A method and system for constructing a dynamic response data recovery model for damaged structure loss

Abstract

The present invention discloses a method and system for constructing a missing dynamic response data recovery model of a damaged structure, which relates to the field of monitoring signal recovery. The present invention includes the following steps: obtaining the original structural response data and cropping the original structural response data by using a sliding window algorithm; establishing an encoder-decoder architecture as the initial structural monitoring response model of the backbone network; training the initial structural monitoring response model by using the cropped original structural response model data, and optimizing the initial structural monitoring response model by using a loss function to obtain a structural monitoring response model. The present invention uses a fully convolutional neural network with built-in residual blocks to establish a non-linear mapping relationship between sensors of a damaged structure, thereby realizing the recovery of data of any channel of interest.

Description

Technical Field

[0001] The present invention relates to the field of monitoring signal recovery, and more specifically to a method and system for constructing a damage structure missing dynamic response data recovery model. Background Art

[0002] The structural dynamic response data has been widely used in damage identification, real-time status warning, and safety assessment of large-scale infrastructure, such as high-rise buildings, long-span bridges, dams, etc. Complete dynamic response data is the key to ensuring the reliability of the identification results. However, due to the influence of sensor failures, the problem of missing structural dynamic response data is inevitable, which will cause deviations in calculation results and even lead to incorrect decisions. Therefore, recovering the missing dynamic response data has important research significance for obtaining reliable identification results and accurately evaluating the safety status of the structure.

[0003] To solve the problem of missing response data, a variety of data-driven methods have been proposed, which mainly utilize the spatio-temporal correlation between sensors and can be roughly divided into three categories of methods, namely, methods based on statistical inference, methods based on machine learning, and methods based on deep learning. Compared with the other two methods, the method based on statistical inference was the first to be proposed and has been well developed. This type of method uses a parameterized model to model the system behavior, and then fits the model parameters through historical data to achieve the recovery of future missing data. However, the methods proposed in the existing stage need to make some basic assumptions about the data characteristics, such as Gaussian distribution, which does not conform to the actual situation. At the same time, the methods based on statistical inference cannot handle the situation of long-term missing data well.

[0004] Another feasible method (i.e., the machine learning method) recovers the missing data by mining the correlation and redundancy of the sensor system. At present, although the machine learning-based methods can recover the missing data well, their recovery ability for large-scale missing data is still limited due to the feature extraction ability.

[0005] Due to the deeper network structure of deep learning models, which can capture the internal distribution and underlying mapping relationships of more complex data, methods for recovering missing data based on deep learning have developed rapidly in recent years. Generally speaking, deep learning-based methods have made great progress in missing data recovery, including the recovery of various types of responses, multi-channel data recovery, etc. However, these methods are all proposed for the responses in the linear elastic stage of intact structures. In the long-term operation process of civil engineering structures, they may encounter extreme loads or structural damages, resulting in the nonlinear characteristics of the structures themselves, and thus the structural responses have stronger nonlinear characteristics. Although deep learning methods have the characteristics of modeling nonlinear mapping relationships, there are no reported methods for recovering the nonlinear response data of damaged structures. In addition, existing methods mainly evaluate the consistency between the recovered results and the original data from a fixed time perspective in the frequency domain through Fourier transform. Since the spectral characteristics of the original monitoring data change with time, it is necessary to develop a time-varying frequency domain evaluation method. Summary of the Invention

[0006] In view of this, the present invention provides a method and system for constructing a recovery model for missing dynamic response data of damaged structures to solve the problems existing in the background technology.

[0007] To achieve the above object, the present invention adopts the following technical solutions:

[0008] A method for constructing a recovery model for missing dynamic response data of damaged structures includes the following steps:

[0009] Obtain the original structural response data, and use the sliding window algorithm to crop the original structural response data;

[0010] Establish an encoder-decoder architecture as the initial structural monitoring response model of the backbone network;

[0011] Use the cropped original structural response model data to train the initial structural monitoring response model, and use the loss function to optimize the initial structural monitoring response model to obtain the structural monitoring response model.

[0012] Optionally, in the encoding stage of the initial structural monitoring response model, one convolutional layer and three residual blocks are used to extract the high-dimensional representation of the input data; the downsampling operation is used to compress the high-dimensional representation and transmit it to the bottleneck layer; in the bottleneck layer, the residual block is used to further extract abstract features; in the upsampling stage, the compressed features from the bottleneck layer are gradually expanded into the length of the input data by deconvolution operations, and are spliced with the underlying features in the downsampling path through skip connections; four residual blocks are used to learn the fused features; two convolutional layers sequentially complete the expansion and extraction of features, and are used to gradually reconstruct the signal to approach the original signal; the original signal is output through the convolutional layer.

[0013] Optionally, the rectified linear unit is adopted for all the non-linear activation functions in the initial structure monitoring response model.

[0014] Optionally, a one-dimensional convolution is adopted for the convolutional layer, and the convolution operation process is as follows:

[0015]

[0016] where y l is the output of the l-th convolutional layer; w l is the convolutional kernel of the l-th convolutional layer; x l-1 is the output of the (l - 1)-th layer; b l is the bias of the l-th convolutional layer; is elementwise; f() is the activation function.

