invention utilizes digital twin technology to obtain acceleration response signals under different damage types. Only one finite element model needs to be established, and then the corresponding Inp file is generated. The Inp file is programmatically modified using Python, the file content is read, various damage type data corresponding to the actual structure is written, and then the calculation is performed by running a script through the Abaqus-Command command window. This method does not require opening the Abaqus-CAE software and can automatically complete the calculation only by calling the solver, improving the calculation efficiency.
[0115] Step A8: Convert the acceleration response signals under different damage types into images to obtain the first time-frequency images under different damage types;
[0116] Step A9: Construct a source domain dataset based on the first time-frequency images under different damage types.
[0117] In the specific implementation manner of the present invention, the target domain dataset is constructed through a structural field test model. Taking a bridge structure as an example, a bridge structure field test model is designed, and acceleration sensors are arranged at key positions of the bridge structure field test model to collect acceleration response signals of the bridge structure under different damage types or damage conditions. Figure 4 The acceleration response signals collected by the acceleration sensors in the bridge structure field test model are shown. During the field test, different damage conditions are simulated by changing the cable force of the bridge stay cables, as shown in Table 1.
[0118] Table 1 Different damage conditions of the cables of the cable-stayed bridge
[0119]
[0120] In this test, the damage of the percentage of the elastic modulus of the materials used is used to model the damage of the stay cables of the bridge structure in order to effectively identify the damage; vehicles with different vehicle weights and speeds are used as external loads. In Table 1, S and N respectively represent the first letters of the numbers of the stay cables on both sides. The damage conditions in this embodiment include the damage location, vehicle speed, vehicle weight, and damage degree. The moving vehicle is used as the external load of the bridge. The vehicle is driven by a motor, and the vehicle speed is controlled by controlling the rotation speed of the motor. Damage condition 1: Healthy, combinations of different vehicle speeds and different vehicle weights; Damage condition 2: The first stay cable S1 on one side is damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%; Damage condition 3: The third stay cable S3 on one side is damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%; Damage condition 4: The fifth stay cable S5 on one side is damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%; Damage condition 5: The first and fourth stay cables S1 / S4 on one side are damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%; Damage condition 6: The second and fifth stay cables S2 / S5 on one side are damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%; Damage condition 7: The fourth stay cable S4 on one side is damaged and the second stay cable N2 on the other side is damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%; Damage condition 8: The sixth stay cable S6 on one side is damaged and the fifth stay cable N5 on the other side is damaged, combinations of different vehicle speeds and different vehicle weights, and the damage degree is 10%, 20%, or 50%. Each damage condition forms multiple sub-conditions through different combinations of vehicle speed, vehicle mass, and damage degree.
[0121] By selecting widely distributed damages, the robustness and accuracy of the present invention in different scenarios can be more comprehensively evaluated. The data of the operating conditions and all damage conditions come from the same excitation scenario to ensure the consistency and comparability of the data. The acceleration response signals under different damage conditions are obtained through the on-site test model of the bridge structure, the acceleration response signals under different damage conditions are converted into time-frequency images, the second time-frequency images under different damage conditions are obtained, and the target domain data set is constructed according to the second time-frequency images under different damage conditions.
[0122] Figure 5 Shows the comparison of the modal parameters of the on-site test model of the bridge structure and the modal parameters of the digital twin model of the bridge structure. Figure 5 It can be seen that the modal parameters of the on-site test model of the bridge structure are very similar to the modal parameters of the digital twin model. At the same time, Table 2, Figure 6 and Figure 7Lists the error values (errors are expressed as percentages) of the first three characteristic frequencies of the in-situ test model of the bridge structure and the digital twin model of the bridge structure, where the maximum difference is only 4.10%, not exceeding 5.00%. Therefore, the modal parameters ( Figure 4 ) and characteristic frequencies (Table 2) indicate that the digital twin model can effectively reflect the dynamic characteristics of the test bridge structure.
