An online self-adaptive correction method for a neural network proxy model

Abstract

The application discloses an online self-adaptive correction method of a neural network proxy model. The method provided by the application combines offline pre-training and online closed-loop correction, takes the error between the measured data at all sensor positions and the model predicted values as an online optimization objective function in the test process, and updates the weight and threshold of the neural network proxy model in real time through back propagation, so that the model parameters continuously approach the real physical state in the test process, eliminates the systematic deviation introduced by pure simulation data training, and improves the accuracy of the full-field response prediction result in the real test environment. At the same time, the measured data at all sensor positions are all involved in error calculation, the sparse point information is diffused to the full field through the nonlinear mapping capability of the neural network, and the accuracy and robustness of the response prediction in the non-point area are improved.

Description

Technical Field

[0001] This invention relates to the technical field of complex equipment testing and monitoring and digital twins, specifically to an online adaptive correction method for a neural network proxy model. Background Technology

[0002] As modern complex equipment (such as large structural components, aircraft, ship equipment, and energy equipment) develops towards high performance and high integration, their three-dimensional full-field dynamic responses (such as displacement, strain, acceleration, and temperature fields) under typical service or test conditions exhibit characteristics such as strong coupling, nonlinearity, wide distribution, and strong time-varying nature. Traditional structural health monitoring and experimental verification methods rely on the deployment of a large number of sensors to obtain measured full-field responses. However, due to constraints such as equipment structural space, wiring costs, and test safety, only a limited number of measurement points can be collected, making it difficult to directly obtain the overall full-field response distribution of the equipment.

[0003] To compensate for the problem that the full-field response is difficult to observe directly due to insufficient measured data, related technologies have introduced methods such as numerical simulation, physical experimental measurement, and full-field reconstruction technology based on surrogate models.

[0004] Firstly, high-fidelity numerical simulation. Before physical testing, a detailed physical model of the equipment is established using numerical simulation tools such as finite element analysis or computational fluid dynamics to simulate the three-dimensional full-field response under various boundary conditions and load conditions. The advantage of this method is that it can systematically explore the influence of design parameters and operating conditions, and theoretically can obtain physical quantities at any location of the structure with high resolution. However, its shortcomings are that the accuracy heavily depends on the accuracy of the constitutive model and boundary condition settings, and it is often difficult to fully reproduce complex factors such as material nonlinearity, assembly gaps, and unknown environmental excitations in real tests, resulting in unavoidable deviations between simulation and actual measurement.

[0005] Secondly, physical experimental measurement and interpolation extrapolation. Sensors are deployed on the experimental equipment to directly measure the physical response at key locations. For locations without sensors, mathematical interpolation or extrapolation based on simplified physical models is used to estimate the overall response. The advantage of this method is that the data comes from the real physical environment, ensuring high reliability. Its limitation is that obtaining sufficiently accurate overall field estimation requires deploying a large number of sensors, which is costly and difficult to implement in space-constrained or extreme environments. Traditional interpolation and extrapolation methods struggle to capture the high-dimensional nonlinear mapping relationships implicit in the responses of complex equipment, and the estimation accuracy drops sharply when the response gradient is large or there are abrupt change regions.

[0006] Third, full-field reconstruction technology based on surrogate models. To balance the full-field information of simulation with the real-time nature of experiments, deep learning-based surrogate model technology has been widely used. This type of method adopts an offline training plus online inference mode: In the offline stage, numerical simulation software is used to calculate the structural response under multiple operating conditions in batches, and a sample dataset of sensor position response and full-field response is constructed; in the training stage, the neural network is trained to establish a nonlinear mapping relationship from sparse measurement points to the full-field response; in the online stage, the pre-trained model is deployed on the experimental system, using a small amount of measured data from sensors as input, and the full-field response of the equipment is quickly inferred through model forward propagation.

[0007] Although the above-mentioned offline training and fixed deployment neural network proxy model method can achieve inference of the whole field with fewer measurement points compared with pure simulation calculation or pure experimental interpolation, and solves the problem of real-time monitoring of the whole field response to a certain extent, it still has the following defects when facing the dynamic and high-fidelity requirements of complex equipment real test scenarios.

[0008] First, the discrepancy between the model and reality leads to insufficient generalization performance. Most existing neural network surrogate models are trained offline entirely based on numerical simulation data, inherently inheriting all the assumptions and errors of the simulation model. In numerical simulations, material properties, geometric dimensions, boundary conditions, etc., are idealized, while the actual physical parameters, installation status, and environmental conditions of the equipment in real-world experimental scenarios inherently deviate from the simulation assumptions. The model itself lacks a mechanism to perceive and correct this data source deviation, resulting in potentially overall biased or distorted predictions based on measured data input.

[0009] Second, there is a fundamental contradiction between model fixation and experimental dynamism. Once the existing surrogate model is trained, its internal parameters are fixed, making it impossible to optimize itself online using real-time measured data during experiments. Real-world experimental environments are full of uncertainties; equipment may experience performance degradation or unexpected operating conditions during testing. Fixed models cannot adapt to these new states or time-varying characteristics not covered in the simulation dataset, leading to a gradual decrease in prediction accuracy in the later stages of the experiment.

[0010] Third, the utilization of measured data is insufficient. Current technologies optimize by minimizing prediction errors on simulation datasets during offline training. While the model may perform well on simulation data, it may not produce optimal full-field predictions under real-world sensor data input. Measured data collected during experiments is typically only used for backend comparison and verification, failing to establish a closed-loop feedback mechanism in the real-time experimental process. This means failing to utilize the error between sensor measurements and model predictions to construct a loss function and adjust network parameters in real-time via backpropagation, resulting in a waste of the informational value of the measured data.

[0011] In summary, in the relevant technologies, under the scenario of reconstructing the full-field response in a one-dimensional vector space of complex equipment testing, there is a technical problem that the neural network proxy model, which is trained offline and fixedly deployed based on multi-condition numerical simulation data, cannot use real-time measured data from all sensor locations to perform online closed-loop correction of the model parameters during the test, resulting in difficulty in eliminating the deviation between simulation and reality. Summary of the Invention

[0012] The technical problem this invention aims to solve is that, in related technologies, under the scenario of reconstructing the full-field response in a one-dimensional vector space during complex equipment testing, there is a technical problem where neural network proxy models trained offline and fixedly deployed based on multi-condition numerical simulation data cannot utilize real-time measured data from all sensor locations for online closed-loop correction of model parameters during the test, leading to difficulties in eliminating the discrepancy between simulation and reality. The purpose is to provide an online adaptive correction method for neural network proxy models, thereby solving the aforementioned technical problem.