[0017] Optionally, it further includes inputting the original signal into the structure monitoring response model to obtain a restored signal, and performing time-domain evaluation and frequency-domain evaluation on the restored signal respectively.

[0018] Optionally, the L2 norm is adopted for time-domain evaluation to calculate the difference between the original signal and the restored result:

[0019]

[0020] In the formula, y′ h represents the restored result of the original signal y h ; N is the number of samples for performance evaluation.

[0021] Optionally, the instantaneous frequency is adopted for frequency-domain evaluation to evaluate the spectral information of the restored result, and the HT algorithm is used to calculate the instantaneous frequency of the signal:

[0022] For any single-channel signal x(t), its complex analytic signal z(t) is constructed through the Hilbert transform, that is:

[0023] z(t) = x(t) + iH[x(t)] = a(t)e iφ(t) ;

[0024] In the formula, is the Hilbert transform, where s is the integration variable, and P represents the Cauchy principle value; The instantaneous amplitude and phase are calculated by the following formula:

[0025] φ(t) = tan -1 + {H[x(t)] / x(t)};

[0026] The instantaneous frequency is defined as the derivative of the instantaneous phase, that is:

[0027]

[0028] The L2 norm of the instantaneous frequency is defined to evaluate the restoration result in the frequency domain, and the corresponding calculation formula is as follows:

[0029]

[0030] In the formula, f h represents the original instantaneous frequency of the h-th data sample; f h ' represents the instantaneous frequency of the restoration result of the h-th data sample.

[0031] A system for constructing a recovery model of missing dynamic response data of a damaged structure includes:

[0032] An original structure response acquisition module: used to acquire original structure response data and crop the original structure response data by using a sliding window algorithm;

[0033] An initial structure monitoring response model establishment module: used to establish an initial structure monitoring response model with an encoder-decoder architecture as the backbone network;

[0034] An initial structure monitoring response model training module: used to train the initial structure monitoring response model by using the cropped original structure response model data, and optimize the initial structure monitoring response model by using a loss function to obtain a structure monitoring response model.

[0035] According to the above technical solutions, compared with the prior art, the present invention provides a method and system for constructing a recovery model of missing dynamic response data of a damaged structure, which uses a fully convolutional neural network with built-in residual blocks to establish a non-linear mapping relationship between sensors of the damaged structure, so as to realize the recovery of data of any channel of interest. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only the embodiments of the present invention. For those of ordinary skill in the art, other drawings can also be obtained according to the provided drawings without creative efforts.

[0037] Figure 1 is the network architecture diagram of the present invention;

[0038] Figure 2 is the schematic diagram of the one-dimensional convolution operation of the present invention;

[0039] Figure 3 is the detailed diagram of the residual block of the present invention;

[0040] Figure 4 It is the parameter diagram of the stiffening skeleton arch rib and the layout diagram of sensors of the present invention;

[0041] Figure 5a It is the intact state diagram of the test arch rib of the present invention and the crack distribution in the failure state;

[0042] Figure 5b It is the diagram of the crown position in the failure state of the test arch rib of the present invention and the crack distribution in the failure state;

[0043] Figure 5c It is the diagram of the position from L / 8 to L / 2 in the failure state of the test arch rib of the present invention and the crack distribution in the failure state;

[0044] Figure 5d It is the diagram of the position from 5L / 8 to 3L / 4 in the failure state of the test arch rib of the present invention and the crack distribution in the failure state;

[0045] Figure 5e It is the diagram of the right arch foot position in the failure state of the test arch rib of the present invention and the crack distribution in the failure state;

[0046] Figure 6a It is the comparison diagram of the recovery results of the data of sample 1 of data type (I), L2 = 0.302, IFL2 = 0.079;

[0047] Figure 6b It is the comparison diagram of the recovery results of the data of sample 2 of data type (I), L2 = 0.302, IFL2 = 0.067;

[0048] Figure 6c It is the comparison diagram of the recovery results of the data of sample 3 of data type (I), L2 = 0.306, IFL2 = 0.068;

[0049] Figure 7a It is the comparison diagram of the recovery results of the data of sample 1 of data type (II), L2 = 0.328, IFL2 = 0.338;

[0050] Figure 7b It is the comparison diagram of the recovery results of the data of sample 2 of data type (II), L2 = 0.337, IFL2 = 0.409;

[0051] Figure 7c It is the comparison diagram of the recovery results of the data of sample 3 of data type (II), L2 = 0.367, IFL2 = 0.581;

[0052] Figure 8a It is the comparison diagram of the recovery results of the data of sample 1 of data type (III), L2 = 0.307, IFL2 = 0.999;

[0053] Figure 8bComparison chart of the recovery results of the data of sample 2 of data type (III), where L2 = 0.305 and IFL2 = 0.648;

[0054] Figure 8c Comparison chart of the recovery results of the data of sample 3 of data type (III), where L2 = 0.293 and IFL2 = 0.806. Specific implementation manner

