A Domain-Adaptive Online Structural Damage Quantification Method

Abstract

This invention proposes a domain-adaptive online structural damage quantification method. It transforms continuous real-valued labels into class labels using fuzzy set theory or clustering methods to accurately measure conditional distribution differences. This allows the proposed method to simultaneously consider the marginal and conditional distribution differences across different domains in regression tasks. Based on this, the invention proposes an online damage quantification framework incorporating domain-adaptive methods. This framework covers the complete damage quantification process, including monitoring data acquisition and processing, damage feature extraction, migration feature mapping, and database management, and holds promise for application in fleet-level structural digital twin construction and management.

Description

Technical Field

[0001] This invention belongs to the field of reliability analysis and failure analysis, and specifically relates to an online structural damage quantification method based on domain adaptation. Background Technology

[0002] Ensuring the structural integrity of aerospace and mechanical systems is a critical research topic. Digital twins (DT) have attracted considerable attention in recent years, aiming to create digital representations of corresponding physical products throughout their lifecycle to support operational and maintenance decisions. As a key task of structural health monitoring (SHM), damage quantification uses sensor monitoring data to determine the real-time damage status of structural components. The results can be used to track and update the status of the digital twin, making it an important component of the digital twin.

[0003] In practical applications, due to differences in manufacturing errors and usage environments, the damage evolution experienced by each component varies, necessitating the construction of a separate damage quantification model for each structure. However, acquiring sufficient labeled data in real-world engineering environments to train digital twin models is difficult and expensive, a problem affecting all supervised learning tasks. Using digital twin virtual simulations to generate large amounts of labeled simulation data to train damage quantification models, followed by deployment in the operational phase, is a feasible approach. However, due to widespread cognitive uncertainty, the fidelity and reliability of digital twins are difficult to guarantee, resulting in poor damage quantification performance. For a real-world structure, a large amount of models and data has accumulated during its design and historical service phases, making it possible to enhance current damage quantification tasks using additional labeled data from similar structures / damage or simulations. However, the problematic dependencies of data and models make applying them to new structures or damages challenging.

[0004] The aforementioned problems can be addressed using domain adaptation methods from transfer learning. Domain adaptation assumes the existence of a large amount of labeled data in the source domain. By mapping two domains to a common latent space where data distributions overlap, it can be used to improve classification or regression tasks in unlabeled (or partially labeled) target domains. The more information shared between the two domains, the easier it is to transfer knowledge between them; otherwise, it becomes more complex and "negative transfer" may occur. Many mature methods exist for domain adaptation, among which Transfer Component Analysis (TCA) and Joint Distribution Adaptation (JDA) are two representative approaches. TCA evaluates the marginal distributions of the two domains. and The differences, and JDA further considers conditional distributions. and The difference lies in the domain adaptation method. Currently, the application of domain adaptation methods in digital twins and structural health monitoring mainly focuses on damage detection, a typical classification problem that can be well handled using the JDA method. However, online damage quantification is a regression problem, requiring new domain adaptation methods.

[0005] However, two challenges currently limit the application of domain adaptation in damage quantification. First, in damage quantification, the responses (features) to damage sizes (labels) differ significantly across locations or structures, meaning their conditional distributions differ. Therefore, traditional domain adaptation methods that only consider edge distributions are only suitable for cases where damages are highly similar. Second, since labels are continuous real values ​​rather than discrete class labels, methods that simultaneously consider differences in conditional distributions (such as JDA) cannot be directly applied due to the difficulty in measuring these differences. Therefore, a novel domain adaptation method is needed to address this issue. Summary of the Invention

[0006] To address the aforementioned technical problems, this invention proposes a domain-adaptive online structural damage quantification method, device, and medium. The specific technical solution is as follows:

[0007] A domain-adaptive online structural damage quantification method includes the following steps:

[0008] Step 1: Collect and build an offline historical database. During the offline phase, two types of available historical data are collected. The first type of data is collected from similar structures or damages, and the second type of data is obtained through virtual simulation using a digital twin model of the actual structure. The available historical data is stored in the twin database for use in the online phase.

[0009] Step 2: Arrange sensors and data acquisition, processing, and transmission systems on the target structure;

[0010] Step 3: Acquire monitoring data related to structure or damage in real time, and extract damage-sensitive features that are sensitive to damage;

[0011] Step 4: Use the online structural damage quantization method to map the damage-sensitive features to a new space and quantize the damage size; the online structural damage quantization method includes the following steps: constructing an input matrix, calculating edge distribution differences, calculating pseudo-classification labels, calculating conditional distribution differences, and calculating an adaptive transformation matrix;

[0012] Step 5: Measure and store the actual damage label in the twin database; if the damage size does not exceed the requirements of the corresponding specification, skip to step 3 to continue monitoring; otherwise, skip to step 6.

