Modal difference based structural parameter variation identification method and system under uncertain boundary constraints

Abstract

This invention discloses a method and system for identifying structural parameter changes in modal differences under uncertain boundary constraints, applicable to structural health monitoring and AI inversion. S1 establishes a dynamic model of structural stiffness changes under unknown actuator constraints, with the parameter to be identified being the change in stiffness at each floor level. S2 performs offline Monte Carlo sampling of actuator constraints and floor stiffness changes, generating modal datasets before and after loading and adding noise. S3 constructs a whitened modal residual feature vector containing indices such as frequency, mode shape, and modal confidence. S4 trains an amortized inferrer, inputting the relationship between modal residuals and floor region stiffness changes, and marginalizing the actuators. S5 online, requiring only a few low-order modal parameters, quickly constructs features and outputs the probability density function of floor stiffness changes. This invention marginalizes actuator stiffness uncertainty offline, reducing calibration and iteration costs; it provides fast and robust online inference, adapting to noise and few modes, and supporting quasi-static and hybrid tests.

Description

Technical Field

[0001] This invention relates to the fields of structural health monitoring and engineering structural dynamics, focusing on data-driven algorithms, systems, and storage media. Under quasi-static testing and in-service online monitoring conditions, it proposes a method and system for identifying structural parameter changes in modal differences under uncertain boundary constraints. The method marginalizes actuator uncertainties in the offline stage and, combined with an efficient online inference framework, achieves point estimation and uncertainty quantification of structural stiffness changes through modal residual whitening, modal guarantee criterion (MAC) constraints, and posterior inference. It aims to improve identification accuracy and robustness in low-modal and noisy environments, and is applicable to quasi-static, mixed testing, and online monitoring scenarios, highlighting the innovations of data-driven approaches, inferential modeling, and uncertainty handling. Background Technology

[0002] Existing structural health monitoring and structural parameter identification methods are widely used in quasi-static tests and in-service online monitoring for floor stiffness and damage identification. Traditional approaches mainly include two categories: one is Bayesian MCMC or least squares inversion based on physical models, which requires precise calibration of external constraints such as boundary constraints and actuator stiffness or iterative solution of high-dimensional posteriors, resulting in high computational costs and sensitivity to initial priors; the other is machine learning methods based on experience or data-driven approaches, which are computationally fast but often ignore or struggle to handle uncertainties in boundary constraints and the lack of modal information under conditions of few modes and strong noise in experiments, leading to unstable identification results or requiring a large amount of labeled data and external calibration support.

[0003] In quasi-static loading scenarios, the stiffness of external constraints such as actuators has a significant impact on the overall structural modes. However, this constraint stiffness is often difficult to measure accurately and may change under different load or displacement conditions, becoming a major bottleneck hindering high-precision, real-time parameter identification. In addition, only a small amount of low-order modal information is usually available on-site, accompanied by high measurement noise. Traditional Bayesian MCMC-based methods often converge slowly or fall into uncertainty accumulation in this situation, affecting their practicality.

[0004] This invention addresses the aforementioned technical bottlenecks by proposing an innovative solution: In the offline phase, Monte Carlo sampling is performed on the uncertainties of actuator stiffness and floor stiffness variations to generate noisy observation modes. Whitened modal residual features are constructed, and an amortized data-driven inference engine implicitly marginalizes actuator stiffness during training. This enables robust and rapid identification of floor stiffness variations under unknown boundary constraints without explicit actuator stiffness calibration or large-scale iterative solutions. This strategy combines the interpretability of physical modeling with the computational efficiency of data-driven methods, effectively overcoming the challenges of few modes, strong noise, and actuator stiffness uncertainty. It significantly improves identification accuracy and online response speed, making it suitable for real-time applications in quasi-static testing of frame structures and in-service monitoring of engineering projects. Summary of the Invention

[0005] This invention provides a method, apparatus, and storage medium for identifying structural stiffness changes under unknown actuator stiffness conditions. The method offline samples actuator stiffness and potential damage scenarios, constructs whitened modal residual features, and trains an amortized data-driven inferrer. This allows for online point estimates or uncertainty measures of stiffness changes based on only a small number of modal observations, avoiding explicit calibration of actuator stiffness or costly iterative inversion. It is suitable for quasi-static tests and in-service structural monitoring.

