A bayesian model fast solution method for structural damage identification based on zero-shot transfer learning

Abstract

The application discloses a kind of structural damage identification bayesian model fast solution method based on zero sample transfer learning, belong to structural damage identification and machine learning technical field.To solve the problem of generalization performance decline of structural damage identification bayesian model.The application includes constructing the bayesian model of structural damage identification;Combined with sparse auto-encoder and adversarial learning, construct and train the adversarial sparse auto-encoder, the adversarial sparse auto-encoder includes source domain sparse auto-encoder module, target domain sparse auto-encoder module and domain discriminator module;PhyCNN proxy model is constructed;Source domain label data set is generated, and source domain PhyCNN proxy model is constructed;Design parameter freezing transfer strategy, construct target domain PhyCNN proxy model;Based on target domain PhyCNN proxy model, sample posterior sample, update structural damage identification bayesian model using posterior sample, calculate the maximum posterior estimation value of structural damage parameter, realize the positioning and quantization of structural damage.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of structural damage identification and machine learning, and particularly relates to a structural damage identification Bayesian model fast solving method based on zero-shot transfer learning. BACKGROUND

[0002] In recent years, Bayesian methods have been widely used in structural damage identification uncertainty analysis, greatly improving the accuracy and robustness of damage identification. However, there are problems such as high-dimensional and strong nonlinear likelihood function calculation cost and complex posterior probability density function solution difficulty in the Bayesian method of structural damage. The existing approximate solution methods (such as variational inference and Markov chain Monte Carlo method) cannot simultaneously consider the calculation accuracy and calculation efficiency, which greatly limits the application of Bayesian methods in civil engineering field.

[0003] Deep learning has made a series of progress in the field of structural damage identification due to its strong nonlinear representation ability. Typical achievements include: damage localization method based on convolutional neural network (CNN), time-varying damage identification model using long short-term memory network (LSTM), and bridge response prediction method based on Transformer. However, these deep learning models are highly dependent on finite element model (FEM) for data labeling.

[0004] Although FEM can generate diversified damage data, there is a significant domain shift between simulation data and real data, mainly in the following aspects: (1) distribution difference of key physical quantities such as material parameters and modal parameters; (2) modeling deviation of environmental uncertainty factors. This domain shift phenomenon will lead to the decline of the generalization performance of the model trained based on finite element data, resulting in performance degradation in practical application, which is specifically manifested as the decline of damage identification result credibility, and seriously restricts the application value of deep learning method in engineering practice. Therefore, it is of important scientific significance and practical value to study and solve the problem of decline of generalization performance of traditional deep learning model based on finite element data training in the deep learning solving method of structural damage identification Bayesian model, and to promote the development of structural damage identification theory. SUMMARY

[0005] The problem to be solved by the present application is the decline of generalization performance of traditional deep learning model based on finite element data training in the deep learning solving method of structural damage identification Bayesian model, and a structural damage identification Bayesian model fast solving method based on zero-shot transfer learning is proposed.

[0006] To achieve the above purpose, the technical scheme of the present application is as follows:

[0007] A structural damage identification Bayesian model fast solving method based on zero-shot transfer learning comprises the following steps:

[0008] S1. Constructing a Bayesian model for structural damage identification, including a prior probability density function of a structural damage parameter, a likelihood function of the structural damage parameter, and a posterior probability density function of the structural damage parameter;

[0009] S2. Constructing and training an adversarial sparse autoencoder by combining a sparse autoencoder and adversarial learning, the adversarial sparse autoencoder including a source domain sparse autoencoder module, a target domain sparse autoencoder module, and a domain discriminator module;

[0010] S3. Constructing a physical information convolutional neural network, designing a sensitivity coefficient matrix of the structural damage parameter, embedding a physical loss based on the sensitivity coefficient matrix of the structural modal parameter into an architecture of the physical information convolutional neural network, and constructing a PhyCNN surrogate model;

[0011] S4. Generating a source domain labeled data set, replacing an input layer of the PhyCNN surrogate model obtained in step S3 with an encoder of the source domain sparse autoencoder module obtained in step S2, training by using the source domain labeled data set, and obtaining a source domain PhyCNN surrogate model;

[0012] S5. Designing a parameter freezing transfer strategy, retaining network architectures and weight parameters of feature learning layers, fully connected layers, and an output layer of the source domain PhyCNN surrogate model obtained in step S4, and replacing the input layer with an encoder of the target domain sparse autoencoder module obtained in step S2, to obtain a target domain PhyCNN surrogate model;

[0013] S6. Sampling posterior samples based on the target domain PhyCNN surrogate model, updating the Bayesian model for structural damage identification obtained in step S1 by using the posterior samples, calculating a maximum a posteriori estimation value of the structural damage parameter, and realizing positioning and quantification of structural damage.