[0055] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0056] Extreme loads or damage are likely to cause the structural system to enter a nonlinear state. Compared with linear systems, the nonlinear characteristics of the response data of nonlinear systems are more significant. At this time, the spatio-temporal correlation between sensors is more difficult to describe. In addition, due to data loss, there will be long-term missing situations, which often involve the mining of long-term spatio-temporal correlations. Therefore, the present invention uses the U-net model as the basic architecture and designs a fully convolutional neural network model for recovering the missing data of damaged structures, and uses sequence convolution layer by layer in an end-to-end manner for feature extraction. On the one hand, by introducing residual blocks, the depth of the network is deepened and the degradation of network performance is avoided. On the other hand, by adding skip connections, the underlying detailed features of the network are retained to enhance the feature extraction ability of the network, so as to better establish the long-term spatio-temporal correlation between sensors in the nonlinear system. To comprehensively evaluate the quality of the recovery results, the present invention not only evaluates the consistency degree between the recovery results and the true results in the time domain, but also introduces evaluation indexes in the frequency domain to judge the accuracy of the recovery results from the details of frequency components. For this reason, the embodiments of the present invention disclose a method for constructing a recovery model for missing dynamic response data of damaged structures, including the following steps:

[0057] S1: Obtain the original structural response data and use the sliding window algorithm to crop the original structural response data;

[0058] S2: Establish an encoder-decoder architecture as the initial structure monitoring response model of the backbone network;

[0059] S3: Use the cropped original structural response model data to train the initial structure monitoring response model, and use the loss function to optimize the initial structure monitoring response model to obtain the structure monitoring response model.

[0060] In S1, in order for the fully convolutional neural network to fully learn the spatio-temporal correlation between sensors, sufficient training samples need to be prepared. Since the actually collected structural response data is of long period and continuously accumulative, and data missing often occurs in a certain time period. Therefore, the original response data can be processed by means of cropping. On the one hand, sufficient training samples can be obtained, and on the other hand, the sample length can be matched to the specified missing segment length to prepare for the design of the model. The present invention uses a sliding window method to crop the original data:

[0061] N = (L - T) / S + 1 (1)

[0062] Wherein, N is the number of samples obtained by cropping, L is the length of the original data, T is the length of the sliding window, and S is the sliding step.

[0063] The samples obtained by cropping are randomly divided into a training set and a validation set at a ratio of 8:2. The training set is used for network training and parameter tuning, while the validation set is used to evaluate the performance of the model. In order to accelerate the convergence speed of the network and improve the accuracy of data recovery, the sample data needs to be normalized. The maximum absolute value element x in the training set samples is extracted max , and by dividing each sample by this absolute value, the sample values are scaled to the interval [-1, 1]:

[0064]

[0065] Wherein, x ijk represents the data of the kth sample, channel j at time point i; represents the normalized data point; C represents the number of channels.

[0066] In S2, to accurately recover the missing data and reduce the complexity of the model, the architecture of the network was carefully designed. The proposed network uses an encoder-decoder architecture as the backbone network, which includes a downsampling path, a bottleneck layer, an upsampling path, and skip connections. The downsampling path, also known as the encoder (En), is responsible for extracting multi-scale hierarchical features and reducing the dimension of the input layer by layer. The bottleneck layer is conducive to automatically extracting higher-level features from the input data step by step, while reducing the noise effect and dimension of the features before the input data undergoes data recovery training. The upsampling path, that is, the decoder (De), performs the opposite process of downsampling. This process is responsible for gradually expanding the compressed abstract features flowing through the bottleneck into the target output with low-level details, and finally completing signal reconstruction. All encoder and decoder layers use convolutional layers, thus constituting a FCN. A significant feature of the designed model is the introduction of residual blocks to increase the network depth without affecting network training, thereby further improving the network's feature learning ability. In addition, skip connections are used to retain the underlying details that are easily overlooked in the downsampling path, which not only speeds up the convergence of network training but also solves the problem of gradient disappearance, improving the training efficiency and accuracy of the network.

[0067] The detailed architecture of the designed FCN is as Figure 1 shown, and the detailed parameters of each layer are shown in Table 1. The backbone of the proposed FCN model is adapted from the classic U-net network. Assume that the input is cropped into samples with a length of 512 points, and the number of sensor channels is C. In the encoding stage, a convolutional layer (i.e., Conv1) and three residual blocks (i.e., R1-R3) are used to extract the high-dimensional representation of the input data, and four downsampling operations (D1-D4) are used to compress these high-dimensional representations and pass them into the bottleneck layer. In the bottleneck layer, a residual block with 1024 convolutional kernels (i.e., R4) is used to further extract higher-level abstract features. After that, the upsampling operation starts. In the upsampling stage, the compressed features from the bottleneck layer are gradually expanded into the length of the input data by four deconvolution operations (i.e., U1-U4) with a kernel size of 2 and a stride of 2, and are concatenated with the underlying features in the downsampling path through skip connections. At the same time, four residual blocks (i.e., R5-R8) are used to learn the fused features. Then, two convolutional layers (i.e., Conv2-Conv3) sequentially complete the expansion and extraction of features, gradually reconstructing the signal to approach the original signal. Finally, the original signal is output through a convolutional layer with 1 convolutional kernel and a stride of 1.