[0006] The above method is implemented through the following steps:

[0007] This invention first provides a method for identifying structural parameter changes using two modal differences under uncertain boundary constraints, comprising the following steps:

[0008] S1. Establish the equivalent stiffness of the actuator containing the unknown actuator. A parameterized model of structural dynamics is defined, defining a parameter vector for structural stiffness variation. The target to be identified is the change in stiffness of each floor; among which For the unknown actuator equivalent stiffness This is a vector of structural stiffness variation parameters. For the number of floors in the structure, For the first Layer stiffness variation parameters ;

[0009] S2. Offline training phase: Within a preset prior range, the equivalent stiffness of the actuator is... With structural stiffness variation parameter vector Random sampling is performed, and the pre-loading stiffness matrix is ​​obtained through forward analysis for each set of sampled parameters. With the stiffness matrix after loading At the same time, the mass matrix is ​​obtained. And by solving the generalized eigenvalue problem: , ;in , Before / after loading Mode shape, , Before / after loading eigenvalues ​​of order 1 , The modal order used; eigenvalues ​​according to the noise model. With mode shape Measurement noise is added to obtain the observed modal parameters;

[0010] S3. Calculate the eigenvalue residuals, mode shape residuals, and mode guarantee criterion (MAC) based on the observed modal parameters before and after loading; then concatenate the eigenvalue residuals, mode shape residuals, and MAC in a preset order to construct the whitened modal residual eigenvector. ;

[0011] S4. Train the amortization inferr using supervised learning or a conditional generation model. To make it possible Point estimation mapping or The posterior mapping; during training, training sample pairs For monitoring signals, and not to As an input variable, make Marginalized in the training distribution; where To amortize the inferrer, It is a posterior distribution;

[0012] S5. Online Application Phase: Obtain modal observation parameters before / after actual loading, and repeat step S3 to obtain the modal residual feature vector. And input the trained Output structural stiffness variation The point estimate or posterior distribution / confidence interval.

[0013] Furthermore, in step S1: the structural dynamics model is The stiffness matrices before and after loading are expressed as follows: (Equivalent model of a multi-story shear wall or finite element model of a frame) , ,in For the first Layer baseline stiffness, For the first Layer stiffness submatrix This is the actuator stiffness submatrix.

[0014] Furthermore, in step S2, the modal parameters are obtained through a generalized eigenvalue problem, namely: ,in For the mode shape matrix, The eigenvalues ​​are used; and the modal guarantees (MAC) are applied to perform stepwise matching of the loaded modes, wherein the MAC is defined as: ,in For the first The first-order mode guarantee criterion, where the superscript T denotes vector transpose.

[0015] Furthermore, the whitening mode residual feature vector mentioned in step S3 Includes the following components and is assembled in a preset order:

[0016] (a) Eigenvalue residuals: , ,in For eigenvalue residuals, As a measure of whitening, The eigenvalue is the relative noise coefficient. For the first The random sampling, at the... The loaded structure identified at each measuring point, degree of freedom, or measurement location. Rank features, For the first The random sampling, at the... The pre-loading structure identified at each measuring point, degree of freedom, or measurement location. Rank features;

[0017] (b) Mode shape residuals: , ,in For mode shape residuals, This is a measure of modal noise. To prevent zero threshold, For modal weighting factors, Before loading the first The first mode shape The components at each measuring point For the first time after loading The first mode shape The components of each measuring point;

[0018] (c) Modal guarantee criterion ;

[0019] Concatenate the residual feature vectors of the whitening mode in sequence. : ,in It is a vectorization operator.

[0020] Furthermore, the amortization inferrer described in step S4 The residual network ResNet structure or the multilayer perceptron (MLP) structure is adopted, and the training sample pairs are used. As a supervisory signal, the point estimation is trained by minimizing the mean squared error loss: ,in For mean square error loss, The number of training samples, It is a 2-norm; when training the output probability model, it is trained by minimizing the negative log-likelihood: ,in For negative log-likelihood loss, The number of training samples, For conditional probability models, For the first The input feature vectors of each training sample are concatenated sequentially to produce the whitening mode residual feature vector. For the first The true structural parameter vector or label corresponding to each training sample is a randomly sampled structural parameter, including the actuator equivalent stiffness constraint parameters. And the structural stiffness variation parameter vector.

[0021] Furthermore, in step S4, when the output posterior distribution... At that time, a generator is constructed using one of the following methods: conditional flow matching model, conditional Rectified Flow, quantile regression, or deep ensemble. After training, the generator is used to perform tests on a given conditional flow. Sampling to obtain The posterior sample or the confidence interval is calculated.

[0022] Furthermore, in step S5, the set of feature vectors obtained from multiple independent measurements... The ensemble averaging or Bayesian posterior synthesis is employed (e.g., combining posteriors based on independent observations under probability output), where For the first The eigenvectors corresponding to each independent measurement , For the number of independent measurements.

[0023] This invention also provides a structural stiffness change identification system under unknown actuator stiffness conditions, comprising: a data acquisition module, a modal parameter preprocessing and matching module, a feature construction module, an amortization inference module, and a result output module; wherein the amortization inference module has a built-in identification model trained according to the above method. The modules are connected and work together according to steps S1 to S5.

[0024] The present invention also provides an electronic device, including a processor, a memory, and a program stored in the memory and executable on the processor, wherein the program, when executed by the processor, implements the above-described method steps.