[0013] This invention is achieved through the following technical solution:

[0014] In a first aspect, the present invention provides an online adaptive correction method for a neural network surrogate model, comprising:

[0015] Obtain a neural network surrogate model trained offline based on a one-dimensional vector dataset from multi-condition numerical simulation.

[0016] During the experiment, one-dimensional response measurement data of the same physical quantity were collected at all sensor locations, and the measurement data at some of the planned sensor locations were extracted; wherein, the planned sensor locations are included in the total sensor locations.

[0017] The measured data from the locations of some of the sensors to be deployed are input into the neural network proxy model to obtain the predicted one-dimensional response of the equipment across the entire field.

[0018] Extract the predicted response values ​​at all sensor locations from the full-field one-dimensional response prediction values;

[0019] The error is calculated based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations, and the weights and thresholds of the neural network surrogate model are fine-tuned online using the error as the online optimization objective function.

[0020] The online fine-tuned neural network proxy model is used to output the current one-dimensional response of the equipment across the entire field.

[0021] Furthermore, the step of obtaining the neural network proxy model obtained through offline training based on a one-dimensional vector dataset from multi-condition numerical simulation includes:

[0022] Establish a three-dimensional finite element model of the equipment, and set material properties, contact relationships and boundary conditions according to the structural characteristics of the equipment;

[0023] Based on the preset test load conditions and load range, batch numerical simulation analysis is carried out;

[0024] Extract the one-dimensional response values ​​of the same physical quantity at some of the sensor locations to be deployed as input data, and extract the one-dimensional response values ​​of the same physical quantity at all nodes of the equipment or dense nodes within the target area as output data to construct a one-dimensional vector dataset.

[0025] The neural network surrogate model is obtained by offline supervised training based on a one-dimensional vector dataset.

[0026] Furthermore, the neural network proxy model includes an input layer, at least one hidden layer, and an output layer;

[0027] The node dimension of the input layer is determined based on the number of sensor locations to be deployed.

[0028] The node dimension of the output layer corresponds to the number of all nodes in the equipment field or the number of dense nodes in the target area, which serve as the output data.

[0029] Furthermore, the process of collecting one-dimensional response measurement data of the same physical quantity at all sensor locations during the experiment, and extracting measurement data from a subset of the sensor locations to be deployed, includes:

[0030] The data acquisition system acquires real-time measured data of the one-dimensional response of the same physical quantity at all sensor locations on the equipment; wherein, the all sensor locations include some sensor locations to be deployed, and also sensor locations used for verification.

[0031] Extract measured data from the locations of the sensors to be deployed from the measured data at all sensor locations.

[0032] Further, the step of calculating the error based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations includes:

[0033] Calculate the root mean square error between the predicted response values ​​at all sensor locations and the measured data at all sensor locations; wherein the root mean square error is the square root of the mean of the squares of the differences between the predicted response values ​​and the corresponding measured data at each sensor location.

[0034] Furthermore, the step of fine-tuning the weights and thresholds of the neural network surrogate model online with error as the online optimization objective function includes:

[0035] With minimizing the root mean square error as the optimization objective, a gradient descent-type optimization algorithm is used to update the weights and thresholds of the neural network surrogate model; wherein, the learning rate used in online fine-tuning is less than the learning rate used in the offline training phase.

[0036] Furthermore, the weights and thresholds of the neural network proxy model are updated, either once at each sampling time step or once every preset number of sampling time steps.

[0037] In a second aspect, the present invention provides an online adaptive correction device for a neural network surrogate model, comprising:

[0038] The acquisition module is used to acquire the neural network proxy model obtained by offline training based on a one-dimensional vector dataset of multi-condition numerical simulation.

[0039] The acquisition module is used to acquire one-dimensional response measured data of the same physical quantity at all sensor locations during the experiment, and to extract measured data at a portion of the sensor locations to be deployed, wherein the portion of the sensor locations to be deployed is included in the total sensor locations.

[0040] The input module is used to input the measured data from the locations of the sensors to be deployed into the neural network proxy model to obtain the predicted one-dimensional response of the equipment across the entire field.

[0041] The extraction module is used to extract the predicted response values ​​at all sensor locations from the full-field one-dimensional response prediction values;

[0042] The fine-tuning module is used to calculate the error based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations, and to fine-tune the weights and thresholds of the neural network surrogate model online with the error as the online optimization objective function.

[0043] The output module is used to output the current one-dimensional response of the equipment across the entire field using an online fine-tuned neural network proxy model.

[0044] Thirdly, the present invention provides an electronic device, comprising: a memory, and one or more processors communicatively connected to the memory; the memory stores instructions executable by the one or more processors, the instructions being executed by the one or more processors to cause the one or more processors to implement the method described above.

[0045] Fourthly, the present invention provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the above-described method.

[0046] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0047] The method provided by this invention combines offline pre-training with online closed-loop correction. During the experiment, the error between the measured data and the model predictions at all sensor locations is used as the online optimization objective function. Backpropagation is used to update the weights and thresholds of the neural network surrogate model in real time, ensuring that the model parameters continuously approximate the real physical state during the experiment. This eliminates the systematic bias introduced by training with purely simulated data and improves the accuracy of the overall response prediction results under real experimental conditions. Simultaneously, measured data from all sensor locations participate in error calculation, diffusing sparse measurement point information to the entire field through the nonlinear mapping capability of the neural network, improving the accuracy and robustness of response prediction in areas without sensor points. Attached Figure Description

[0048] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0049] Figure 1 This is an architecture diagram of an online adaptive correction method for a neural network proxy model provided in the embodiments of this specification;

[0050] Figure 2 A flowchart illustrating an online adaptive correction method for a neural network proxy model provided in the embodiments of this specification;

[0051] Figure 3 This is a schematic diagram illustrating the training process of a typical part's three-dimensional full-field response neural network surrogate model provided in the embodiments of this specification;

[0052] Figure 4 This is a block diagram of an online adaptive correction device for a neural network proxy model provided in the embodiments of this specification;

[0053] Figure 5 This is a block diagram of an electronic device provided in the embodiments of this specification. Detailed Implementation

[0054] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0055] In related technologies, real-time monitoring of the three-dimensional full-field dynamic response (displacement, strain, acceleration, temperature field, etc.) of complex equipment (e.g., large structural components, aircraft, ship equipment, energy equipment, etc.) under typical test conditions is a key link in structural health assessment and experimental verification. Due to limitations in equipment structure installation space, wiring costs, and test safety, sensors can often only be deployed at limited locations on the surface or inside the equipment. This results in the direct acquisition of response data at sparse measurement points, making it impossible to directly obtain the overall full-field response distribution of the equipment.

