Structural displacement reconstruction method and system based on finite element model correction, and medium

Abstract

This invention provides a structural displacement reconstruction method, system, and medium based on finite element model correction. The method includes: acquiring a dual-network strain modal prediction model, including a first network model and a second network model; inputting the current measured modal information of the structure under test into the first network model to invert and obtain the predicted finite element model parameters of the preset finite element model; inputting the predicted finite element model parameters into the second network model to predict the predicted strain modes of the structure; solving for the modal coordinates based on the measured strain response and predicted strain modes during the operation of the structure under test; and reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure. Using this invention, indirect reconstruction from measurable strain response to target displacement is achieved, improving the overall accuracy of displacement reconstruction of the structure under test.

Description

Technical Field

[0001] This invention relates to the field of structural health monitoring technology, specifically to a structural displacement reconstruction method, system, and medium based on finite element model correction. Background Technology

[0002] As the core load-bearing unit in engineering, structures are widely used in various engineering scenarios, such as bridges and slab-beam composite structures. Their displacement response is a crucial characteristic for structural condition assessment and safety monitoring. Existing displacement acquisition methods mainly include direct measurement methods such as laser displacement measurement, visual measurement, and contact displacement measurement. However, these methods have high requirements for the measurement environment, installation space, and reference benchmarks, limiting their application in complex boundary conditions and long-term online monitoring scenarios. In contrast, structural strain response is easier to measure, and methods that indirectly reconstruct structural displacement by measuring strain have broad application value. Furthermore, displacement mode and frequency information can be readily obtained through modal testing. Therefore, indirectly inferring structural parameters based on measurable modal information and combining it with measured strain information to complete displacement reconstruction has become an important direction for technological development.

[0003] However, existing technologies still have the following shortcomings in displacement reconstruction of plate-beam composite structures: First, finite element models are usually established based on design parameters, while real structures are affected by factors such as manufacturing errors, local stiffness deviations and boundary changes, resulting in significant mismatch between the model and the actual object; Second, strain modes are the key basis for displacement reconstruction, but it is difficult to directly measure strain modes with high precision, making traditional mode conversion methods lack reliable strain mode support. Therefore, it is necessary to construct a method that can effectively solve the finite element model mismatch problem, overcome the difficulty in obtaining strain modes, and improve the displacement reconstruction accuracy of structures. Summary of the Invention

[0004] In view of this, it is necessary to provide a structural displacement reconstruction method, system and medium based on finite element model correction, in order to solve the technical problem of low displacement reconstruction accuracy in existing technologies.

[0005] To address the aforementioned technical problems, in a first aspect, the present invention provides a structural displacement reconstruction method based on finite element model correction, comprising: A pre-constructed dual-network strain modal prediction model is obtained, wherein the dual-network strain modal prediction model includes a cascaded first network model and a second network model. The first network model is used to establish the mapping relationship between the measured modal information of the structure to be tested and the parameters of the corresponding preset finite element model. The second network model is used to establish the mapping relationship between the finite element parameters and the strain modes of the structure. The current measured modal information of the structure is input into the first network model, and the predicted finite element model parameters of the preset finite element model are obtained by inversion. The predicted finite element model parameters are input into the second network model to predict the predicted strain modes of the structure. Based on the measured strain response and the predicted strain modes during the operation of the structure, the modal coordinates are solved. Based on the modal coordinates and the measured displacement modal information of the structure, the dynamic or static displacement of the structure is reconstructed.

[0006] In one possible implementation, the prediction step for predicting finite element model parameters includes: Modal analysis was performed on the measured frequency response information, and the corresponding order frequency and modal information were extracted.

[0007] Modal analysis is performed on the current measured modal information to extract the measured point displacement modal sequence and measured frequency data of a preset order; Feature extraction is performed on the measured frequency data to obtain frequency features; Temporal and spatial correlation features are extracted from the displacement mode sequence of the measurement point to obtain displacement mode features; The frequency features and the displacement mode features are fused to obtain the fused features; The parameters of the finite element model are predicted based on the fusion features.

[0008] In one possible implementation, the prediction step for the predicted strain modes includes: The finite element model parameters predicted by the first network model are subjected to feature interaction and enhancement to obtain interactive enhancement features; Temporal correlation features are extracted from the interaction enhancement features to obtain temporal features; The strain mode is predicted based on the time-series characteristics.

[0009] One possible implementation also includes: Sampling is performed within a preset range of the parameters to be inverted in the preset finite element model to generate multiple sets of finite element model parameter samples; Modal analysis was performed on the parameter samples of each group of finite element models to extract the corresponding displacement modal features, frequency features, and strain modal features; Based on the displacement modal features and frequency features, a first training sample set is constructed, and the first network model is trained to fit the mapping relationship between the measured modal information and the finite element model parameters. A second training sample set is constructed based on the finite element model parameter samples and the corresponding strain mode features, and the second network model is trained to fit the mapping relationship between the finite element model parameters and the strain modes.

[0010] In one possible implementation, the finite element model parameters of the preset finite element model are structural parameters characterizing the structure, including at least one of material parameters, geometric parameters, and boundary parameters.

[0011] In one possible implementation, solving for the modal coordinates based on the measured strain response and the predicted strain modes during the structure's operation includes: Solve for the modal coordinates using the following formula: ; Where t is the time variable, For modal coordinates, To measure the strain response, Let q be the predicted strain mode, and q be the modal coordinate variable to be solved.

[0012] In one possible implementation, reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure includes: Reconstruct dynamic or static displacements using the following formula: ; in, For dynamic or static displacement, To measure displacement modal information, These are modal coordinates.

[0013] In one possible implementation, after reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure, the method further includes: If a reconstruction command for the full-field displacement of the structure is received, the preset finite element model is corrected based on the prediction parameters output by the dual-network strain modal prediction model to obtain the corrected finite element model. The full-field displacement mode matrix is ​​extracted using the modified finite element model. Based on the full-field displacement mode matrix and the modal coordinates, the full-field displacement distribution of the structure is reconstructed.