[0123] Table 2 Characteristic Frequencies of the In-situ Test Model and Digital Twin Model of the Bridge Structure
[0124]
[0125] Preprocess the acceleration response signals obtained from the digital twin model and the in-situ test model, and then convert the preprocessed acceleration response signals into time-frequency images. The acceleration response signals obtained from the digital twin model correspond to the first time-frequency image, and the acceleration response signals obtained from the in-situ test model correspond to the second time-frequency image. In this embodiment, the preprocessing includes normalization processing and filtering processing. The normalization processing process is as follows: calculate the maximum and minimum values of the acceleration response signals, and normalize the amplitude of each acceleration response signal so that it is mapped to the interval [-1, 1] to ensure consistency. The filtering processing is used to eliminate noise and outliers.
[0126] There are various ways to convert one-dimensional time series signals (i.e., acceleration response signals) into two-dimensional time-frequency images, such as Markov Transfer Field (MTF), Gram Angular Difference Field (GADF), Recurrence Plot (RT), Short-Time Fourier Transform (STFT), etc. Conventional methods for converting time series to two-dimensional time-frequency images often face limitations in batch processing when dealing with time series of different lengths. Since the lengths of the acceleration response signals are not consistent under different external loads, and the lengths of the acceleration response signals also vary during each measurement, this makes the signal length an important influencing factor in feature classification.
[0127] To solve the above problems, the present invention uses Spectral Markov Transfer Field (SMTF) to convert the acceleration response signals into time-frequency images, specifically including:
[0128] Step 1.1: Calculate the spectral signal of the acceleration response signal, and the calculation formula is:
[0129]
[0130] where s(k) represents the k-th component in the spectral signal, x(i) represents the value of the i-th sampling point in the acceleration response signal, n represents the number of sampling points or the length of the acceleration response signal, abs() represents the modulus function, and j represents the imaginary unit. The k-th component s(k) in the spectral signal is a complex number, and the k-th component s(k) represents the amplitude and phase information at frequency k. Represents the Fourier kernel function.
[0131] Step 1.2: Normalize each component in the spectral signal to obtain the normalized components of the spectral signal.
[0132] In this embodiment, the min-max normalization method is used to normalize each component in the spectral signal, and the specific formula is:
[0133]
[0134] where u(k) represents the k-th normalized component of the spectral signal, s max represents the maximum component in the spectral signal, s min represents the minimum component in the spectral signal.
[0135] Step 1.3: Uniformly divide the value range of the amplitude set to obtain Q sub-intervals; where the amplitude set includes the amplitudes of all normalized components of the spectral signal.
[0136] Since each amplitude in the amplitude set has been normalized, the value range of the amplitude set is [0, 1]. Uniformly dividing the value range of the amplitude set is to uniformly divide the numerical interval [0, 1] to obtain Q sub-intervals, and each sub-interval can be expressed as q j , j ∈ [1, Q].
[0137] Step 1.4: Map each amplitude in the amplitude set to a sub-interval; where the specific mapping formula is:
[0138]
[0139] where A k represents the k-th amplitude in the amplitude set; q j represents the j-th sub-interval; argmin j represents finding the j that makes the function reach the minimum value, that is, finding the j that makes the smallest. Through formula (3), it can be determined which sub-interval each amplitude in the amplitude set is currently in.
[0140] Step 1.5: Generate a spectral Markov transition field matrix according to the probability that each amplitude transfers from the current sub-interval to other sub-intervals.
[0141] In this embodiment, the spectral Markov transition field matrix of size n×n can be expressed as:
[0142]
[0143]
[0144] where p(A a ∈q i ∣A b ∈q j ) represents the conditional probability that the amplitude is in qj at frequency k = b and is in q i after multiple state changes at k = a.
[0145] Step 1.6: Convert the spectral Markov transfer field matrix into a two-dimensional time-frequency image.
[0146] The element value at each position in the spectral Markov transfer field matrix represents the gray value of the corresponding pixel in the image, thereby generating a two-dimensional time-frequency image. Before converting the spectral Markov transfer field matrix into a two-dimensional time-frequency image, the spectral Markov transfer field matrix is first normalized so that the gray value of each pixel in the image is between 0 and 255, which is convenient for subsequent image processing and pattern recognition. The time-frequency image is saved in the PNG image format for subsequent analysis and processing.