[0068] Since the structural monitoring response can be regarded as a one-dimensional time series, all convolutional layers in the network use one-dimensional convolutions. In addition, to prevent overfitting, dropout technology is applied in the upsampling stage. All non-linear activation functions in the network use rectified linear units.

[0069] Table 1 Detailed Parameters of the Network Model

[0070] Layer Input Size Output Size Number of Kernels Kernel Size Stride Padding Activation Function Input 512×C - - - - - - Conv1 512×C 512×64 64 3 1 Same Relu D1 512×64 256×64 - 2 2 Valid - R1 256×64 256×128 128 3 1 Same Relu D2 256×128 128×128 - 2 2 Valid - R2 128×128 128×256 256 3 1 Same Relu D3 128×256 64×256 - 2 2 Valid - R3 64×256 64×512 512 3 1 Same Relu D4 64×512 32×512 - 2 2 Valid - R4 32×512 32×1024 1024 3 1 Same Relu U1 32×1024 64×512 512 2 2 Valid - R5 64×1024 64×256 256 3 1 Same Relu U2 64×256 128×256 256 2 2 Valid - R6 128×512 128×128 128 3 1 Same Relu U3 128×128 256×128 128 2 2 Valid - R7 256×256 256×64 64 3 1 Same Relu U4 256×64 512×64 64 2 2 Valid - R8 512×128 512×64 64 3 1 Same Relu Conv2 512×64 512×64 64 2 1 Same Relu Conv3 512×64 512×64 64 2 1 Same Relu Output 512×64 512×1 1 1 1 Valid -

[0071] The convolutional layer consists of feature maps obtained by convolutional operations of several convolutional kernels. The convolutional kernels have the characteristics of local perception and parameter sharing, and can significantly reduce the number of model parameters while learning multiple feature representations. One-dimensional convolution is used to process the case where the input is one-dimensional data (see Figure 2 ), and its convolutional operation process is as follows:

[0072]

[0073] where, y l is the output of the l-th convolutional layer; w l is the convolutional kernel of the l-th convolutional layer; x l-1 is the output of the (l - 1)-th (i.e., the previous layer); b l is the bias of the l-th convolutional layer; is elementwise; f() is the activation function.

[0074] The deep convolutional neural network uses pooling layers to gradually reduce the size of the feature maps and achieve downsampling of the feature maps. After multiple poolings, the size of the feature maps will be greatly reduced compared to the original input image. In the fully convolutional network, it is required to output a pixel-level feature map with the same size as the original image, so it is necessary to upsample the pooled feature maps. The upsampling layer is implemented by transposed convolution. Transposed convolution is mainly applied to the recovery of downsampled feature maps, visualization of intermediate layers of the convolutional network, etc. Through transposed convolution, the features output by the bottleneck layer are fused in the time and space dimensions, and then these features are gradually expanded along the upsampling path, and thus a feature map with the same size as the input image can be obtained. The calculation formula for the transposed convolution operation is as follows:

[0075] O T =(W T - 1)×S T +K T - 2P T (4)

[0076] In the formula, O T represents the height or width of the output; W T represents the height or width of the input; S T represents the stride; K T represents the size of the convolutional kernel; P T represents the size of the padding.

[0077] The pooling process often leads to information loss. Based on the features of the last pooling layer, the feature maps generated by upsampling are often rather rough. Considering adding more detailed information from the previous layers, by introducing skip connections from high-resolution feature maps to fuse the features of multiple layers and taking into account both local and global information, the roughness of the classification results can usually be improved. In Figure 1 each layer's feature map is passed through a skip connection to the upsampling path before downsampling. Then, it is connected to the output of the transposed convolution along the feature dimension. The skip connection bypasses the downsampling and bottleneck layers, which not only facilitates the preservation of low-level details but also regulates the gradient flow and alleviates the vanishing gradient problem.

[0078] If the size of the input matrix is small, the problem of loss of detailed information of the original data will occur after only a few samplings. However, simply reducing the network depth directly will reduce the model's ability to encode input information and affect the accuracy of data recovery. To increase the network depth without affecting network training, a residual network is introduced based on U-Net. The residual network (ResNet) uses residual blocks to solve the problem of network performance degradation caused by the deepening of the network hierarchy. The residual block is realized by short-circuit connecting the forward neural network and includes a direct mapping part and a residual part. The structure is as Figure 3 shown, and the formula is:

[0079] x l+1 = h(x l ) + F(x l , w l ) (5)

[0080] where x l and x l+1 are the input and output of the residual block respectively; w l is the weight of the residual block, that is, the convolution operation; h(x l ) is the direct mapping, which is reflected as the upper curve in Figure 3 ; F(x l , w l ) is the output result after passing through the convolutional layer, that is, the residual part, which consists of two convolutional operations, namely the part containing the convolution in the lower part of Figure 3 ;

[0081] For the stacked non-linear layers with short-circuit connections, the input is passed to the output through the short-circuit connection. Just making the training target of the non-linear layer F(x l , w l ) approach 0 can enable the residual block to learn the identity mapping. After adding the short-circuit connection, the derivative of the output with respect to the input is:

[0082]

[0083] In Equation (6), x l+1 with respect to xl The partial derivative of l+1 is greater than 1, solving the problem of gradient vanishing. When x

[0084] is the identity mapping, the constraint that information can only be passed layer by layer between network layers is eliminated, enabling information to skip multiple layers and solving the problem of network degradation that occurs as the network deepens.