[0014] Secondly, the present invention also provides a structural displacement reconstruction system based on finite element model correction, comprising: An acquisition unit is used to acquire a pre-constructed dual-network strain mode prediction model, wherein the dual-network strain mode prediction model includes a cascaded first network model and a second network model. The first network model is used to establish a mapping relationship between the measured modal information of the structure to be tested and the parameters of the corresponding preset finite element model. The second network model is used to establish a mapping relationship between the parameters of the finite element model and the strain modes of the structure. The first prediction unit is used to input the current measured modal information of the structure into the first network model and invert to obtain the prediction parameters of the preset finite element model; The second prediction unit is used to input the prediction finite element model parameters into the second network model to predict the predicted strain mode of the structure. The determination unit is used to solve for the modal coordinates based on the measured strain response and the predicted strain modes during the operation of the structure. The reconstruction unit is used to reconstruct the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure.

[0015] Thirdly, the present invention also provides an electronic device, including a memory and a processor, wherein, The memory is used to store programs; The processor, coupled to the memory, is used to execute the program stored in the memory to implement the steps in the structural displacement reconstruction method based on finite element model correction described in any of the above implementations.

[0016] Fourthly, the present invention also provides a computer-readable storage medium for storing a computer-readable program or instruction, which, when executed by a processor, can implement the steps in the structural displacement reconstruction method based on finite element model correction described in any of the above implementations.

[0017] The beneficial effects of this invention are: The structural displacement reconstruction method based on finite element model correction provided by this invention obtains a pre-constructed dual-network strain mode prediction model, which includes a cascaded first network model and a second network model. The first network model is used to establish the mapping relationship between the measured modal information of the structure under test and the parameters of the corresponding preset finite element model. The second network model is used to establish the mapping relationship between the finite element model parameters and the strain modes of the structure. The current measured modal information of the structure under test is input into the first network model, and the predicted finite element model parameters of the preset finite element model are obtained through inversion, thus correcting the parameters of the initial finite element model and making the corrected model closer to the real structure. This effectively reduces the mismatch error between the real structure and the initial finite element model. The predicted finite element model parameters are input into the second network model to predict the predicted strain modes of the structure, achieving efficient mapping from finite element model parameters to strain modes. This effectively avoids the difficulties of direct measurement and can obtain a strain mode basis that matches the real structure, providing reliable support for subsequent modal coordinate solving. Based on the measured strain response and predicted strain modes during the operation of the structure under test, the modal coordinates are solved. Based on modal coordinates and measured displacement modal information of the structure, the dynamic or static displacement of the structure is reconstructed, realizing indirect reconstruction from measurable strain response to target displacement, thus improving the overall accuracy of displacement reconstruction of the structure under test. Attached Figure Description

[0018] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0019] Figure 1 A schematic flowchart of an embodiment of the structural displacement reconstruction method based on finite element model correction provided by the present invention; Figure 2 The overall flowchart of the structural displacement reconstruction method provided by the present invention; Figure 3 A schematic diagram of the structure of the first network model provided by the present invention; Figure 4 This is a schematic diagram of the structure of the second network model provided by the present invention; Figure 5 A schematic diagram of the structural displacement reconstruction system based on finite element model correction provided by the present invention. Detailed Implementation

[0020] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0021] In the description of the embodiments of the present invention, unless otherwise stated, "a plurality of" means two or more.

[0022] The terms "first," "second," etc., used in the embodiments of this invention are for descriptive purposes only and should not be construed as indicating or implying their relative importance or implicitly specifying the number of technical features indicated. Therefore, a technical feature defined with "first" or "second" may explicitly or implicitly include at least one of that feature.

[0023] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of the invention. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0024] This invention provides a structural displacement reconstruction method, system, and medium based on finite element model correction, which are described below.

[0025] The execution subject of the structural displacement reconstruction method based on finite element model correction in this application embodiment can be the structural displacement reconstruction system based on finite element model correction provided in this application embodiment, or an electronic device that integrates the structural displacement reconstruction system based on finite element model correction. This application embodiment does not make specific limitations in this regard.

[0026] Figure 1 This is a schematic flowchart of an embodiment of the structural displacement reconstruction method based on finite element model correction provided by the present invention, as shown below. Figure 1 As shown, the structural displacement reconstruction method based on finite element model correction includes: S101. Obtain a pre-constructed dual-network strain mode prediction model, wherein the dual-network strain mode prediction model includes a cascaded first network model and a second network model. The first network model is used to establish the mapping relationship between the measured modal information of the structure to be tested and the parameters of the corresponding preset finite element model. The second network model is used to establish the mapping relationship between the parameters of the finite element model and the strain modes of the structure.

[0027] The structure to be measured refers to the engineering structural entity that requires displacement reconstruction. This structure can be various engineering structures such as bridges and slab-beam composite structures. In practical applications, sensors need to be deployed on the structure to collect its measured modal information and strain response data during operation, which will be used for subsequent finite element model correction and displacement reconstruction.

[0028] The dual-network strain mode prediction model is a deep learning model pre-built in this embodiment, used to predict the strain modes of the structure based on the measured modal information of the structure to be tested.

[0029] The first network model is the first sub-network in the dual-network strain modal prediction model. It is used to establish the mapping relationship between the measured modal information of the structure under test and the finite element model parameters of the corresponding preset finite element model. Specifically, this model takes the measured modal information (including the displacement modal sequence of the measurement points and the measured frequency data) as input and outputs finite element model parameters that can characterize the true structural state of the structure under test. Through this mapping relationship, the first network model realizes the parameter correction of the preset finite element model.

[0030] The second network model is the second sub-network in the dual-network strain mode prediction model. Its function is to establish a mapping relationship between the finite element model parameters and the strain modes of the structure under test. Specifically, this model takes the finite element model parameters output by the first network model as input and outputs the predicted strain modes of the structure under test. Through this mapping relationship, the second network model achieves efficient inference from structural parameters to strain modes, obtaining the strain modes without direct measurement.

[0031] The first network model and / or the second network model is a deep neural network, a convolutional neural network, or a recurrent neural network.

[0032] A pre-defined finite element model is a numerical analysis model established based on the design parameters or initial geometric information of the structure to be measured. This model can be based on design drawings and standard parameters, without considering manufacturing errors, local stiffness deviations, boundary variations, or other factors. The pre-defined finite element model contains several adjustable finite element model parameters, including material parameters (such as elastic modulus and density), geometric parameters (such as plate thickness and beam height), and boundary parameters (such as support stiffness). The predicted finite element model parameters obtained through inversion from the first network model can be used to correct the pre-defined finite element model, making it closer to the actual structure.