[0025] The present invention also provides a computer-readable storage medium having a computer program stored thereon, wherein the computer program, when executed by a processor, implements the above-described method steps.

[0026] Compared with existing technologies, the advantages of this invention are as follows: by sampling the equivalent stiffness of the unknown actuator in the offline stage and implicitly marginalizing it in the training stage, explicit calibration of boundary constraints is avoided; by constructing whitened modal residual features that fuse eigenvalue / frequency residuals, mode shape residuals and MAC, the recognition stability under few modes and strong noise conditions is improved; through amortized posterior inference, the point estimate and confidence interval / posterior distribution of stiffness changes can be quickly output in the online stage, thus taking into account accuracy, real-time performance and interpretable uncertainty quantification capabilities, and is particularly suitable for quasi-static tests, mixed tests and in-service monitoring scenarios. Attached Figure Description

[0027] Figure 1 This is a flowchart of the overall process of the present invention;

[0028] Figure 2 Offline training and online recognition core process

[0029] Figure 3 A schematic diagram of an equivalent model of an N-story shear tower including actuator stiffness;

[0030] Figure 4 This is a schematic diagram showing the comparison results of the posterior means in a 20-layer numerical simulation example.

[0031] Figure 5 A comparison plot of posterior probability densities for 20 parameters;

[0032] Figure 6 Diagram showing the layout of measurement points for frame modal testing;

[0033] Figure 7 A schematic diagram of the finite element model of the frame structure (including actuator constraints);

[0034] Figure 8 A schematic diagram showing the region division (45 regions) for the frame finite element model;

[0035] Figure 9 This is a schematic diagram of the posterior probability density of damage factors in a frame structure (5×9 subplot).

[0036] Figure 10 This is a map showing the actual damage. Detailed Implementation

[0037] The specific implementation process of the present invention will be further described below with reference to the accompanying drawings, through numerical examples and specific embodiments of frame structure engineering. However, the scope of protection of the present invention is not limited to the following embodiments. Those skilled in the art can modify and adjust this embodiment according to the technical solution of the present invention and the prior art, and all such modifications and adjustments fall within the scope of protection of the present invention.

[0038] Reference Figure 1 The present invention provides a method for identifying structural parameter changes using two modal differences under uncertain boundary constraints, comprising the following steps, the core process of which is as follows: Figure 2 As shown:

[0039] S1. Establish a parameterized model of structural dynamics containing the equivalent stiffness of unknown actuators, and define the structural stiffness variation parameter vector.

[0040] 1. Structural Dynamics Model Establishment: An equivalent shear floor model or equivalent finite element model is used to characterize the structure's dynamic properties. Taking a shear tower model as an example, the stiffness matrix before and after loading. and It can be represented as: , ,in For the first Layer baseline stiffness, For the first Layer stiffness submatrix This is the actuator stiffness submatrix. In this model... It is considered an unknown parameter, and its specific value will be represented in parameterized form in subsequent steps and implicitly marginalized.

[0041] 2. Definition of structural stiffness variation parameter vector: Define the structural stiffness variation parameter vector. This is a vector of structural stiffness variation parameters. For the number of floors in the structure, ,in Indicates the first Layer (or the first) stiffness reduction ratio of the element Indicates no damage. (This indicates a complete loss of stiffness).

[0042] S2. Offline Training Phase: Randomly sample the changes in actuator stiffness and structural stiffness within a preset prior range, and generate training data.

[0043] 1. Parameter sampling: Within a preset prior range, for the unknown actuator equivalent stiffness... With structural stiffness variation parameter vector Perform random sampling. This can be achieved using Monte Carlo methods, for example, on... and Sampling is performed on a distribution (such as a uniform distribution or a Gaussian distribution).

[0044] 2. Forward analysis and modal parameter acquisition: For each set of samples... and Forward analysis using a structural dynamics model yields the stiffness matrices before and after loading. and and the corresponding quality matrix Then, the modal parameters are obtained by solving the generalized eigenvalue problem: , ;in For the quality matrix, , Before / after loading Mode shape, , Before / after loading eigenvalues ​​of order 1 , The modal order used; according to the noise model. and Measurement noise is added to obtain the observed modal parameters;

[0045] 3. Generation of observation modal parameters: Simulating noise in the actual measurement process, and generating characteristic values. and mode By adding measurement noise, the observed modal parameters are obtained. The noise model can be additive Gaussian noise or other noise models that conform to the actual situation.

[0046] S3. Construct the whitening mode residual feature vector from the observed mode parameters before / after loading. They were then assembled and whitened in a predetermined order.

[0047] 1. Modal Matching: The post-loading modes are matched sequentially with the pre-loading modes using the Modal Assurance Criterion (MAC) according to their order. MAC is defined as: ,in For the first The modal guarantee criterion, where the superscript T denotes vector transpose, ensures the consistency of the modes under different loading states, facilitating subsequent residual calculations.