[0014] Further, the specific implementation method of step S1 includes the following steps:

[0015] S1.1. Constructing a prior probability density function of a structural damage parameter θ, expressed as:

[0016]

[0017] wherein π(θ|β) is the prior probability density function of the structural damage parameter θ, β i is a hyperparameter corresponding to the i th structural damage parameter θ i , i is the sequential number of the damage parameter, and n is the total number of damage parameters;

[0018] S1.2. Obtaining an observation data set of structural modal parameters through a modal test The measurement error e of the rth natural frequency and the modal shape is introduced respectively r and the measurement error E of the modal shape r , the expression is:

[0019]

[0020] Where ω r (θ) and are the rth natural frequency and the modal shape of the structure damage parameter θ respectively, γ r and α r are the hyperparameters of the rth natural frequency and the modal shape respectively, is the observed value of the rth natural frequency, represents a normal distribution, represent the mean and variance respectively, is the observed value of the rth modal shape, and I is a unit matrix;

[0021] Assuming that each order modal parameter is independent of each other, the likelihood function of the structure damage parameter is constructed, and the expression is:

[0022]

[0023] Where, is the likelihood function, is the likelihood function corresponding to the natural frequency, is the likelihood function corresponding to the modal shape;

[0024]

[0025] Where N o is the total number of modal orders, and N m is the measured degree of freedom;

[0026] S1.3. Based on the Bayesian formula, the posterior probability density function of the structure damage parameter is constructed The expression is:

[0027]

[0028] Where c is the evidence value.

[0029] Further, the specific implementation method of step S2 includes the following steps:

[0030] S2.1. Constructing an adversarial sparse autoencoder, including a source domain sparse autoencoder module SAE s , a target domain sparse autoencoder module SAE t and a domain discriminator module Dis;

[0031] SAE sis responsible for mapping source domain data to source domain latent space q s (z) and reconstructing data is a vector space where source domain data resides.

[0032] SAE t is responsible for mapping target domain data to target domain latent space q t (z) and reconstructing data is a vector space where target data resides.

[0033] Dis is responsible for distinguishing is from q s (z) or q t (z), z is data in latent space, q s (z) and q t (z) are aligned through adversarial training, realizing that source domain data and target domain data are mapped to the same feature space;

[0034] S2.2. Constructing the loss function of the adversarial sparse autoencoder, including the reconstruction loss, sparse loss and adversarial loss of the adversarial sparse autoencoder.

[0035] The expression of the reconstruction loss L rec of the adversarial sparse autoencoder is as follows:

[0036]

[0037] Wherein, L rec,s is the reconstruction loss of the source domain, and L rec,t is the reconstruction loss of the target domain.

[0038] The expression of the sparse loss L spar of the adversarial sparse autoencoder is as follows:

[0039]

[0040] Wherein, and respectively represent the average activation value of the i-th latent space node of SAE s and SAE t , KL is KL divergence, N z is the dimension of latent space data z.

[0041] The expression of the adversarial loss L adver of the adversarial sparse autoencoder is as follows:

[0042]

[0043] where Dis(·) is the output of the discriminator, which is between 0 and 1.

[0044] The expression of the total loss of the adversarial sparse autoencoder is obtained as follows:

[0045] L ASAE = L rec,s + L rec,t + L spar + L adver (11)

[0046] S2.3. Constructing an adversarial training mechanism to realize the parameter update of the adversarial sparse autoencoder by alternating optimization: for the source domain sparse autoencoder module SAE s , its network parameters are optimized by minimizing L rec,s + L spar + L adver ; for the target domain sparse autoencoder module SAE t , its network parameters are updated by minimizing L rec,t + L spar + L adver ; and for the domain discriminator module Dis, the network parameter optimization is realized by maximizing the adversarial loss L adver .

[0047] Further, the specific implementation method of step S3 includes the following steps:

[0048] S3.1. Constructing a physical information convolutional neural network including an input layer, a feature learning layer FL, a fully connected layer FC, and an output layer, wherein the feature learning layer is used to extract features from the input or the output of the previous feature learning layer, and is composed of a convolutional layer, a Batch Norm layer, and a nonlinear activation function PReLU;

[0049] S3.2. Designing the sensitivity coefficients of the rth order natural frequency and mode shape to the structural damage parameter , which is expressed as:

[0050]

[0051]

[0052] where is the sensitivity coefficient of the rth order natural frequency corresponding to the structural damage parameter , is the sensitivity coefficient of the rth order mode shape corresponding to the structural damage parameter , l is the coefficient corresponding to the lth order modal shape, and N d is the number of degrees of freedom of the structural system.