[0013] Step 6: End monitoring and prepare for repair or replacement of the structure.

[0014] Furthermore, step 4 includes extracting tagged data of the source domain from the database. and the currently available labeled data. Combined with unlabeled features extracted from sensors This forms the input based on the domain adaptive algorithm; then the above data is mapped to a common latent space, in which an adaptive regression model f is trained to quantify the damage size in real time;

[0015] The input to the domain-adaptive algorithm includes: features within the source domain. and tags Features available in the target domain and tags and current unlabeled features .

[0016] Furthermore, the step of constructing the input matrix specifically includes:

[0017] Make the matrix Includes all features, Includes all labeled features. Includes all available tags; where the superscript or subscript 's' represents a parameter in the source domain, and the superscript or subscript 't' represents a parameter in the target domain. The source domain has labeled features. for Corresponding tags The target domain contains labeled features. for Corresponding tags For unlabeled features of the target domain.

[0018] Furthermore, the step of calculating the edge distribution difference specifically includes:

[0019] To reduce the distribution at the source domain edge Distribution at the edge of the target domain The difference between them is measured by the maximum mean difference, which is used as the distance metric for comparing different distributions.

[0020] The maximum mean difference is calculated using formula (1) as the distance between the sample means of the source domain data and the target domain data after kernel function mapping and neighborhood adaptive transformation:

[0021]

[0022] in For the source domain data set, For the first in the source domain One sample, The number of samples in the source domain. For the target domain sample set, For the first in the source domain One sample, The number of samples in the target domain. For adaptive transformation matrix, For kernel function, For the kernel matrix; The trace of the matrix, The MMD matrix for edge distribution is calculated as follows:

[0023]

[0024] Furthermore, multi-kernel maximum mean difference is used to measure the distributional difference between the source and target domains, where the kernel function associated with the feature map is used in the multi-kernel maximum mean difference. All feasible solutions Defined as;

[0025]

[0026] in For predefined One kernel function, Constrain each of its corresponding weight coefficients. And the sum of weights ;

[0027] The optimal kernel for MK-MMD is searched by jointly maximizing test power and minimizing type II error. parameter:

[0028]

[0029] in Indicates the kernel function Calculated distribution and MK-MMD value, For the first A group of quaternions, A quad array The MK-MMD value. The estimated variance of MK-MMD. , To calculate the expected function;

[0030] Formula (4) can be simplified to a quadratic programming (QP) problem:

[0031]

[0032] in The weight coefficients are in vector form. The covariance of MK-MMD can be expressed as follows: Computation with time complexity, , ,and ; A small regularization parameter is used to avoid ill-conditioned problems;

[0033] The optimal weights are obtained by solving formula (5). Thus, multi-core ;

[0034] Considering the discrepancy between the number of samples in the source domain and the target domain, It is obtained by averaging the results of several random runs; in the 1st... In this run, random sampling is used to extract samples from the domain containing a larger number of samples, so that the two domains have the same number of samples. Then, the results are calculated using the method in formula (5). ;at last, We obtain it from the following formula:

[0035]

[0036] in This represents the number of random sampling operations.

[0037] Furthermore, the step of calculating the pseudo-classification label specifically includes:

[0038] First, a regression model is trained using all the labeled data to predict unlabeled features. pseudo-tags Combine it with available tags to form Then, the continuous real-valued labels in damage quantification are converted into pseudo-classification labels using fuzzy set or clustering methods.

[0039] Furthermore, the step of calculating the difference in conditional distribution specifically includes:

[0040] Considering the common data in the sample There are 10 categories, namely Referring to the JDA method operations, use the first... Class conditional distribution and To replace conditional distribution ;

[0041] If the labels are hard labels, use the following formula to calculate the maximum mean difference of each type of conditional distribution between the source and target domains:

[0042]

[0043] in Indicates the first element belonging to the source domain. Sample set of the class, Indicates the first Sample The pseudo-tags, and Accordingly, Indicates a class belonging to the target domain. The sample set, Indicates the first Sample The pseudo-tags, and Therefore, class tags are involved. Maximum mean difference matrix The calculation is as follows:

[0044]

[0045] If the labels are soft labels, the calculation of the maximum mean difference of the conditional distribution needs to be modified as follows:

[0046]

[0047] in An improved version, its first Okay, number The formula for calculating column elements is:

[0048]

[0049] The standard form obtained according to the following formula:

[0050]

[0051] in It is the first For the nth sample Membership degree or probability of a class.

