A Real-Time Early Warning Method for Cable-stayed Structures Based on Deep-FCSVDD

Abstract

A real-time early warning method for cable-stayed structures based on Deep-FCSVDD is proposed, comprising the following steps: acquiring the lateral acceleration response of the cable-stayed structure; creating a frequency domain dataset; training a 1D-CAE; determining the center vector based on the 1D-CAE calculation results; using the encoder weights trained in the 1D-CAE as the initial weights for Deep-FCSVDD; optimizing the initialized Deep-FCSVDD model using gradient descent; selecting the optimal model weights and saving the network weight parameters; training a Deep-FCSVDD model independently for each cable; extracting low-dimensional abstract features of the lateral acceleration response of the cable in a healthy state using the trained Deep-FCSVDD model, and defining a damage threshold using a proposed damage index. This method not only possesses the powerful feature extraction capabilities of deep learning algorithms but also provides an interpretable damage index.

Description

Technical Field

[0001] This invention belongs to the field of real-time early warning technology for cable structures, and particularly relates to a real-time early warning and damage localization method for cable structures based on a deep fully convolutional support vector data description model. Background Technology

[0002] Cable-stayed structures, due to their high load-bearing capacity and excellent aerodynamic / seismic performance, are widely used in the design and construction of long-span bridges, building roofs, stadiums, and other structures. However, unlike traditional beams and columns, cables typically have a shorter design lifespan, and their actual service life is often even shorter. Cables are more susceptible to damage, and cable failure can directly lead to the collapse of the entire structure. Therefore, early detection of potential damage in cables is crucial.

[0003] Cables are frequently damaged due to broken wires, loose anchor heads, corrosion, and other reasons. Currently, there are three main methods for cable damage detection: vibration response-based methods, static parameter-based methods, and non-destructive testing (NDT) methods. Vibration response methods (such as acceleration and displacement) are widely used due to their high accuracy and low cost. The extracted vibration frequency or cable force is used as a damage indicator; a sudden and irreversible decrease in these indicators suggests cable damage. However, these indicators are not sensitive enough to minor damage, and abnormal changes may be masked by noise. Strain measured by strain gauges and cable end pressure measured by pressure sensors are another type of damage indicator, but both are inconvenient to install and remove. NDT techniques such as acoustic emission, magnetic flux leakage, and guided wave detection can also be used for on-site inspection of cable structures due to their high accuracy, but the equipment is expensive, the operation is complex, and some techniques are not suitable for long-term monitoring. Deep learning methods, due to their powerful feature extraction capabilities, can extract minor damage features from the structural vibration response under white noise excitation, making them suitable for real-time early warning of cable damage. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a real-time early warning method for cable-stayed structures based on Deep-FCSVDD. This method is applicable to online monitoring of single or multiple cables in cable-stayed structures (including cable-stayed bridges and suspension bridges).

[0005] The technical solution of this invention:

[0006] A real-time early warning method for cable-stayed structures based on Deep-FCSVDD, comprising the following steps:

[0007] S1. Collect the lateral acceleration response of each cable in the cable structure;

[0008] S1.1 The lateral acceleration response of the cable refers to the acceleration response of the cable perpendicular to the direction of traffic flow. The acceleration response is collected using an accelerometer, and its sampling frequency is generally 100Hz.

[0009] S2. Perform independent dataset splitting on the acceleration response of each cable, and preprocess the acceleration response in each generated dataset. Each cable corresponds to a training set, a validation set, and a test set.

[0010] The acceleration response of each cable is split into independent datasets:

[0011] S2.1. The collected acceleration responses in both healthy and unknown (including healthy and damaged) states of the cable are divided into three datasets according to the proportion: training set, validation set, and test set. The training set and validation set are used for training the Deep-FCSVDD model and for model selection, respectively. They can only contain data in the healthy state of the cable. The test set contains data in the unknown state of the cable (including healthy and damaged) and is used to test the performance of the algorithm for early warning of the cable.

[0012] S2.1.1 A healthy state refers to a state in which the cable is not damaged, while an unknown state refers to a state in which the cable may have been damaged but has not yet been detected and requires further assessment.

[0013] Preprocess the accelerated responses in each dataset generated in S2.1:

[0014] S2.2 Preprocessing includes two steps: data augmentation and frequency domain processing. Data augmentation is used to expand the dataset and improve model accuracy, while frequency domain preprocessing is used to extract effective information from the acceleration response and reduce the learning difficulty of the model.