[0056] To infer the full-field response from sparse measurement points, a full-field reconstruction method based on a neural network surrogate model has been introduced in related technologies. This method typically employs a three-stage approach: offline training and fixed deployment. In the first stage, a high-fidelity three-dimensional finite element model of the equipment is established, with multiple typical load conditions preset. The structural response under each condition is calculated in batches using numerical simulation analysis. The simulated response values ​​at the locations of the sensors to be deployed are extracted as input samples, and the simulated response values ​​at all full-field nodes are used as output labels, constructing a multi-condition numerical simulation dataset. In the second stage, the neural network is trained offline under supervised supervision using this simulation dataset. The network weights and thresholds are iteratively updated through backpropagation, enabling the network to learn the nonlinear mapping relationship from sparse measurement point responses to the full-field response. After training, the model parameters are fixed and saved, resulting in the neural network surrogate model. In the third stage, during the experiment, this fixed model is deployed in a data acquisition system. Measured data collected by a small number of sensors is used as input, and the model's forward propagation calculates the predicted full-field response, achieving rapid inference from sparse measured data to the full-field response.

[0057] However, the aforementioned offline training and fixed deployment mode has the following problems. During the establishment of the numerical simulation model, material properties, geometric dimensions, boundary conditions, etc., are all idealized. However, there are inherent deviations between the actual physical parameters, installation status, and environmental conditions of the equipment in the actual test scenario and the simulation assumptions. The neural network proxy model trained based on pure simulation data has its internal parameters fixed after offline training, inherently inheriting all the assumptions and errors of the simulation model. When this fixed model is deployed in a real test, facing physical realities inconsistent with the simulation assumptions, the model itself lacks a mechanism to perceive and correct this deviation originating from the data source. This leads to an overall offset or distortion in the full-field response prediction results generated based on measured data input; that is, the deviation between simulation and reality is difficult to eliminate. Furthermore, the measured data collected by all sensors actually deployed in the test, exceeding the model input requirements, is only used for backend comparison and verification, not for online optimization of model parameters. The information value reflecting the true physical state of the equipment contained in the measured data is not fully utilized.

[0058] In summary, the relevant technologies have the following technical problems: In the scenario of reconstructing the full-field response in a one-dimensional vector space of complex equipment testing, the neural network proxy model, which is trained offline and fixedly deployed based on multi-condition numerical simulation data, cannot use real-time measured data from all sensor locations to perform online closed-loop correction of the model parameters during the test, making it difficult to eliminate the deviation between simulation and reality.

[0059] The inventive concept of this invention is as follows: During the experiment, the real-time measured data at all sensor locations are compared with the predicted values ​​of the neural network surrogate model at the same locations. The error between the two is used as the objective function for online optimization. The model weight parameters and threshold parameters are updated online through backpropagation, forming an online closed loop of prediction-comparison-correction. This allows the model parameters to continuously approach physical reality during the experiment, thereby eliminating the deviation between simulation and reality.

[0060] like Figures 1-3 As shown, this embodiment provides an online adaptive correction method for a neural network proxy model. This method can be applied to full-field response reconstruction scenarios during complex equipment testing. The complex equipment can be large structural components, aircraft, ship equipment, or energy equipment.

[0061] The method can be implemented by a computer device deployed at a complex equipment testing site, such as an industrial control computer, embedded processing unit, edge computing node, or a high-speed computing platform integrated with a data acquisition system. This computer device can communicate with the data acquisition system via a data interface, receive measured response data collected by various sensors deployed on the target equipment, and run a deployed neural network proxy model on the computer device to perform forward propagation calculations, error calculations, backpropagation parameter updates, and output the overall response prediction results. In a distributed deployment scenario, the aforementioned data acquisition, forward propagation calculations, and backpropagation parameter updates can also be completed collaboratively by different processing units, with data transmission and command interaction between the processing units via a field data bus or network.

[0062] The method may include:

[0063] Step S11: Obtain the neural network surrogate model obtained by offline training based on the one-dimensional vector dataset of multi-condition numerical simulation.

[0064] In this embodiment, the neural network proxy model is a deep neural network that has been pre-trained offline. This model receives one-dimensional response values ​​of the same physical quantity at some of the sensor locations to be deployed on the equipment, and outputs predicted one-dimensional response values ​​of the same physical quantity at corresponding nodes across the entire equipment. The input-output mapping relationship of this model is established offline using a one-dimensional vector dataset from multi-condition numerical simulation.

[0065] In this embodiment, the multi-condition numerical simulation one-dimensional vector dataset is a sample set formed during the offline preparation phase. This dataset includes multiple sets of samples, each set containing input and output data. The input data consists of one-dimensional response values ​​of the same physical quantity calculated through numerical simulation at the locations of the sensors to be deployed under corresponding load conditions. The output data consists of one-dimensional response values ​​of the same physical quantity calculated through numerical simulation at all nodes of the equipment under the same load conditions.

[0066] Specifically, the load condition coverage test includes typical load types such as static load, impact load, resonant load, and operational load. Multiple load conditions can be generated based on a preset load range, and batch numerical simulation analysis can be performed based on the equipment's three-dimensional finite element model.

[0067] It should be noted that the one-dimensional vector data refers to a single physical quantity that is represented by the values ​​of that physical quantity at different sensor locations or different nodes in a single model run.

[0068] In this embodiment, offline training is a supervised learning process performed on the neural network based on a dataset. During training, the input data of each group of samples is input into the neural network to obtain the corresponding full-field response prediction value. Then, the full-field response prediction value is compared with the output data to calculate the prediction error, and the weights and thresholds in the network are iteratively updated based on the prediction error. When the model meets the preset training termination condition, the current network parameters are saved, resulting in a neural network proxy model. The input layer node dimension of the neural network proxy model matches the number of sensor locations to be deployed, the output layer node dimension matches the number of nodes equipped with the full-field response, and the hidden layer is used to realize the nonlinear mapping from sparse input to full-field output.

[0069] Step S12: During the experiment, collect the one-dimensional response measurement data of the same physical quantity at all sensor locations, and extract the measurement data at some of the sensor locations to be deployed, wherein the partial sensor locations to be deployed are included in the total sensor locations.

[0070] In this embodiment, after the equipment test begins, the data acquisition system continuously collects measured data of the one-dimensional response of the same physical quantity at all sensor locations on the equipment according to a preset sampling frequency. The proposed partial sensor locations are included in the total sensor locations. Measured data at the proposed partial sensor locations can be extracted from the real-time measured data at all sensor locations as the input data source for the subsequent neural network proxy model. At the same time, complete measured data at all sensor locations are retained for subsequent error calculation.