[0147] Figure 8 shows the process of converting the acceleration response signal into a two-dimensional time-frequency image, Figure 9 shows the two-dimensional time-frequency images obtained by converting different acceleration response signals using the spectral Markov transfer field. Converting the one-dimensional time series signal into a two-dimensional time-frequency image can better capture the time and frequency characteristics of the signal through time-frequency analysis. These characteristics may not be directly or fully represented in the original one-dimensional time series signal, while the time-frequency diagram can reveal the local characteristics and trends of the signal.
[0148] Step 2: Extract features from each first time-frequency image to obtain first feature vectors; combine all the first feature vectors to obtain a first feature matrix.
[0149] Step 3: Extract features from each second time-frequency image to obtain second feature vectors; combine all the second feature vectors to obtain a second feature matrix.
[0150] Directly performing Transfer Component Analysis (TCA) on the source domain dataset and the target domain dataset may not fully capture the differences between the source domain and the target domain, or may lead to unstable results. This is because the original data usually contains noise or redundant information, which may interfere with the effectiveness of TCA. Before performing transfer component analysis, feature extraction is carried out first, especially using deep learning models (such as the convolutional neural network model CNN), which can extract more stable and discriminative features, enabling transfer component analysis to better align the data distributions of the source domain and the target domain. The dimension of the original data is usually very high, and directly performing transfer component analysis may lead to excessive computational complexity. Through feature extraction, the dimension of the data can be reduced, thereby reducing the computational complexity of transfer component analysis and improving the computational efficiency. Directly performing transfer component analysis on high-dimensional original data may cause the damage recognition model to overfit to the source domain dataset and cannot generalize well to the target domain; through the feature extraction of time-frequency images, the data can be simplified and the risk of overfitting can be reduced. Therefore, performing feature extraction first and then transfer component analysis can make transfer component analysis more effective and reliable. Especially when dealing with high-dimensional and complex original data, feature extraction can greatly improve the overall performance and robustness of transfer learning.
[0151] In a specific embodiment of the present invention, a pre-trained convolutional neural network model is used to extract features from the first time-frequency image and the second time-frequency image, that is, the pre-trained convolutional neural network model is used to extract features from the first time-frequency image to obtain a first feature vector, and the pre-trained convolutional neural network model is used to extract features from the second time-frequency image to obtain a second feature vector. The API provided by PyTorch is called to load the convolutional neural network model. In this embodiment, the convolutional neural network model selects the ResNet-50 model, and the ResNet-50 model is used to extract the features of the first time-frequency image or the second time-frequency image. During the feature extraction process, the parameters of all layers in the ResNet-50 model are frozen to avoid parameter modification during feature extraction. The ResNet-50 model has been pre-trained on the ImageNet dataset and has strong image feature extraction capabilities.
[0152] The original ResNet-50 model consists of multiple convolutional layers, pooling layers, fully connected layers, etc., and has the ability to extract multi-level image features. In order to make the ResNet-50 model a feature extractor, the last fully connected layer is removed, that is, the ResNet-50 model of the present invention does not include a fully connected layer. The ResNet-50 model of the present invention includes multiple convolutional layers and a global average pooling layer, and the 2048-dimensional feature vector output by the global average pooling layer is the feature vector required by the present invention.
[0153] In this embodiment, the image processing library PIL is used to load the time-frequency image for which features need to be extracted, ensuring that the loaded image has the correct format and is not damaged. The loaded time-frequency image is adjusted to the input size (224×224) required by the ResNet-50 model. In addition, the time-frequency image needs to be normalized using the mean and standard deviation of ImageNet for normalization.
[0154] The convolutional neural network model can learn richer feature expressions from the time-frequency image; when the convolutional neural network model extracts image features, it often automatically performs dimensionality reduction processing, retains the most important features, and reduces noise interference.