[0052] Furthermore, the step of calculating the adaptive transformation matrix specifically includes:

[0053] The optimal adaptive matrix is ​​computed using the following constrained optimization problem. :

[0054]

[0055] in It is a constraint that the variance of the data must remain unchanged before and after the transformation. It is a central matrix. It is the identity matrix. It is a regularization parameter that ensures the optimization problem is well-defined. If the improved conditional distribution maximum mean difference matrix is ​​not applied, ; Denotes the F-norm of a matrix;

[0056] The constraint optimization in formula (12) can be solved by constructing its Lagrangian function:

[0057]

[0058] in They are Lagrange multipliers;

[0059] make We can obtain the generalized eigenvalue decomposition:

[0060]

[0061] Finally, by solving formula (14) The optimal adaptive transformation matrix can be obtained by computing the smallest eigenvectors. .

[0062] Furthermore, step 5 specifically includes: measuring the actual damage label through non-destructive testing. , will be with features Pair them and store them in a twin database.

[0063] Furthermore, the sensors in step (2) include, but are not limited to, one or more of strain sensors, piezoelectric sensors, and accelerometers; the feature extraction methods used in step (3) include, but are not limited to, Fourier transform, wavelet transform, empirical mode decomposition, and autoregressive or autoencoder methods based on machine learning. The methods for converting continuous real-valued labels in damage quantification into pseudo-classification labels in step (6) include, but are not limited to, fuzzy set methods and clustering methods, wherein the clustering methods include, but are not limited to, K-means clustering, fuzzy C-means clustering, Gaussian mixture model, spectral clustering, hierarchical clustering, etc.

[0064] The present invention also provides an electronic device comprising: a processor; a memory; and a program, wherein the program is stored in the memory and configured to be executed by the processor, the program including methods described above.

[0065] The present invention also provides a computer-readable storage medium having a computer program stored thereon, characterized in that the computer program is executed by a processor using the above-described method.

[0066] Beneficial effects:

[0067] This invention proposes a domain-adaptive online structural damage quantification method, device, and medium. First, it proposes a novel domain-adaptive method that converts continuous real-valued labels into class labels using fuzzy set theory or clustering methods, thereby accurately measuring the differences in conditional distributions. This allows the proposed method to simultaneously consider the marginal and conditional distribution differences across different domains in regression tasks. Based on this, the invention proposes an online damage quantification framework that combines the domain-adaptive method. This framework covers the complete damage quantification process, involving the acquisition and processing of monitoring data, extraction of damage features, migration feature mapping, and database management, and is expected to be applied to the construction and management of fleet-level structural digital twins. Attached Figure Description

[0068] Figure 1 This is a framework diagram of the domain-adaptive online structural damage quantification method of the present invention;

[0069] Figure 2 This is a schematic diagram of the domain adaptive method of the present invention;

[0070] Figure 3 This is a schematic diagram of the fuzzy set of the present invention, wherein (a) represents the fuzzy set of the source domain and (b) represents the fuzzy set of the target domain;

[0071] Figure 4 This is a schematic diagram of the hard clustering and soft clustering of the present invention;

[0072] Figure 5 This is a schematic diagram showing the aluminum alloy reinforced wall panel structure and the positions of the seven rivets used in Embodiment 1 of the present invention;

[0073] Figure 6 This is a schematic diagram of the finite element model of the aluminum alloy stiffened wall panel in Embodiment 1 of the present invention;

[0074] Figure 7 This is a schematic diagram of the results in Embodiment 1 of the present invention, where the dataset at rivet 1 is the source domain and the crack datasets at the other 6 rivets are the target domains.

[0075] Figure 8 This is a schematic diagram of the composite material debonding sample in Example 2 of the present invention;

[0076] Figure 9 This is a schematic diagram of the debonding location of the composite material debonding sample in Example 2 of the present invention;

[0077] Figure 10 This is a schematic diagram of the finite element model of the composite debonding sample in Embodiment 2 of the present invention;

[0078] Figure 11 This is a schematic diagram of the damage quantification results from the first sample to the second sample in Embodiment 2 of the present invention;

[0079] Figure 12 This is a schematic diagram illustrating the damage quantification results from simulation model data to the first sample in Embodiment 2 of the present invention. Detailed Implementation

[0080] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0081] The implementation flowchart of the domain-adaptive online structural damage quantification method of the present invention is as follows: Figure 1 As shown.

[0082] Step 1: Collect and build an offline historical database

[0083] Before applying the domain-adaptive online structural damage quantification method proposed in this invention to the online damage quantification of actual structures, all available historical data is first collected offline. This data mainly consists of two types. The first type is data collected from similar structures or damage, such as structures in the same fleet with more severe damage, which helps in the damage quantification of structures with less severe damage. The second type of data is obtained through virtual simulation using a digital twin model of the actual structure. Although the digital twin model still deviates from the actual structure, the useful information it contains is still helpful in the damage quantification of the current structure. This data is stored in a twin database for use in the online phase.