[0033] Specifically, a pre-constructed dual-network strain modal prediction model is obtained. This dual-network strain modal prediction model includes a cascaded first network model and a second network model. The first network model is used to establish the mapping relationship between the measured modal information of the structure under test and the parameters of the corresponding preset finite element model. The second network model is used to establish the mapping relationship between the parameters of the finite element model and the strain modes of the structure. This model has been trained with a large number of finite element simulation samples before application and has the ability to invert the finite element model parameters from the measured modal information and predict the strain modes from the finite element model parameters.

[0034] S102. Input the current measured modal information of the structure into the first network model, and invert to obtain the prediction parameters of the preset finite element model.

[0035] Among them, the predicted finite element model parameters can characterize the true structural state of the structure under test, including but not limited to material parameters, geometric parameters and boundary parameters.

[0036] Measured modal information can be obtained by arranging sensors on the structure and conducting modal tests.

[0037] Specifically, the current measured modal information of the structure under test is input into the first network model. The first network model inverts the input measured modal information to obtain the predicted parameters of the preset finite element model, thus correcting the parameters of the initial finite element model and making the corrected model closer to the real structure. This effectively reduces the mismatch error between the real structure and the initial finite element model.

[0038] S103. Input the predicted finite element model parameters into the second network model to predict the predicted strain modes of the structure.

[0039] Among them, the strain mode is the spatial derivative of the displacement mode, which describes the strain distribution of the structure under each mode.

[0040] Specifically, the predicted finite element model parameters output by the first network model are input into the second network model. The second network model predicts the predicted strain modes of the structure based on the input finite element model parameters, realizing an efficient mapping from finite element model parameters to strain modes. The strain modes can be obtained without direct measurement, thus effectively avoiding the difficulties of direct measurement. Moreover, it can obtain a strain mode basis that matches the real structure, providing reliable support for subsequent modal coordinate solving.

[0041] Understandably, by constructing a cascaded first and second network model, this embodiment forms a two-step chain algorithm framework of "inversion parameters - predicted strain modes". This framework decomposes the complex displacement reconstruction problem into sub-steps with clear physical meanings, each step being supported by a corresponding physical model, thus balancing the fitting ability of data-driven methods with the interpretability of structural dynamics models.

[0042] S104. Based on the measured strain response and the predicted strain mode during the operation of the structure, solve for the modal coordinates.

[0043] The measured strain response changes over time, reflecting the real-time deformation state of the structure under dynamic loads. During the operation of the structure, strain sensors arranged on the structure can be used to collect the measured strain response.

[0044] Modal coordinates are weighted coefficients that describe the contribution of each mode to the structural response. According to the principle of modal superposition, the strain response of a structure can be expressed as a linear combination of strain modes, and the combination coefficients are the modal coordinates.

[0045] Specifically, the modal coordinates can be obtained by multiplying the pseudo-inverse of the predicted strain mode with the measured strain response.

[0046] S105. Based on the modal coordinates and the measured displacement modal information of the structure, reconstruct the dynamic displacement or static displacement of the structure.

[0047] Among them, the measured displacement modal information can be obtained through modal tests, reflecting the displacement distribution pattern of the structure under each mode.

[0048] Specifically, based on the modal superposition principle, the measured displacement modal information can be multiplied by the solved modal coordinates to obtain the dynamic or static displacement response of the structure. This achieves indirect reconstruction from the measurable strain response to the target displacement. Because the finite element model parameters obtained by the inversion of the first network model can characterize the real structural state, the strain modes predicted by the second network model avoid the deviation of direct measurement, and the accuracy of each link is transferred to the reconstructed dynamic or static displacement, the overall accuracy of the displacement reconstruction of the structure under test is improved.

[0049] Furthermore, this embodiment avoids directly outputting displacement from a black-box network. By decomposing displacement reconstruction into multiple sub-steps with clear physical meaning, such as parameter inversion and strain prediction, it can leverage the nonlinear fitting capability of data-driven methods while preserving the interpretability of the structural dynamics model.

[0050] In summary, the structural displacement reconstruction method based on finite element model correction provided in this invention obtains a dual-network strain mode prediction model containing a cascaded first network and a second network, and sequentially executes operations of inversion parameters, predicted strain modes, and displacement reconstruction. This forms a two-step chain algorithm framework with clear physical meaning, improving the physical interpretability of the displacement reconstruction process. Inputting the measured modal information into the first network inversion yields the predicted finite element model parameters, enabling the inversion results to characterize the true structural state and effectively reducing the mismatch error between the real structure and the initial finite element model. Inputting the predicted finite element model parameters into the second network predicts the strain modes, achieving efficient mapping from structural parameters to strain modes and avoiding the engineering problem of difficult direct measurement of strain modes. Based on the solved modal coordinates and measured displacement modal information, dynamic or static displacement is reconstructed, achieving stable and accurate reconstruction from measurable strain response to target displacement, thus improving the overall accuracy of displacement reconstruction.

[0051] like Figure 2 The diagram shown is the overall flowchart of the structural displacement reconstruction method. The specific process is as follows: The measured frequencies and displacement modes, along with the frequencies and displacement modes of the finite element model, are input into the finite element model correction network, which outputs the finite element model parameters. These finite element model parameters are then input into the strain mode regression network, which outputs the finite element strain modes. In practical applications, the measured frequencies and displacement modes are input into the finite element model correction network, which outputs the finite element model parameters. These parameters are then input into the strain mode regression network, which outputs the network's predicted strain modes.

[0052] The network-predicted strain modes and the measured strain are input into the mode conversion module, which processes the measured displacement modes and finally outputs the predicted displacement.

[0053] In one specific implementation, taking a plate-beam composite structure as an example, the displacement reconstruction process includes: Step 1: Establish a parametric finite element model of the plate-beam composite structure. The model includes the plate region and the beam region connected to it. Displacement modal measurement points are set at several locations on the structure; frequency information extraction points are set at the structural boundaries or representative response locations; and strain response measurement points are set at the target strain acquisition locations.

