Interpolation method for missing data of structural health monitoring, electronic equipment and program product

Abstract

The invention provides an interpolation method for structural health monitoring missing data, electronic equipment and a program product, and relates to the technical field of computers. The structure health monitoring missing data interpolation method comprises the following steps: acquiring time sequence observation data containing a plurality of sensor channels for a target structure, and generating a mask matrix corresponding to the time sequence observation data; according to the mask matrix, filling a data missing position in the time sequence observation data with random noise to obtain a target input matrix; inputting the target input matrix into a generative interpolation network, wherein the generative interpolation network comprises a generator and a discriminator; adversarial learning joint training is carried out on the generator and the discriminator, a target data interpolation model is obtained, and in the adversarial learning joint training process, a joint training loss function at least comprises a physical consistency loss item; and performing data interpolation on the to-be-interpolated time sequence observation data according to the target data interpolation model.

Description

Technical Field

[0001] This disclosure relates to the field of computer technology, and in particular to a method, electronic device and program product for interpolating missing data in structural health monitoring. Background Technology

[0002] Structural Health Monitoring (SHM) systems continuously collect dynamic response data of engineering structures (such as bridges, buildings, and tunnels) by deploying multiple types of sensors at key locations, providing data support for structural safety assessment and damage identification. In actual operation, however, sensor failures, communication interruptions, and other factors often lead to continuous and asynchronous data loss from multiple sensors, severely impacting subsequent structural condition assessments.

[0003] Among the current technical solutions, one is the discriminative method based on convolutional or recurrent neural networks, which relies on partial observation data at each time step and is difficult to handle the situation where all sensors are simultaneously and continuously missing. Another is the generative method based on generative adversarial networks. Although this method can model the data distribution, it does not fully consider the low-order characteristics of the structural dynamic response, and the generated data is prone to deviating from the physical laws under high missing rate. A third method is to introduce an explicit physical model as a constraint. This method mostly relies on an accurate finite element model, and traditional kernel norm regularization is prone to excessive decay of singular values, making it difficult to accurately maintain the dominant modal characteristics. Summary of the Invention

[0004] This disclosure provides a method, electronic device, and program product for interpolating missing data in structural health monitoring.

[0005] According to one aspect of this disclosure, a method for imputing missing data in structural health monitoring is provided, comprising: Acquire time-series observation data containing multiple sensor channels for a target structure, and generate a mask matrix corresponding to the time-series observation data. The time-series observation data contains continuous and synchronous missing data from multiple sensors, and the mask values ​​in the mask matrix are used to identify the missing data locations in the time-series observation data. Based on the mask matrix, random noise is filled at the missing data locations in the time series observation data to obtain the target input matrix; The target input matrix is ​​input into a generative interpolation network, which includes a generator and a discriminator. The generator generates interpolated complete time series data based on the target input matrix, and the discriminator determines whether the data value in the complete time series data is real data or interpolated data. The generator and the discriminator are jointly trained using adversarial learning to obtain the trained generator, which is then used as the target data interpolation model. During the adversarial learning joint training process, the joint training loss function includes at least a physical consistency loss term, which is used to constrain the interpolated data generated by the generator to maintain the low-order dynamic characteristics of the structural response. Based on the target data interpolation model, data interpolation is performed on the time series observation data to be interpolated where there are continuous and synchronous missing data from multiple sensors.

[0006] According to one technical solution, by acquiring time-series observation data containing multiple sensor channels and generating a corresponding mask matrix, the locations of continuous and synchronously missing data in the time-series observation data are clearly identified, providing structured missing information for subsequent processing. Next, a target input matrix is ​​constructed by filling the missing locations with random noise, and this matrix is ​​input into a generative interpolation network. This generative interpolation network includes a generator and a discriminator. An adversarial learning mechanism between the generator and the discriminator drives the generator to generate interpolated data that conforms to the real data distribution.

[0007] Furthermore, during the adversarial learning joint training process, a physical consistency loss term is introduced to constrain the generator's output, forcing its imputation results to maintain the low-order dynamic characteristics of the structural response. This ensures the physical rationality and consistency of the reconstructed data without pre-setting precise physical equations. Consequently, the trained generator can be directly used for fast and stable imputation of data with similar missing patterns. This effectively solves the data recovery problem in scenarios of continuous synchronous data loss, significantly improving the physical reliability and engineering applicability of the imputation results.

[0008] According to the structural health monitoring missing data imputation method of at least one embodiment of this disclosure, a physical consistency loss term is constructed, including: Perform a Hankel transform on the complete time series data to obtain the corresponding Hankel matrix; Singular value decomposition is performed on the Hankel matrix to obtain multiple singular values ​​corresponding to the Hankel matrix; Apply a non-convex penalty function to each of the singular values ​​to obtain the penalty amount corresponding to each of the singular values; Based on the penalty amounts corresponding to the multiple singular values, a physical consistency loss term is constructed.

[0009] According to the technical solution of this embodiment, the low-order dynamic characteristics of the structural response can be maintained more accurately, so that the constructed physical consistency loss term can enable the generator to generate interpolated data that conforms to the physical laws of the structure even when the monitoring data of multiple sensors is continuously and synchronously missing.

[0010] According to at least one embodiment of the structural health monitoring missing data imputation method of the present disclosure, the generator includes a dilated temporal convolutional network, the dilated temporal convolutional network including multiple one-dimensional causal dilated convolutional layers; The generator generates interpolated complete time series data based on the target input matrix, including: The target input matrix is ​​subjected to time series feature extraction through multiple one-dimensional causal dilated convolutional layers to obtain multi-channel time series features; Based on the multi-channel time series characteristics, complete time series data after data interpolation is generated.

[0011] According to the technical solution of this embodiment, the multi-layer causal dilated convolutional structure of the dilated temporal convolutional network enables the model to effectively capture the long-range temporal dependencies in the structural dynamic response, ensuring the causality of the temporal prediction, avoiding future information leakage, and meeting the physical rationality requirements of structural health monitoring data processing.

[0012] According to the structural health monitoring missing data imputation method of at least one embodiment of the present disclosure, the dilation rate of the multilayer one-dimensional causal dilated convolutional layers increases layer by layer, and the receptive field of each one-dimensional causal dilated convolutional layer is fixed.

[0013] According to the technical solution of this embodiment, the dilated temporal convolutional network can obtain a huge receptive field covering the entire long-term continuous missing interval with a relatively small number of layers. This enables the explicit capture and generation of coherent temporal data that spans long missing intervals and conforms to evolutionary patterns. Furthermore, by keeping the receptive field fixed in each one-dimensional causal dilated convolutional layer (which can be achieved by fixing the convolutional kernel width), the structure of the dilated temporal convolutional network can be more regular and modular, reducing the complexity of hyperparameter design and ensuring the stability and convergence efficiency of model training.