[0084] Step 2: Place sensors on the target structure

[0085] Appropriate sensors and data acquisition, processing, and transmission systems are deployed within the actual structure to obtain real-time monitoring data related to structural damage for processing in step 3. Sensors that can be used here include, but are not limited to, strain sensors, piezoelectric sensors, and accelerometers.

[0086] Step 3: Extract damage-sensitive features from sensor data.

[0087] Based on the monitoring data obtained in step 2, damage-sensitive features are extracted using feature extraction techniques. Feature extraction transforms the raw data into features that are more strongly correlated with damage. Widely used methods include, but are not limited to, Fourier transform, wavelet transform, empirical mode decomposition, and machine learning-based methods such as autoregression and autoencoders.

[0088] Step 4: Use the domain adaptation method proposed in this invention to map the features to a new space and quantize the damage size.

[0089] Extract labeled data from the source domain from the database. and the currently available labeled data. Combined with unlabeled features extracted from sensors This forms the input to the domain adaptation algorithm. Then, these data are mapped to a common latent space, where an adaptive regression model is trained. This allows for real-time quantification of damage size. A specific illustration is shown below. Figure 2 As shown.

[0090] The input to the domain adaptation algorithm includes: features within the source domain. and tags Features available in the target domain and tags and current unlabeled features .

[0091] Step 4.1: Construct the input matrix

[0092] In step 4.1, the matrix Includes all features, Includes all labeled features. Includes all available tags; where the superscript or subscript 's' represents a parameter in the source domain, and the superscript or subscript 't' represents a parameter in the target domain. The source domain has labeled features. for Corresponding tags The target domain contains labeled features. for Corresponding tags For unlabeled features of the target domain.

[0093] Step 4.2: Calculate the marginal distribution differences

[0094] To reduce the distribution at the source domain edge Distribution at the edge of the target domain The difference between the two distributions is measured using the maximum mean difference as the distance metric for comparing the different distributions. Specifically, MMD calculates the distance between the sample means of the source domain data and the target domain data after kernel function mapping and neighborhood adaptive transformation using formula (1):

[0095]

[0096] in For the source domain data set, For the first in the source domain One sample, The number of samples in the source domain. For the target domain sample set, For the first in the source domain One sample, The number of samples in the target domain. For adaptive transformation matrix, For kernel function, For the kernel matrix; The trace of the matrix, The MMD matrix for edge distribution is calculated as follows:

[0097]

[0098] Here, multi-kernel maximum mean difference (MK-MMD) can be further used to measure the distributional difference between the source and target domains. The kernel function associated with the feature map in MK-MMD... All feasible solutions Defined as;

[0099]

[0100] in For predefined One kernel function, Constrain each of its corresponding weight coefficients. And the sum of weights .

[0101] The optimal kernel β parameter for MK-MMD is searched by jointly maximizing test power and minimizing type II error:

[0102]

[0103] in Indicates the kernel function Calculated distribution and MK-MMD value, For the first A group of quaternions, A quad array The MK-MMD value. The estimated variance of MK-MMD. , To calculate the expected function;

[0104] Formula (4) can be simplified to a quadratic programming (QP) problem:

[0105]

[0106] in The weight coefficients are in vector form. The covariance of MK-MMD can be expressed as follows: Computation with time complexity, , ,and ; A small regularization parameter is used to avoid ill-conditioned problems; therefore, by solving formula (5), we obtain a multi-core... .

[0107] However, the above steps require This is insufficient for online damage quantification. In this invention, It is obtained by averaging the results of several random runs. In the... In this run, random sampling is used to extract samples from the domain containing a larger number of samples, so that the two domains have the same number of samples. Then, the method of formula (5) is used to calculate... .at last, We obtain it from the following formula:

[0108]

[0109] in This represents the number of random sampling operations.

[0110] Step 4.3: Calculate pseudo-classification labels

[0111] First, a regression model is trained using all the labeled data to predict unlabeled features. pseudo-tags Combine it with available tags to form Then, fuzzy set or clustering methods are used to convert the continuous real-valued labels in damage quantification into pseudo-classification labels.

[0112] (1) Generate fuzzy class labels using fuzzy set method

[0113] Each element in a fuzzy set has a degree of membership to that set, typically represented by a number between 0 and 1, ranging from low to high. By assigning labels from samples to several fuzzy sets according to their membership degrees, fuzzy labels can be obtained. Fuzzy sets are suitable for handling one-dimensional labels.

[0114] Take three fuzzy sets with triangular membership functions as an example. First, for those already scaled to... of consecutive labels Calculate its using kernel density estimation (KDE) , and Quantiles were used, and based on them, three fuzzy sets of triangles were defined, labeled as small, medium, and large, respectively, as follows: Figure 3 As shown. For each real-valued label, its membership degree can be calculated according to the membership relationship of the three fuzzy sets. Based on the above method, a continuous set of labels can be converted into three fuzzy classes.