[0054] First, construct a set of candidate finite element model parameters based on the set of structural design variables. Then, determine the parameter vector to be inverted based on sensitivity analysis, correlation analysis, or empirical selection principles.

[0055] (1) In equation (1), p is the parameter vector of the finite element model to be inverted;p i For the first i One parameter to be inverted; m The number of parameters to be inverted.

[0056] Step 2: Construct a finite element simulation sample set for parameter inversion. Sampling is performed within a preset range for each parameter to be inverted, generating multiple sets of finite element model parameter samples. Modal analysis is performed on each set of parameter samples to extract the corresponding displacement modal features and frequency features, and a training sample set for the first network is constructed. The displacement modal features preferably use a displacement modal matrix composed of N displacement modal measurement points and an L-order mode, and the frequency features preferably use the frequency vector corresponding to the 6th order mode.

[0057] (2) (3) In equation (2), The displacement mode characteristic matrix; φ u,i For the first i The displacement mode vector; N is the number of displacement mode measurement points; S is the selected mode order.

[0058] In equation (3), For the first i The order is the first i Frequency data corresponding to the first displacement mode vector.

[0059] (4) In equation (4), For the first k Group 1 network training samples; For the first k The displacement modal feature matrix of the sample group; For the first k Frequency feature vector of a group of samples; For the first k The finite element model parameter vector corresponding to the group of samples; k This is the sample number.

[0060] Step 3: Train the first network model and establish the mapping relationship between displacement modes and frequencies and finite element model parameters. Based on the training samples constructed in Step 2, train the first network model to establish the mapping relationship between displacement mode features and frequency features and finite element model parameters.

[0061] (5) In equation (5), The parameter vector of the finite element model obtained from the prediction of the first network; f1(·) is the nonlinear mapping function of the first network; Φ u and ω These are the input displacement mode matrix and frequency vector, respectively.

[0062] Correspondingly, the training objective function of the first network can be the parameter prediction error loss function.

[0063] (6) In equation (6), L 1 represents the parameter prediction error loss function of the first network; N p is the total number of training samples; (k) For the first k The true parameter vector of the group of samples; For the first k The predicted parameter vector of the group of samples; ||·|2 is the L2 norm.

[0064] By training on finite element simulation samples, the first network acquires the ability to invert the parameters of the finite element model based on the measured displacement modes and measured frequency information, thereby realizing the parameter correction of the finite element model of the real structure.

[0065] Step 4: Construct a finite element simulation sample set for strain mode prediction. For the parameterized finite element model established in Step 1, extract the corresponding strain mode samples after parameter sampling to form the training sample set for the second network. Let the... k If the strain modes corresponding to the parameter samples of the finite element model are a set of strain mode matrices, then the training samples of the second network consist of parameter vectors and strain modes.

[0066] (7) In equation (7), For the first k Group 2 network training samples; p (k) For the first k The finite element model parameter vector corresponding to the group of samples; For the first k The strain modes corresponding to the group of samples; k This is the sample number.

[0067] For the parameterized finite element model established in step one, after parameter sampling, the corresponding strain mode samples are further extracted to form the training sample set of the second network. Let the first... k If the strain modes corresponding to the parameter samples of the finite element model are a set of strain mode matrices, then the training samples of the second network consist of parameter vectors and strain modes.

[0068] Step 5: Train the second network model and establish the mapping relationship from finite element model parameters to strain modes. Based on the training samples constructed in Step 4, train the second network model and establish the mapping relationship from finite element model parameters to strain modes.

[0069] (8) In equation (8), To predict strain modes; f 2(·) is the nonlinear mapping function of the second network; p is the input finite element model parameter vector.

[0070] In this system, the finite element model parameter vector serves as the input to the second network, and the predicted strain modes serve as the output of the second network.

[0071] Correspondingly, the training objective function of the second network can be the strain mode prediction error loss function.

[0072] (9) In equation (9), L2 is the strain mode prediction error loss function of the second network; N The total number of training samples; For the first k The true strain modes of the sample group; For the first k Predicted strain modes of the sample group.

[0073] This step establishes a nonlinear mapping relationship between finite element model parameters and strain modes, enabling further inference of strain modes using the predicted finite element model parameters in practical applications.

[0074] Step Six: Obtain the measured displacement modes and measured frequency information, and invert the finite element model parameters. Conduct modal tests on the actual plate-beam composite structure to obtain the measured displacement modal characteristics and corresponding measured frequency information. Input the measured displacement modal characteristics and measured frequency information into the first network model to obtain the predicted finite element model parameter vector of the structure.

[0075] (10) In equation (10), This refers to the parameter vector of the finite element model obtained by inversion based on measured modal information. These are the measured displacement modal characteristics; ω m To measure the frequency characteristics, the parameters of the finite element model of the real structure are corrected.

[0076] Step 7: Infer the strain modes based on the predicted finite element model parameters. Input the predicted finite element model parameter vector obtained in Step 6 into the second network model to obtain the predicted strain modes.

[0077] (11) In equation (11), This step enables the inference of strain modes from the corrected structural parameters to the strain modes, thus avoiding the difficulty of directly measuring the strain modes with high precision.

[0078] Step 8: Acquire measured strain response and establish mode transformation relationship. During the actual operation of the structure, use strain sensors to acquire the measured strain response of the structure. Using the strain modes predicted in Step 7 as the strain mode basis, the relationship between strain response and modal coordinates can be established.

[0079] (12) In equation (12), ε(t) For a moment t The measured strain response vector; For predicting strain modal basis; q( t ( ) for time t The modal coordinate vector, where the modal coordinate vector is the variable to be determined.

[0080] Step 9: Solve for modal coordinates using mode transformation: (13) In equation (13), (t) represents the modal coordinate estimate obtained after regularization; arg min_q(·) represents minimization with respect to q.

[0081] Furthermore, the above regularization problem can be written in analytical form: (14) In equation (14), (t) represents the analytical solution for the modal coordinates; for The false rebellion.

[0082] Step 10: Reconstruct the actual displacement based on the displacement modes and modal coordinates. Using the measured high-fidelity displacement modes and the modal coordinates obtained in Step 9, the dynamic or static displacement of the structure can be reconstructed.