[0015] S2.2.1 Data augmentation refers to slicing the time-domain signal of the cable acceleration response using a sliding window. First, an initial window of size NT is selected, and the time-domain data points contained in the window are taken as samples. Then, the window is moved along the positive direction of the time axis with a specific step size. After the movement, the data points contained in the window are taken as new samples. The window movement is repeated until the window reaches the end of the data.

[0016] In step S2.2.1, the size of the initial window NT needs to be determined based on the fundamental frequency of the cable, and its calculation method is as follows:

[0017]

[0018] Where f represents the fundamental frequency of the cable, and the frequency resolution Δf is required to be no less than 1% of f. s This represents the sampling frequency, taken as 100Hz. f represents rounding down. max f represents the highest frequency of the selected frequency band. min This represents the lowest frequency of the selected frequency band;

[0019] S2.2.2 Frequency domain preprocessing refers to converting the samples in S2.2.1 to the frequency domain through fast Fourier transform, calculating their power spectral density (PSD), then extracting a frequency band with a high signal-to-noise ratio from the PSD, and finally standardizing the PSD data within the extracted frequency band to complete the frequency domain preprocessing.

[0020] S3. Copy all three datasets of Lasso and mix the copied datasets together according to the category to form an overall training set, an overall validation set and an overall test set. Use these three overall datasets to train and test a one-dimensional fully convolutional autoencoder (1D-CAE). Finally, save the best weights of the 1D-CAE.

[0021] S3.1, Copying all three datasets of all LAS and mixing the copied datasets together according to category means copying all LAS training sets, mixing the copied datasets together, and then randomly shuffling them. The validation set and test set are handled in the same way as the training set.

[0022] S3.2, Using these three overall datasets to train and test 1D-CAE refers to constructing a 1D-CAE, then using the overall training and validation sets constructed in S3.1 to train and select the model, and finally saving the selected optimal weights.

[0023] The 1D-CAE mainly consists of an encoder and a decoder. The encoder is composed of a one-dimensional convolutional layer, a one-dimensional normalization layer, a one-dimensional max pooling layer, and two non-linear activation functions. The detailed architecture is as follows: Input -> One-dimensional convolutional layer -> One-dimensional normalization layer -> LeakyReLU -> One-dimensional max pooling layer -> One-dimensional convolutional layer -> One-dimensional normalization layer -> LeakyReLU -> One-dimensional max pooling layer -> One-dimensional convolutional layer -> One-dimensional normalization layer -> LeakyReLU -> One-dimensional max pooling layer -> One-dimensional convolutional layer ->ReLU->Low-dimensional features; The decoder consists of a one-dimensional transposed convolutional layer, a one-dimensional normalization layer, an upsampling layer, and two non-linear activation functions. The detailed architecture is as follows: Low-dimensional features->One-dimensional transposed convolutional layer->One-dimensional normalization layer->LeakyReLU->Upsampling layer->One-dimensional transposed convolutional layer->One-dimensional normalization layer->LeakyReLU->Upsampling layer->One-dimensional transposed convolutional layer->One-dimensional normalization layer->LeakyReLU->Upsampling layer->One-dimensional convolutional layer->Tanh->Reconstructed input;

[0024] The original Deep-SVDD model uses a 2D convolutional autoencoder with a fully connected layer. Only by replacing its fully connected layer with a 1D convolutional layer and ReLU can the low-dimensional features extracted from the vibration response by 1D-CAE remain interpretable, and thus the interpretable damage index proposed in step S7 can be used.

[0025] S4. Build a Deep-FCSVDD model for each cable. The model architecture is the encoder part of 1D-CAE, and the initial weights are the optimal weights of 1D-CAE saved in S3. Input the training and test sets of each cable into the corresponding initialized Deep-FCSVDD model to obtain the features of each sample in the dataset in the low-dimensional feature space. Then, average these low-dimensional features to obtain the center vector. Define the loss function using the center vector and the output of the Deep-FCSVDD model.

[0026] S4.1, "Building a Deep-FCSVDD model for each cable" means building a Deep-FCSVDD model with the same network architecture for each cable.

[0027] S4.2 The model architecture is the encoder part of 1D-CAE, which means that the encoder part in 1D-CAE is separated from the 1D-CAE model and used as the network architecture of Deep-FCSVDD model. Other parts in the 1D-CAE model are directly discarded.

[0028] S4.2 The initial weights are the optimal weights of the 1D-CAE saved in S3. This means that the weights of the encoder part in the 1D-CAE are copied to the Deep-FCSVDD model according to the names of the network modules, and the Deep-FCSVDD model defined and initialized for each cable is completely equal.