[0155] Combine all the first feature vectors to obtain the first feature matrix Combine all the second feature vectors to obtain the second feature matrix where n s represents the number of samples in the source domain dataset, n t represents the number of samples in the target domain dataset, and d represents the dimension of the first feature vector or the second feature vector. In this embodiment, d is 2048.
[0156] Step 4: Concatenate the first feature matrix and the second feature matrix to obtain the joint feature matrix.
[0157] The joint feature matrix X can be expressed as
[0158] Step 5: Perform transfer component analysis on the joint feature matrix to obtain the source domain feature vector and the target domain feature vector in the common feature space.
[0159] The goal of transfer component analysis is to find a projection matrix A such that the distribution difference between the projected source domain and target domain in the common feature space is minimized while retaining the discriminant information of the data.
[0160] In the specific implementation manner of the present invention, performing transfer component analysis on the joint feature matrix includes:
[0161] Step 5.1: Construct a joint Gaussian kernel matrix according to the joint feature matrix X, and the specific formula is:
[0162]
[0163] where k ij represents the element in the i-th row and j-th column of the joint Gaussian kernel matrix; x i and x j represent two feature vectors in the joint feature matrix; σ represents the bandwidth of the Gaussian kernel function. The joint Gaussian kernel matrix can be expressed as K ij = kij (x i , x j ), the joint Gaussian kernel matrix K is obtained by calculating the kernel function values between any two eigenvectors in the joint feature matrix.
[0164] To capture complex feature relationships, a kernel TCA variant is used to map the original feature space to a high-dimensional feature space. The similarity between samples is calculated through the kernel function. Since the image feature vectors are high-dimensional, TCA faces computational challenges in processing this data. Therefore, the Gaussian kernel function adopted in the present invention can help handle complex non-linear relationships.
[0165] Step 5.2: Construct a joint centered kernel matrix according to the joint Gaussian kernel matrix. The specific formula is:
[0166] K c = HKH (7)
[0167]
[0168] where K c represents the joint centered kernel matrix, that is, the distribution difference matrix between the source domain and the target domain; H represents the centering matrix; I and 1 both represent all-ones matrices.
[0169] Step 5.3: To measure the distribution difference between the source domain and the target domain, the maximum mean discrepancy is used as a metric to construct a maximum mean discrepancy matrix, which is expressed as:
[0170]
[0171] where M represents the maximum mean discrepancy matrix; 1 a×b represents an all-ones matrix of size a×b.
[0172] Step 5.4: Construct an objective function according to the joint centered kernel matrix and the maximum mean discrepancy matrix.
[0173] In this embodiment, the expression of the objective function is:
[0174]
[0175] where A represents the projection matrix; the superscript T represents the transpose; λ represents the regularization parameter; tr() represents the trace of the matrix; represents solving for the optimal projection matrix to minimize the distribution difference between the source domain and the target domain in the common feature space. The first term on the right side of the objective function represents the distribution difference between the source domain and the target domain, and the second term is the regularization term used to avoid overfitting.
[0176] Step 5.5: Solve the objective function to obtain the projection matrix.
[0177] In this embodiment, the generalized eigenvalue decomposition is used to solve the objective function, including:
[0178] Convert the objective function into a generalized eigenvalue problem:
[0179] (K c MK c +λK c )A = K c AΛ (11)
[0180] where Λ represents the diagonal matrix of eigenvalues, and the diagonal matrix of eigenvalues contains the first k smallest eigenvalues. Select the eigenvectors corresponding to the smallest eigenvalues as the column vectors of the projection matrix to obtain the projection matrix.
[0181] Step 5.6: Construct the first centralized kernel matrix according to the first eigenmatrix and the joint eigenmatrix, and obtain the source domain eigenvectors according to the first centralized kernel matrix and the projection matrix.