[0053] The sensitivity coefficient matrix H of the structural damage parameters is constructed, and its expression is:

[0054] H = [H] ω(θ) H ψ(θ) (15)

[0055] S3.3. Embed the physical loss based on the sensitivity coefficient matrix of structural damage parameters into the convolutional neural network architecture of the physical information obtained in step S3.1 to construct the PhyCNN surrogate model. The loss function of the PhyCNN surrogate model is L. PhyCNN The expression is:

[0056]

[0057] Where R represents the output values ​​of the modal parameters of the finite element model (FEM). This represents the modal parameter output values ​​of the PhyCNN surrogate model, including natural frequencies and mode shapes.

[0058] Furthermore, the specific implementation method of step S4 includes the following steps:

[0059] S4.1. Generating source domain label dataset based on FEM: N is generated from the prior probability density function of the structural damage parameters in equation (1) using the inverse sampling method. PhyCNN A sample, represented as:

[0060]

[0061] Calculate N using FEM PhyCNN Sample The corresponding modal parameters are expressed as:

[0062]

[0063] The sample is calculated based on equations (12) to (14). The corresponding sensitivity coefficient matrix is ​​represented as follows:

[0064]

[0065] Then based on N PhyCNN The source domain label dataset consists of 10 samples, their corresponding modal parameters, and their corresponding sensitivity coefficient matrices.

[0066] S4.2. SAE s The encoder module replaces the input layer of the PhyCNN proxy model to obtain the source domain PhyCNN proxy model, which is then trained based on the source domain label dataset.

[0067] Furthermore, the target domain PhyCNN proxy model in step S5 does not require additional training and can directly replace FEM to calculate the modal parameters of the target domain, thus achieving zero-sample transfer from the source domain to the target domain.

[0068] Furthermore, the specific implementation method of step S6 includes the following steps:

[0069] S6.1. Generate posterior samples based on the target domain PhyCNN surrogate model. When generating posterior samples using the Metropolis-Hastings algorithm, the target domain PhyCNN surrogate model replaces FEM to evaluate candidate samples in order to generate posterior samples.

[0070] S6.2. Constructing the hyperparameter α of the Bayesian model for structural damage identification i β r and γ r The update formula is expressed as:

[0071]

[0072] in, The mean inside the parentheses is calculated based on the posterior sample.

[0073] S6.3. Based on the posterior samples generated in step S6.1, update the Bayesian model hyperparameter γ using equations (20), (21), and (22). r α r and β i The maximum a posteriori estimate of the damage parameter is identified, and the above operation is repeated until the iteration meets the pre-set convergence condition, thereby realizing the localization and quantification of structural damage.

[0074] The beneficial effects of this invention are:

[0075] This invention presents a fast solution method for Bayesian models of structural damage identification based on zero-shot transfer learning. This method automates the entire process, from cross-domain feature alignment between the source and target domains, to the construction and transfer of surrogate models, and finally, the rapid solution of the Bayesian model for structural damage identification. The algorithm boasts short computation time and high recognition accuracy, significantly improving the efficiency of solving Bayesian models for structural damage identification.

[0076] The present invention discloses a fast solution method for Bayesian models of structural damage recognition based on zero-shot transfer learning. The proposed adversarial sparse autoencoder utilizes an adversarial learning mechanism to perform cross-domain feature distribution matching, realizing zero-shot transfer of the source domain pre-trained model to the target domain. This significantly reduces the computational cost and data dependence of the target domain, and solves the problem of balancing accuracy and efficiency in cross-domain damage recognition under small sample conditions.

[0077] The present invention provides a fast solution method for a Bayesian model for structural damage identification based on zero-shot transfer learning. This method exhibits good generalization and transfer performance. The proposed PhyCNN surrogate model can be flexibly embedded into other sampling algorithms and applied to fast Bayesian inference in other complex systems.

[0078] The present invention provides a fast solution method for Bayesian models of structural damage identification based on zero-shot transfer learning, which can guarantee a structural damage identification accuracy of over 98% and a speed improvement of approximately 31 times.

[0079] The present invention provides a fast solution method for Bayesian models of structural damage identification based on zero-shot transfer learning, which can be applied to the damage identification problem of large and complex engineering structural systems. Attached Figure Description

[0080] Figure 1 This is a schematic diagram of a cable-stayed bridge in an embodiment of the present invention;

[0081] Figure 2 The diagram shows the structure of a fast solution method for a Bayesian model for structural damage recognition based on zero-shot transfer learning, as described in this invention. (a) represents the construction and training of an adversarial sparse autoencoder, (b) represents the construction and training of a PhyCNN surrogate model, and (c) represents the solution of the Bayesian model for structural damage in the target domain.

[0082] Figure 3 This is a comparison diagram of the first 6 natural frequencies of the low-fidelity model and the high-fidelity model in an embodiment of the present invention;

[0083] Figure 4 This is a comparison diagram of the first 6 mode shapes of the low-fidelity model and the high-fidelity model in an embodiment of the present invention;

[0084] Figure 5 This is a schematic diagram illustrating the weight sharing mechanism between the source domain sparse autoencoder and the target domain sparse autoencoder in an embodiment of the present invention.