[0014] According to at least one embodiment of the structural health monitoring missing data imputation method of the present disclosure, the generator further includes a local sparse multi-head attention module; Based on the multi-channel time series characteristics, complete time series data after data interpolation is generated, including: Based on the local sparse multi-head attention module, in the time region where real data exists in the target input matrix, a cross-channel correlation matrix is ​​determined between multiple sensor channels. The cross-channel correlation matrix is ​​used to describe the correlation between the monitoring data of each sensor when multiple sensors monitor the same structure. Based on the multi-channel time series characteristics and the cross-channel correlation matrix, complete time series data after data interpolation is generated.

[0015] According to the technical solution of this embodiment, the cross-channel correlation matrix between sensors is explicitly modeled in the real data time region by a local sparse multi-head attention module. By making full use of the spatial continuity prior of the structural dynamic response, the generator can infer the reasonable response of other sensor channels in the same time region based on the real data of some sensor channels, and provide a spatial dimension constraint for data interpolation in the missing areas of continuous synchronization of monitoring data.

[0016] According to at least one embodiment of the structural health monitoring missing data imputation method of this disclosure, the discriminator determines whether the data value in the complete time series data is real data or imputed data, including: The discriminator performs binary classification on each data value in the complete time series data based on the complete time series data and the corresponding cue matrix, and outputs the probability of each data value being real data. The cue matrix is ​​generated based on the mask matrix and is used to partially reveal whether each data value in the complete time series data is real data or imputed data.

[0017] According to the technical solution of this embodiment, by providing partially real missing information (i.e., a cue matrix) as "cues," it is equivalent to providing a weak supervision signal for the discriminator's learning process. This helps alleviate the pattern collapse and instability problems commonly found in generative adversarial network training, guides the discriminator and generator to converge more efficiently, accelerates the overall training speed, and improves the training success rate.

[0018] According to at least one embodiment of the structural health monitoring missing data imputation method of this disclosure, the joint training loss function further includes an adversarial loss term and an observation consistency loss term, wherein the adversarial loss term is used to constrain the imputation data generated by the generator to be consistent with the real data in terms of data distribution; the observation consistency loss term is used to constrain the values ​​at the existing real data positions in the complete time series data generated by the generator to be consistent with the original real data.

[0019] According to the technical solution of this embodiment, the weighted combination of the three loss terms enables the generator to maintain the accuracy of the observation data and generate imputation data that conforms to physical laws and has a real distribution in the scenario of continuous synchronous missing data of multi-sensor monitoring data. This significantly improves the imputation accuracy and robustness under high missing rate conditions and overcomes the technical defects of a single loss function that makes it difficult to take into account the authenticity of data, the consistency of observation and the physical rationality.

[0020] According to at least one embodiment of the structural health monitoring missing data interpolation method of the present disclosure, the time series observation data includes one or more of multi-channel vibration, displacement, acceleration or strain data for the target structure.

[0021] The technical solution of this embodiment can cover a variety of monitoring needs, from dynamic characteristic analysis to static condition assessment. This allows the method to be flexibly deployed in structural health monitoring systems for various important infrastructures (bridges, buildings, dams, etc.).

[0022] According to another aspect of this disclosure, an interpolation device for missing structural health monitoring data is provided, the device comprising: The acquisition module is used to acquire time-series observation data containing multiple sensor channels for the target structure and generate a mask matrix corresponding to the time-series observation data. The time-series observation data contains continuous synchronous missing data from multiple sensors, and the mask values ​​in the mask matrix are used to identify the missing data locations in the time-series observation data. The filling module is used to fill random noise at the missing data positions in the time series observation data according to the mask matrix to obtain the target input matrix; An input module is used to input the target input matrix into a generative interpolation network. The generative interpolation network includes a generator and a discriminator. The generator generates interpolated complete time series data based on the target input matrix, and the discriminator judges whether the data value in the complete time series data is real data or interpolated data. The training module is used to perform adversarial learning joint training on the generator and the discriminator to obtain the trained generator and use it as the target data imputation model. In the process of adversarial learning joint training, the joint training loss function includes at least a physical consistency loss term. The physical consistency loss term is used to constrain the imputation data generated by the generator to maintain the low-order dynamic characteristics of the structural response. The processing module is used to perform data interpolation on the time series observation data to be interpolated that has continuous synchronous missing data from multiple sensors, based on the target data interpolation model.

[0023] According to another aspect of this disclosure, an electronic device is provided, comprising: a memory storing execution instructions; and a processor executing the execution instructions stored in the memory, causing the processor to perform a structural health monitoring missing data interpolation method according to any embodiment of this disclosure.

[0024] According to another aspect of this disclosure, a readable storage medium is provided, wherein executable instructions are stored therein, which, when executed by a processor, are used to implement a method for interpolating missing structural health monitoring data according to any embodiment of this disclosure.

[0025] According to another aspect of this disclosure, a computer program product is provided, including a computer program that, when executed by a processor, implements a method for interpolating missing structural health monitoring data according to any embodiment of this disclosure.

[0026] The beneficial technical effect of this disclosure is that by constraining the low-order dynamic characteristics of the interpolation results through physical consistency loss, it ensures the rationality and consistency of the reconstructed data in a physical sense without relying on precise physical equations, thus solving the problem of data recovery from continuous synchronization loss of all sensors. Attached Figure Description

[0027] The accompanying drawings illustrate exemplary embodiments of the present disclosure and, together with the description thereof, serve to explain the principles of the present disclosure. These drawings are included to provide a further understanding of the present disclosure and are incorporated in and constitute a part of this specification.

[0028] Figure 1 This is a flowchart illustrating a method for interpolating missing structural health monitoring data according to one embodiment of this disclosure.

[0029] Figure 2 This is a flowchart illustrating the process of constructing a physical consistency loss term in a method for imputing missing structural health monitoring data according to one embodiment of this disclosure.

[0030] Figure 3 This is a schematic diagram of the generator's processing flow in a structural health monitoring missing data interpolation method according to one embodiment of this disclosure.

[0031] Figure 4 This is a flowchart illustrating step S320 of a structural health monitoring missing data interpolation method according to one embodiment of this disclosure.

[0032] Figure 5 This is a schematic diagram of the processing flow of a method for interpolating missing structural health monitoring data according to another embodiment of this disclosure.

[0033] Figure 6-11 This is a schematic diagram of the data interpolation result in the time domain of a structural health monitoring missing data interpolation method according to an embodiment of the present disclosure.