[0182] Project the source domain dataset and the target domain dataset into the common feature space through the projection matrix. To ensure that the distributions of the source domain and the target domain in the common feature space are closer, project the centralized kernel matrix of the source domain (i.e., the first centralized kernel matrix) and the centralized kernel matrix of the target domain (i.e., the second centralized kernel matrix). The construction process of the first centralized kernel matrix is as follows:
[0183] First, construct the source domain Gaussian kernel matrix according to the first eigenmatrix and the joint eigenmatrix. The specific formula is:
[0184]
[0185] where Ks represents the source domain Gaussian kernel matrix, (K s ) ij represents the feature of the i-th row and j-th column in the source domain Gaussian kernel matrix; represents the i-th first eigenvector in the first eigenmatrix, x j represents the j-th eigenvector (the first eigenvector or the second eigenvector) in the joint eigenmatrix. The source domain Gaussian kernel matrix K s represents the kernel matrix between the first eigenmatrix and the joint eigenmatrix. Each row of the source domain Gaussian kernel matrix K s corresponds to a first eigenvector of the first eigenmatrix, and each column corresponds to an eigenvector of the first eigenmatrix or the second eigenmatrix. In this way, the source domain Gaussian kernel matrix K s captures the similarity between the first eigenmatrix (i.e., the source domain) and the joint eigenmatrix (i.e., the source domain + the target domain).
[0186] Referring to formula (7) and formula (8), for the source domain Gaussian kernel matrix Ks Perform centering processing to obtain the first centered kernel matrix Project the first centered kernel matrix to obtain the source domain feature vectors. The projection formula is:
[0187]
[0188] where Z s represents the source domain feature vectors.
[0189] Step 5.7: Construct the second centered kernel matrix based on the second feature matrix and the joint feature matrix, and obtain the target domain feature vectors according to the second centered kernel matrix and the projection matrix.
[0190] The construction process of the second centered kernel matrix is as follows:
[0191] First, construct the target domain Gaussian kernel matrix based on the second feature matrix and the joint feature matrix. The specific formula is:
[0192]
[0193] where Kt represents the target domain Gaussian kernel matrix, (K t ) ij represents the feature at the i-th row and j-th column in the target domain Gaussian kernel matrix; represents the i-th second feature vector in the second feature matrix, and x j represents the j-th feature vector (the first feature vector or the second feature vector) in the joint feature matrix. The target domain Gaussian kernel matrix K t represents the kernel matrix between the second feature matrix and the joint feature matrix. Each row of the target domain Gaussian kernel matrix K t corresponds to a second feature vector in the second feature matrix, and each column corresponds to a feature vector in the first feature matrix or the second feature matrix. In this way, the target domain Gaussian kernel matrix K t captures the similarity between the second feature matrix (i.e., the target domain) and the joint feature matrix (i.e., the source domain + the target domain).
[0194] Referring to formula (7) and formula (8), perform centering processing on the target domain Gaussian kernel matrix K t to obtain the second centered kernel matrix Project the second centered kernel matrix to obtain the target domain feature vectors. The projection formula is:
[0195]
[0196] where Z t represents the target domain feature vectors.
[0197] Step 6: Construct a damage identification model, and perform supervised training on the damage identification model by using the source domain feature vectors and the damage types of the source domain dataset.
[0198] In a specific embodiment of the present invention, the damage identification model selects a support vector machine classifier. Perform supervised training on the support vector machine classifier by using the source domain feature vectors and the damage types of the source domain dataset. The specific expression is:
[0199] Classifier = SVM().fit(Z s , Y s ) (16)
[0200] Among them, Classifier represents the variable name of the support vector machine classifier, SVM() represents the constructor of the support vector machine classifier, fit represents calling the fit method of the support vector machine classifier to train the support vector machine classifier, and Y s represents the damage type of the source domain dataset, that is, the true label corresponding to the source domain feature vectors. Z represents the source domain feature vectors s Each row of represents a sample. Formula (16) means creating a support vector machine classifier and using the source domain feature vectors Z s and the true label Y s for training. The trained damage identification model is saved in the variable Classifier.
[0201] Step 7: Perform unsupervised training on the damage identification model after supervised training by using the target domain feature vectors.