[0048] 2. Construction of whitening mode residual eigenvectors: whitening mode residual eigenvectors It contains the following components, which are assembled in a preset order:

[0049] (a) Eigenvalue residuals: , ,in For eigenvalue residuals, As a measure of whitening, The eigenvalue is the relative noise coefficient; For the first The random sampling, at the... The loaded structure identified at each measuring point, degree of freedom, or measurement location. Rank features, For the first The random sampling, at the... The pre-loading structure identified at each measuring point, degree of freedom, or measurement location. Rank features;

[0050] (b) Mode shape residuals: , ,in For mode shape residuals, As a measure of whitening, This is a measure of modal noise. To prevent zero threshold, For modal weighting factors, Before loading the first The first mode shape The components at each measuring point For the first time after loading The first mode shape The components of each measuring point;

[0051] (c) Concatenate the residual eigenvectors of the whitening mode in sequence. : ,in It is a vectorization operator.

[0052] Whitening helps eliminate correlations between features and gives the data zero mean and unit variance, thereby improving the training efficiency and recognition performance of subsequent inferrs.

[0053] S4, Offline Training Amortization Inferr :

[0054] 1. Inferrer Structure: Amortized inferrs can employ neural network structures such as ResNet or Multilayer Perceptron (MLP). These networks are able to extract features from the input feature vector. Learn the structural stiffness variation parameter vector The mapping.

[0055] 2. Training Objective: During the training phase, offline-generated sample pairs are used as training targets. As a monitoring signal. The key to this invention is that the actuator stiffness is not controlled during the training process. As an input variable, thus They are implicitly marginalized in the training distribution.

[0056] Point estimation training: If the goal is to obtain The point estimates are then trained by minimizing the mean squared error (MSE) loss: ,in For mean square error loss, The total number of training samples, For the first The input feature vectors of each training sample are concatenated sequentially to produce the whitening mode residual feature vector. For the first The true structural parameter vector or label corresponding to each training sample is a randomly sampled structural parameter, including the actuator equivalent stiffness constraint parameters. And the structural stiffness variation parameter vector.

[0057] Probabilistic model training: If the goal is to train a model that outputs posterior probability... Then, training is performed by minimizing the negative log-likelihood (NLL): Among them, For negative log-likelihood loss, The number of training samples, It is a conditional probability model.

[0058] 3. Posterior Distribution Implementation: In step S4, when the inferr outputs the posterior distribution... At this time, generator mechanisms such as Conditional Normalizing Flow (CFM), Conditional Rectified Flow, quantile regression, or deep ensemble can be used for construction. After training, for a given input feature... The uncertainty of identification can be characterized by sampling posterior samples from the generator or by calculating confidence intervals based on these samples.

[0059] S5. Online Application Phase: Obtain modal observation parameters before / after actual loading, and output point estimates of structural stiffness changes. Or posterior distribution / confidence interval.

[0060] 1. Online data acquisition: In practical applications (such as quasi-static tests or online monitoring), the actual modal observation parameters of the structure before and after loading are obtained.

[0061] 2. Feature Vector Generation: Repeat step S3 to construct the whitening mode residual feature vector using the online acquired modal observation parameters. .

[0062] 3. Stiffness variation identification: The generated feature vector Input into the trained amortization inferr In the middle, the structural stiffness change is directly output. The point estimate (if trained with MSE) or the posterior distribution / confidence interval (if trained with NLL or a conditional generative model).

[0063] 4. Integrated averaging / Bayesian synthesis (optional): For a set of feature vectors obtained from multiple independent measurements, an integrated averaging method (e.g., taking the mean of point estimates) or a Bayesian synthesis method that combines the posterior of independent observations under probability output can be used to further improve recognition stability and reduce the impact of measurement noise.

[0064] Example 1: Numerical example of shear floor ( ) =20)

[0065] This embodiment aims to demonstrate a typical Ns-story shear building numerical model (set) =20), verifying the effectiveness and robustness of the structural stiffness change identification method proposed in this invention.

[0066] 1. Model building and parameterization

[0067] See attached document Figure 3 (Diagram of equivalent model of Ns-story shear tower) In this example, the structural model is set as a 20-story shear tower, and only one translational degree of freedom (lateral displacement degree of freedom) is considered for each floor.

[0068] Floor stiffness: Let the first floor be stiffness. The baseline stiffness of the layer is denoted as The structural stiffness variation parameter vector is defined as follows: This is a vector of structural stiffness variation parameters. For the number of floors in the structure, For the first Layer stiffness variation parameters To verify the recognition performance of this invention, this example sets the actual structural stiffness. The change decreases linearly with the floor height, and its value range is [0.1, 0.4], that is, the stiffness of the bottom floor changes more significantly, while the change of the upper floor is smaller.