[0071] In some implementations, the total sensor locations include not only the locations of the sensors to be deployed, but also additional calibration sensor locations. The measured data at these additional calibration sensor locations are not used as model input, but are involved in subsequent error calculations.

[0072] Step S13: Input the measured data from the locations of the sensors to be deployed into the neural network proxy model to obtain the predicted one-dimensional response of the equipment across the entire field.

[0073] In this embodiment, the measured data at the locations of the sensors to be deployed, extracted in step S12, can be assembled into an input data vector according to the order corresponding to the input layer nodes of the neural network proxy model, and the input data vector can be input into the neural network proxy model at the current moment.

[0074] The neural network proxy model performs forward propagation calculations and outputs a one-dimensional response prediction value for the entire equipment field. Each element in the one-dimensional response prediction value corresponds to the one-dimensional response prediction result of the same physical quantity at each node in the entire equipment field.

[0075] Step S14: Extract the predicted response values ​​at all sensor locations from the full-field one-dimensional response prediction values.

[0076] In this embodiment, the full-field one-dimensional response prediction value output by the neural network surrogate model covers all nodes of the equipment. Based on a pre-established correspondence, the predicted response values ​​for all sensor locations can be extracted from the full-field one-dimensional response prediction value. This correspondence characterizes the relationship between each sensor location and the corresponding node in the full-field prediction result. After extraction, a set of predicted response values ​​for all sensor locations is obtained, and this set corresponds positionally to the measured data for all sensor locations collected in step S12.

[0077] Step S15: Calculate the error based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations, and fine-tune the weights and thresholds of the neural network surrogate model online using the error as the online optimization objective function.

[0078] In this embodiment, the predicted response values ​​at all sensor locations obtained in step S14 can be compared with the measured data at all sensor locations collected in step S12, and the error between the two can be calculated. The error calculation can use the root mean square error method. Specifically, the difference between the predicted response value and the corresponding measured data at each sensor location is calculated, each difference is squared, the average of all squared results is calculated, and then the square root of the average value is taken to obtain the error value at the current time.

[0079] The error value is used as the objective function for online optimization, and online fine-tuning is performed on the neural network surrogate model. During online fine-tuning, with the goal of minimizing the error value, backpropagation is performed to obtain the gradient information corresponding to the weights and thresholds of each layer in the neural network surrogate model, and gradient descent-type optimization algorithms are used to update the weights and thresholds. The learning rate used in the online fine-tuning stage is lower than the learning rate used in the offline training stage to reduce the disturbance of the mapping relationship obtained by offline training during the online update process.

[0080] In this embodiment, the error calculation, objective function construction, and parameter update processes are executed cyclically during the experiment. In one specific implementation, parameter updates are performed once at each sampling time; in another specific implementation, parameter updates are performed once every fixed time window.

[0081] Step S16: Utilize the online fine-tuned neural network proxy model to output the current one-dimensional response of the equipment across the entire field.

[0082] In this embodiment, after the online fine-tuning of weights and thresholds is completed in step S15, the updated neural network proxy model can be invoked to output the equipment's one-dimensional response prediction result at the current moment. This equipment one-dimensional response prediction result serves as the monitoring result at the current moment, characterizing the distribution of the equipment's response in its current state.

[0083] In this embodiment, steps S12 to S16 constitute an online closed loop. As measured data is continuously collected during the experiment, data extraction, full-field prediction, error calculation, parameter updating, and result output are repeatedly executed, enabling the neural network proxy model to continuously correct itself based on real-time measured data and output the equipment's full-field one-dimensional response prediction result corresponding to the current experimental state.

[0084] In some implementations, the step of obtaining the neural network surrogate model obtained by offline training based on a one-dimensional vector dataset from multi-condition numerical simulation includes:

[0085] Step S111: Establish a three-dimensional finite element model of the equipment, and set material properties, contact relationships and boundary conditions according to the structural characteristics of the equipment.

[0086] In this embodiment, during the offline preparation phase, a three-dimensional geometric model of the equipment can first be established, and a three-dimensional finite element model for numerical simulation analysis can be generated based on the three-dimensional geometric model. Then, according to the structural characteristics of the equipment, material properties, contact relationships, and boundary conditions are set on the three-dimensional finite element model.

[0087] Specifically, the material properties are used to characterize the response characteristics of each part of the equipment under load. The contact relationships are used to characterize the connection interface relationships between the various components of the equipment. The boundary conditions are used to characterize the installation, fixation, and constraint states of the equipment under test conditions.

[0088] The above settings ensure that the established three-dimensional finite element model corresponds to the test state of the equipment.

[0089] In one specific implementation scheme, on the three-dimensional finite element model, corresponding material properties can be set for each mesh region based on the actual material type of each component of the equipment. Material properties can include elastic modulus, Poisson's ratio, density, and damping coefficient. For composite material structures, the fiber orientation angle and ply thickness of each layup can also be set.

[0090] In one specific implementation, contact relationships are set for the connection interfaces between components on a three-dimensional finite element model. Contact types can include bonded contact (the two components remain fully connected at the contact surface), frictional contact (the two components can slide relative to each other, and the sliding resistance is determined by the coefficient of friction), and frictionless contact (allowing free sliding).

[0091] In a specific implementation plan, boundary conditions can be set according to the actual installation and fixing method of the equipment in the test. Boundary conditions can include displacement constraints and force constraints. Displacement constraints limit the translation or rotation of the corresponding node in the finite element model in a specified direction to 0 or a preset value, and are used to simulate the constraint effect of clamps, bolted connections or support structures. Force constraints apply concentrated forces, distributed pressures or moments to the corresponding nodes in the finite element model, and are used to simulate the external loads in the test.

[0092] Step S112: Based on the preset test load conditions and load range, perform batch numerical simulation analysis.

[0093] In this embodiment, the load conditions and load range corresponding to the equipment in the test can be determined in advance.

[0094] Specifically, the load conditions include static load conditions, impact load conditions, resonant load conditions, and operational load conditions. The load range is used to define the range of load variation under different load conditions. Multiple sets of load conditions can be generated based on the test load conditions and load ranges, and each set of load conditions can be applied to the three-dimensional finite element model established in step S111 to perform batch numerical simulation analysis and obtain the full-field response results of the equipment under different load conditions.

[0095] In a specific implementation plan, within the load parameter range corresponding to each load condition type, multiple specific load condition combinations can be generated through sampling methods. The sampling method can employ Latin hypercube sampling, which divides the value range of each load parameter into equally probable intervals, randomly selects a value within each interval, and then randomly combines the selected values ​​of different parameters to ensure that the generated load condition combinations are evenly distributed within the load parameter space, avoiding the concentration of load conditions in localized areas.