[0115] (2) Generate soft / hard labels for the corresponding categories using clustering methods.

[0116] Clustering methods aim to group a set of objects such that objects in the same group (called a cluster) are (in some sense) more similar to each other than objects in other groups (clusters). Generally, they can be divided into two types: hard clustering and soft clustering, such as... Figure 4 As shown, the main difference is that a sample is clustered into only one class through hard clustering, but a sample is included in multiple classes with probabilities or membership degrees through soft clustering. Clustering methods are suitable for both one-dimensional and multi-dimensional labels.

[0117] Clustering methods output either hard labels or soft labels. A hard label indicates that an element definitively belongs to only one cluster, while a soft label, such as [0.25, 0.75], means that the sample has a 0.25 probability of belonging to the first cluster and a 0.75 probability of belonging to the second cluster. Labels obtained using the fuzzy C-means method and the fuzzy labels obtained using the fuzzy set method both represent the degree of membership to a particular cluster, while labels obtained using a Gaussian mixture model represent the probability of belonging to a particular cluster.

[0118] Step 4.4: Calculate the differences in distribution conditions

[0119] In this invention, the common elements in the sample are considered. There are 10 categories, namely Referring to the JDA method operations, use the first... Class conditional distribution and To replace conditional distribution .

[0120] In step 4.3, the continuous labels of the regression problem are converted into pseudo-labels of the categories using fuzzy sets or clustering methods. If the labels are hard labels, the MMD of the conditional distributions for each category between the source and target domains is calculated using the following formula.

[0121]

[0122] in Indicates the first element belonging to the source domain. Sample set of the class, Indicates the first Sample The pseudo-tags, and Accordingly, Indicates a class belonging to the target domain. The sample set, Indicates the first Sample The pseudo-tags, and Therefore, class tags are involved. Maximum mean difference matrix The calculation is as follows:

[0123]

[0124] If the labels are soft labels, the calculation of the maximum mean difference of the conditional distribution needs to be modified as follows:

[0125]

[0126] in An improved version, its first Okay, number The formula for calculating column elements is:

[0127]

[0128] The standard form obtained according to the following formula:

[0129]

[0130] in It is the first For the nth sample Membership degree or probability of a class.

[0131] Step 4.5: Calculate the adaptive transformation matrix

[0132] The optimal adaptive matrix is ​​computed using the following constrained optimization problem. .

[0133]

[0134] in It is a constraint that the variance of the data must remain unchanged before and after the transformation. It is a central matrix. It is the identity matrix. These are regularization parameters that ensure the optimization problem is explicitly defined. If the improved conditional distribution MMD matrix is ​​not applied, . This represents the F-norm of the matrix.

[0135] The constraint optimization in formula (12) can be solved by constructing its Lagrangian function:

[0136]

[0137] in It is a Lagrange multiplier.

[0138] make We can obtain the generalized eigenvalue decomposition:

[0139]

[0140] Finally, by solving formula (14) The optimal adaptive transformation matrix can be obtained by computing the smallest eigenvectors. .

[0141] Step 5: Measure and store the actual damage tags.

[0142] Once the true damage label can be measured using non-destructive testing (which can be combined with physics-based models), , will be with features Pair and store in a twin database. If the damage size does not exceed the requirements of the corresponding specification, skip to step 3 to continue monitoring; otherwise, skip to step 6.

[0143] Step 6 concludes the monitoring and prepares for repair or replacement of the structure.

[0144] The present invention will be described in detail below with reference to specific embodiments.

[0145] Example 1

[0146] In this embodiment, consider an aluminum alloy stiffened wall panel, such as Figure 5 As shown, the panel consists of a skin reinforced with four riveted longitudinal beams and additional fasteners at the top and bottom edges, generating a stress field consistent with that experienced by the actual structure by distributing the applied load along the entire width of the panel. The skin is made of Al2024-T6 alloy, the four L-shaped longitudinal beams are made of Al7075-T76 alloy, and the panel is equipped with a network of 20 FBG (fiber Bragg grating) strain sensors located on the L-shaped longitudinal beams.

[0147] The damage characteristics were selected based on the values ​​of 20 strain sensors. Here, the following method is used: Figure 6 The finite element model shown generates simulation datasets with cracks of different lengths at seven different rivet locations, as illustrated in the figure. The labels (crack lengths) are then assigned... The spacing from arrive Equally spaced samples were taken, and finite element simulations were performed to calculate the strain response at the corresponding locations. Each dataset consists of 100 samples. These seven datasets are represented as follows: .