[0034] Figure 12 This is a schematic structural block diagram of a device for interpolating missing data in structural health monitoring according to one embodiment of the present disclosure.

[0035] Figure 13 This is a schematic structural block diagram of an electronic device according to one embodiment of the present disclosure. Detailed Implementation

[0036] The present disclosure will now be described in further detail with reference to the accompanying drawings and examples. It should be understood that the specific examples described herein are for illustrative purposes only and are not intended to limit the scope of the disclosure. Furthermore, it should be noted that, for ease of description, only the parts relevant to the present disclosure are shown in the accompanying drawings.

[0037] It should be noted that, where there is no conflict, the embodiments and features described in this disclosure can be combined with each other. The technical solutions of this disclosure will now be described in detail with reference to the accompanying drawings and embodiments.

[0038] Existing technologies struggle to balance the accuracy of data distribution with constraints on low-order structural dynamics when processing missing data from multiple sensors in structural health monitoring, especially when observational information is lacking in the missing regions. This results in interpolation results that easily deviate from physical laws and lack accuracy.

[0039] To address this, this disclosure proposes the following technical solution: by acquiring time-series observation data containing multiple sensor channels and generating a corresponding mask matrix, the locations of continuous and synchronously missing data in the time-series observation data are clearly identified, providing structured missing information for subsequent processing. Next, a target input matrix is ​​constructed by filling the missing locations with random noise, and this matrix is ​​input into a generative interpolation network. This generative interpolation network includes a generator and a discriminator. An adversarial learning mechanism between the generator and the discriminator drives the generator to generate interpolated data that conforms to the real data distribution.

[0040] Furthermore, during the adversarial learning joint training process, a physical consistency loss term is introduced to constrain the generator's output, forcing its imputation results to maintain the low-order dynamic characteristics of the structural response. This ensures the physical rationality and consistency of the reconstructed data without pre-setting precise physical equations. Consequently, the trained generator can be directly used for fast and stable imputation of data with similar missing patterns. This effectively solves the data recovery problem in scenarios of continuous synchronous data loss, significantly improving the physical reliability and engineering applicability of the imputation results.

[0041] Figure 1 This is a flowchart illustrating a method for interpolating missing structural health monitoring data according to one embodiment of this disclosure. This method can be applied to terminal devices (such as smartphones, tablets, laptops, etc.) or servers. The following explanation uses the application of this method to a server as an example.

[0042] like Figure 1 As shown, the method for interpolating missing data in structural health monitoring preferably includes steps S110 to S150.

[0043] In step S110, time-series observation data containing multiple sensor channels for the target structure is acquired, and a mask matrix corresponding to the time-series observation data is generated. The time-series observation data contains continuous and synchronous missing data from multiple sensors, and the mask value in the mask matrix is ​​used to identify the missing data locations in the time-series observation data.

[0044] The time-series observation data consists of periodically collected monitoring data from a structural health monitoring system that is not part of the target structure (such as a bridge or high-rise building), and includes multiple sensor channels. Each sensor channel corresponds to an independent physical sensor (such as an accelerometer or strain gauge), and the monitoring data recorded in chronological order constitute a time series. Therefore, the time-series observation data can be represented as a multidimensional matrix. ,in N For the number of sensor channels, T This refers to the duration of the time.

[0045] Preferably, the time-series observation data includes one or more of the following: multi-channel vibration, displacement, acceleration, or strain data for the target structure. By supporting the processing of the four core response data types in structural health monitoring systems—vibration, displacement, acceleration, and strain—this disclosed technical solution can cover a variety of monitoring needs, from dynamic characteristic analysis to static state assessment. This allows the method to be flexibly deployed in structural health monitoring systems for various important infrastructures (bridges, buildings, dams, etc.) to repair their critical monitoring data, significantly improving the applicability and market application potential of this disclosed technical solution.

[0046] Continuous synchronous data loss from multiple sensors refers to the phenomenon where multiple sensor channels simultaneously experience data loss within the same continuous time period during structural health monitoring. The loss pattern manifests as multiple sensor channel rows exhibiting consecutive data loss within the same time interval.

[0047] The mask matrix is ​​a binary matrix with the same dimensions as the time series observation data. M ∈{0,1} N×T In the mask matrix M In the diagram, a mask value of 1 indicates that the corresponding position contains actual observation data, while a mask value of 0 indicates that the corresponding position contains missing data.

[0048] In this embodiment, the server obtains raw monitoring data from multiple sensor channels within a target time period from a structural health monitoring system deployed for the target structure, and aligns the raw monitoring data from multiple sensor channels in time to form time-series observation data.

[0049] The server iterates through each element in the time-series observation data. If the element's value exceeds a pre-defined range or is null, it assigns a value of 0 to the corresponding position in the mask matrix; if the element's value is not null and falls within the pre-defined range, it assigns a value of 1 to the corresponding position in the mask matrix. After iterating through all elements, the resulting data has a dimension of [dimension value missing]. N × T The mask matrix.

[0050] It should be noted that, for scenarios where continuous synchronization of multi-sensor monitoring data is missing, the mask matrix will present a blocky missing pattern where multiple channel rows are simultaneously zero within consecutive time column intervals. This missing pattern differs from random missing or single-channel missing data, posing a greater challenge to data imputation.

[0051] In step S120, random noise is filled at the missing data locations in the time series observation data according to the mask matrix to obtain the target input matrix.

[0052] In this implementation, the server generates a random matrix with the same dimension as the time series observation data. Each element in the random matrix is ​​independently sampled from a preset data distribution (such as a standard normal distribution), which is a random noise value.

[0053] The server iterates through the mask matrix, checking the coordinates of positions where the mask value is 0. It then replaces the data values ​​in the time-series observation data corresponding to these coordinates with random noise values ​​from the corresponding positions in a random matrix, thus obtaining the target input matrix.

[0054] Thus, in the resulting target input matrix, the original real data is retained at the positions with a mask value of 1, while random noise is filled at the positions with a mask value of 0. By introducing random noise at the missing data positions in the time series observation data instead of simply filling in zero values ​​or the mean, the generator is provided with an initial uncertain input, avoiding the supervised "input-output" mapping assumption. This prompts the generator to actively learn the conditional probability distribution from noise to real data rather than a fixed functional relationship during the adversarial learning joint training process.

[0055] In step S130, the target input matrix is ​​input into a generative interpolation network, which includes a generator and a discriminator. The generator generates complete time series data after data interpolation based on the target input matrix, and the discriminator determines whether the data value in the complete time series data is real data or interpolated data.