[0202] Step 8: Perform performance evaluation on the damage identification model after unsupervised training by using the target domain feature vectors and the damage types of the target domain dataset to obtain a target identification model.
[0203] Use the damage identification model after unsupervised training to perform damage identification on the target domain feature vectors to obtain predicted labels. Compare the predicted labels with the corresponding damage types in the target domain dataset to determine the recognition accuracy rate, and perform performance evaluation according to the recognition accuracy rate. The target identification model after supervised and unsupervised training has a very high damage recognition accuracy rate.
[0204] Step 9: Online identification of structural damage.
[0205] Obtain the real-time acceleration response signal of the structure, and convert the real-time acceleration response signal into a real-time time-frequency image; use a pre-trained convolutional neural network model to extract features from the real-time time-frequency image to obtain a real-time feature vector; use an object recognition model to perform online damage recognition on the real-time feature vector, which can identify the damage types of the real-time acceleration response signals from real structures, effectively improving the accuracy and automation of real structure health monitoring.
[0206] To verify the effectiveness of the method of the present invention, use an object recognition model (i.e., a trained support vector machine classifier) to perform damage recognition on the first time-frequency image of the source domain dataset. t-distributed stochastic neighbor embedding is a visualization tool that can be used to obtain a clear intuition of the data feature space. To realize the visualization of the damage recognition results of the object recognition model (i.e., the trained support vector machine classifier) for the first time-frequency image, use t-distributed stochastic neighbor embedding to realize the display of the damage recognition results, as Figure 10 shown. Figure 10 In it, solid circles of different colors mark different damage types. It can be seen that the object recognition model of the present invention can well identify the damage categories of the first time-frequency image.
[0207] To illustrate the advantages of the present invention, compare the damage recognition results of the method without using TCA for the target domain dataset with the damage recognition results of the method of the present invention for the target domain dataset, as Figure 11 and Figure 12 shown. From Figure 11 and Figure 12 it can be seen that when TCA is not used, the damage recognition results are messy, the distribution overlaps seriously, and they do not form clusters, which means that the features extracted by CNN contribute little to class separation, resulting in very poor recognition accuracy; while the method of the present invention clearly clusters and separates the damage recognition results, indicating that the method of the present invention has good damage recognition ability.
[0208] Figure 13 shows the recognition accuracies of 8 damage categories on the target domain dataset without using TCA and using TCA (i.e., the method of the present invention). From Figure 13 it can be seen that the recognition accuracy of the method of the present invention for each damage category is better than that of the method without using TCA. Figure 14 shows the damage recognition confusion matrix of the method of the present invention on the target domain dataset. The number of samples on the diagonal of the recognition confusion matrix is the number of samples correctly predicted. The object recognition model of the present invention shows a high damage recognition accuracy.
[0209] Embodiment 2
[0210] An embodiment of the present invention further provides an electronic device, which includes: a memory, a processor, and a computer program / instructions stored on the memory, and the processor executes the computer program / instructions to implement the structural damage identification method in the embodiments of the present application.
[0211] Although not shown, the electronic device includes a processor, which can perform various appropriate operations and processes according to the programs and / or data stored in the read-only memory (ROM) and / or the programs and / or data loaded from the storage section into the random access memory (RAM). The processor can be a multi-core processor or can include multiple processors. In some embodiments, the processor can include a general main processor and one or more special coprocessors, for example, a central processing unit, a graphics processing unit (GPU), a neural network processing unit (NPU), a digital signal processor (DSP), and so on. In the RAM, various programs and data required for device operation are also stored. The processor, ROM, and RAM are connected to each other through a bus. The input / output (I / O) interface is also connected to the bus.
[0212] The above-mentioned processor and memory are jointly used to execute the programs / instructions stored in the memory, and when the programs / instructions are executed by a computer, they can implement the methods, steps, or functions described in the above embodiments.
[0213] Although not shown, an embodiment of the present invention further provides a computer-readable storage medium, on which a computer program / instructions are stored, and when the computer program / instructions are executed by a processor, they implement the structural damage identification method in the embodiments of the present application.