[0029] S4.2 Input the training and test sets of each cable into the corresponding initial Deep-FCSVDD model to obtain the features of each sample in the low-dimensional feature space. This means that before updating the weights of the Deep-FCSVDD model, it is necessary to use the initial Deep-FCSVDD model corresponding to a certain cable to perform an inference on the corresponding training and test sets to obtain low-dimensional features.

[0030] S4.2.1 Low-dimensional features refer to the output dimension of the Deep-FCSVDD model being smaller than the input dimension.

[0031] S4.3, averaging these low-dimensional features to obtain the center vector means stacking all the low-dimensional features (vectors) obtained in S4.2 by row and then averaging them by row.

[0032] S4.4. Define the loss function using the center vector and the output of the Deep-FCSVDD model. This means that when training the Deep-FCSVDD model, the model's output and center vector will be used to calculate its Euclidean distance and use this distance as the loss function.

[0033] S5. Adjust the hyperparameters and input the training set and validation set established for each cable into the corresponding Deep-FCSVDD model for training.

[0034] S5.1 Setting hyperparameters during training, including initial learning rate, maximum number of training epochs, batch size, model convergence criterion, Momentum, and Weightdecay;

[0035] S5.2 Determine whether the loss function tends to converge with the increase of iterations during the training process; if convergence is satisfied, proceed to step S5.3; if convergence is not satisfied, return to S5.1, adjust the parameters and continue training.

[0036] S5.3. Does the validation set result meet the requirements? If the validation set prediction result meets the requirements, proceed to step S6; if not, return to S5.1, adjust the parameters, and continue training.

[0037] S6. Complete the training of the Deep-FCSVDD model and save the training weight parameters corresponding to the best results on the validation set.

[0038] S7. Provide real-time warnings for each cable based on the defined damage indicators and warning thresholds;

[0039] S7.1 The damage index consists of two parts. The first part is the DI defined based on the autocorrelation function. a The first part is used to detect large losses, and the second part is the DI defined based on the cross-correlation function. c Used to detect minor damage.

[0040] DI a and DI c The calculation method is as follows:

[0041] DI a (x)=argpeak(R z(x) )-argpeak(R c (4)

[0042] DI c (x)=argmax(R z(x),c (5)

[0043] Where argpeak represents the x-coordinate of the first peak, argmax represents the x-coordinate of the maximum value, z(x) represents the output of Deep-FCSVDD, and R z(x) R represents the autocorrelation function with respect to z(x). c R represents the autocorrelation function with respect to c. z(x),c This represents the cross-correlation function with respect to z(x) and c;

[0044] S7.2 The warning threshold refers to the damage index calculated based on the training set and validation set corresponding to each cable, and then the damage threshold is determined by the 3σ principle.

[0045] The beneficial effects of this invention are as follows: The real-time early warning method for cable structures in this invention leverages the powerful low-dimensional feature extraction capability of the Deep-FCSVDD model, proposes two interpretable damage indices, and achieves real-time early warning for cables. To reduce the training difficulty of the network, this invention performs frequency domain preprocessing on the original accelerated response, and by selecting appropriate frequency bands, it retains effective information while significantly reducing the training difficulty of the network. In terms of network structure, by using 1D-CAE, the interpretability of low-dimensional features is preserved, and based on this, two interpretable damage indices are proposed, solving the mutual influence between cables caused by the redistribution of cable forces. Based on the above, the Deep-FCSVDD real-time early warning method for cables proposed in this invention can provide timely warnings of minor damage to cables, and it is expected to be applied in engineering practice for real-time early warning of cable damage. Attached Figure Description

[0046] Figure 1 This is a schematic diagram of the real-time early warning method for cable structures based on Deep-FCSVDD.

[0047] Figure 2 This is a schematic diagram of data collection, segmentation, and preprocessing.

[0048] Figure 3 This is a schematic diagram of the 1D-CAE model and the Deep-FCSVDD model.

[0049] Figure 4 This is the warning result when the 1% damage to cables 13-15 occurs.

[0050] Figure 5 This is the warning result when cable #1 is 1% damaged. Detailed Implementation

[0051] The specific embodiments of the present invention will be further described below with reference to the accompanying drawings and technical solutions. The accompanying drawings illustrate implementation examples of the present invention, and their purpose is to provide a more specific explanation of the disclosure of the present invention.

[0052] like Figure 1 As shown, this invention provides a real-time early warning method for cable-stayed structures based on Deep-FCSVDD, comprising seven steps S1-S7:

[0053] Furthermore, such as Figure 2 As shown, collecting the lateral acceleration response of each cable in S1 refers to collecting the acceleration response of each cable in the Z direction.