[0056] In this embodiment, the server uses the target input matrix generated in the aforementioned steps as input to a generative interpolation network for corresponding data processing. This generative interpolation network includes a generator and a discriminator. The generator processes the data based on the target input matrix, outputting a complete time series dataset with the same dimensions as the target input matrix, where all positions are filled with data values. The discriminator identifies the data values ​​in the complete time series dataset, determining whether the data value is real data or interpolated data.

[0057] In step S140, the generator and the discriminator are jointly trained using adversarial learning to obtain the trained generator, which is then used as the target data interpolation model. During the adversarial learning joint training process, the joint training loss function includes at least a physical consistency loss term, which is used to constrain the interpolated data generated by the generator to maintain the low-order dynamic characteristics of the structural response.

[0058] Among them, adversarial learning joint training refers to the process of generator and discriminator cooperating in training through alternating optimization. The generator aims to generate imputed data that is difficult for the discriminator to distinguish, while the discriminator aims to accurately identify real data and imputed data.

[0059] The joint training loss function is the objective function used to guide the updating of model parameters during the joint training process of adversarial learning.

[0060] The physical consistency loss term is a regularization constraint term constructed based on low-order structural dynamics characteristics. It is used to constrain the interpolated data generated by the generator to maintain the low-order dynamic characteristics of the structural response. These low-order dynamic characteristics are typically manifested as strong correlations between multi-channel time series signals (such as complete time series data generated by the generator) in the time and spatial domains. The matrix formed by these signals, or the matrix after certain transformations, has low rank. Maintaining these low-order dynamic characteristics means that the interpolated data generated by the generator should not disrupt this inherent correlation structure.

[0061] In this implementation, during adversarial learning joint training, the target input matrix is ​​input into the generator, and the generator performs corresponding data processing based on the target input matrix to output a complete time series data after data interpolation.

[0062] Next, the complete time series data is input into the discriminator, which identifies the data values ​​in the complete time series data and outputs the judgment result for each data value as either real data or imputed data.

[0063] Based on the generator's output (i.e., complete time-series data) and the discriminator's output (i.e., the judgment result of whether it is real data or imputed data), a joint training loss function is constructed. The model parameters of the generator or discriminator are then optimized based on the loss value of this joint training loss function until a preset number of training epochs or convergence of the loss value is achieved. At this point, the trained generator can be used as the target data imputation model to impute time-series observation data in real-world application scenarios where there are continuous synchronous gaps in multi-sensor monitoring data.

[0064] It is worth noting that the joint training loss function includes at least a physical consistency loss term. By introducing a physical consistency loss term into the joint training loss function, the problem of excessive decay of singular values ​​caused by traditional nuclear norm regularization is effectively overcome, enabling the interpolated data generated by the generator to accurately maintain the dominant modal characteristics and low-order dynamic properties of the structural response.

[0065] In step S150, data interpolation is performed on the time series observation data to be interpolated that has continuous synchronous missing data from multiple sensors, according to the target data interpolation model.

[0066] Among them, the time series observation data to be interpolated can be newly generated during the actual operation of the structural health monitoring system or historical archived monitoring data that needs data repair.

[0067] In this embodiment, after acquiring the time series observation data to be interpolated that has continuous synchronous missing data from multiple sensors, the time series observation data to be interpolated can be subjected to the same data preprocessing as in the model training stage, such as channel normalization and outlier removal.

[0068] Next, a corresponding mask matrix is ​​generated based on the time series observation data to be interpolated. Then, based on the mask matrix, random noise with the same data distribution as the training phase is filled into the missing data positions in the time series observation data to be interpolated, so as to obtain the target input data corresponding to the time series observation data to be interpolated.

[0069] The target input data is fed into the trained generator (i.e., the target data interpolation model), and the generator outputs the complete time series data after data interpolation, thus completing the data interpolation process.

[0070] Thus, the technical solution disclosed herein, by acquiring time-series observation data containing multiple sensor channels and generating a corresponding mask matrix, clearly identifies the locations where continuous synchronization is missing in the time-series observation data, providing structured missing information for subsequent processing. Next, a target input matrix is ​​constructed by filling the missing locations with random noise, and this matrix is ​​input into a generative interpolation network. This generative interpolation network includes a generator and a discriminator, and the generator is driven to generate interpolated data that conforms to the real data distribution through an adversarial learning mechanism between the generator and the discriminator.

[0071] Furthermore, during the adversarial learning joint training process, a physical consistency loss term is introduced to constrain the generator's output, forcing its imputation results to maintain the low-order dynamic characteristics of the structural response. This ensures the physical rationality and consistency of the reconstructed data without pre-setting precise physical equations. Consequently, the trained generator can be directly used for fast and stable imputation of data with similar missing patterns. This effectively solves the data recovery problem in scenarios of continuous synchronous data loss, significantly improving the physical reliability and engineering applicability of the imputation results.

[0072] In some embodiments of this disclosure, constructing the physical consistency loss term preferably includes steps S210 to S240, please refer to... Figure 2 .

[0073] In step S210, the complete time series data is subjected to Hankel transformation to obtain the corresponding Hankel matrix.

[0074] In step S220, singular value decomposition is performed on the Hankel matrix to obtain multiple singular values ​​corresponding to the Hankel matrix.

[0075] In step S230, a non-convex penalty function is applied to each of the singular values ​​to obtain the penalty amount corresponding to each of the singular values.

[0076] In step S240, a physical consistency loss term is constructed based on the penalty amounts corresponding to the multiple singular values.

[0077] In this implementation, the complete time series data output by the generator is subjected to a Hankel transformation to obtain the corresponding Hankel matrix (i.e., a matrix structure in which the sum of the row index and the column index is a constant and the elements have the same value, which can effectively characterize the time-shift invariant properties of the time series data).

[0078] Next, singular value decomposition is performed on the transformed Hankel matrix to calculate the multiple singular values ​​corresponding to the Hankel matrix. Each singular value is then substituted into a non-convex penalty function (such as the SCAD (Smoothly Clipped Absolute Deviation) penalty function) to calculate the penalty amount for each singular value. It should be noted that by applying a non-convex penalty function to each singular value, a stronger penalty can be imposed on smaller singular values ​​to promote sparsity, while a weaker penalty can be imposed on larger singular values ​​to avoid excessive decay.

[0079] Once the penalty for each singular value is calculated, the penalties for all singular values ​​can be summed to obtain the corresponding physical consistency loss term.

[0080] Preferably, a Hankel transform is performed on the time series data of each sensor channel in the complete time series data. Singular value decomposition is then performed on the Hankel matrix corresponding to each sensor channel, and a non-convex penalty function is applied. The penalty amounts of each singular value for the same sensor channel are summed to obtain the physical constraint loss for that sensor channel. Then, the physical constraint losses of all sensor channels are averaged to obtain the physical consistency loss term corresponding to the complete time series data.