[0096] In a specific implementation plan, for each load combination, a numerical simulation solver can be invoked to solve the established three-dimensional finite element model. Based on the set loads and boundary conditions, the solver iteratively calculates the full-field response distribution of the target equipment when it reaches force equilibrium under that load condition. For problems involving material nonlinearity or geometric nonlinearity, the solver iterates multiple times within each load increment step until convergence, ultimately outputting the converged full-field response result.

[0097] Step S113: Extract the one-dimensional response value of the same physical quantity at the locations of some sensors to be deployed as input data, and extract the one-dimensional response value of the same physical quantity at all nodes of the equipment or dense nodes in the target area as output data to construct a one-dimensional vector dataset.

[0098] In a specific implementation plan, the following extraction operation can be performed on the simulation calculation results for each set of load conditions:

[0099] (1) Extract input data.

[0100] From all nodes of the 3D finite element model, determine the nodes that spatially correspond to the locations of the sensors to be deployed in the experiment. For each corresponding node, extract the one-dimensional response value of the same physical quantity under that operating condition. When the sensor measures temperature, extract the temperature value of the corresponding node. When the sensor measures the displacement component in a certain direction, extract the displacement value of the corresponding node in that direction. When the sensor measures the strain component in a certain direction, extract the strain value of the corresponding node in that direction. The same physical quantity refers to the extracted quantities at all planned sensor locations in the model belonging to the same physical quantity type and the same directional component. Arrange the extracted response values ​​at each sensor location in a predetermined order to form the input data vector for that set of operating conditions.

[0101] (2) Extract the output data.

[0102] The scope of output data extraction can include two options. The first option is to extract the one-dimensional response value of the same physical quantity at all nodes across the entire equipment, meaning that the response value of this physical quantity is extracted for each mesh node of the finite element model, forming the output data vector for this set of working conditions. The second option is to extract the one-dimensional response value of the same physical quantity at densely packed nodes within the target area, meaning that only a subset of nodes in the critical structural regions of interest are extracted. The target area is a local region within the equipment with complex stress states, large response gradients, or critical significance for structural safety assessment. Densifying the nodes within this area can provide a more refined description of the response distribution. Under the second option, the output data vector only covers the nodes within the target area.

[0103] In this embodiment, input data vectors and output data vectors extracted under the same set of operating conditions can be paired to form a sample. Samples corresponding to all operating conditions are then aggregated to form a one-dimensional vector dataset. Each sample in this dataset includes an input data vector and a corresponding output data vector. The dimension of the input data vector is equal to the number of sensor locations to be deployed, and the dimension of the output data vector is equal to the number of all nodes in the field or the number of dense nodes within the target area.

[0104] Step S114: Perform offline supervised training on the neural network based on the one-dimensional vector dataset to obtain the neural network surrogate model.

[0105] In this embodiment, the input layer node dimensions and output layer node dimensions of the neural network can be determined based on a one-dimensional vector dataset. The input layer node dimensions correspond to the number of locations of the partial sensors to be deployed, and the output layer node dimensions correspond to the dimension of the output data vector. At least one hidden layer can be set between the input and output layers to establish a non-linear mapping relationship between the input data vector and the output data vector.

[0106] In this embodiment, the one-dimensional vector dataset can be divided into a training set and a validation set, and offline supervised training of the neural network can be performed based on the training set. During training, the input data vectors in the training set can be input into the neural network to obtain the corresponding predicted output vectors. The predicted output vectors are then compared with the corresponding output data vectors to calculate the prediction error. Backpropagation can be performed based on the prediction error, and the weights and thresholds in the neural network can be iteratively updated. The system repeatedly executes the processes of input data reading, prediction output generation, prediction error calculation, backpropagation, and parameter updating until a preset training termination condition is met. After the preset training termination condition is met, the system saves the weights and thresholds in the current neural network to obtain the neural network surrogate model.

[0107] In some implementations, the neural network proxy model includes an input layer, at least one hidden layer, and an output layer.

[0108] In this embodiment, the neural network proxy model employs a hierarchical structure to organize neuron nodes. This hierarchical structure may sequentially include an input layer, at least one hidden layer, and an output layer.

[0109] In one possible and specific implementation, the specific structure of a neural network proxy model for a typical component (26,688 grid responses) is shown in Table 1.

[0110] Table 1. Typical Structure of Neural Network Surrogate Model for Real-Time Calculation of 3D Full-Field Response of a Typical Part

[0111]

[0112] In one possible and specific implementation, the training parameters of the neural network proxy model for this part are shown in Table 2.

[0113] Table 2 Training parameters of a typical part's three-dimensional full-field response neural network surrogate model

[0114]

[0115] Specifically, in the basic feedforward structure, there may be no connections between neurons within each layer. Neurons in adjacent layers are fully or partially connected through directed weighted connections, with each connection corresponding to a weight parameter. In addition to the input layer, each neuron in each layer also corresponds to a threshold parameter. The input layer receives one-dimensional response data from the locations of the sensors to be deployed and passes this data to subsequent hidden layers. The hidden layer, located between the input and output layers, performs layer-by-layer nonlinear feature transformations on the input data, gradually mapping the low-dimensional sparse measurement point responses to a high-dimensional latent space representation, and then gradually mapping the high-dimensional latent space representation to the representation required by the output layer. The output layer converts the output of the last hidden layer into predicted response values ​​for all nodes of the target equipment.

[0116] Understandably, the mapping from the locations of some sensors to the overall response is often highly nonlinear. If only a direct linear connection is established between the input and output layers, the network can only express linear mappings and cannot capture the nonlinear characteristics of the response distribution caused by material nonlinearity, geometric nonlinearity, and contact nonlinearity prevalent in complex equipment structures. By introducing at least one hidden layer and using a nonlinear activation function, the network gains the ability to express arbitrary nonlinear mappings and can reconstruct the overall response distribution containing nonlinear response characteristics from sparse discrete measurement point data. The number of hidden layers can be determined based on the mapping complexity; that is, when the difference between the number of input sensors and the number of output nodes is large, or when the mechanical response nonlinearity of the target equipment is high, multiple hidden layers can be used to extract and combine features step by step.

[0117] The node dimension of the input layer is determined based on the number of sensor locations to be deployed.

[0118] In this implementation, when the one-dimensional response data of the same physical quantity collected at each sensor location is a single value, the dimension of the input layer node is equal to the number of sensor locations to be deployed. Each input layer node corresponds to one sensor location, and this node receives the current measured response value at the corresponding sensor location each time the model runs.

[0119] The node dimension of the output layer corresponds to the number of all nodes in the equipment field or the number of dense nodes in the target area, which serve as the output data.