[0085] Figure 6 The diagram shows the posterior probability density function of structural damage parameters in this embodiment of the invention, where (a) is the posterior probability density function of unit 2 and (b) is the posterior probability density function of unit 132.

[0086] Figure 7 These are damage identification result diagrams for different methods in the embodiments of the present invention, wherein (a) is the damage identification result diagram for working condition 1 of different methods, and (b) is the damage identification result diagram for working condition 2 of different methods.

[0087] Figure 8 This is a flowchart of a method for fast solution of a Bayesian model for structural damage identification based on zero-shot transfer learning, as described in this invention. Detailed Implementation

[0088] 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 specific embodiments. It should be understood that the specific embodiments described herein are only for explaining the invention and are not intended to limit the invention; that is, the described specific embodiments are merely a part of the embodiments of the invention, and not all of them. The components of the specific embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations, and the invention may also have other embodiments.

[0089] Therefore, the following detailed description of specific embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected specific embodiments of the invention. All other specific embodiments obtained by those skilled in the art based on these specific embodiments without inventive effort are within the scope of protection of this invention.

[0090] To further understand the invention's content, features, and effects, the following specific embodiments are provided, along with accompanying drawings. Figure 1 - Appendix Figure 8 Detailed explanation is as follows:

[0091] Example 1:

[0092] A fast solution method for a Bayesian model for structural damage recognition based on zero-shot transfer learning includes the following steps:

[0093] S1. Construct a Bayesian model for structural damage identification, including the prior probability density function of structural damage parameters, the likelihood function of structural damage parameters, and the posterior probability density function of structural damage parameters.

[0094] Furthermore, the specific implementation method of step S1 includes the following steps:

[0095] S1.1. Construct the prior probability density function of the structural damage parameter θ, the expression of which is:

[0096]

[0097] Where π(θ|β) is the prior probability density function of the structural damage parameter θ, and β i To be related to the i-th structural damage parameter θ i The corresponding hyperparameters are i, which is the sequential number of the damage parameter, and n, which is the total number of damage parameters.

[0098] S1.2. Obtain the observation dataset of structural modal parameters through modal testing. Introduce measurement errors e for the natural frequencies of the r-th order natural frequencies and mode shapes respectively. r Measurement error E of mode shape r The expression is:

[0099]

[0100] Where, ω r (θ) and These are the r-th natural frequency and mode shape of the structural damage parameter θ, respectively, and γ r and α r These are the hyperparameters of the r-th natural frequency and the hyperparameters of the mode shape, respectively. Let r be the observed value of the r-th natural frequency. It represents a normal distribution. These represent the mean and variance, respectively. Let I be the observed value of the r-th mode shape, and I be the element matrix.

[0101] Assuming that the modal parameters are independent of each other, the likelihood function of the structural damage parameters is constructed as follows:

[0102]

[0103] in, Let be the likelihood function. Let be the likelihood function corresponding to the natural frequency. This is the likelihood function for the corresponding mode shape;

[0104]

[0105] Where, N o N represents the total number of modal orders. m To measure degrees of freedom;

[0106] S1.3. Based on Bayes' theorem, construct the posterior probability density function of structural damage parameters. The expression is:

[0107]

[0108] Where c is the evidence value.

[0109] S2. Construct and train an adversarial sparse autoencoder by combining sparse autoencoders and adversarial learning. The adversarial sparse autoencoder includes a source domain sparse autoencoder module, a target domain sparse autoencoder module, and a domain discriminator module.

[0110] Furthermore, the specific implementation method of step S2 includes the following steps:

[0111] S2.1. Constructing an adversarial sparse autoencoder, including a source domain sparse autoencoder module (SAE). s Target Domain Sparse Autoencoder Module (SAE) t Dis;

[0112] SAE s Responsible for transferring source domain data Mapped to the source domain latent space q s (z), and reconstructed into data The vector space where the source domain data resides;

[0113] SAE t target domain data Mapped to the target domain latent space q t (z), and reconstruct the data The vector space where the target data resides;

[0114] Dis is responsible for distinguishing It comes from q s (z) or q t (z), where z is ***, and q is achieved through adversarial training. s (z) and q t Alignment of the distribution of (z) enables the source domain data and the target domain data to be mapped to the same feature space;

[0115] S2.2. Construct the loss function for adversarial sparse autoencoders, including the reconstruction loss, sparsity loss, and adversarial loss for adversarial sparse autoencoders;

[0116] Reconstruction loss L against sparse autoencoders rec The expression is:

[0117]

[0118] Among them, L rec,s L is the reconstruction loss of the source domain. rec,t The reconstruction loss is for the target domain;

[0119] Sparse loss L for adversarial sparse autoencoders spar The expression is:

[0120]