[0214] In the embodiments of the present invention, the storage medium includes permanent and non-permanent, removable and non-removable articles that can implement information storage by any method or technology. Examples of storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, magnetic disk storage or other magnetic storage devices, or any other non-transmission medium that can be used to store information that can be accessed by a computing device.
[0215] A readable storage medium includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. The information can be computer-readable instructions, data structures, program modules, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technologies, compact disc read-only memory (CD-ROM), digital versatile disc (DVD) or other optical storage, magnetic cassette tapes, disk storage or other magnetic storage devices, or any other non-transitory medium that can be used to store information that can be accessed by a computing device. As defined herein, computer-readable media do not include transitory computer-readable media, such as modulated data signals and carrier waves.
[0216] Although not shown, embodiments of the present invention also provide a computer program product, including: computer programs / instructions, which, when executed by a processor, implement the structural damage identification method in the embodiments of the present application.
[0217] The above-disclosed are only specific embodiments of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art within the technical scope disclosed by the present invention can easily think of changes or variations, which should all be covered within the protection scope of the present invention.
Claims
1. A structural damage identification method based on digital twin and feature migration, characterized in that: The identification method comprises: Constructing a source domain dataset and a target domain dataset; wherein each sample in the source domain dataset includes a first time-frequency image of the structure and its damage type, and each sample in the target domain dataset includes a second time-frequency image of the structure and its damage type, and the first time-frequency image and the second time-frequency image are both converted from the acceleration response signal of the structure; the source domain dataset is constructed using a digital twin model of the structure; Performing feature extraction on each of the first time-frequency images to obtain a first feature vector; combining all the first feature vectors to obtain a first feature matrix; performing feature extraction on each of the second time-frequency images to obtain a second feature vector; combining all the second feature vectors to obtain a second feature matrix; Concatenating the first feature matrix and the second feature matrix to obtain a joint feature matrix; Performing migration component analysis on the joint feature matrix to obtain a source domain feature vector and a target domain feature vector in a common feature space; Constructing a damage recognition model, and performing supervised training on the damage recognition model using the source domain feature vector and the damage type of the source domain data set; Using the target domain feature vector to perform unsupervised training on the supervised trained damage recognition model; The target domain feature vector and the damage type of the target domain data set are used to evaluate the performance of the damage recognition model after unsupervised training to obtain a target recognition model.
2. The structural damage identification method according to claim 1, characterized in that: Use the digital twin model of the structure to build the source domain dataset, including: Step A1: construct a parametric finite element model of the structure; Step A2: performing dynamic analysis on the parameterized finite element model and exporting an Inp file; Step A3: using a Python script to open the Inp file, and parsing the unit set and its material properties in the Inp file; Step A4: modify the material properties of the unit set according to different damage types of the structure, update the material properties of different damage locations, and obtain Inp files of different damage types; Step A5: Use the subprocess module to perform ABAQUS simulation calculations on the Inp files of different damage types to obtain ODB result files of different damage types; Step A6: Use Python script to open the ODB result files of different damage types, extract the acceleration response signals of the structural nodes from the ODB result files of different damage types, and obtain the acceleration response signals under different damage types; Step A7: converting the acceleration response signals under different damage types into images to obtain first time-frequency images under different damage types; Step A8: construct a source domain dataset according to the first time-frequency images under different damage types.
3. The structural damage identification method according to claim 1, characterized in that: The acceleration response signal of the structure is converted into a first time-frequency image or a second time-frequency image by using a spectral Markov transfer field, including: The frequency spectrum signal of the acceleration response signal is calculated using the following formula: Wherein, s(k) represents the kth component in the spectrum signal, x(i) represents the value of the i-th sampling point in the acceleration response signal, n represents the number of sampling points of the acceleration response signal, abs() represents the modulus value function, and j represents the imaginary unit; Performing normalization processing on each component in the spectrum signal to obtain a normalized component of the spectrum signal; The value range of the amplitude set is evenly divided to obtain Q sub-intervals; wherein the amplitude set includes the amplitudes of all normalized components of the spectrum signal; Each amplitude in the amplitude set is mapped to a subinterval; wherein the specific mapping formula is: Among them, A k represents the kth amplitude in the amplitude set, q j represents the jth subinterval, argmin j It means finding j that makes the function reach the minimum value; Generate a spectral Markov transition field matrix according to the probability of each amplitude being transferred from the current subinterval to other subintervals; The spectral Markov transfer field matrix is converted into a two-dimensional image to obtain a first time-frequency image or a second time-frequency image.