[0069] Actuator stiffness: The equivalent stiffness of the actuator is denoted as... It is represented in the model in the form of parameters and is marginalized in the offline stage.

[0070] Stiffness matrix: The stiffness matrix before loading (baseline state) and after loading (damage or stiffness change state), as well as the corresponding mass matrix, are constructed according to the method described in step S1 of this invention. The mass matrix is ​​a diagonal matrix, and the mass of each floor can be equally divided or allocated according to the actual engineering situation.

[0071] 2. Modal solution and modal matching (corresponding to S2)

[0072] By solving the generalized eigenvalue problem of the model, several low-order eigenvalues ​​and mode shapes of the structure can be obtained.

[0073] To ensure correct modal matching and avoid modal confusion, this embodiment uses the Modal Assurance Criterion (MAC) to perform step-by-step matching and verification of modalities before and after loading. Modalities that do not meet the preset MAC threshold (e.g., 0.8 or 0.9) will be eliminated or reordered to ensure the reliability of the matching.

[0074] 3. Construct whitening mode residual features (corresponding to S3)

[0075] Based on the observed modal parameters before and after loading, and following the method described in step S3 of this invention, whitened modal residual eigenvectors are constructed. These eigenvectors include components such as eigenvalue residuals, mode shape residuals, and modal guarantee criterion (MAC) values. After splicing and whitening of all components, the final whitened modal residual eigenvectors are obtained. (See attached figure.) Figure 2 The S3 step (feature construction) is shown in the diagram.

[0076] 4. Offline sampling and training (corresponding to S2 and S4)

[0077] Sampling interval setting: Actuator equivalent stiffness The sampling interval is set to [ The stiffness variation of each layer of the structure The sampling interval is set to [-0.5, 0.5].

[0078] Training data generation: For each generated sample, a corresponding structural model is first constructed, and then the modal parameters are solved through forward analysis. Based on this, measurement noise is injected into the obtained modal parameters to simulate actual observation conditions. In this embodiment, Gaussian noise is injected into the frequencies and mode shapes respectively to simulate real observation conditions when generating modal data. This method supports multiple noise level settings (e.g., 1%, 3%, 5% standard deviation), and specifically, for generating observation modal data for online identification, the relative standard deviation of the frequency is set to 3%, and the relative standard deviation of the mode shape is set to 5%. Finally, according to the method described in step 3 of this invention, a whitened modal residual feature vector is constructed. and based on the sampled true stiffness variation As the corresponding monitoring signal.

[0079] Inferrer Training: In this embodiment of the invention, the inferrer can be implemented using a neural network structure such as ResNet or Multilayer Perceptron (MLP). Depending on the specific training objective, an appropriate loss function is selected for optimization: if the objective is to obtain a point estimate of stiffness variation, the mean squared error (MSE) loss function is used; if the objective is to obtain a probability output of stiffness variation, the negative log-likelihood (NLL) loss function is used.

[0080] 5. Online recognition process

[0081] For each set of independent observation data, repeat step 3 to construct the whitening mode residual features. And input it into the trained amortization inferrer In this process, point estimates and / or posterior samples of stiffness variation are obtained.

[0082] Results analysis:

[0083] Identification accuracy (see attached document) Figure 4 ): Figure 4 This paper compares the identification results of the method of this invention and the traditional baseline method (which fixes the equivalent stiffness of the actuator to a nominal value) on 20 parameters (i.e., the stiffness of 20 floors) for the true stiffness variation of the structure. The figure shows that the posterior mean curve identified by the method of this invention (blue bar) closely matches the true value (gray bar), and its accuracy is far higher than that of the traditional baseline method (orange bar), which shows a significant deviation from the true value. Quantitative analysis shows that the root mean square error (RMSE) of the method of this invention is 0.001, indicating that it can achieve near-zero error in accurate identification; in contrast, the RMSE of the traditional baseline method is as high as 0.033. This clearly demonstrates that the method of this invention can more accurately locate the stiffness variation of each floor, and the identified posterior mean error is significantly smaller than that of traditional methods that do not consider actuator uncertainties or use fixed actuator stiffness for identification.