[0121] in, and They represent SAE respectively s and SAE t The average activation value of the i-th latent space node, KL is the KL divergence, N z Let z be the dimension of the potential spatial data;

[0122] Adversarial loss L against sparse autoencoders adver The expression is:

[0123]

[0124] Where Dis(·) is the output of the discriminator, which is between 0 and 1;

[0125] The expression for the total loss against sparse autoencoders is obtained as follows:

[0126] L ASAE =L rec,s +L rec,t +L spar +L adver (11)

[0127] S2.3. Constructing an adversarial training mechanism to achieve parameter updates for the adversarial sparse autoencoder through alternating optimization: For the source domain sparse autoencoder module SAE s By minimizing L rec,s +L spar +L adver Optimize its network parameters; for the target domain sparse autoencoder module SAE t By minimizing L rec,t +L spar +L adver To update its network parameters; for the domain discriminator module Dis, by maximizing the adversarial loss L adver To optimize network parameters.

[0128] S3. Construct a physical information convolutional neural network, design a sensitivity coefficient matrix for structural damage parameters, embed the physical loss based on the sensitivity coefficient matrix of structural modality parameters into the physical information convolutional neural network architecture, and construct the PhyCNN surrogate model.

[0129] Furthermore, the specific implementation method of step S3 includes the following steps:

[0130] S3.1. Constructing a physical information convolutional neural network includes an input layer, a feature learning layer (FL), a fully connected layer (FC), and an output layer. The feature learning layer is used to extract features from the input or the output of the previous feature learning layer, and consists of three parts: a convolutional layer, a batch normalized layer, and a non-linear activation function (PReLU).

[0131] S3.2. Design the impact of the r-th natural frequency and mode shape on structural damage parameters. The sensitivity coefficient is expressed as:

[0132]

[0133] in, The r-th natural frequency corresponds to the structural damage parameter. The sensitivity coefficient, The r-th mode shape corresponds to the structural damage parameters. The sensitivity coefficient, τ l These are the coefficients corresponding to the l-th mode shape, N d The number of degrees of freedom of the structural system;

[0134] The sensitivity coefficient matrix H of the structural damage parameters is constructed, and its expression is:

[0135] H = [H] ω(θ) H ψ(θ) (15)

[0136] S3.3. Embed the physical loss based on the sensitivity coefficient matrix of structural damage parameters into the convolutional neural network architecture of the physical information obtained in step S3.1 to construct the PhyCNN surrogate model. The loss function of the PhyCNN surrogate model is L. PhyCNN The expression is:

[0137]

[0138] Where R represents the output values ​​of the modal parameters of the finite element model (FEM). This represents the modal parameter output values ​​of the PhyCNN surrogate model, including natural frequencies and mode shapes.

[0139] S4. Generate a source domain label dataset, replace the encoder of the source domain sparse autoencoder module obtained in step S2 with the input layer of the PhyCNN proxy model obtained in step S3, and train it using the source domain label dataset to obtain the source domain PhyCNN proxy model.

[0140] Furthermore, the specific implementation method of step S4 includes the following steps:

[0141] S4.1. Generating source domain label dataset based on FEM: N is generated from the prior probability density function of the structural damage parameters in equation (1) using the inverse sampling method. PhyCNN A sample, represented as:

[0142]

[0143] Calculate N using FEM PhyCNN Sample The corresponding modal parameters are expressed as:

[0144]

[0145] The sample is calculated based on equations (12) to (14). The corresponding sensitivity coefficient matrix is ​​represented as follows:

[0146]

[0147] Then based on N PhyCNN The source domain label dataset consists of 10 samples, their corresponding modal parameters, and their corresponding sensitivity coefficient matrices.

[0148] S4.2. SAE s The encoder module replaces the input layer of the PhyCNN proxy model to obtain the source domain PhyCNN proxy model, which is then trained based on the source domain label dataset.

[0149] S5. Design a parameter freezing migration strategy, retain the network architecture and weight parameters of the feature learning layer, fully connected layer and output layer of the source domain PhyCNN surrogate model obtained in step S4, and replace the input layer with the encoder of the target domain sparse autoencoder module obtained in step S2 to obtain the target domain PhyCNN surrogate model.

[0150] Furthermore, the target domain PhyCNN proxy model in step S5 does not require additional training and can directly replace FEM to calculate the modal parameters of the target domain, thus achieving zero-sample transfer from the source domain to the target domain.

[0151] S6. Based on the target domain PhyCNN surrogate model, sample posterior samples, update the Bayesian model for structural damage identification obtained in step S1 using the posterior samples, calculate the maximum posterior estimate of the structural damage parameters, and realize the localization and quantification of structural damage.

[0152] Furthermore, the specific implementation method of step S6 includes the following steps:

[0153] S6.1. Generate posterior samples based on the target domain PhyCNN surrogate model. When generating posterior samples using the Metropolis-Hastings algorithm, the target domain PhyCNN surrogate model replaces FEM to evaluate candidate samples in order to generate posterior samples.