[0081] Thus, the complete time series data is transformed into a matrix structure that can characterize time-shift invariant properties through Hankel transformation. Combined with singular value decomposition, the dominant modal features of the structural response are effectively extracted. Then, a physical consistency loss term is constructed using a non-convex penalty function. Compared with traditional kernel norm regularization methods that apply a uniform penalty to all singular values, this method can more accurately preserve the low-order dynamic characteristics of the structural response. This allows the constructed physical consistency loss term to enable the generator to generate interpolated data that conforms to the physical laws of the structure even when there is a continuous synchronous loss of multi-sensor monitoring data.

[0082] In some embodiments of this disclosure, the generator includes a dilated temporal convolutional network comprising multiple layers of one-dimensional causal dilated convolutional layers. The generator generates interpolated complete time-series data based on the target input matrix, preferably including steps S310 to S320, as detailed below. Figure 3 .

[0083] In step S310, the target input matrix is ​​subjected to time series feature extraction through multiple one-dimensional causal dilated convolutional layers to obtain multi-channel time series features.

[0084] In step S320, complete time series data after data interpolation is generated based on the multi-channel time series characteristics.

[0085] Among them, the dilated temporal convolutional network is a temporal feature extraction network built based on causal dilated convolutional operations.

[0086] A one-dimensional causal dilated convolutional layer is a convolutional layer in which the convolution kernel is only convolved with the current time step and the historical time step (i.e., it does not depend on future information and strictly guarantees the causality of the time series data generation process), and an dilation coefficient is introduced in the time dimension.

[0087] In this implementation, the target input matrix is ​​fed into multiple one-dimensional causal dilated convolutional layers. In each one-dimensional causal dilated convolutional layer, the input undergoes one-dimensional dilation convolution. After passing through multiple one-dimensional causal dilated convolutional layers, the output is a multi-channel time-series feature corresponding to the target input matrix. Through this hierarchical structure (i.e., multiple one-dimensional causal dilated convolutional layers), shallow networks capture short-term, localized change patterns, while deep networks, due to the cumulative effect of the dilation rate, possess a receptive field covering the entire missing interval or even a longer historical context, thus enabling the modeling of long-term evolutionary trends.

[0088] Preferably, after each one-dimensional causal dilated convolutional layer, a nonlinear activation function (such as ReLU), a normalization layer (optionally, such as a weight normalization layer) and a residual connection are sequentially connected, which are used to stabilize training.

[0089] Next, after obtaining the multi-channel time series features, the generator maps the high-dimensional multi-channel time series features back to the original physical data space through one or more subsequent network layers (such as using a one-dimensional convolutional layer with a kernel width of 1 as the output layer), and finally generates a matrix with the same dimension as the target input matrix, which is the complete time series data after data interpolation.

[0090] Thus, by using the multi-layer causal dilated convolutional structure of the dilated temporal convolutional network, the model can effectively capture the long-range temporal dependencies in the structural dynamic response, ensuring the causality of the temporal prediction, avoiding future information leakage, and meeting the physical rationality requirements of structural health monitoring data processing.

[0091] In some embodiments of this disclosure, the dilation rate of the multilayer one-dimensional causal dilated convolutional layers increases layer by layer, and the receptive field of each one-dimensional causal dilated convolutional layer is fixed.

[0092] The dilation rate is used to compensate for the spacing between kernel elements in a one-dimensional causal dilated convolutional layer, and is used to control the sampling span of the convolution operation in the time dimension.

[0093] The receptive field is the number of time steps that a given output unit in a one-dimensional causal dilated convolutional layer covers on its direct input (i.e., the output of the previous layer).

[0094] In this embodiment, the dilation rate of each layer in a multi-layer one-dimensional causal dilation convolutional layer is increased progressively according to a predetermined pattern. Preferably, the dilation rate of the multi-layer one-dimensional causal dilation convolutional layer increases progressively in a geometric progression (e.g., base 2). For example, the dilation rate of the first causal dilation convolutional layer is 1, the dilation rate of the second causal dilation convolutional layer is 2, the dilation rate of the third causal dilation convolutional layer is 4, ..., and the dilation rate of the Lth causal dilation convolutional layer is 2. L-1 .

[0095] Thus, dilated temporal convolutional networks can obtain a large receptive field covering the entire long-term continuous missing interval with a relatively small number of layers. This enables the explicit capture and generation of coherent and evolution-compliant temporal data spanning long missing intervals.

[0096] Furthermore, in each one-dimensional causal dilated convolutional layer, the receptive field is kept fixed (which can be achieved by fixing the kernel width), making the dilated temporal convolutional network structure more regular and modular, reducing the complexity of hyperparameter design, and ensuring the stability and convergence efficiency of model training.

[0097] In some embodiments of this disclosure, the generator further includes a locally sparse multi-head attention module; step S320, generating the complete time series data after data interpolation based on the multi-channel time series characteristics, preferably includes steps S321 to S322, please refer to... Figure 4 .

[0098] In step S321, based on the local sparse multi-head attention module, a cross-channel correlation matrix is ​​determined in the time region where real data exists in the target input matrix. The cross-channel correlation matrix is ​​used to describe the correlation between the monitoring data of each sensor when multiple sensors monitor the same structure.

[0099] In step S322, complete time series data after data interpolation is generated based on the multi-channel time series characteristics and the cross-channel correlation matrix.

[0100] Among them, the local sparse multi-head attention module refers to a neural network module that divides the input sequence into multiple local time windows and performs sparse attention calculations in each window. By limiting the scope of attention calculations and sparse attention weights, it significantly reduces computational complexity while maintaining modeling capabilities.

[0101] In this implementation, the multi-channel time series feature tensor is divided into non-overlapping local windows of a predetermined window length according to the time dimension. This predetermined window length is set based on the dominant frequency period of the structural dynamic response (e.g., twice the dominant frequency period). Within each local window, for the real data time region with a mask value of 1, feature vectors from each sensor channel are extracted to construct a query matrix Q, a key matrix K, and a value matrix V, where Q, K, and V all have a dimension of N×d. k N is the number of sensor channels, d k For feature dimensions.

[0102] Then, the attention weight matrix is ​​calculated and sparsified (e.g., the top-k attention weights with the largest absolute values ​​in each row are retained (k is 20% of the number of sensor channels N, and k≥3), and the remaining weights are reset to zero) to form a sparse attention weight matrix. The value matrix V is then weighted and fused using the sparse attention weight matrix to obtain a feature representation of cross-channel correlation.