[0084] Uncertainty Quantification (see Appendix) Figure 5 ): Figure 5The figure shows the posterior probability density functions for 20 floor stiffness variation parameters. As can be seen from the figure, the posterior PDF distribution obtained by the method of this invention (orange solid line) exhibits a significant advantage over the baseline method (blue dashed line): its curves are generally narrower and have higher peak values, indicating higher concentration and confidence. For example, in most parameters (such as #1 to #20), the peak value of the PDF obtained by the method of this invention (orange solid line) is significantly higher than that of the peak value of the baseline method (blue dashed line), and the distribution range is more compact, reflecting a significant reduction in the uncertainty of stiffness variation estimation. Simultaneously, the center position of the posterior PDF curve (i.e., the posterior mean) of the method of this invention is generally closer to the true value (shown by the vertical dashed line). For example, on the 15th floor (#15), the peak value of the method of this invention is almost aligned with the true value, while the baseline method shows a significant offset. In summary, the method of this invention not only provides more accurate point estimates (as shown in the attached figure), but also... Figure 5 As shown in the figure, it can also provide a more compact posterior distribution that is closer to the true level of uncertainty, effectively quantifying the uncertainty of the recognition results, thereby significantly enhancing the reliability of the recognition results.

[0085] Example 2: Engineering Case of Frame Structure with Actuator Constraints

[0086] This embodiment aims to verify the applicability and effectiveness of the structural stiffness change identification method proposed in this invention in real engineering scenarios using an engineering frame specimen with actuator constraints.

[0087] 1. Engineering background and finite element model (corresponding to S1, and refer to the appendix) Figure 6 Appendix Figure 7 Appendix Figure 8 )

[0088] See attached document Figure 6 (Frame Modal Test Measurement Point Layout Diagram) and Appendix Figure 7 (Schematic diagram of finite element model of frame structure, including actuator constraints) The identification object in this embodiment is a three-story, two-span engineering frame specimen.

[0089] Actuator loading and stiffness uncertainty: such as Figure 7 As shown, the frame specimen is connected to the reaction wall via an actuator on the left and subjected to a quasi-static load. During this process, the equivalent stiffness of the actuator-clamp... This can change and is difficult to accurately obtain through individual calibration. This invention addresses this change. As an uncertainty parameter, it is parametrically represented in the finite element model, and its influence on the structural stiffness identification result is effectively eliminated through marginalization processing in the subsequent offline training stage.

[0090] Finite element model construction: based on Figure 7 For the engineering frame specimen shown, establish its finite element model and follow the attached... Figure 8 The structure is divided into 45 identification regions. This model accurately reflects the geometric dimensions, material properties, and boundary conditions of the frame structure, and can accurately simulate its dynamic characteristics. The stiffness matrix and mass matrix of the model are constructed according to the method described in step S1 of this invention.

[0091] Modal solution and modal matching: Modal analysis is performed on the established finite element model to obtain the eigenvalues ​​and mode shapes of the structure. The modes before loading (baseline state) and after loading (damage or stiffness change state) are matched using the Modal Assurance Criterion (MAC) to ensure the correctness of the modal correspondence.

[0092] 2. Offline sampling and training (corresponding to S2, S4)

[0093] Sampling interval setting: Actuator equivalent stiffness The sampling interval is set to [ The sampling range for structural stiffness variation (damage factor) in each region (45 regions in total) is set to [-0.5, 0.5].

[0094] Training data generation: A large number of training samples are generated for the finite element model of the engineering frame specimen. Each sample contains simulated real stiffness changes and actuator stiffness. Modal parameters are solved through forward analysis, and Gaussian noise is injected to simulate actual observation conditions. In this embodiment, to simulate the noise level of actual engineering tests, preset levels of Gaussian noise are injected into the frequencies and mode shapes. Specifically, the relative standard deviation of the frequency is set to 3%, and the relative standard deviation of the mode shape is set to 5%. Finally, according to the method described in step 3 of this invention, a whitened modal residual feature vector is constructed, and the sampled real stiffness changes are used as the corresponding monitoring signals.

[0095] Inferrer Training: A neural network architecture (e.g., ResNet or MLP) is used as the inferrer for offline training. The mean squared error (MSE) or negative log-likelihood (NLL) loss function is selected for optimization based on the specific training objective.

[0096] 3. Feature Construction and Online Recognition (corresponding to S3, S5)

[0097] Feature Construction: In the actual online identification process, by loading a small amount of measurement data of low-order modal parameters before and after loading, these modal parameters are extracted according to the method described in step S3 of this invention, and MAC matching and whitening residual feature construction are performed. These feature vectors contain components such as eigenvalue residuals, mode shape residuals, and modal guarantee criterion (MAC) values.

[0098] Online identification: The constructed whitening modal residual feature vector is input into the amortized inferrer trained offline. The inferrer will output the posterior mean of the damage factor (stiffness change) for each region (45 regions) and the uncertainty measure (e.g., confidence interval or posterior sample) in real time.

[0099] 4. Recognition Results (Refer to Figures 8 and 9) Figure 10 )

[0100] Identification accuracy and stiffness variation distribution (based on appendix) Figure 9 With appendix Figure 10 (cross-verification)

[0101] Appendix Figure 10 (The actual damage marker diagram) visually illustrates the macroscopic physical damage state of the three-story frame specimen after loading. Cracks are mainly concentrated at beam ends, beam-column joints, and near the horizontal members of the floors, exhibiting obvious spatial non-uniformity (some members / areas have dense cracks, while some areas have sparse cracks or even almost no cracks). This indicates that the structural stiffness degradation does not occur uniformly throughout, but rather manifests as significant stiffness changes in several local areas coexisting with slight or near-zero changes in other areas.