[0154] S6.2. Constructing the hyperparameter α of the Bayesian model for structural damage identification i β r and γ r The update formula is expressed as:

[0155]

[0156] in, The mean inside the parentheses is calculated based on the posterior sample.

[0157] S6.3. Based on the posterior samples generated in step S6.1, update the Bayesian model hyperparameter γ using equations (20), (21), and (22). r α r and β i The maximum a posteriori estimate of the damage parameter is identified, and the above operation is repeated until the iteration meets the pre-set convergence condition, thereby realizing the localization and quantification of structural damage.

[0158] This embodiment conducts actual experiments to verify the experimental results as follows:

[0159] by Figure 1 The cable-stayed bridge shown is modeled using multi-scale finite element methods: the low-fidelity model (source domain) uses 77 coarse-grained elements for the main girder, which reduces the computational cost of modal analysis by 28.3% compared to the high-fidelity model (target domain) with 312 fine-grained elements. This is based on the ZS-PhyCNN method (…). Figure 2 It enables cross-domain damage identification from low-fidelity models to high-fidelity models, providing an efficient solution for damage identification of large and complex structures.

[0160] The low-fidelity model is updated based on the modal parameters of the high-fidelity model in its complete state. Figure 3 The results show that the average error of the first six vertical natural frequencies of the low-fidelity model decreased from the initial 0.96% to 0.09%. Figure 4 Modal confidence criterion (MAC) analysis shows that the updated model's mode shape MAC values ​​are all stable above 98%, verifying the spatial consistency of the two models in terms of dynamic characteristics. The updated low-fidelity model not only reconstructs the dynamic characteristics of the high-fidelity model well, but also provides efficient training data support for the subsequent construction of deep learning surrogate models by establishing a high-precision-low-cost parameter mapping relationship.

[0161] The latent space dimension of the ASAE domain adaptation module is set to 312, and other key hyperparameter configurations are detailed in Table 1. During training, to ensure q s (z) and q t The consistent convergence of (z) employs a weight-sharing mechanism: specifically, the source domain sparse autoencoder (SAE) achieves this. s Sparse Autoencoder (SAE) for Target Domain t The weight parameters connecting the hidden layer and the latent space layer are designed to be shared parameters, and the architectural design details are as follows: Figure 5 As shown.

[0162] Table 1. Network hyperparameters against sparse autoencoders

[0163]

[0164] Table 2 shows the detailed configuration of the proxy model for the three methods.

[0165]

[0166] The synergistic effect of physical constraint mechanism and cross-domain migration strategy was verified by using the controlled variable method. The experimental design included two key comparisons: (1) verification of the effectiveness of physical constraints: constructing ablation experimental groups of ZS-PhyCNN (with physical constraints) and ZS-CNN (without physical constraints); (2) verification of cross-domain damage recognition performance: comparing and analyzing cross-domain damage recognition (ZS-PhyCNN) with target domain recognition (MH-PhyCNN). The three surrogate models adopted a unified network structure except for the input layer, namely 4 FL layers and 1 FC layer. The detailed configuration is shown in Table 2.

[0167] For model training, a comparative dataset was constructed based on a multi-fidelity modeling strategy: 3000 samples were generated using a low-fidelity model to train a cross-domain model (ZS-PhyCNN / ZS-CNN), while an equal number of samples were used to train a benchmark model within the domain (MH-PhyCNN) using a high-fidelity model. This experimental design effectively decoupled the impact of physical constraint mechanisms and cross-domain transfer effects on the accuracy of damage recognition. ZS-CNN served as a blank control group, intuitively reflecting the role of physical information embedding in improving the model's generalization ability.

[0168] Damage to cable-stayed bridges is simulated by reducing the Young's modulus of the beam elements. Table 3 introduces two damage scenarios for the target domain of the cable-stayed bridge, i.e., the high-fidelity model. For cable-stayed bridges with hundreds of structural elements, damage to only two elements will result in only minor changes in their modal parameters, as detailed in Table 4.

[0169] Table 3 Information on three damage conditions in the high-fidelity model.

[0170]

[0171] Table 4 Modal parameters of the high-fidelity model before and after damage

[0172]

[0173] Table 5 Comparison of damage identification results from different methods

[0174]

[0175] Table 5 compares the damage identification results of four methods: ZS-PhyCNN, ZS-CNN, MH-PhyCNN, and the MH method (MH-FEM) based on a high-fidelity finite element model. Figure 6 The posterior probability density function of working condition 2 based on the ZS-PhyCNN method is shown. Figure 7The damage identification results of several methods are compared using a three-dimensional bar chart. Compared with ZS-PhyCNN, the DS1 damage identification result of ZS-CNN has a larger error, and the DS2 damage localization is incorrect (damage localization units are 1, 2, and 129, while the actual damage units are 2 and 132). This indicates that for deep neural networks trained on the same dataset, physically constrained neural networks have significantly improved the prediction performance of structural modal parameters. Compared with MH-PhyCNN, the damage identification errors of ZS-PhyCNN are similar, but the former reduces the training data acquisition cost by about 28.3%, indicating that ZS-PhyCNN achieves the ability to train high-precision deep surrogate models at low cost. In addition, compared with the traditional MH-FEM method, ZS-PhyCNN achieves a damage identification error of less than 1.5% and improves computational efficiency by 31 times.