[0120] In this implementation, when the output data consists of one-dimensional response values ​​at all nodes across the entire equipment, the output layer node dimension equals the total number of nodes. When the output data consists of one-dimensional response values ​​at dense nodes within the target region, the output layer node dimension equals the number of dense nodes within the target region. This correspondence between the output layer node dimension and the size of the output data nodes in the dataset ensures that the input-output mapping learned by the proxy model during offline training can be directly reproduced during online deployment. Each output layer node corresponds to a specific grid node in the discretized target equipment space or a specific dense node within the target region, and this correspondence remains unchanged throughout the entire offline training and online application process.

[0121] In some implementations, the step of collecting one-dimensional response measurement data of the same physical quantity at all sensor locations during the experiment, and extracting measurement data from a subset of the sensor locations to be deployed, includes:

[0122] Step S121: Real-time acquisition of one-dimensional response data of the same physical quantity at all sensor locations on the equipment through the data acquisition system; wherein, the all sensor locations include some sensor locations to be deployed, and the all sensor locations also include sensor locations used for verification.

[0123] In this embodiment, the total sensor positions may specifically include two sets of sensor positions, which are mutually exclusive and whose union is equal to the total sensor positions.

[0124] Specifically, the first group represents the proposed locations of some sensors. These sensor locations are consistent with the sensor installation locations used to extract input data during the offline phase of building the one-dimensional vector dataset. This group of sensors will serve a dual function during the online phase.

[0125] More specifically, on the one hand, the measured data collected by the sensor group is extracted and used as the input vector of the neural network surrogate model, driving the model to perform forward propagation to generate the full-field response prediction value. On the other hand, the deviation between the predicted value at the sensor location (extracted from the full-field response prediction value output by the model) and the measured data is incorporated into the calculation of the online optimization objective function.

[0126] Specifically, the second group consists of sensor locations used for verification. These locations are not among the planned deployment locations; that is, the response values ​​at these locations were not used as input data when constructing the one-dimensional vector dataset offline. This group of sensors performs a single function online. More specifically, the deviation between the predicted values ​​(extracted from the model's full-field response predictions) at these sensor locations and the measured data is also included in the calculation of the online optimization objective function. The measured data collected by this group of sensors is not input into the neural network surrogate model.

[0127] It is understandable that when the number of sensor locations involved in the online optimization objective function calculation is greater than the number of sensor locations in the model input, the objective function obtains prediction bias information from more spatial locations, and the gradient direction is jointly determined by the biases of more independent locations. This reduces the underestimation of local errors that may occur when the input sensor location happens to be in a region of gradual response change, and makes the direction of model parameter correction subject to more comprehensive spatial constraints.

[0128] In this embodiment, after the physical test of the target equipment begins, the data acquisition system can perform synchronous sampling on all sensor channels at a preset sampling frequency. The preset sampling frequency can be determined based on the rate of change of the test response and the hardware capabilities of the data acquisition system.

[0129] At each sampling time, the data acquisition system obtains a measured data vector. The dimension of this vector is equal to the number of all sensor locations. Each element in the vector corresponds to a measured data value of the one-dimensional response of the same physical quantity at that sensor location at that sampling time. Among the elements corresponding to all sensor locations, the elements belonging to the planned deployment sensor locations constitute the first subset of the vector, and the elements belonging to the sensor locations used for verification constitute the second subset of the vector. The first and second subsets do not intersect.

[0130] Step S122: Extract the measured data of the partial sensor locations to be deployed from the measured data of all sensor locations.

[0131] In this embodiment, a sensor location index mapping relationship can be pre-established. This mapping relationship records the index position of each sensor location in the total sensor measured data vector, and marks whether the sensor location belongs to the part of the sensor locations to be deployed or to the sensor locations used for verification.

[0132] After obtaining the measured data vector of all sensor locations in step S121, according to all the indices marked as the locations of the sensors to be deployed in the mapping relationship, the values ​​at the corresponding index positions are sequentially extracted from the measured data vector and assembled into an input vector in a manner consistent with the arrangement order of the input layer nodes of the neural network proxy model.

[0133] In some embodiments, the step of calculating the error based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations includes:

[0134] Step S151: Calculate the root mean square error between the predicted response values ​​at all sensor locations and the measured data at all sensor locations; wherein the root mean square error is the square root of the mean of the squares of the differences between the predicted response values ​​at each sensor location and the corresponding measured data.

[0135] In this embodiment, the difference between the predicted response value and the corresponding measured data at all sensor locations can be calculated to obtain the prediction error for each sensor location. The prediction errors for all sensor locations can be squared to eliminate the influence of the positive or negative direction of the error on the overall error calculation result. Then, the average of all squared errors is calculated, and the square root of the obtained average is calculated to obtain the root mean square error (RMSE) between the predicted response values ​​and the measured data at all sensor locations. The RMS error comprehensively reflects the overall degree of deviation between the predicted response values ​​and the measured data at all sensor locations.

[0136] In one specific implementation, the total sensor locations include the locations of some sensors to be deployed and the locations of sensors used for verification. Therefore, when calculating the root mean square error (RMSE), the errors between the predicted response values ​​and measured data at the locations of some sensors to be deployed, as well as the errors between the predicted response values ​​and measured data at the locations of sensors used for verification, can be used simultaneously to calculate the RMSE, so that the RMSE can reflect the overall consistency between the predicted results and the measured results at all sensor locations.

[0137] In some implementations, the step of fine-tuning the weights and thresholds of the neural network surrogate model online with error as the online optimization objective function includes:

[0138] Step S152: With minimizing the root mean square error as the optimization objective, the weights and thresholds of the neural network proxy model are updated using a gradient descent-type optimization algorithm; wherein the learning rate used in the online fine-tuning is less than the learning rate used in the offline training stage.

[0139] In this embodiment, the backpropagation parameter update during the online fine-tuning phase can specifically employ a gradient descent-type optimization algorithm. Specifically, the gradient descent-type optimization algorithm can include stochastic gradient descent and adaptive moment estimation algorithms.

[0140] In a specific implementation, at the current sampling time, after the root mean square error (RMSE) for that time has been calculated, this RMSE value can be used as the objective function value. Starting from the output layer of the neural network surrogate model, the partial derivatives of the objective function with respect to each weight parameter and each threshold parameter can be calculated layer by layer in reverse order along the network hierarchy. For each weight parameter, the partial derivative of the objective function value with respect to that parameter is calculated, yielding the gradient value for that parameter. The gradient value is also calculated for each threshold parameter. The gradient value indicates the local direction and rate of change of the objective function at the current parameter value. A positive gradient value indicates that increasing the parameter will lead to an increase in the objective function, while a negative gradient value indicates that increasing the parameter will lead to a decrease in the objective function. The absolute value of the gradient indicates the sensitivity of the objective function to changes in that parameter.