[0102] Corresponding Appendix Figure 9 In the (posterior probability density map of damage factors in frame structures), the method of this invention successfully achieved damage factors for up to 45 local units of the entire structure. The invention provides refined identification of damage distribution. Specifically, the damage distribution identified by this invention covers an extremely wide range, accurately mapping the true "sparse / localized" physical damage characteristics: on the one hand, for attached... Figure 10 In severely damaged areas with dense cracks, the corresponding damage factor identification values ​​deviate significantly from zero, exhibiting severe stiffness degradation (e.g., The peak values ​​are concentrated around 0.55. The peak value is as high as 0.58. The peak value is around 0.42); on the other hand, for the attached Figure 10 In areas with no obvious cracks and no significant damage, the posterior distribution of the corresponding parameters is tightly concentrated in a very small interval close to 0 (e.g., The peak value is below 0.05. The peak values ​​are concentrated at an extremely low level of 0.02.

[0103] This highly differentiated and refined distribution at the level of mathematical parameters perfectly maps the attached... Figure 10The present invention addresses the complex physical state of a real structure, characterized by both localized severe cracking and localized minor damage. From the perspective of consistency between the actual crack location and the location of parameter changes, this invention can accurately pinpoint the main areas where stiffness changes occur and provide a stiffness change distribution that conforms to the physical damage morphology. This fully demonstrates its extremely high accuracy in capturing the spatial distribution of real stiffness changes, rather than mistakenly spreading damage to a large number of crack-free areas.

[0104] Uncertainty Quantification and Reliability (Based on Appendix) Figure 9 (posterior probability distribution characteristics)

[0105] Appendix Figure 9 This fully demonstrates the core advantages of the method in uncertainty quantification. Unlike traditional identification methods that only output a single definite value, this invention comprehensively depicts the statistical characteristics of all 45 parameters through the posterior probability density function (PDF, orange dashed line in the figure). Its main advantages are reflected in the following two specific features:

[0106] First, it possesses extremely high confidence in parameter estimation. In a large number of key parameter subplots (e.g.) to ,as well as to In the region where these parameters are located, the posterior PDF curves exhibit an extremely steep and sharp single-peak shape. Specifically, the peak values ​​(vertical axis) of the PDF for these parameters are generally as high as 40–60 (e.g., ...). Peak value exceeded 60 and The peak value reaches 50), and the horizontal axis span is extremely narrow (usually concentrated in an extremely narrow range with a width of less than 0.05). This indicates that the method of the present invention can still accurately lock these local stiffness changes with a very high degree of confidence under complex conditions of unknown boundary constraints, and the estimated random fluctuations and uncertainties are reduced to an extremely low level.

[0107] Secondly, it accurately reflects the differences in sensitivity to structural information. (Combined with appendix) Figure 10 It is known that the actual distribution of cracks exhibits engineering patterns of local concentration and correlation with the stress path of the component, leading to differences in the amount of information in the observation data at different locations. (Appendix) Figure 10 This difference was objectively quantified: for some parameters (such as...) , The PDF curves of these models are relatively wide (horizontal axis span can reach 0.3 to 0.4) and have low peak values ​​(vertical axis peak values ​​are only between 6 and 8), even exhibiting a broad multi-peak shape. This reflects the model's weak ability to identify the degree of damage at these specific locations, objectively presenting a state of "insufficient evidence." The method of this invention does not forcibly provide a potentially misleading absolute single value, but rather quantifies and explicitly expresses this uncertainty through probability distribution, thereby greatly improving the interpretability and engineering reliability of the conclusions.

[0108] In summary, the method of this invention can not only accurately depict complex spatial damage distributions, but also transparently and rigorously quantify the reliability of the identification results by providing a compact and well-defined posterior probability distribution, greatly enhancing the scientific basis for engineering diagnosis.