[0083] (15) In equation (14), û(t) is the vector of dynamic or static displacement obtained by reconstruction; For the measured high-fidelity displacement mode matrix; (t) represents the modal coordinate vector obtained in step nine. The reconstructed result is the time history of the dynamic or static displacement of the target measurement point, key node, or target region.

[0084] In some embodiments of the present invention, the prediction step for predicting finite element model parameters includes: performing modal analysis on the current measured modal information to extract a preset order of measurement point displacement modal sequence and measured frequency data; performing feature extraction on the measured frequency data to obtain frequency features; extracting temporal and spatial correlation features from the measurement point displacement modal sequence to obtain displacement modal features; fusing the frequency features and the displacement modal features to obtain fused features; and predicting the finite element model parameters based on the fused features.

[0085] The measured modal information refers to the response data collected from the structure under test through modal testing, including the displacement mode sequence at measurement points and the measured frequency data. The displacement mode sequence at measurement points refers to the displacement mode shape data collected at multiple measurement points on the structure, reflecting the displacement distribution of the structure under each mode; the measured frequency data refers to the natural frequency values ​​of the structure under each mode.

[0086] Specifically, after inputting the current measured modal information into the first network model, the first network model first extracts features from the measured frequency data to obtain frequency features. These frequency features are used to characterize the frequency distribution information of the structure under each modal order. Simultaneously, the first network model extracts temporal and spatial correlation features from the displacement modal sequence of the measurement points to obtain displacement modal features. The temporal features refer to the variation law of displacement modal data with modal order, while the spatial features refer to the displacement correlation relationship between different measurement points. Subsequently, the first network model fuses the frequency features and displacement modal features to obtain fused features. This fusion process integrates frequency domain information and spatial domain information, so that the fused features simultaneously contain the frequency characteristics and mode shape characteristics of the structure. Finally, the first network model predicts finite element model parameters based on the fused features. These finite element model parameters can characterize the true structural state of the structure under test.

[0087] Understandably, this embodiment extracts features from the measured frequency data and the displacement mode sequence of the measurement point, and fuses the extracted frequency features with the displacement mode features, so that the first network model can simultaneously use the frequency information and mode shape information of the structure to perform parameter inversion, thereby improving the accuracy of parameter inversion of the finite element model.

[0088] In one specific implementation, such as Figure 3The diagram shown is a schematic representation of the first network model. This first network model is used to invert the finite element model parameters based on the measured modal information of the structure under test. It includes a frequency encoder, a recurrent neural network layer, an average pooling layer, a feature fusion unit, and a parameter prediction decoder.

[0089] The frequency encoder takes measured frequency data as input and uses a multilayer perceptron as its basic network structure. It contains linear layers and activation functions to extract features from the frequency data and output frequency features.

[0090] The input to the recurrent neural network layer is the displacement mode sequence of the measurement point, and its basic network structure is a bidirectional gated recurrent unit. This layer extracts the implicit temporal dependencies and spatial correlation features in the sequence by performing forward and backward processing on the displacement mode sequence, and outputs preliminary features.

[0091] The average pooling layer is connected to the recurrent neural network layer to receive the preliminary features output by the recurrent neural network layer, and then performs global average pooling on them to compress the sequence dimension and output displacement mode features.

[0092] The feature fusion unit is connected to the frequency encoder and the average pooling layer respectively, and is used to concatenate the frequency features and displacement mode features in terms of dimensions to output fused features.

[0093] The parameter prediction decoder is connected to the feature fusion unit. Its basic network structure is a fully connected neural network, which includes a normalization layer to predict the parameters of the finite element model based on the fused features.

[0094] In practical applications, measured frequency data is input to a frequency encoder and processed by a multilayer perceptron to obtain frequency features. The displacement modal sequence of the measurement points is input to a recurrent neural network layer, processed by a bidirectional gated recurrent unit, and then subjected to global average pooling to obtain displacement modal features. A feature fusion unit concatenates the frequency features and displacement modal features dimensionally to form fused features. A parameter prediction decoder receives the fused features, processes them through a fully connected neural network, and outputs predicted values ​​for the finite element model parameters.

[0095] Through the above structure, the first network model can simultaneously utilize the structure's frequency and mode shape information for parameter inversion. The introduction of bidirectional gated recurrent units enables the model to learn the temporal patterns and spatial correlations in the displacement mode sequence, while the average pooling layer effectively compresses the feature dimension, reducing subsequent computational load. The fusion of frequency and displacement mode features allows the model to comprehensively predict parameters using multi-source information, improving the accuracy of finite element model parameter inversion.

[0096] In some embodiments of the present invention, the step of predicting the strain mode includes: performing feature interaction and enhancement on the finite element model parameters predicted by the first network model to obtain interactive enhancement features; extracting temporal correlation features from the interactive enhancement features to obtain temporal features; and predicting the strain mode based on the temporal features.

[0097] Feature interaction refers to the multi-dimensional feature crossing and fusion of the input finite element model parameters in order to uncover the nonlinear correlation between the parameters.

[0098] Temporal correlation features refer to the dependencies between parameters or implicit states extracted from parameter sequences or implicit state sequences, which are used to capture the dynamic mapping between finite element model parameters and strain modes.

[0099] Strain modes refer to the strain distribution pattern of a structure under various modes. They are the spatial derivatives of displacement modes and are used to describe the spatial distribution pattern of the strain field during vibration.

[0100] Specifically, in this embodiment, the operation of predicting strain modes is performed in the second network model. The finite element model parameters output from the first network model are input into a feature interaction layer. This layer uses a multi-head attention mechanism to perform feature interaction and enhancement processing on the finite element model parameters, obtaining interactively enhanced features. The multi-head attention mechanism can simultaneously capture the interdependencies between parameters from multiple subspaces, enhancing the expressive power of the features. Subsequently, the interactively enhanced features are input into a temporal feature extraction layer. This layer uses a bidirectional gated recurrent unit to extract temporal correlation features from the interactively enhanced features, obtaining temporal features. The bidirectional gated recurrent unit can simultaneously utilize forward and backward sequence information, more comprehensively capturing the temporal dependencies between features. Finally, the temporal features are input into a result decoder, which is composed of a fully connected neural network, to predict the strain modes of the output structure based on the temporal features.