[0103] The output features of all local windows are concatenated along the time dimension to obtain the cross-channel correlation matrix between multiple sensor channels. This matrix is ​​then residually connected to the multi-channel time series features output by the dilated time convolutional network. Finally, it is processed by a feedforward neural network layer to generate the complete time series data after data interpolation.

[0104] In this way, by explicitly modeling the cross-channel correlation matrix between sensors in the real data time region through the local sparse multi-head attention module, the spatial continuity prior of the structural dynamic response is fully utilized, enabling the generator to infer the reasonable response of other sensor channels in the same time region based on the real data of some sensor channels, providing a spatial dimension constraint for data interpolation in the missing regions of continuous synchronization of monitoring data.

[0105] In some embodiments of this disclosure, the discriminator's determination of whether the data value in the complete time series data is real data or interpolated data preferably includes: The discriminator performs binary classification on each data value in the complete time series data based on the complete time series data and the corresponding cue matrix, and outputs the probability of each data value being real data. The cue matrix is ​​generated based on the mask matrix and is used to partially reveal whether each data value in the complete time series data is real data or imputed data.

[0106] In this embodiment, based on the complete time-series data output by the generator, a cue matrix of the same dimension as the complete time-series data is generated. The data values ​​in this cue matrix are generated based on a mask matrix, thereby selectively and partially revealing whether the data values ​​in the complete time-series data are real data or imputed data. Preferably, some elements in the mask matrix can be randomly inverted (e.g., some "0"s can be replaced with "1", or some "1"s can be replaced with "0") to obtain the cue matrix, thus providing only incomplete real information as clues to the discriminator.

[0107] The complete time series data output by the generator and the cue matrix are used as input to the discriminator. In the discriminator, multiple fully connected layers and nonlinear activation functions are used to perform multiple nonlinear transformations to extract deep discriminative features from the input data. The last fully connected layer outputs a probability value for each data value in the complete time series data, representing the likelihood that the data is a real data point. This probability value ranges from 0 to 1; the closer the probability value is to 1, the more confident the discriminator is that the data is real; the closer the probability value is to 0, the more confident the discriminator is that the data is imputed data generated by the generator.

[0108] Thus, by providing partially true missing information (i.e., the cue matrix) as "cues," it is equivalent to providing a weak supervision signal for the discriminator's learning process. This helps alleviate the pattern collapse and instability problems commonly found in generative adversarial network training, guiding the discriminator and generator to converge more efficiently, accelerating the overall training speed, and improving the training success rate.

[0109] In some publicly disclosed implementations, the joint training loss function further includes an adversarial loss term and an observation consistency loss term, wherein the adversarial loss term is used to constrain the imputation data generated by the generator to be consistent with the real data in terms of data distribution; and the observation consistency loss term is used to constrain the values ​​at existing real data positions in the complete time series data generated by the generator to be consistent with the original real data.

[0110] Among them, the adversarial loss term is a component of the loss function constructed based on the adversarial game between the generator and the discriminator, which is used to measure the difference between the data distribution of the imputed data generated by the generator and the data distribution of the real data.

[0111] The observation consistency loss term is the loss function component that ensures the constraint generator output remains consistent with the original real data at the positions marked as valid observations in the mask matrix (i.e., positions with a mask value of 1).

[0112] In this implementation, when constructing the joint training loss function, in addition to considering the physical consistency loss term, adversarial loss term and observation consistency loss term can also be considered.

[0113] Preferably, when constructing the adversarial loss term, the discriminator loss is calculated using binary cross-entropy loss based on the discriminator's output. Then, based on the principle of minimizing the discriminator's output, the generator's adversarial loss term is calculated. By minimizing this adversarial loss term, the generator attempts to make the discriminator give a high-probability output at the missing position.

[0114] Preferably, when constructing the observation consistency loss term, the position coordinates of all positions with a mask value of 1 are extracted from the mask matrix, and the mean square error between the generator's generated data and the original real data at the corresponding position coordinates is calculated, thereby obtaining the observation consistency loss term.

[0115] Thus, by synergistically combining the three components of the joint training loss function (i.e., the adversarial loss term, the observation consistency loss term, and the physical consistency loss term), an organic integration of data-driven and physical constraints is achieved. The adversarial loss term drives the generator to produce interpolated data whose distribution approximates the true structural response distribution (i.e., the distribution of the real data), enhancing the statistical realism and diversity of the interpolation results and avoiding the oversmoothing phenomenon produced by discriminative methods. The observation consistency loss term strictly constrains the generator to maintain the original data at the real data locations, ensuring that the data interpolation process does not destroy existing real information and maintains data integrity. The physical consistency loss term guides the generator to produce interpolated data that conforms to the low-order characteristics of structural dynamics, compensating for the lack of observational information in continuously missing synchronous regions. The weighted combination of the three loss terms enables the generator to maintain the accuracy of the observational data and generate interpolated data that conforms to physical laws and has a realistic distribution in scenarios with continuously missing synchronous multi-sensor monitoring data. This significantly improves the interpolation accuracy and robustness under high missing rate conditions, overcoming the technical shortcomings of a single loss function that cannot simultaneously consider data authenticity, observation consistency, and physical rationality.

[0116] Figure 5 This is a schematic diagram of the processing flow of a method for interpolating missing structural health monitoring data according to another embodiment of this disclosure.

[0117] like Figure 5 As shown, in the Input stage (left half of the attached diagram), Features represent the time-series observation data from multiple sensor channels. The "xxx" in the matrix indicates a situation where multiple sensor monitoring data are continuously and synchronously missing, meaning that multiple sensors simultaneously lack data within the same time period. Time represents the time dimension, and the row direction of the matrix represents the time step sequence.

[0118] Missing data, marked with "xxx" in the figure, represents the continuous synchronous missing data caused by sensor failure or communication interruption during the target structure monitoring process.

[0119] A mask matrix is ​​a binary matrix with the same dimension as the time series observation data. A "1" indicates the presence of valid observation data (true data) at that location, while a "0" indicates missing data at that location. The mask matrix is ​​used to accurately identify the locations of missing data in the time series observation data, providing location guidance for subsequent processing.

[0120] Random noise is a random numerical sequence used to fill in missing positions. It is sampled from a preset probability distribution (such as the standard normal distribution) and provides the generator with initial uncertainty input.

[0121] In the input phase, a mask matrix is ​​generated based on the time-series observation data. Then, based on the mask matrix, random noise is filled into the missing data locations in the time-series observation data (i.e., locations where the mask value is 0), forming a complete target input matrix. The target input matrix preserves the integrity of the original real data, introducing uncertainty only into the missing regions.