[0085]

[0086] Among them, M represents the number of training samples in each batch; x h represents the model input; FCN is simplified to the parameterized non - linear model f φ (x h ), that is, the recovery result; y h represents the original signal. Therefore, the goal of the training process is to minimize the loss based on the entire dataset.

[0087] Furthermore, in the present invention, in order to quantitatively evaluate the recovery performance of the proposed method in the time domain, the L2 norm is used to calculate the difference between the original signal and the recovery result:

[0088]

[0089] In the formula, y′ h represents the recovery result of the original signal y h ; N is the number of samples used for performance evaluation.

[0090] In addition to maintaining the consistency of the signal time - domain characteristics, the goal of data recovery should also ensure the integrity of the signal spectrum information as much as possible. Therefore, generally, in addition to evaluating the time - domain recovery result of the signal, relevant literature also compares its spectrum characteristics through the Fourier transform of the signal. However, the spectrum information of non - stationary data may change over time, especially for non - linear data, whose spectrum information may change even more significantly over time. The instantaneous frequency (IF) is usually used to represent the frequency - domain transient characteristics of non - stationary and non - linear signals. Therefore, compared with traditional methods, the present invention introduces instantaneous frequency to evaluate the spectrum information of the recovery result, and the HT algorithm is used here to calculate the instantaneous frequency of the signal.

[0091] For any single - channel signal x(t), its complex analytic signal z(t) can be constructed through the Hilbert transform, that is:

[0092] z(t) = x(t)+iH[x(t)] = a(t)e iφ(t) (9)

[0093] In the formula, is the Hilbert transform, where s is the integration variable and P represents the Cauchy principal value; The instantaneous amplitude and phase can be calculated by the following equations:

[0094]

[0095] Based on Equation (9), the instantaneous frequency is defined as the derivative of the instantaneous phase, i.e.:

[0096]

[0097] On this basis, the present invention defines the L2 norm of the instantaneous frequency (IFL2) for evaluating the restoration result in the frequency domain. The corresponding calculation formula is as follows:

[0098]

[0099] In the formula, f h represents the original instantaneous frequency of the h-th data sample; f′ h represents the instantaneous frequency of the restoration result of the h-th data sample.

[0100] To verify the effectiveness of the proposed method, a loading failure test of a concrete-filled steel tubular arch with stiffening skeleton was carried out, and the acceleration data of each damaged state of the arch rib were collected for case study. The model arch rib was designed by scaling down an actual bridge, with a span of 12 m, a rise of 2.55 m, and an arch axis coefficient of 1.8, as Figure 4 shown. The model arch is a single-rib arch, using dumbbell-shaped concrete-filled steel tubes as the stiffening skeleton. The test arch section is 32.2 cm high and 14 cm wide, and the thickness of the top and bottom plates is 10 cm. The concrete outside the arch rib is of C60 grade, and the concrete filled inside is of C80 grade. The main chord tubes are made of Q345 steel tubes with a diameter of 65 mm and a wall thickness of 4 mm, while the web members are made of Q345 steel tubes with a diameter of 32 mm and a wall thickness of 4 mm. The steel bars are of HRB400 type, and the vertical main steel bars are while the transverse and longitudinal structural steel bars are

[0101] The finished steel tubular stiffening skeleton was manufactured in the processing factory according to the design drawings, and then transported to the laboratory for the pouring of the concrete inside the tubes and the binding and pouring of the steel bars and concrete outside the tubes. Finally, the arch rib was installed at the pre-cast arch seat position by a truss crane. The arch rib was loaded by a jack installed at the crown, as Figure 5aAs shown in the figure. At 100 kN, microcracks began to appear at the lower edge of the cross-section at the crown (L / 2). At 130 kN, the number of cracks in the crown area increased, the crack range expanded, and continued to develop towards the upper edge of the cross-section. The cracks below the crown developed upwards, and the cracks on both sides of the crown developed obliquely upwards. The number of cracks in the 2L / 8 and 6L / 8 areas increased, and cracks began to appear at the upper edge of the cross-section in the L / 8 and 7 / 8 areas. At 249 kN, tiny cracks appeared at the two arch feet on the left and right. Starting from the loading force greater than 250 kN, crushing cracks began to appear at the upper edge of the cross-section in the loading area of the crown of the test arch, but the jack loading force could still continue to increase. At 265.713 kN, the upper edge of the crown area was completely crushed, the jack could not hold the load, the entire arch could not continue to bear the load, and the test arch reached the ultimate bearing capacity. The crack distribution after the arch rib failure is as Figure 5b - Figure 5e shown.