[0101] Understandably, this embodiment, through feature interaction and enhancement processing of the finite element model parameters, can fully explore the nonlinear correlations between the parameters and enhance the richness of feature representation. By extracting the temporal correlation features of the interactive enhancement features, the dynamic mapping law between the finite element model parameters and strain modes is effectively captured. Based on the above processing, this embodiment achieves efficient mapping from finite element model parameters to strain modes, avoiding the difficulties of directly measuring strain modes, and improving the accuracy of strain mode prediction.

[0102] In one specific implementation, such as Figure 4The diagram shows the second network model. This second network model is used to map the finite element model parameters to strain modes. The input to the second network model is the finite element parameters, which are multi-dimensional physical parameter vectors. The input parameters first enter the feature interaction fusion layer, which uses a multi-head attention mechanism as the basic network to perform feature interaction and fusion processing on the input finite element model parameters, fusing three-way sequence information to uncover the nonlinear correlation between the parameters.

[0103] The output of the feature interaction fusion layer enters the temporal feature extraction layer. This layer uses a bidirectional gated recurrent unit as the basic network to extract forward and backward temporal spatial correlation features and capture the dynamic mapping law between finite element model parameters and strain modes.

[0104] A sequence generation layer is set before the temporal feature extraction layer to construct three enhanced sequence inputs to enrich the diversity of feature representation.

[0105] The output of the temporal feature extraction layer enters the feature extraction module, which uses an enhanced noise reduction autoencoder as the base network and includes batch normalization and linear layers to perform dimensionality reduction and enhancement processing on temporal features.

[0106] The output of the feature extraction module enters the result decoder, which uses a fully connected neural network as the base network, including layer normalization and activation functions, to predict the output strain modes based on the extracted features. The output strain mode data has a shape of 73×6, representing the 6th order strain modes at 73 measurement points.

[0107] In some embodiments of the present invention, the method further includes: sampling within a preset range of the parameters of the finite element model to be inverted in the preset finite element model to generate multiple sets of finite element model parameter samples; performing modal analysis on each set of finite element model parameter samples to extract corresponding displacement modal features, frequency features, and strain modal features; constructing a first training sample set based on the displacement modal features and frequency features, and training the first network model to fit the mapping relationship between measured modal information and finite element model parameters; constructing a second training sample set based on the finite element model parameter samples and the corresponding strain modal features, and training the second network model to fit the mapping relationship between finite element model parameters and strain modes.

[0108] Sampling refers to randomly selecting multiple sets of parameter values ​​within a preset range of parameters of the finite element model to be inverted, in order to generate diverse finite element model instances.

[0109] Modal analysis refers to solving the vibration modes of a structure at various natural frequencies using the finite element method, and obtaining the distribution of displacement modes and strain modes.

[0110] Displacement modal characteristics refer to the relative distribution of displacement at each measuring point of the structure under each mode; frequency characteristics refer to the natural frequency values ​​corresponding to each mode; and strain modal characteristics refer to the relative distribution of strain at each measuring point of the structure under each mode.

[0111] Specifically, this embodiment first determines the finite element model parameters to be inverted in a preset finite element model. These parameters include at least one of material parameters, geometric parameters, and boundary parameters, and a preset range for each parameter is set. Sampling is performed within this preset range to generate multiple sets of finite element model parameter samples. Modal analysis is performed on each set of parameter samples to extract the corresponding displacement modal features, frequency features, and strain modal features. A first training sample set is constructed based on the displacement modal features and frequency features. Each training sample consists of displacement modal features, frequency features, and the corresponding finite element model parameters, used to train the first network model to fit the mapping relationship between measured modal information and finite element model parameters. A second training sample set is constructed based on the finite element model parameter samples and the corresponding strain modal features. Each training sample consists of finite element model parameters and the corresponding strain modes, used to train the second network model to fit the mapping relationship between finite element model parameters and strain modes. As an example, for a plate-beam composite structure, 27 displacement modal measurement points and 6th-order modes can be selected to construct a displacement modal feature matrix and a frequency feature vector.

[0112] Understandably, this embodiment generates diverse finite element model parameter samples within a preset range, covering various parameter combinations that may occur in the structure, thus improving the comprehensiveness of the training samples. Displacement modes, frequencies, and strain modes are extracted through modal analysis, providing accurate input and output data for network training. Based on the constructed training sample set, the first and second networks are trained, enabling both networks to learn the nonlinear mapping relationships between measured modal information and finite element model parameters, as well as between finite element model parameters and strain modes, respectively, laying a reliable foundation for subsequent inversion and prediction.

[0113] In some embodiments of the present invention, the finite element model parameters of the preset finite element model are structural parameters characterizing the structure, including at least one of material parameters, geometric parameters, and boundary parameters.

[0114] In this context, finite element model parameters refer to adjustable variables used to describe the physical properties of a pre-defined finite element model. Material parameters include, but are not limited to, elastic modulus, density, and Poisson's ratio, used to characterize the mechanical properties of structural materials. Geometric parameters include, but are not limited to, plate thickness, beam height, beam width, and cross-sectional area, used to characterize the geometric dimensions of structural members. Boundary parameters include, but are not limited to, support stiffness and connection stiffness, used to characterize structural boundary conditions and the connection characteristics between members.

[0115] Specifically, the finite element model parameters of the preset finite element model are the structural parameters to be inverted. When constructing the training sample set for the dual-network strain modal prediction model, sampling is performed within a preset range of the finite element model parameters to be inverted from the preset finite element model, generating multiple sets of finite element model parameter samples. Each set of samples contains at least one of material parameters, geometric parameters, and boundary parameters. By performing modal analysis on each set of parameter samples, the corresponding displacement modal features, frequency features, and strain modal features are extracted to form the training sample set. The first network model learns from these samples to establish an inversion mapping relationship from measured modal information to finite element model parameters.

[0116] Understandably, this embodiment, by using material parameters, geometric parameters, and boundary parameters as the parameters of the finite element model to be inverted, can comprehensively cover the key factors affecting the dynamic characteristics of the structure. Through the inversion and correction of these parameters, the corrected finite element model can accurately characterize the physical properties of the real structure, effectively reducing the mismatch error between the real structure and the initial finite element model, and providing an accurate parameter basis for subsequent strain mode prediction and displacement reconstruction.