[0122] In the generator processing stage, the target input matrix is ​​fed into the Dilated TCN (Dilated Temporal Convolutional Network). This network processes the target input matrix through multiple one-dimensional causal dilated convolutional layers to obtain the Dilated TCN Output (i.e., multi-channel time series features). The dilation rate of each of the one-dimensional causal dilated convolutional layers in the network increases progressively (e.g., 1, 2, 4), while the receptive field remains fixed (e.g., 5).

[0123] Building upon the multi-channel time-series features extracted by Dilated TCN, a Local Sparse Multi-Head Attention mechanism is introduced. This mechanism calculates cross-channel correlations (i.e., spatial attention) between different sensor channels only within local time regions where valid historical observation data (i.e., real data) exists. This learned cross-channel correlation is then used to guide the generation of data in completely missing time regions. Specifically, Heads=4 indicates that the attention mechanism is divided into four parallel "heads" for computation, each focusing on a different feature subspace. Window=32 indicates that the time-series data is divided into local windows of length 32, with attention computation performed within each window.

[0124] After processing by Dilated TCN and Local Sparse Multi-Head Attention, the output is the complete time series data (i.e., the generator's output) through Sigmoid Activation.

[0125] During the discriminator processing stage, the generated data (i.e., the complete time series data output by the generator) and the hint matrix are input into the discriminator. The discriminator identifies the data values ​​in the complete time series data based on the input, determining whether the data value is real data or imputed data generated by the generator, and outputs the corresponding probability matrix, whose data values ​​are used to represent the probability of each data value being real data or imputed data.

[0126] During the loss calculation phase, the Loss (total loss function, i.e., joint training loss function) includes PhyLoss (physical consistency loss term), adversarial loss term, and observation consistency loss term. Among them, the physical consistency loss term is obtained from the complete time series data through processing steps such as Hankel Transformation, singular value decomposition, and application of a non-convex penalty function.

[0127] During the Update phase, the network parameters of the generator and discriminator are alternately updated based on the calculated Loss using the backpropagation algorithm.

[0128] Thus, the structural health monitoring data interpolation method disclosed herein can effectively interpolate structural health monitoring data where there are continuous and synchronous missing data from multiple sensors.

[0129] Figure 6-11This diagram illustrates the time-domain data interpolation results of a structural health monitoring missing data interpolation method according to an embodiment of this disclosure. It includes six sets of time-domain data imputation results, labeled a through f. Each set of results contains two views: a Full View on the left, displaying the entire time series; and a Zoom In view on the right, focusing on detailed comparisons within a specific time period for easy observation of interpolation accuracy.

[0130] In each set of time-domain data repair results, the horizontal axis represents Time (s), indicating the time point of data sampling, in seconds. The vertical axis represents Acceleration (m / s). 2 The figure (), represents acceleration, measured in meters per second squared. The purple curve represents Original data, which is the complete data sequence actually collected during the target structure monitoring process. The blue curve or dots represent Imputation data, representing the result after repairing missing data using the technical solution disclosed herein. Blue dots represent Missing points, indicating the missing portions in the original monitoring data.

[0131] from Figure 6-11 As can be seen, regardless of whether it is a simple periodic signal, a complex nonlinear waveform, noisy data, or a signal with a long-term trend change, the technical solution disclosed herein can accurately recover the temporal characteristics of the missing data region. The interpolation results are highly consistent with the original data in terms of amplitude, frequency, phase, and waveform details. Furthermore, it achieves a smooth transition at the edge of the missing data region without obvious boundary effects, while effectively preserving the noise characteristics and periodicity of the original signal. This fully verifies the superiority and robustness of the interpolation method that integrates physical consistency constraints and dilated temporal convolutional networks in maintaining low-order characteristics of structural dynamics, handling large-scale continuous synchronous missing data, and adapting to various types of monitoring signals.

[0132] Figure 12 This is a schematic structural block diagram of a device for interpolating missing data in structural health monitoring according to one embodiment of the present disclosure.

[0133] like Figure 12 As shown, the interpolation device includes an acquisition module 1210, a filling module 1220, an input module 1230, a training module 1240, and a processing module 1250.

[0134] The acquisition module 1210 is used to acquire time-series observation data containing multiple sensor channels for the target structure and generate a mask matrix corresponding to the time-series observation data. The time-series observation data contains continuous synchronous missing data from multiple sensors, and the mask value in the mask matrix is ​​used to identify the missing data position in the time-series observation data.

[0135] The filling module 1220 is used to fill random noise at the missing data positions in the time series observation data according to the mask matrix to obtain the target input matrix.

[0136] The input module 1230 is used to input the target input matrix into a generative interpolation network. The generative interpolation network includes a generator and a discriminator. The generator generates complete time series data after data interpolation based on the target input matrix. The discriminator judges whether the data value in the complete time series data is real data or interpolated data.

[0137] The training module 1240 is used to perform adversarial learning joint training on the generator and the discriminator to obtain the trained generator and use it as the target data interpolation model. In the process of adversarial learning joint training, its joint training loss function includes at least a physical consistency loss term. The physical consistency loss term is used to constrain the interpolation data generated by the generator to maintain the low-order dynamic characteristics of the structural response.

[0138] The processing module 1250 is used to perform data interpolation on the time series observation data to be interpolated that has continuous synchronous missing data from multiple sensors, according to the target data interpolation model.

[0139] In some embodiments of this disclosure, when constructing the physical consistency loss term, the training module 1240 is used to: perform Hankel transformation on the complete time series data to obtain the corresponding Hankel matrix; perform singular value decomposition on the Hankel matrix to obtain multiple singular values ​​corresponding to the Hankel matrix; apply a non-convex penalty function to each of the singular values ​​to obtain the penalty amount corresponding to each of the singular values; and construct the physical consistency loss term based on the penalty amounts corresponding to the multiple singular values.

[0140] This disclosure also provides an electronic device. Figure 13 A schematic diagram of the hardware implementation using the processing system is shown.

[0141] like Figure 13As shown, the hardware structure of electronic device 1000 can be implemented using a bus architecture. The bus architecture can include any number of interconnect buses and bridges, depending on the specific application and overall design constraints of the hardware. Bus 1100 connects various circuits including one or more processors 1200, memory 1300, and / or hardware modules. Bus 1100 can also connect various other circuits 1400 such as peripherals, voltage regulators, power management circuits, external antennas, etc. Bus 1100 can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Component (EISA) bus, etc. Buses can be categorized as address buses, data buses, control buses, etc. For ease of illustration, only one connection line is used in this figure, but this does not indicate that there is only one bus or one type of bus.