[0102] During the test, when the loading force increased by 10 kN each time, the jack was held for a period of time, and the specific position was excited by a rubber hammer to make the arch rib generate vibration response. Seven channels of acceleration sensors were evenly arranged along the span direction from left to right, and the acceleration time history data was collected at a sampling frequency of 1024 Hz for subsequent missing data recovery.

[0103] Each time when collecting, the arch rib was hammered many times with a rubber hammer, and the acceleration data with a duration of 300 s was collected, which contained 307,200 data points. Based on the acceleration data under 250 kN loading in the present invention, only the data of two channels (i.e., channel 1 and channel 3) were used. Among them, channel 1 was used as the data channel to be recovered, and channel 3 was used as the intact data channel. In order to prepare sufficient data samples for the training of the fully convolutional neural network and prevent overfitting, the acceleration data segments were cropped by means of data sliding window. The length of the sliding window was taken as 512, and the step size was taken as 128. Therefore, a total of 2,397 samples with a length of 512 were generated. On this basis, the acceleration data samples were randomly divided into a training set and a validation set, where the training set contained 1,918 samples, and the validation set contained 479 samples. Finally, in order to accelerate the training speed of the network and improve the recovery accuracy, the data set was normalized.

[0104] The present invention uses the Adam algorithm to train the model, where the learning rate is set to 0.0005, and β1 and β2 are set to 0.9 and 0.99 respectively. The network parameters are initialized by he_uniform. According to the scale of the sample data, the BatchSize is set to 32 and the epoch is set to 100. Based on the Kears 2.6.0 deep learning framework, the training is carried out in the operating environment with a computer configuration of 14 AMD EPYC 7453 CPUs, an RTX 4090 graphics card, 24 GB of GPU, and 64.4 GB of memory.

[0105] To visually display the recovery results of the validation set samples, some typical samples were selected. Since there are free vibrations and ambient excitation vibrations during the vibration test, the collected acceleration data contains the results generated by high-amplitude excitation, low-amplitude excitation, and mixed-amplitude excitation. Therefore, to explore the recovery performance of the proposed method for different types of acceleration data, the acceleration data in the present invention was divided into three types according to the amplitude size. Type I is the high-amplitude response, that is, the response generated by free vibration; Type II is the low-amplitude response, that is, the response generated by ambient excitation; Type III is the mixed-amplitude response, that is, the first half of the response is generated by ambient excitation and the second half of the response is generated by free vibration.

[0106] Figure 6a - Figure 6c 、 Figure 7a - Figure 7c 、 Figure 8a - Figure 8c respectively show the recovery results of three validation set samples of three types of responses randomly selected, including the time-domain recovery results and the instantaneous frequencies corresponding to the recovery results. At the same time, the time-frequency domain evaluation indexes of each selected sample were calculated. Through careful analysis, the following conclusions can be drawn:

[0107] (1) The method proposed in the present invention can better recover the nonlinear response of the damaged structure. For example, Figure 8a - Figure 8c for the three validation samples of data type III, whether it is the low-amplitude response part or the high-amplitude response part, there is a high degree of coincidence between the time history of the recovery result and the original data. In addition, although there are differences between the instantaneous frequencies of the recovery results and the original data at some time points, the overall consistency is good.

[0108] (2) High-amplitude response data (i.e., data type I) is easier to recover. For example, Figure 6a - Figure 6c for the three validation samples of data type I, the recovery results maintain good consistency with the original data in the time-frequency domain, with an average L2 of 0.303 and an average IFL2 of 0.071; while Figure 7a - Figure 7c for the three validation samples of data type II, the recovery results only maintain good consistency with the original data in the time domain, but there are serious disagreements at some data points in the frequency domain, with an average L2 of 0.344 and an average IFL2 of 0.443. Obviously, the error of the recovery result of data type I is less than that of data type II, that is, high-amplitude response data (i.e., data type I) is easier to recover.

[0109] (3) The instantaneous frequency evaluation technique can be used as an effective tool for comparing the recovery performance in the frequency domain. For example, just looking at the recovery results in the time domain, the average L2 of the recovery results of data type I is 0.303, and the average L2 of the recovery results of data type III is 0.302. The two are almost close, and it is impossible to judge the quality of the recovery results. However, since the instantaneous frequency is more sensitive to data changes, that is, the average IFL2 of the recovery results of data type I is 0.071, and the average IFL2 of the recovery results of data type III is 0.818. Based on this, it can be accurately judged that the recovery results of data type I are better.

[0110] To verify the recovery performance of the proposed method under different working conditions, the present invention discusses and analyzes the influence of the spatial position of the input channels and the number of input channels on the recovery results. In addition, the performance of the proposed method in recovering multi-channel data and cross-state recovery scenarios is also studied.