[0117] In some embodiments of the present invention, the step of solving for the modal coordinates based on the measured strain response and the predicted strain modes during the operation of the structure includes: Solve for the modal coordinates using the following formula: ; Where t is the time variable, For modal coordinates, To measure the strain response, Let q be the predicted strain mode, and q be the modal coordinate variable to be solved.

[0118] Specifically, in this embodiment, after obtaining the predicted strain mode and the measured strain response, the modal coordinates are solved using a modal transformation method. The solution process is based on the following optimization problem: finding the modal coordinates q that minimize the sum of the fitting error term and the regularization term. Wherein, the fitting error term... To ensure that the solution matches the measured strain response, t is a time variable during the solution process, indicating that the modal coordinates at each time point are solved independently.

[0119] In some embodiments of the present invention, reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure includes: Reconstruct dynamic or static displacements using the following formula: ; in, For dynamic or static displacement, To measure displacement modal information, These are modal coordinates.

[0120] Dynamic displacement refers to the displacement response of a structure as it changes over time during operation, describing the deformation state of each measuring point at different times. Static displacement refers to the displacement response of a structure under constant load that does not change over time, describing the deformation distribution of the structure in equilibrium. In this embodiment, the displacement can be either dynamic or static, depending on the actual monitoring requirements or load type. When the structure is subjected to dynamic loads that change over time (such as vehicle traffic on a bridge or wind loads), it is necessary to reconstruct the dynamic displacement to capture the real-time vibration response of the structure. When the structure is subjected to constant or quasi-static loads (such as static tests or long-term settlement monitoring), the same method can be used to reconstruct the static displacement, in which case the time variable t can be considered a constant or a single moment.

[0121] Measured displacement modal information refers to the displacement modal matrix obtained through modal testing, which reflects the displacement distribution of the structure under each mode and is an inherent property of the structure.

[0122] Modal coordinates are weighted coefficient vectors obtained by solving modal changes, used to represent the contribution of each mode to the dynamic response of the structure.

[0123] Specifically, the dynamic or static displacement of the structure can be reconstructed based on the modal superposition principle. The measured displacement modal information is multiplied by the solved modal coordinates to obtain the dynamic or static displacement vector of the structure.

[0124] Understandably, this embodiment multiplies the modal coordinates with the measured displacement modal information using the modal superposition principle, thereby realizing the displacement transformation from modal space to physical space and obtaining the dynamic or static displacement response of the structure in the time domain. This process is directly based on the measured displacement modal information, avoiding the errors that may be introduced by relying on the finite element model to extract displacement modes, and improving the accuracy of displacement reconstruction.

[0125] In some embodiments of the present invention, after reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure, the method further includes: if a reconstruction instruction for the full-field displacement of the structure is received, then the preset finite element model is modified based on the predicted finite element model parameters output by the dual-network strain modal prediction model to obtain a modified finite element model; the full-field displacement modal matrix is ​​extracted using the modified finite element model; and the full-field displacement distribution of the structure is reconstructed based on the full-field displacement modal matrix and the modal coordinates.

[0126] The corrected finite element model refers to the updated model obtained by substituting the predicted finite element model parameters output by the dual-network strain modal prediction model into the preset finite element model.

[0127] The full-field displacement modal matrix refers to the displacement modal basis extracted from the modified finite element model, covering all nodes of the structure, and is used to describe the displacement distribution of the structure in the entire field. The full-field displacement distribution refers to the set of displacement values ​​of all nodes of the structure during the dynamic response process. Compared with the dynamic or static displacement of preset measurement points, the full-field displacement distribution can provide deformation information of the entire structure.

[0128] Specifically, after reconstructing the dynamic or static displacement based on modal coordinates and measured displacement modal information, if a full-field displacement reconstruction command for the structure is received, the preset finite element model is first modified according to the predicted finite element model parameters output by the dual-network strain modal prediction model to obtain the modified finite element model. Subsequently, modal analysis is performed using the modified finite element model to extract the full-field displacement modal matrix covering all nodes of the structure. Finally, based on the full-field displacement modal matrix and the modal coordinates obtained in the aforementioned steps, the full-field displacement distribution of the plate-beam composite structure is reconstructed according to equation (16): (16) In equation (16), To reconstruct the full-field displacement distribution at time t, This is the full-field displacement mode matrix extracted from the modified finite element model.

[0129] Understandably, this embodiment, by receiving a full-field displacement reconstruction command, triggers further correction of the preset finite element model and extraction of the full-field displacement mode matrix, achieving extended reconstruction from point displacement to full-field displacement. The full-field displacement mode matrix extracted based on the corrected finite element model better matches the physical characteristics of the actual structure, improving the accuracy of the full-field displacement reconstruction. This method can obtain overall structural deformation information without the need for additional sensors, providing more comprehensive data support for structural health monitoring and condition assessment.

[0130] To better implement the structural displacement reconstruction method based on finite element model correction in the embodiments of the present invention, based on the structural displacement reconstruction method based on finite element model correction, as follows: Figure 5 As shown, this embodiment of the invention also provides a structural displacement reconstruction system based on finite element model correction. The structural displacement reconstruction system 500 based on finite element model correction includes: The acquisition unit 501 is used to acquire a pre-constructed dual-network strain mode prediction model, wherein the dual-network strain mode prediction model includes a cascaded first network model and a second network model. The first network model is used to establish a mapping relationship between the measured modal information of the structure to be tested and the finite element model parameters of the corresponding preset finite element model. The second network model is used to establish a mapping relationship between the finite element model parameters and the strain modes of the structure. The first prediction unit 502 is used to input the current measured modal information of the structure into the first network model and invert to obtain the predicted finite element model parameters of the preset finite element model. The second prediction unit 503 is used to input the prediction finite element model parameters into the second network model to predict the predicted strain mode of the structure. The determining unit 504 is used to solve for the modal coordinates based on the measured strain response and the predicted strain modes during the operation of the structure. The reconstruction unit 505 is used to reconstruct the dynamic displacement or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure.