Claims

1. A method for identifying structural parameter changes using two modal differences under uncertain boundary constraints, characterized in that, Includes the following steps: S1. Establish the equivalent stiffness of the actuator containing the unknown actuator. A parameterized model of structural dynamics is defined, defining a parameter vector for structural stiffness variation. The target to be identified is the change in stiffness of each floor; among which For the unknown actuator equivalent stiffness This is a vector of structural stiffness variation parameters. For the number of floors in the structure, For the first Layer stiffness variation parameters ; S2. Offline training phase: Within a preset prior range, the equivalent stiffness of the actuator is... With structural stiffness variation parameter vector Random sampling is performed, and the pre-loading stiffness matrix is ​​obtained through forward analysis for each set of sampled parameters. With the stiffness matrix after loading At the same time, the mass matrix is ​​obtained. And by solving the generalized eigenvalue problem: , ;in , Before / after loading Mode shape, , Before / after loading eigenvalues ​​of order 1 , The modal order used; eigenvalues ​​according to the noise model. With mode shape Measurement noise is added to obtain the observed modal parameters; S3. Calculate the eigenvalue residuals, mode shape residuals, and mode guarantee criterion MAC based on the observed modal parameters before and after loading. Then, the eigenvalue residuals, mode shape residuals, and modal guarantee criterion (MAC) are concatenated in a preset order to construct the whitened modal residual eigenvector. ; S4. Train the amortization inferr using supervised learning or a conditional generation model. To make it possible Point estimation mapping or The posterior mapping; during training, training sample pairs For monitoring signals, and not to As an input variable, make Marginalized in the training distribution; where To amortize the inferrer, It is a posterior distribution; S5. Online Application Phase: Obtain modal observation parameters before / after actual loading, and repeat step S3 to obtain the modal residual feature vector. And input the trained Output structural stiffness variation The point estimate or posterior distribution / confidence interval.

2. The method according to claim 1, characterized in that, In step S1: the structural dynamics model is The stiffness matrices before and after loading are expressed as follows: (Equivalent model of a multi-story shear wall or finite element model of a frame) , ,in For the first Layer baseline stiffness, For the first Layer stiffness submatrix This is the actuator stiffness submatrix.

3. The method according to claim 1, characterized in that, In step S2, the modal parameters are obtained through the generalized eigenvalue problem, i.e.: ,in For the mode shape matrix, The eigenvalues ​​are used; and the modal guarantees (MAC) are applied to perform stepwise matching of the loaded modes, wherein the MAC is defined as: ,in For the first The first-order mode guarantee criterion, where the superscript T denotes vector transpose.

4. The method according to claim 3, characterized in that, The whitening mode residual feature vector mentioned in step S3 Includes the following components and is assembled in a preset order: (a) Eigenvalue residuals: , ,in For eigenvalue residuals, As a measure of whitening, The eigenvalue is the relative noise coefficient. For the first The random sampling, at the... The loaded structure identified at each measuring point, degree of freedom, or measurement location. Rank features, For the first The random sampling, at the... The pre-loading structure identified at each measuring point, degree of freedom, or measurement location. Rank features; (b) Mode shape residuals: , ,in For mode shape residuals, This is a measure of modal noise. To prevent zero threshold, For modal weighting factors, Before loading the first The first mode shape The components at each measuring point For the first time after loading The first mode shape The components of each measuring point; (c) Modal guarantee criterion ; Concatenate the residual feature vectors of the whitening mode in sequence. : ,in It is a vectorization operator.

5. The method according to claim 4, characterized in that, The amortization inferrer described in step S4 The residual network ResNet structure or the multilayer perceptron (MLP) structure is adopted, and the training sample pairs are used. As a supervisory signal, the point estimation is trained by minimizing the mean squared error loss: ,in For mean square error loss, The number of training samples, It is a 2-norm; when training the output probability model, it is trained by minimizing the negative log-likelihood: ,in For negative log-likelihood loss, The number of training samples, For conditional probability models, For the first The input feature vectors of each training sample are concatenated sequentially to produce the whitening mode residual feature vector. For the first The true structural parameter vector or label corresponding to each training sample is a randomly sampled structural parameter, including the actuator equivalent stiffness constraint parameters. And the structural stiffness variation parameter vector.

6. The method according to claim 1, characterized in that, In step S4, when the output posterior distribution... At that time, a generator is constructed using one of the following methods: conditional flow matching model, conditional Rectified Flow, quantile regression, or deep ensemble. After training, the generator is used to perform tests on a given conditional flow. Sampling to obtain The posterior sample or the confidence interval is calculated.

7. The method according to claim 1, characterized in that, In step S5, the set of feature vectors obtained from multiple independent measurements The ensemble averaging or Bayesian posterior synthesis is employed (e.g., combining posteriors based on independent observations under probability output), where For the first The eigenvectors corresponding to each independent measurement , For the number of independent measurements.

8. A structural stiffness change identification system under unknown actuator stiffness conditions, characterized in that, include: The module includes a data acquisition module, a modal parameter preprocessing and matching module, a feature construction module, an amortization inference module, and a result output module. The amortization inference module has a built-in recognition model trained according to the method of any one of claims 1 to 7. The modules are connected and work together according to steps S1 to S5.

9. An electronic device comprising a processor, a memory, and a program stored in the memory and executable on the processor, characterized in that, When the program is executed by the processor, it implements the steps of the method described in any one of claims 1 to 7.

10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by a processor, it implements the steps of the method described in any one of claims 1 to 7.

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