[0111] To explore the influence of different input channels on the recovery results, channels 2 (C2), 4 - 7 (C4 - C7) are respectively used as input channels to recover the data of channel 1. The data set preparation and parameter settings under different input channels are the same as those in the previous case. Table 2 shows the time-frequency domain evaluation indexes of the recovery results of the validation set samples under different input channels. Table 2 also quantitatively verifies this phenomenon, that is, when using channel 5 as the input, the L2 and IFL2 of the recovery results of the validation set samples are 0.159 and 0.229 respectively, while when using channel 2 as the input, the L2 and IFL2 of the recovery results of the validation set samples are 0.282 and 0.308 respectively.

[0112] Table 2 Evaluation indexes of recovery results under different input channels

[0113]

[0114] To reveal how the differences in input channels affect the recovery results, the absolute value of the correlation coefficient (AVCC) between each input channel (i.e., C2 - C7) and the output channel (i.e., C1) is calculated.

[0115] Increasing the number of input channels may facilitate the modeling of the spatial correlation between sensors. Therefore, the present invention explores the influence of the number of input channels on the recovery results, and sets five working conditions with different numbers of input channels, namely S1 - S5, corresponding to the number of input channels being 1 - 5 respectively. The detailed input channels of each working condition are shown in Table 3. To make the calculation results more comparable, except for the difference in the network input channels, the remaining network parameter settings under different working conditions are kept the same.

[0116] Table 3 Working condition settings for different numbers of channels

[0117] Operating Condition Number of Input Channels Input Channel S1 1 C3 S2 2 C3, C4 S3 3 C3, C4, C5 S4 4 C3, C4, C5, C6 S5 5 C3, C4, C5, C6, C7

[0118] Table 4 lists the time-frequency domain evaluation indexes of the recovery results under different numbers of input channels. It can be seen that the original signals under various working conditions have been well recovered. However, there are slight differences in the accuracy of the recovery results under different working conditions, that is, the more the number of input channels, the higher the coincidence degree between the recovery result and the original data. According to the overall evaluation indexes of the recovery results of the validation set samples in Table 4, it can be clearly observed that as the number of input channels increases, the error of the recovery result gradually decreases. Generally speaking, the increase in the number of input channels does not bring a very large improvement in the accuracy of the recovery result, which also shows that the FCN can establish a complex non-linear mapping relationship between the input and output through a relatively small number of input channels, so as to achieve the accurate recovery of missing data.

[0119] Table 4 Evaluation indexes of the recovery results under different numbers of input channels

[0120]

[0121] Since multiple sensors may fail simultaneously during the operation of the structural health monitoring system, it is very necessary to recover the data of multiple channels simultaneously. The present invention uses Channel 1 as the input data and simultaneously recovers the data of 4 output channels (i.e., Channels 4 to 7) to verify the ability of the proposed method to perform multi-channel data recovery. To achieve multi-channel data output, only the number of convolution kernels in the output layer of the network model in Table 1 needs to be adjusted to the number of output channels, which is 4 in this embodiment. Specifically, the accuracy of the recovery result of Channel 5 may be the highest, followed by Channel 6, while the accuracy of the recovery results of Channels 4 and 7 may be the lowest. To verify the above conjecture, the evaluation indexes of the recovery results of all validation set samples of each channel are calculated, as shown in Table 5. It can be intuitively seen from the table that the L2 and IFL2 of the recovery result of Channel 5 are 0.144 and 0.247, respectively, and the error is the smallest. The L2 and IFL2 of the recovery result of Channel 4 are 0.351 and 0.598, respectively, and the error is the largest. This result is related to the correlation between the input and output channels, that is, the correlation between Channel 5 and Channel 1 is the highest, so the best recovery result is obtained, while the correlations between Channels 4, 6, and 7 and Channel 1 are slightly lower, so the errors of the recovery results are relatively large. Generally speaking, the proposed method can use the data of a single channel to recover the data of multiple target output channels, and the error of the recovery result of the output channel with a relatively low correlation with the input channel will be relatively large.

[0122] Table 5 Evaluation indexes of the recovery results of each output channel

[0123]

[0124] Since the change in the structural state cannot be detected in advance, in actual situations, it may be possible to use the model trained in the previous state to recover the missing channel data in the next state. Therefore, it is necessary to discuss the feasibility of cross-state recovery. Taking Channel 3 as the input, the data of Channel 1 is recovered, and the training set samples and validation set samples are constructed respectively using the acceleration data collected under the external loads of 220 kN and 250 kN by the model arch. Whether in the time domain or the frequency domain, the recovery results better depict the change trend of the original data, but there is a certain deviation in the amplitude of the time-domain results. This indicates that the change in the structural state has led to a significant change in the nonlinear correlation between channels. Therefore, there will be a certain error in using the nonlinear neural network model established in the previous state to recover the missing data in the subsequent state. For this reason, it is recommended to add the latest training samples to the trained fully convolutional neural network model in real time to update the nonlinear relationship between channels, thereby improving the reliability of data recovery.