[0148] Predicted step size The number of unlabeled samples in each prediction is determined, thus significantly affecting the quality of adaptation and prediction accuracy. In this embodiment, three prediction step sizes are employed.

[0149] 1. Defined as a small step size, this means that once unlabeled data is processed, domain adaptation is performed, labels are predicted, and then the actual length is measured.

[0150] 2. Defined as a medium step size, this means that once five unlabeled data points have been collected, they are processed and measured.

[0151] 3. Defined as a large stride, this means that once ten unlabeled data points have been collected, the lifecycle is considered complete. The data will be processed and measured.

[0152] In this embodiment, since the labels are one-dimensional, fuzzy sets are used to calculate pseudo-classification labels. This method is abbreviated as OFJDAR, representing an online fuzzy set-based joint distribution adaptive method for regression. The number of fuzzy sets is... The quantiles are 5, 50, and 95, respectively. Regularization parameter Minimum number of eigenvectors Using the Rivet 1 dataset As the source domain arrive The six datasets are used as source domains.

[0153] Four benchmark methods were selected for comparison:

[0154] Using source domain data only (OSD): Only labeled strain data from the source domain are selected to train the regression model, due to the different... The impact of cracks at the rivet location varies, so this method may have significant deviations. Figure 5 As shown.

[0155] Use Target Domain Data Only (OTD): Select only the target domain. The regression model is trained using available labeled data (with smaller damage sizes), and the predictions made by this regression model are essentially extrapolations because the damage size of unlabeled samples is larger than that of available labeled samples.

[0156] Source domain and target domain simple combination (CTD): Source domain and target domain The labeled data in the dataset is directly combined to train the regression model.

[0157] Online migration component analysis (OTCAR): The same online damage quantification framework as this invention, but using migration component analysis (TCA), thus only considering the differences in marginal distributions and ignoring the differences in conditional distributions.

[0158] The root mean square error (RMSE) function is used to evaluate the method.

[0159]

[0160] in For the first A real label value, For the first Each predicted label value, This represents the number of samples to be evaluated.

[0161] In the online damage quantification task, the crack lengths predicted using the method proposed in this invention and four baseline methods will be stored at each step. When all predictions are made, the RMSE will be calculated using formula (14).

[0162] Figure 7 The final calculation results are presented. Overall, the performance of OTD is relatively stable across all domains, while the performance of CTD varies considerably, indicating that direct combination involves significant uncertainty, thereby reducing prediction accuracy. In most cases, the proposed method OFJDAR exhibits the best performance and outperforms OTCAR, while the latter shows greater fluctuations with increasing prediction step size.

[0163] When the step size is small, the proposed method exhibits the best accuracy across all target domains. At this point, the influence of pseudo-labels is minimal, thus ensuring domain adaptation quality. OTCAR's accuracy is lower than the proposed method, but it still outperforms other baseline methods without adaptation. When the step size is medium, the proposed method, except for... Out-of-dataset still exhibits the best performance, while OTCAR's accuracy shows significant fluctuations.

[0164] This embodiment illustrates that the method proposed in this invention can effectively address the problem of crack length quantification in metal structures because it can simultaneously consider the differences in edge distribution and conditional distribution.

[0165] Example 2

[0166] The object of this embodiment is a large crack lap shear (CLS) specimen. The damage mode of this specimen is debonding, and its basic structure is as follows: Figure 8 As shown. Figure 9 The layout and debonding locations of the sample are shown. The adhesive on the sample is a laminate consisting of 8 layers of F593 / W3T282 woven fabric, stacked in the following order: The designed thickness of each layer after curing is approximately... The total thickness of the laminate is The adhesive used was Loctite EA9695030 double-layer adhesive with a designed thickness of 0.137 mm. A Kapton® film was inserted between the adhesive layers using a Z-shaped insert as a pre-fabricated release mechanism. The specimen withstood a peak stress of 40 kN applied by four bonded steel sheets, compared to... Cyclic load.

[0167] In this embodiment, the large CLS specimen is equipped with 12 FBG sensors, and all strain values ​​are measured at... The lengths were measured and averaged under short-term sustained loads. During the experiment, the debonding lengths were measured on the lower and upper sides, and are expressed as follows: and .

[0168] In this embodiment, a finite element model of the specimen was also constructed, such as... Figure 10 As shown. First, multiple parts are modeled independently, then connected together in the assembly using TIE constraints between different surfaces. Both the laminate and adhesive are modeled using SC8R type continuum shell elements to describe material behavior near the debonding front.