[0142] This disclosure also provides a readable storage medium storing a computer program that, when executed by a processor, is used to implement the methods described above. A "readable storage medium" can be any means that can contain a program for storage, communication, propagation, or transmission for use by or in conjunction with an instruction execution system, apparatus, or device. More specific examples of a readable storage medium include: an electrical connection with one or more wires (electronic device), a portable computer disk drive (magnetic device), random access memory (RAM), read-only memory (ROM), erasable and programmable read-only memory (EPROM or flash memory), fiber optic devices, and portable read-only memory (CDROM), etc.

[0143] This disclosure also provides a computer program product, the methods of which can be implemented wholly or partially through software, hardware, firmware, or any combination thereof. When implemented in software, it can be implemented wholly or partially as a computer program product. The computer program product includes one or more computer programs or instructions. When the computer program or instructions are loaded and executed, all or part of the processes or functions of this disclosure are performed.

[0144] Computer programs or instructions can be stored in a readable storage medium or transferred from one readable storage medium to another. For example, the computer program or instructions can be transferred from one website, computer, server, or data center to another website, computer, server, or data center via wired or wireless means. The readable storage medium can be any available medium capable of access, or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium, such as a floppy disk, hard disk, or magnetic tape; an optical medium, such as a digital video optical disc; or a semiconductor medium, such as a solid-state drive. The computer-readable storage medium can be a volatile or non-volatile storage medium, or it can include both volatile and non-volatile types of storage media.

[0145] Those skilled in the art will understand that embodiments of this disclosure can be provided as methods, systems, or computer program products. Therefore, this disclosure can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this disclosure can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0146] This disclosure is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus, and computer program products according to this disclosure. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0147] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0148] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0149] In the description of this specification, the references to terms such as "one embodiment / mode," "some embodiments / modes," "example," "specific example," or "some examples," etc., refer to specific features, structures, or characteristics described in connection with that embodiment / mode or example, which are included in at least one embodiment / mode or example of this disclosure. In this specification, the illustrative expressions of the above terms do not necessarily refer to the same embodiment / mode or example. Moreover, the specific features, structures, or characteristics described may be combined in any suitable manner in one or more embodiments / modes or examples. Furthermore, without contradiction, those skilled in the art can combine and integrate the different embodiments / modes or examples described in this specification, as well as the features of different embodiments / modes or examples.

[0150] Those skilled in the art should understand that the above embodiments are merely for illustrating the present disclosure and are not intended to limit the scope of the disclosure. Those skilled in the art can make other changes or modifications based on the above disclosure, and these changes or modifications still fall within the scope of the present disclosure.

Claims

1. A method for imputing missing data in structural health monitoring, characterized in that, include: Acquire time-series observation data containing multiple sensor channels for a target structure, and generate a mask matrix corresponding to the time-series observation data. The time-series observation data contains continuous and synchronous missing data from multiple sensors, and the mask values ​​in the mask matrix are used to identify the missing data locations in the time-series observation data. Based on the mask matrix, random noise is filled at the missing data locations in the time series observation data to obtain the target input matrix; The target input matrix is ​​input into a generative interpolation network, which includes a generator and a discriminator. The generator generates interpolated complete time series data based on the target input matrix, and the discriminator determines whether the data value in the complete time series data is real data or interpolated data. The generator and the discriminator are jointly trained using adversarial learning to obtain a trained generator, which is then used as the target data imputation model. During the joint adversarial learning training, the joint training loss function includes at least a physical consistency loss term, which constrains the imputation data generated by the generator to maintain the low-order dynamic characteristics of the structural response. Based on the target data interpolation model, data interpolation is performed on the time series observation data to be interpolated where there is a continuous synchronous missing data from multiple sensors. The physical consistency loss term is constructed as follows: Perform a Hankel transform on the complete time series data to obtain the corresponding Hankel matrix; Singular value decomposition is performed on the Hankel matrix to obtain multiple singular values ​​corresponding to the Hankel matrix; Applying a non-convex penalty function to each of the singular values ​​yields a penalty amount corresponding to each singular value; and Based on the penalty amounts corresponding to the multiple singular values, a physical consistency loss term is constructed.

2. The method for interpolating missing structural health monitoring data as described in claim 1, characterized in that, The generator includes a dilated temporal convolutional network, which comprises multiple one-dimensional causal dilated convolutional layers. The generator generates interpolated complete time series data based on the target input matrix, including: The target input matrix is ​​subjected to time series feature extraction through multiple one-dimensional causal dilated convolutional layers to obtain multi-channel time series features; as well as Based on the multi-channel time series characteristics, complete time series data after data interpolation is generated.

3. The method for interpolating missing structural health monitoring data as described in claim 2, characterized in that, The dilation rate of the multilayer one-dimensional causal dilated convolutional layers increases layer by layer, and the receptive field of each one-dimensional causal dilated convolutional layer is fixed.

4. The method for interpolating missing structural health monitoring data as described in claim 2, characterized in that, The generator also includes a local sparse multi-head attention module; Based on the multi-channel time series characteristics, complete time series data after data interpolation is generated, including: Based on the local sparse multi-head attention module, in the time region where real data exists in the target input matrix, a cross-channel correlation matrix is ​​determined between multiple sensor channels. The cross-channel correlation matrix is ​​used to describe the correlation between the monitoring data of each sensor when multiple sensors monitor the same structure. as well as Based on the multi-channel time series characteristics and the cross-channel correlation matrix, complete time series data after data interpolation is generated.

5. The method for interpolating missing structural health monitoring data as described in claim 1, characterized in that, The discriminator determines whether the data values ​​in the complete time series data are real data or imputed data, including: The discriminator performs binary classification on each data value in the complete time series data based on the complete time series data and the corresponding cue matrix, and outputs the probability of each data value being real data. The cue matrix is ​​generated based on the mask matrix and is used to partially reveal whether each data value in the complete time series data is real data or imputed data.

6. The method for interpolating missing structural health monitoring data as described in claim 1, characterized in that, The joint training loss function also includes an adversarial loss term and an observation consistency loss term. The adversarial loss term is used to constrain the imputation data generated by the generator to be consistent with the real data in terms of data distribution. The observation consistency loss term is used to constrain the values ​​at the existing real data positions in the complete time series data generated by the generator to be consistent with the original real data.

7. The method for interpolating missing structural health monitoring data as described in any one of claims 1-6, characterized in that, The time-series observation data includes one or more of the following: multi-channel vibration, displacement, acceleration, or strain data for the target structure.

8. An electronic device, characterized in that, include: The memory stores execution instructions; as well as A processor that executes execution instructions stored in the memory, causing the processor to perform the method for interpolating missing structural health monitoring data as described in any one of claims 1 to 7.

9. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the method for interpolating missing structural health monitoring data as described in any one of claims 1 to 7.

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