[0125] The various embodiments in this specification are described in a progressive manner. The key point of each embodiment is to illustrate the differences from other embodiments. The same or similar parts among the embodiments can be referred to each other. For the devices disclosed in the embodiments, since they correspond to the methods disclosed in the embodiments, the descriptions are relatively simple. For the relevant parts, refer to the description in the method section.

[0126] The above description of the disclosed embodiments enables those skilled in the art to implement or use the present invention. Various modifications to these embodiments will be obvious to those skilled in the art. The general principles defined in the present invention can be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to these embodiments shown in the present invention, but will conform to the widest scope consistent with the principles and novel features disclosed in the present invention.

Claims

1. A method for constructing a recovery model of dynamic response data with missing damage structure, characterized in that, It includes the following steps: Obtain the original structural response data and crop the original structural response data using a sliding window algorithm; Establish an encoder-decoder architecture as the initial structural monitoring response model of the backbone network; In the encoding stage of the initial structural monitoring response model, a convolutional layer and three residual blocks are used to extract the high-dimensional representation of the input data; the downsampling operation is used to compress the high-dimensional representation and transmit it to the bottleneck layer; in the bottleneck layer, the residual block is used to further extract the abstract features; in the upsampling stage, the compressed features from the bottleneck layer are gradually expanded into the length of the input data by deconvolution operations and are concatenated with the underlying features in the downsampling path through skip connections; Four residual blocks are used to learn the fused features; Two convolutional layers sequentially complete the expansion and extraction of features, which are used to reconstruct the signal to be close to the original signal; the original signal is output through the convolutional layer; Use the cropped original structural response model data to train the initial structural monitoring response model, and use the loss function to optimize the initial structural monitoring response model to obtain the structural monitoring response model.

2. The method for constructing a recovery model of dynamic response data with missing damage structure according to claim 1, characterized in that, The nonlinear activation functions in the initial structural monitoring response model all use rectified linear units.

3. The method for constructing a recovery model of dynamic response data with missing damage structure according to claim 1, characterized in that, The convolutional layer uses one-dimensional convolution, and the convolution operation process is as follows: where y l is the output of the l-th convolutional layer; w l is the convolutional kernel of the l-th convolutional layer; x l-1 is the output of the (l-1)-th layer; b l is the bias of the l-th convolutional layer; is element-wise multiplication; f() is the activation function.

4. The method for constructing a recovery model of dynamic response data with missing damage structure according to claim 1, characterized in that, It also includes inputting the original signal into the structural monitoring response model to obtain the restored signal, and performing time-domain evaluation and frequency-domain evaluation on the restored signal respectively.

5. The method for constructing a recovery model of dynamic response data with missing damage structure according to claim 4, characterized in that, The time-domain evaluation uses the L2 norm to calculate the difference between the original signal and the restored result: where y h ′ represents the recovery result of the original signal y h ; N is the number of samples used for performance evaluation.

6. The method for constructing a recovery model of dynamic response data with missing damage structure according to claim 4, characterized in that, The frequency-domain evaluation uses the instantaneous frequency to evaluate the spectral information of the restored result, and the Hilbert-Huang algorithm is used to calculate the instantaneous frequency of the signal: For any single-channel signal x(t), its complex analytic form z(t) is constructed through the Hilbert transform, that is: z(t) = x(t) + iH[x(t)] = a(t)e iφ(t) ; In the formula, is the Hilbert transform, where s is the integration variable and P represents the Cauchy principal value; The instantaneous amplitude and phase are calculated by the following formula: φ(t) = tan -1 + {H[x(t)] / x(t)}; The instantaneous frequency is defined as the derivative of the instantaneous phase, that is: Define the L2 norm of the instantaneous frequency for the evaluation of the restored result in the frequency domain, and the corresponding calculation formula is as follows: where f h represents the original instantaneous frequency of the h-th data sample; f h ' represents the instantaneous frequency of the recovery result of the h-th data sample.

7. A system for constructing a recovery model of dynamic response data with missing damage structure, characterized in that, It includes: Original structural response acquisition module: used to obtain the original structural response data and crop the original structural response data using a sliding window algorithm; Initial structural monitoring response model establishment module: used to establish an encoder-decoder architecture as the initial structural monitoring response model of the backbone network; in the encoding stage of the initial structural monitoring response model, a convolutional layer and three residual blocks are used to extract the high-dimensional representation of the input data; the downsampling operation is used to compress the high-dimensional representation and transmit it to the bottleneck layer; in the bottleneck layer, the residual block is used to further extract the abstract features; in the upsampling stage, the compressed features from the bottleneck layer are gradually expanded into the length of the input data by deconvolution operations and are concatenated with the underlying features in the downsampling path through skip connections; Four residual blocks are used to learn the fused features; Two convolutional layers sequentially complete the expansion and extraction of features, which are used to reconstruct the signal to be close to the original signal; the original signal is output through the convolutional layer; Initial structural monitoring response model training module: used to train the initial structural monitoring response model using the cropped original structural response model data, and use the loss function to optimize the initial structural monitoring response model to obtain the structural monitoring response model.

Images