[0176] It should be noted that relational terms such as "first" and "second" are used merely to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0177] Although this application has been described above with reference to specific embodiments, various modifications can be made and components can be replaced with equivalents without departing from the scope of this application. In particular, as long as there is no structural conflict, the features in the specific embodiments disclosed in this application can be combined with each other in any way. The lack of an exhaustive description of these combinations in this specification is merely for the sake of brevity and resource conservation. Therefore, this application is not limited to the specific embodiments disclosed herein, but includes all technical solutions falling within the scope of the claims.

Claims

1. A fast solution method for a Bayesian model of structural damage recognition based on zero-shot transfer learning, characterized in that, Includes the following steps: S1. Construct a Bayesian model for structural damage identification, including the prior probability density function of structural damage parameters, the likelihood function of structural damage parameters, and the posterior probability density function of structural damage parameters; S2. Construct and train an adversarial sparse autoencoder by combining sparse autoencoders and adversarial learning, wherein the adversarial sparse autoencoder includes a source domain sparse autoencoder module, a target domain sparse autoencoder module, and a domain discriminator module; S3. Construct a physical information convolutional neural network, design a sensitivity coefficient matrix for structural damage parameters, embed the physical loss based on the sensitivity coefficient matrix of structural modality parameters into the physical information convolutional neural network architecture, and construct the PhyCNN surrogate model; The specific implementation method of step S3 includes the following steps: S3.

1. Constructing a physical information convolutional neural network includes an input layer, a feature learning layer (FL), a fully connected layer (FC), and an output layer. The feature learning layer is used to extract features from the input or the output of the previous feature learning layer, and consists of three parts: a convolutional layer, a BatchNorm layer, and a non-linear activation function (PReLU). S3.

2. Design the impact of the r-th natural frequency and mode shape on structural damage parameters. The sensitivity coefficient is expressed as: ； ； ； in, and These are structural damage parameters The r-th natural frequency and mode shape, The r-th natural frequency corresponds to the structural damage parameter. The sensitivity coefficient, The r-th mode shape corresponds to the structural damage parameters. The sensitivity coefficient, These are the coefficients corresponding to the l-th mode shape, N d The number of degrees of freedom of the structural system; Constructing the sensitivity coefficient matrix of structural damage parameters The expression is: ； S3.

3. Embed the physical loss based on the sensitivity coefficient matrix of structural damage parameters into the convolutional neural network architecture of the physical information obtained in step S3.1 to construct the PhyCNN surrogate model. The loss function of the PhyCNN surrogate model is... The expression is: ； in, This represents the output values ​​of the modal parameters of the finite element model (FEM). This represents the modal parameter output values ​​of the PhyCNN surrogate model, including natural frequencies and mode shapes. S4. Generate a source domain label dataset, replace the input layer of the PhyCNN proxy model obtained in step S3 with the encoder of the source domain sparse autoencoder module obtained in step S2, and train it using the source domain label dataset to obtain the source domain PhyCNN proxy model. S5. Design a parameter freezing transfer strategy to retain the network architecture and weight parameters of the feature learning layer, fully connected layer and output layer of the source domain PhyCNN surrogate model obtained in step S4, and replace the input layer with the encoder of the target domain sparse autoencoder module obtained in step S2 to obtain the target domain PhyCNN surrogate model. S6. Based on the target domain PhyCNN surrogate model, sample posterior samples, update the Bayesian model for structural damage identification obtained in step S1 using the posterior samples, calculate the maximum posterior estimate of the structural damage parameters, and realize the localization and quantification of structural damage.

2. The fast solution method for a Bayesian model of structural damage recognition based on zero-shot transfer learning according to claim 1, characterized in that, The specific implementation method of step S1 includes the following steps: S1.

1. Constructing structural damage parameters The prior probability density function is expressed as: ； in, Structural damage parameters The prior probability density function, To the i-th structural damage parameter The corresponding hyperparameters are i, which is the sequential number of the damage parameter, and n, which is the total number of damage parameters. S1.