[0131] The structural displacement reconstruction system 500 based on finite element model correction provided in the above embodiments can realize the technical solutions described in the above embodiments of the structural displacement reconstruction method based on finite element model correction. The specific implementation principles of each module or unit can be found in the corresponding content in the above embodiments of the structural displacement reconstruction method based on finite element model correction, and will not be repeated here.

[0132] Accordingly, this application also provides a computer-readable storage medium for storing computer-readable programs or instructions. When the programs or instructions are executed by a processor, they can implement the steps or functions of the structural displacement reconstruction method based on finite element model correction provided in the above-described method embodiments.

[0133] Those skilled in the art will understand that all or part of the processes of the methods described in the above embodiments can be implemented by a computer program instructing related hardware (such as a processor, controller, etc.), and the computer program can be stored in a computer-readable storage medium. The computer-readable storage medium may be a disk, optical disk, read-only memory, or random access memory, etc.

[0134] The above provides a detailed description of the structural displacement reconstruction method, system, and medium based on finite element model correction provided by this invention. Specific examples have been used to illustrate the principles and implementation methods of this invention. The descriptions of the above embodiments are only for the purpose of helping to understand the method and core ideas of this invention. At the same time, for those skilled in the art, there will be changes in the specific implementation methods and application scope based on the ideas of this invention. Therefore, the content of this specification should not be construed as a limitation of this invention.

Claims

1. A structural displacement reconstruction method based on finite element model correction, characterized in that, include: A pre-constructed dual-network strain mode prediction model is obtained, wherein the dual-network strain mode prediction model includes a cascaded first network model and a second network model. The first network model is used to establish the mapping relationship between the measured modal information of the structure to be tested and the finite element model parameters of the corresponding preset finite element model. The second network model is used to establish the mapping relationship between the finite element model parameters and the strain modes of the structure. The current measured modal information of the structure is input into the first network model, and the predicted finite element model parameters of the preset finite element model are obtained by inversion. The predicted finite element model parameters are input into the second network model to predict the predicted strain modes of the structure. Based on the measured strain response and the predicted strain modes during the operation of the structure, the modal coordinates are solved. Based on the modal coordinates and the measured displacement modal information of the structure, the dynamic or static displacement of the structure is reconstructed.

2. The structural displacement reconstruction method based on finite element model correction according to claim 1, characterized in that, The prediction steps for the finite element model parameters include: Modal analysis is performed on the current measured modal information to extract the measured point displacement modal sequence and measured frequency data of a preset order; Feature extraction is performed on the measured frequency data to obtain frequency features; Temporal and spatial correlation features are extracted from the displacement mode sequence of the measurement point to obtain displacement mode features; The frequency features and the displacement mode features are fused to obtain the fused features; The parameters of the finite element model are predicted based on the fusion features.

3. The structural displacement reconstruction method based on finite element model correction according to claim 2, characterized in that, The prediction steps for the predicted strain modes include: The predicted finite element model parameters obtained from the first network model are subjected to feature interaction and enhancement to obtain interactive enhancement features; Temporal correlation features are extracted from the interaction enhancement features to obtain temporal features; The strain mode is predicted based on the time-series characteristics.

4. The structural displacement reconstruction method based on finite element model correction according to claim 1, characterized in that, Also includes: Sampling is performed within a preset range of the parameters of the finite element model to be inverted in the preset finite element model to generate multiple sets of finite element model parameter samples; Modal analysis was performed on the parameter samples of each group of finite element models to extract the corresponding displacement modal features, frequency features, and strain modal features; Based on the displacement modal features and frequency features, a first training sample set is constructed, and the first network model is trained to fit the mapping relationship between the measured modal information and the finite element model parameters. A second training sample set is constructed based on the finite element model parameter samples and the corresponding strain mode features, and the second network model is trained to fit the mapping relationship between the finite element model parameters and the strain modes.

5. The structural displacement reconstruction method based on finite element model correction according to claim 1, characterized in that, The finite element model parameters of the preset finite element model are structural parameters that characterize the structure, including at least one of material parameters, geometric parameters, and boundary parameters.

6. The structural displacement reconstruction method based on finite element model correction according to claim 1, characterized in that, The process of solving for modal coordinates based on the measured strain response and the predicted strain modes during the operation of the structure includes: Solve for the modal coordinates using the following formula: ； Where t is the time variable, For modal coordinates, To measure the strain response, Let q be the predicted strain mode, and q be the modal coordinate variable to be solved.

7. The structural displacement reconstruction method based on finite element model correction according to claim 1, characterized in that, The process of reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure includes: Reconstruct dynamic or static displacements using the following formula: ； in, For dynamic or static displacement, To measure displacement modal information, These are modal coordinates.

8. The structural displacement reconstruction method based on finite element model correction according to any one of claims 1-7, characterized in that, After reconstructing the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure, the method further includes: If a reconstruction command for the full-field displacement of the structure is received, the preset finite element model is corrected based on the predicted finite element model parameters output by the dual-network strain modal prediction model to obtain the corrected finite element model. The full-field displacement mode matrix is ​​extracted using the modified finite element model. Based on the full-field displacement mode matrix and the modal coordinates, the full-field displacement distribution of the structure is reconstructed.

9. A structural displacement reconstruction system based on finite element model correction, characterized in that, include: The acquisition unit is used to acquire a pre-constructed dual-network strain mode prediction model, wherein the dual-network strain mode prediction model includes a cascaded first network model and a second network model. The first network model is used to establish a mapping relationship between the measured modal information of the structure to be tested and the finite element model parameters of the corresponding preset finite element model. The second network model is used to establish a mapping relationship between the finite element model parameters and the strain modes of the structure. The first prediction unit is used to input the current measured modal information of the structure into the first network model and invert to obtain the predicted finite element model parameters of the preset finite element model. The second prediction unit is used to input the prediction finite element model parameters into the second network model to predict the predicted strain mode of the structure. The determination unit is used to solve for the modal coordinates based on the measured strain response and the predicted strain modes during the operation of the structure. The reconstruction unit is used to reconstruct the dynamic or static displacement of the structure based on the modal coordinates and the measured displacement modal information of the structure.

10. A computer-readable storage medium, characterized in that, Used to store computer-readable programs or instructions, which, when executed by a processor, can implement the steps in the structural displacement reconstruction method based on finite element model correction as described in any one of claims 1 to 8.

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