[0141] In this embodiment, the learning rate used in the online fine-tuning phase is lower than that used in the offline training phase. The learning rate in the offline training phase can be set to a relatively large value based on the network's convergence speed and training stability to ensure that the parameters are fully updated within a limited number of training epochs.

[0142] Understandably, during the offline training phase, the network parameters learn from a random initial state, requiring a large parameter update step size to quickly approach the optimal parameter region. After offline training, the network parameters are in a relatively optimal state, possessing the basic ability to infer the overall response from sparse measurement points. In the online fine-tuning phase, the goal of parameter updates is to fine-tune the current experimental physical reality while maintaining the learned physical laws, rather than relearning the input-output mapping relationship. If the online learning rate is too large, or the single update step size is too large, it may cause the parameters to deviate from the physical laws learned in the offline training phase, resulting in a decrease in prediction accuracy at subsequent sampling times. Using a smaller online learning rate, with each update making only small adjustments to the parameters, allows the model to gradually approach the current physical state, eliminating simulation-reality discrepancies while maintaining the stability of the mapping relationship from sparse measurement points to the overall response established during offline training.

[0143] In some implementations, the weights and thresholds of the neural network proxy model are updated once at each sampling time step, or once every preset number of sampling time steps.

[0144] In this embodiment, during the experiment, the data acquisition system can continuously acquire the measured one-dimensional response data of the same physical quantity at all sensor locations according to a preset sampling frequency. Each data acquisition completes one sampling time step. After completing steps S121 to S152 in each sampling time step, the weights and thresholds of the neural network surrogate model can be updated online according to a preset parameter update strategy.

[0145] In one specific implementation, weight and threshold updates can be performed at each sampling time step. That is, immediately after the root mean square error (RMSE) is calculated at the current sampling time step, the RMS error is used as the online optimization objective function to update the weights and thresholds of the neural network surrogate model. The updated neural network surrogate model is then used to process the measured data acquired at the next sampling time step. By performing parameter updates at each sampling time step, the neural network surrogate model can continuously adjust its network parameters based on the latest collected measured data, improving the model's adaptability to changes in the equipment's current response state.

[0146] In another specific implementation, the weights and thresholds can be updated every preset number of sampling time steps. After completing data acquisition, full-field response prediction, and root mean square error calculation for multiple consecutive sampling time steps, when the preset number of sampling time steps is reached, the weights and thresholds of the neural network surrogate model are updated online using the root mean square error corresponding to the current sampling time step. Between two adjacent parameter updates, the neural network surrogate model keeps its current parameters unchanged and performs response prediction on the data from each sampling time step.

[0147] In a specific and possible implementation, this method is applied to the real-time reconstruction and correction of full-field strain during the structural static test of a key connecting component of an air wing.

[0148] In this implementation scheme, a key connecting component of the wing is used as the target equipment. The test is conducted on a static test bench, where a multi-point coordinated loading system is used to apply static loads to the wing, and the full-field strain distribution of the key connecting component is monitored in real time to obtain the structural response state under load.

[0149] In the offline preparation phase of this implementation plan, numerical simulation analysis and dataset construction were performed. A high-precision finite element model of the wing connection component was established using finite element analysis software, with a total of approximately 200,000 model elements. The loading condition range was set according to the test outline, with the wingtip deflection ranging from 0 mm to 1200 mm and the loading angle ranging from -5 degrees to +5 degrees. Five hundred different loading condition combinations were generated within the above load range using the Latin hypercube sampling method, and nonlinear static analysis was performed on each combination.

[0150] During data extraction, single strain components at nodes corresponding to the 10 measurement points to be arranged in the physical experiment were extracted from the finite element model as input data. Simultaneously, the same strain component at all nodes of the key connecting components of the wing was extracted as output data, covering approximately 200,000 nodes. The system paired the input and output data for each set of working conditions to construct a one-dimensional vector dataset containing 500 samples.

[0151] In a specific and possible implementation, a fully connected deep neural network can be built as a neural network proxy model. The input layer node dimension of this model is equal to the number of sensor locations to be deployed, which is 10 in this implementation. Four hidden layers, each containing 256 neurons, can be set between the input and output layers, using a linear rectified activation function. The output layer node dimension corresponds to the total number of nodes in the target equipment, which is approximately 200,000 in this implementation. In this implementation, a direct output method is used.

[0152] The aforementioned one-dimensional vector dataset can be used to perform offline supervised training on the neural network. The optimizer employs the adaptive moment estimation algorithm, with an initial learning rate set to 0.001 and a loss function of the root mean square error at all nodes. Training is stopped when the loss value on the validation set no longer decreases, and the current weights and thresholds are saved, resulting in the initial neural network surrogate model.

[0153] During the test phase, the loading system was activated, and the data acquisition system collected measured strain data at all 30 sensor locations at a sampling frequency of 10 Hz.

[0154] During the forward inference process at the current sampling moment, measured data from 10 planned sensor locations are extracted from the measured data stream, constructed as input vectors, and input into the current neural network proxy model. After forward propagation, the predicted strain response values ​​at all nodes of the equipment are output.

[0155] During error calculation, predicted response values ​​corresponding to all 30 sensor locations are extracted from the predicted full-field strain response values. Simultaneously, the system acquires the actual measured values ​​at all 30 sensor locations at that moment. The root mean square error between the predicted response values ​​and the actual measured values ​​at these 30 sensor locations is calculated and used as the online optimization objective function for the current moment.

[0156] In a specific and possible implementation, a preset warning threshold can be set to control the triggering conditions for online fine-tuning. When the root mean square error calculated at the current moment exceeds the preset warning threshold, it can be determined that there is a large deviation between the prediction result of the current neural network surrogate model and the physical experimental state, triggering the online optimization mechanism. In this implementation, the preset warning threshold is set to 50 microstrains.

[0157] After triggering online optimization, the current input vector can be kept unchanged, and the optimization objective is to minimize the root mean square error at the current time step. One or more gradient descent updates are performed on the weights and thresholds of the neural network surrogate model. The weight parameters can be iteratively adjusted along the inverse direction of the gradient of the objective function with respect to the weight parameters, using the product of the learning rate and the gradient value as the update step size. In this implementation, the learning rate for online fine-tuning is set to 10 to the power of -5 to ensure the stability of parameter updates.

[0158] The forward propagation can be re-executed using the updated weights and thresholds to calculate and output the strain response values ​​at all nodes of the equipment at the current moment.