[0169] In this embodiment, strain values ​​from 12 FBG sensors were selected as damage features, and three datasets were constructed, forming three domains. Two experimental datasets were extracted from two sample experiments. The first dataset... The first dataset consists of 71 samples, while the second dataset... It consists of 68 samples. (Simulation dataset) The simulation was generated by numerical simulations of different debonding fronts, consisting of 18 parallel leading edges (…). ) samples and 174 straight leading edges ( The sample composition.

[0170] In this embodiment, since the decoupling problem involves multidimensional labels, a clustering method is used to calculate pseudo-classification labels. This method is abbreviated as OCJDAR, representing an online clustering-based joint distribution adaptive method for regression, and MK-MMD is used. The number of clusters is... Regularization parameters Minimum number of eigenvectors Random sampling operands in MK-MMD computation . The baseline and evaluation methods are the same as in Example 1. This example demonstrates two adaptive scenarios.

[0171] In the first scenario, using the first experimental dataset As the source domain, the second experimental dataset As the source domain. The result is as follows: Figure 11 As shown in the image. It can be seen that the OSD directly uses... The trained model is used to quantize The debonding state will exhibit significant deviations across all three step sizes. Furthermore, OTD only uses the available marker data. Quantifying the subsequent deadhesion state can lead to significant errors at certain points because OTD is essentially an extrapolation. The error of OTD increases significantly with increasing step size. The CTD method directly combines the available labeled data from both domains, achieving better results than OSD and OTD. However, as shown in Example 1, in some cases, simple combination can lead to worse predictions. As a baseline domain adaptation method, OTCAR's performance is inconsistent. At times, it performs better than CTD, but when and At other times, its performance is even worse. The OCJDAR method used in this invention outperforms the benchmark method at all step sizes, and the results are relatively stable.

[0172] In the second scenario, using a simulated dataset As the source domain, the first experimental dataset As the source domain. This is a common scenario for damage quantization, and the result is as follows. Figure 12 As shown, all methods perform worse than in the first scenario, due to the greater domain difference between the simulation and experimental datasets. The OSD result curves have been removed, and the numerical values ​​are shown in the figure. It can be seen that the OSD method has a very high RMSE. This is because in simulation, many factors such as geometry, material properties, and contact parameters affect model fidelity, causing significant differences between the numerical model and the actual structure. CTD still outperforms OTD, while OCJDAR in this invention still performs best, indicating that the useful information contained in the simulation dataset helps improve the accuracy of damage diagnosis for actual structures.

[0173] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A domain-adaptive online structural damage quantification method, characterized in that, Specifically, the steps include the following: Step 1: Collect and construct an offline historical database. During the offline phase, two types of available historical data are collected. The first type of data is collected from similar structures or damages, and the second type of data is obtained through virtual simulation using a digital twin model of the actual structure. The available historical data is stored in the twin database for use in the online phase. Step 2: Arrange sensors and data acquisition, processing, and transmission systems on the target structure; Step 3: Acquire monitoring data related to structure or damage in real time, and extract damage-sensitive features that are sensitive to damage; Step 4: Map the damage-sensitive features to a new space and quantize the damage size using the online structural damage quantization method; the online structural damage quantization method includes the following steps: constructing an input matrix, calculating edge distribution differences, calculating pseudo-classification labels, calculating conditional distribution differences, and calculating an adaptive transformation matrix, including: Extract labeled data from the source domain from the database. and the currently available labeled data. Combined with unlabeled features extracted from sensors This forms the input based on a domain-adaptive algorithm; then, the above data is mapped to a common latent space, where an adaptive regression model is trained. This allows for real-time quantification of damage size; The input to the domain-adaptive algorithm includes: features within the source domain. and tags Features available in the target domain and tags and current unlabeled features ; The steps for calculating pseudo-classification labels specifically include: First, a regression model is trained using all the labeled data to predict unlabeled features. pseudo-tags Combine it with available tags to form Then, the continuous real-valued labels in damage quantification are converted into pseudo-classification labels using fuzzy set or clustering methods. Step 5: Measure and store the actual damage label in the twin database; if the damage size does not exceed the requirements of the corresponding specification, skip to step 3 to continue monitoring; otherwise, skip to step 6. Step 6: End monitoring and prepare for repair or replacement of the structure.

2. The domain-adaptive online structural damage quantification method according to claim 1, characterized in that: The steps for constructing the input matrix specifically include: Make the matrix Includes all features, Includes all labeled features. Includes all available tags; where the superscript or subscript 's' represents a parameter in the source domain, and the superscript or subscript 't' represents a parameter in the target domain. The source domain has labeled features. for Corresponding tags The target domain contains labeled features. for Corresponding tags For unlabeled features of the target domain.