4. The structural damage identification method according to claim 1, characterized in that: A pre-trained convolutional neural network model is used to perform feature extraction on the first time-frequency image and the second time-frequency image; wherein the pre-trained convolutional neural network model does not include a fully connected layer.
5. The structural damage identification method according to claim 1, characterized in that: Performing migration component analysis on the joint feature matrix includes: A joint Gaussian kernel matrix is constructed according to the joint feature matrix. The specific formula is: Among them, k ij represents the element in the i-th row and j-th column of the joint Gaussian kernel matrix; x i 、x j represents the two eigenvectors in the joint feature matrix; σ represents the bandwidth of the Gaussian kernel function; The joint centralized kernel matrix is constructed according to the joint Gaussian kernel matrix. The specific formula is: Among them, K c represents the joint centralized kernel matrix; K represents the joint Gaussian kernel matrix; H represents the centralized matrix; I a×b Represents a matrix of size a×b with all 1s; n s Represents the number of samples in the source domain dataset, n t Indicates the number of samples in the target domain dataset; A maximum mean difference matrix is constructed, which is expressed as: Where M represents the maximum mean difference matrix; The objective function is constructed according to the joint centralized kernel matrix and the maximum mean difference matrix; wherein the expression of the objective function is: Where A represents the projection matrix, superscript T represents the transpose, λ represents the regularization parameter, and tr() represents the trace of the matrix; It means solving the optimal projection matrix so that the distribution difference between the source domain and the target domain in the common feature space is minimized; Solving the objective function to obtain a projection matrix; constructing a first centralized kernel matrix according to the first feature matrix and the joint feature matrix, and obtaining a source domain feature vector according to the first centralized kernel matrix and the projection matrix; A second centralized kernel matrix is constructed according to the second feature matrix and the joint feature matrix, and a target domain feature vector is obtained according to the second centralized kernel matrix and the projection matrix.
6. The structural damage identification method according to claim 5, characterized in that: The objective function is solved by generalized eigenvalue decomposition, including: Convert the objective function into a generalized eigenvalue problem: (K c MK c +λK c )A=K c AL; Where Λ represents the eigenvalue diagonal matrix, which contains the first k smallest eigenvalues; The eigenvector corresponding to the minimum eigenvalue is selected as the column vector of the projection matrix to obtain the projection matrix.
7. The structural damage identification method according to any one of claims 1 to 6, characterized in that: The identification method further comprises: Acquiring a real-time acceleration response signal of the structure, and converting the real-time acceleration response signal into a real-time time-frequency image; Extracting features from the real-time time-frequency image to obtain a real-time feature vector; The target recognition model is used to perform online damage recognition on the real-time feature vector.
8. An electronic device comprising a memory, a processor, and a computer program / instruction stored in the memory, characterized in that: The processor executes the computer program / instructions to implement the structural damage identification method according to any one of claims 1 to 7.
9. A computer-readable storage medium having a computer program / instruction stored thereon, characterized in that: When the computer program / instructions are executed by a processor, the structural damage identification method according to any one of claims 1 to 7 is implemented.
10. A computer program product comprising a computer program / instructions, characterized in that When the computer program / instructions are executed by a processor, the structural damage identification method according to any one of claims 1 to 7 is implemented.
Citation Information
Patent Citations
Residential car elevator fault diagnosis method and device, electronic equipment and storage medium
CN114676741A
Waste household appliance recovery cost evaluation system based on online migration component analysis
CN118096213A