[0159] During the testing of this implementation scheme, when the wing was loaded to 80% of its design load, the relative error of strain prediction at the wing root using the neural network surrogate model without online correction was 15%. After enabling the real-time correction mechanism, the model parameters were fine-tuned online using measured data from all 30 sensor locations, reducing the relative error of strain prediction at all nodes across the entire field to within 5%. This corrected prediction result reflects the local stiffness distribution changes that the simulation model failed to capture.

[0160] According to embodiments of the present invention, such as Figure 4 As shown, an online adaptive correction device for a neural network surrogate model is provided, comprising:

[0161] The acquisition module is used to acquire the neural network proxy model obtained by offline training based on a one-dimensional vector dataset of multi-condition numerical simulation.

[0162] The acquisition module is used to acquire one-dimensional response measured data of the same physical quantity at all sensor locations during the experiment, and to extract measured data at a portion of the sensor locations to be deployed, wherein the portion of the sensor locations to be deployed is included in the total sensor locations.

[0163] The input module is used to input the measured data from the locations of the sensors to be deployed into the neural network proxy model to obtain the predicted one-dimensional response of the equipment across the entire field.

[0164] The extraction module is used to extract the predicted response values ​​at all sensor locations from the full-field one-dimensional response prediction values;

[0165] The fine-tuning module is used to calculate the error based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations, and to fine-tune the weights and thresholds of the neural network surrogate model online with the error as the online optimization objective function.

[0166] The output module is used to output the current one-dimensional response of the equipment across the entire field using an online fine-tuned neural network proxy model.

[0167] According to an embodiment of the present invention, an electronic device is provided; please refer to... Figure 5 The electronic device in this embodiment may include one or more of the following components: a processor, a network interface, memory, non-volatile memory, and one or more application programs, wherein the one or more application programs may be stored in non-volatile memory and configured to be executed by one or more processors, and the one or more programs are configured to perform the methods as described in the foregoing method embodiments.

[0168] According to embodiments of the present invention, a computer-readable storage medium is provided having a computer program stored thereon, which, when executed by a computer, causes the computer to perform the method described in any of the above embodiments.

[0169] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for online adaptive correction of a neural network surrogate model, characterized in that, include: Obtain a neural network surrogate model trained offline based on a one-dimensional vector dataset from multi-condition numerical simulation. During the experiment, one-dimensional response measurement data of the same physical quantity were collected at all sensor locations, and the measurement data at some of the planned sensor locations were extracted; wherein, the planned sensor locations are included in the total sensor locations. The measured data from the locations of some of the sensors to be deployed are input into the neural network proxy model to obtain the predicted one-dimensional response of the equipment across the entire field. Extract the predicted response values ​​at all sensor locations from the full-field one-dimensional response prediction values; The error is calculated based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations, and the weights and thresholds of the neural network surrogate model are fine-tuned online using the error as the online optimization objective function. The online fine-tuned neural network proxy model is used to output the current one-dimensional response of the equipment across the entire field.

2. The method according to claim 1, characterized in that, The steps for obtaining the neural network proxy model obtained through offline training based on a one-dimensional vector dataset from multi-condition numerical simulation include: Establish a three-dimensional finite element model of the equipment, and set material properties, contact relationships and boundary conditions according to the structural characteristics of the equipment; Based on the preset test load conditions and load range, batch numerical simulation analysis is carried out; Extract the one-dimensional response values ​​of the same physical quantity at some of the sensor locations to be deployed as input data, and extract the one-dimensional response values ​​of the same physical quantity at all nodes of the equipment or dense nodes within the target area as output data to construct a one-dimensional vector dataset. The neural network surrogate model is obtained by offline supervised training based on a one-dimensional vector dataset.

3. The method according to claim 2, characterized in that, The neural network proxy model includes an input layer, at least one hidden layer, and an output layer; The node dimension of the input layer is determined based on the number of sensor locations to be deployed. The node dimension of the output layer corresponds to the number of all nodes in the equipment field or the number of dense nodes in the target area, which serve as the output data.

4. The method according to claim 1, characterized in that, The process of collecting one-dimensional response measurement data of the same physical quantity at all sensor locations during the experiment, and extracting measurement data from a subset of the sensor locations to be deployed, includes: The data acquisition system acquires real-time measured data of the one-dimensional response of the same physical quantity at all sensor locations on the equipment; wherein, the all sensor locations include some sensor locations to be deployed, and also sensor locations used for verification. Extract measured data from the locations of the sensors to be deployed from the measured data at all sensor locations.

5. The method according to claim 4, characterized in that, The step of calculating the error based on the predicted response values ​​at all sensor locations and the measured data at all sensor locations includes: Calculate the root mean square error between the predicted response values ​​at all sensor locations and the measured data at all sensor locations; wherein the root mean square error is the square root of the mean of the squares of the differences between the predicted response values ​​and the corresponding measured data at each sensor location.

6. The method according to claim 5, characterized in that, The step of fine-tuning the weights and thresholds of the neural network surrogate model online with error as the online optimization objective function includes: With minimizing the root mean square error as the optimization objective, a gradient descent-type optimization algorithm is used to update the weights and thresholds of the neural network surrogate model; wherein, the learning rate used in online fine-tuning is less than the learning rate used in the offline training phase.

7. The method according to claim 6, characterized in that, The weights and thresholds of the neural network proxy model are updated once at each sampling time step, or once every preset number of sampling time steps.

8. An online adaptive correction device for a neural network surrogate model, characterized in that, include: The acquisition module is used to acquire the neural network proxy model obtained by offline training based on a one-dimensional vector dataset of multi-condition numerical simulation. The acquisition module is used to acquire one-dimensional response measured data of the same physical quantity at all sensor locations during the experiment, and to extract measured data at a portion of the sensor locations to be deployed, wherein the portion of the sensor locations to be deployed is included in the total sensor locations. The input module is used to input the measured data from the locations of the sensors to be deployed into the neural network proxy model to obtain the predicted one-dimensional response of the equipment across the entire field. The extraction module is used to extract the predicted response values ​​at all sensor locations from the full-field one-dimensional response prediction values; The fine-tuning module is used to calculate the error based on the predicted response values ​​and measured data at all sensor locations, and to fine-tune the weights and thresholds of the neural network surrogate model online using the error as the online optimization objective function. The output module is used to output the current one-dimensional response of the equipment across the entire field using an online fine-tuned neural network proxy model.

9. An electronic device, characterized in that, include: A memory, and one or more processors communicatively connected to the memory; The memory stores instructions that can be executed by the one or more processors to cause the one or more processors to implement the method as described in any one of claims 1 to 7.

10. A computer-readable storage medium, characterized in that, The readable storage medium stores a computer program that, when executed by a processor, implements the method of any one of claims 1 to 7.

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