2. Obtain the observation dataset of structural modal parameters through modal testing. The measurement error of the natural frequency is introduced into the r-th natural frequency and the mode shape, respectively. Measurement error of mode shape The expression is: ； ； in, and These are structural damage parameters The r-th natural frequency and mode shape, and These are the hyperparameters of the r-th natural frequency and the hyperparameters of the mode shape, respectively. Let r be the observed value of the r-th natural frequency. It represents a normal distribution. These represent the mean and variance, respectively. For the observed values ​​of the r-th mode shape, It is a unit matrix; Assuming that the modal parameters are independent of each other, the likelihood function of the structural damage parameters is constructed as follows: ； in, Let be the likelihood function. Let be the likelihood function corresponding to the natural frequency. This is the likelihood function for the corresponding mode shape; ； ； Where, N o N represents the total number of modal orders. m To measure degrees of freedom; S1.

3. Constructing the posterior probability density function of structural damage parameters based on Bayes' theorem. The expression is: ； Where c is the evidence value.

3. A fast solution method for a Bayesian model of structural damage recognition based on zero-shot transfer learning according to claim 1 or 2, characterized in that, The specific implementation method of step S2 includes the following steps: S2.

1. Constructing an adversarial sparse autoencoder, including the source domain sparse autoencoder module SAE. s Target Domain Sparse Autoencoder Module (SAE) t Dis; SAE s Responsible for transferring source domain data Mapped to the source domain latent space q s (z), and reconstructed into data , The vector space where the source domain data resides; SAE t target domain data Mapped to the target domain latent space q t (z), and reconstruct the data , The vector space where the target data resides; Dis is responsible for distinguishing It comes from q s (z) or q t (z), q is achieved through adversarial training. s (z) and q t Alignment of the distribution of (z) enables the source domain data and the target domain data to be mapped to the same feature space; S2.

2. Construct the loss function for adversarial sparse autoencoders, including the reconstruction loss, sparsity loss, and adversarial loss for adversarial sparse autoencoders; Reconstruction loss against sparse autoencoders The expression is: ； in, The reconstruction loss of the source domain, The reconstruction loss is for the target domain; Sparse loss for adversarial sparse autoencoders The expression is: ； in, and They represent SAE respectively s and SAE t The average activation value of the i-th potential space node. L is the KL divergence, N z Let z be the dimension of the potential spatial data; Adversarial loss against sparse autoencoders The expression is: ； in, This is the output of the discriminator, located between 0 and 1; The expression for the total loss against sparse autoencoders is obtained as follows: ； S2.

3. Constructing an adversarial training mechanism to achieve parameter updates for the adversarial sparse autoencoder through alternating optimization: For the source domain sparse autoencoder module SAE s By minimizing L rec,s + L spar + L adver Optimize its network parameters; for the target domain sparse autoencoder module SAE t By minimizing L rec,t + L spar + L adver To update its network parameters; for the domain discriminator module Dis, by maximizing the adversarial loss L adver To optimize network parameters.

4. The fast solution method for a Bayesian model of structural damage recognition based on zero-shot transfer learning according to claim 3, characterized in that, The specific implementation method of step S4 includes the following steps: S4.

1. Generating source domain label dataset based on FEM: N is generated from the prior probability density function of structural damage parameters in equation (1) using the inverse sampling method. PhyCNN A sample, represented as: ； Calculate N using FEM PhyCNN Sample The corresponding modal parameters are expressed as: ； The sample is calculated based on equations (12) to (14). The corresponding sensitivity coefficient matrix is ​​represented as follows: ； Then based on N PhyCNN The source domain label dataset consists of 10 samples, their corresponding modal parameters, and their corresponding sensitivity coefficient matrices. S4.

2. SAE s The encoder module replaces the input layer of the PhyCNN proxy model to obtain the source domain PhyCNN proxy model, which is then trained based on the source domain label dataset.

5. The fast solution method for a Bayesian model of structural damage recognition based on zero-shot transfer learning according to claim 4, characterized in that, The target domain PhyCNN proxy model in step S5 does not require additional training and can directly replace FEM to calculate the modal parameters of the target domain, thus achieving zero-sample transfer from the source domain to the target domain.

6. The fast solution method for Bayesian model of structural damage recognition based on zero-shot transfer learning according to claim 5, characterized in that, The specific implementation method of step S6 includes the following steps: S6.

1. Generate posterior samples based on the target domain PhyCNN surrogate model. When generating posterior samples using the Metropolis-Hastings algorithm, the target domain PhyCNN surrogate model replaces FEM to evaluate candidate samples in order to generate posterior samples. S6.

2. Constructing the hyperparameters of a Bayesian model for structural damage identification , as well as The update formula is expressed as: ； ； ； in, The mean inside the parentheses is calculated based on the posterior sample. S6.

3. Based on the posterior samples generated in step S6.1, update the hyperparameters of the Bayesian model using equations (20), (21), and (22). , as well as The maximum a posteriori estimate of the damage parameter is identified, and the above operation is repeated until the iteration meets the pre-set convergence condition, thereby realizing the localization and quantification of structural damage.

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