3. The domain-adaptive online structural damage quantification method according to claim 2, characterized in that: The steps for calculating the edge distribution differences specifically include: To reduce the distribution at the source domain edge Distribution at the edge of the target domain The difference between them is measured by the maximum mean difference, which is used as the distance metric for comparing different distributions. The maximum mean difference is calculated using formula (1) as the distance between the sample means of the source domain data and the target domain data after kernel function mapping and neighborhood adaptive transformation: in For the source domain data set, For the first in the source domain One sample, The number of samples in the source domain. For the target domain sample set, For the first in the source domain One sample, The number of samples in the target domain. For adaptive transformation matrix, For kernel function, For the kernel matrix; The trace of the matrix, The MMD matrix with marginal distribution is calculated as follows:

4. The domain-adaptive online structural damage quantification method according to claim 3, characterized in that: Furthermore, the multi-kernel maximum mean difference (MK-MMD) is used to measure the distributional difference between the source and target domains. The kernel function associated with the feature map in the multi-kernel maximum mean difference is... All feasible solutions Defined as; in For predefined One kernel function, Constrain each of its corresponding weight coefficients. And the sum of weights ; The optimal kernel for MK-MMD is searched by jointly maximizing test power and minimizing type II error. parameter: in Indicates the kernel function Calculated distribution and MK-MMD value, For the first A group of quaternions, A quad array The MK-MMD value, and the estimated variance of MK-MMD. , To calculate the expected function; Formula (4) can be simplified to a quadratic programming (QP) problem: in The weight coefficients are in vector form. The covariance of MK-MMD can be expressed as follows: Computation with time complexity, , ,and ; A small regularization parameter is used to avoid ill-conditioned problems; The optimal weights are obtained by solving formula (5). Thus, multi-core ; Considering the discrepancy between the number of samples in the source domain and the target domain, It is obtained by averaging the results of several random runs; In the In this run, random sampling is used to extract samples from the domain containing a larger number of samples, so that the two domains have the same number of samples. Then, the results are calculated using the method in formula (5). ;at last, We obtain it from the following formula: in This represents the number of random sampling operations.

5. The domain-adaptive online structural damage quantification method according to claim 1, characterized in that: The steps for calculating the difference in conditional distribution specifically include: Considering the common data in the sample There are 10 categories, namely Referring to the JDA method operations, use the first... Class conditional distribution and To replace conditional distribution ; If the labels are hard labels, use the following formula to calculate the maximum mean difference of each type of conditional distribution between the source and target domains: in Indicates the first element belonging to the source domain. Sample set of the class, Indicates the first Sample The pseudo-tags, and Accordingly, Indicates a class belonging to the target domain. The sample set, Indicates the first Sample The pseudo-tags, and Therefore, class tags are involved. Maximum mean difference matrix The calculation is as follows: If the labels are soft labels, the calculation of the maximum mean difference of the conditional distribution needs to be modified as follows: in An improved version, its first Okay, number The formula for calculating column elements is: The standard form obtained according to the following formula: in It is the first For the nth sample Membership degree or probability of a class.

6. The domain-adaptive online structural damage quantification method according to claim 5, characterized in that: The steps for calculating the adaptive transformation matrix specifically include: The optimal adaptive matrix is ​​computed using the following constrained optimization problem. : in It is a constraint that the variance of the data must remain unchanged before and after the transformation. It is a central matrix. It is the identity matrix. It is a regularization parameter that ensures the optimization problem is explicitly defined. If the improved conditional distribution maximum mean difference matrix is ​​not applied, ; Denotes the F-norm of a matrix; The constraint optimization in formula (12) can be solved by constructing its Lagrangian function: in They are Lagrange multipliers; make We can obtain the generalized eigenvalue decomposition: Finally, by solving formula (14) The optimal adaptive transformation matrix can be obtained by computing the smallest eigenvectors. .

7. The domain-adaptive online structural damage quantification method according to claim 1, characterized in that: Step 5 specifically includes: The true damage label was measured using non-destructive testing. , will be with features Pair them and store them in a twin database.

8. The domain-adaptive online structural damage quantification method according to claim 1, characterized in that: The sensors used in step 2 include, but are not limited to, one or more strain sensors, piezoelectric sensors, and accelerometers. The feature extraction methods used in step 3 include, but are not limited to, Fourier transform, wavelet transform, empirical mode decomposition, and autoregressive or autoencoder methods based on machine learning. The methods for converting continuous real-valued labels in damage quantification into pseudo-classification labels in step 6 include, but are not limited to, fuzzy set methods and clustering methods, where clustering methods include K-means clustering, fuzzy C-means clustering, Gaussian mixture models, spectral clustering, or hierarchical clustering.

9. An electronic device, characterized in that... include: processor; Memory; And a program, wherein the program is stored in the memory and configured to be executed by a processor, the program comprising methods for performing any one of claims 1-8.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that: The computer program is executed by a processor according to any one of claims 1-8.

Images