[0054] In step S2.1, dividing the data into three datasets proportionally, namely the training set, validation set, and test set, means dividing the corresponding acceleration response of each cable into the training set, validation set, and test set in a ratio of 8:1:1.

[0055] Furthermore, the size of the initial window NT in step S2.2.1 needs to be determined based on the fundamental frequency of the cable, and its calculation method is as follows:

[0056]

[0057] Where f represents the fundamental frequency of the cable, and the frequency resolution Δf is required to be no less than 1% of f. s This represents the sampling frequency, taken as 100Hz. f represents rounding down. max f represents the highest frequency of the selected frequency band. min This represents the lowest frequency of the selected frequency band.

[0058] Furthermore, the standardization in step S2.2.2 refers to linearly scaling the data within the selected frequency band to the range of [-1, 1].

[0059] Furthermore, in step S3, the 1D-CAE model comprises an encoder and a decoder, the specific configurations of which are shown in Table 1. Here, LeakyReLU, ReLU, and Tanh represent nonlinear activation functions.

[0060] Table 1. Network architecture of a one-dimensional fully convolutional autoencoder

[0061]

[0062]

[0063] d represents the number of data points in the input sample.

[0064] Furthermore, in step S4.2, the training and test sets of each cable are input into the corresponding initial Deep-FCSVDD model to obtain the features of each sample in the dataset in the low-dimensional feature space. This means that before updating the weights of the Deep-FCSVDD model, the initial Deep-FCSVDD model corresponding to a certain cable needs to perform an inference on the corresponding training and test sets to obtain the low-dimensional features.

[0065] Furthermore, in step S4.2.1, the low-dimensional features refer to the output of the Deep-FCSVDD model.

[0066] Furthermore, in step S4.3, taking the average of these low-dimensional features to obtain the center vector means stacking all the low-dimensional features (vectors) obtained in S4.2 by row and then taking the average by row.

[0067] Furthermore, in step S4.4, the loss function is defined using the center vector and the output of the Deep-FCSVDD model. This means that when training the Deep-FCSVDD model, the model's output and the center vector will be used to calculate its Euclidean distance and use this distance as the loss function.

[0068] The center vector is calculated according to the following formula:

[0069]

[0070] Where c represents the center vector, n represents the total number of samples, φ represents the Deep-FCSVDD model after the corresponding LAX initialization is completed, and x i represents the i-th sample in the corresponding Lasso dataset, and W represents the weights of the Deep-FCSVDD model.

[0071] Define the loss function using the center vector and the output of the Deep-FCSVDD model:

[0072]

[0073] Where c represents the center vector, n represents the total number of samples, φ represents the Deep-FCSVDD model after the corresponding LAX initialization is completed, and x i represents the i-th sample in the corresponding Lasso dataset, and W represents the weights of the Deep-FCSVDD model.

[0074] S5 is the training process of the method of the present invention, which includes forward propagation and backward propagation processes. At the same time, the completion of training must meet the requirements of training and testing.

[0075] In step S5.1, the hyperparameters are specifically set as follows: initial learning rate is 0.005, number of training epochs is 200, batch size is 2, Momentum is 0.9, and Weightdecay is 0.0001.

[0076] In step S5.2, the loss function is backpropagated, and the weights are updated using stochastic gradient descent (SGD). This allows the loss function error to be propagated layer by layer from the last layer forward, updating the parameters of each layer with the goal of minimizing the loss function. The number of iterations is set to 200. Training stops when the model reaches the maximum number of iterations and the loss function has decreased to convergence.

[0077] In step S5.3, if the losses of both the training set and the validation set no longer decrease, and the loss of the validation set is no higher than 120% of the loss of the training set, then the training process and results of S5 are considered to have reached the applicable standard.

[0078] S7.1 The damage index consists of two parts. The first part is the DI defined based on the autocorrelation function. a The first part is used to detect large damage; the second part is the DI defined based on the cross-correlation function. c Used to detect minor damage.

[0079] DI a and DI c The calculation method is as follows:

[0080] DI a (x)=argpeak(R z(x) )-argpeak(R c (4)

[0081] DI c (x)=argmax(R z(x),c (5)

[0082] Where argpeak represents the x-coordinate of the first peak, argmax represents the x-coordinate of the maximum value, z(x) represents the output of Deep-FCSVDD, and R z(x) R represents the autocorrelation function with respect to z(x). c R represents the autocorrelation function with respect to c. z(x),c This represents the cross-correlation function of z(x) and c.

[0083] S7.2 The warning threshold refers to the damage index calculated based on the training set and validation set corresponding to each cable, and then the damage threshold is determined by the 3σ principle.

[0084] The 3σ principle states that a cable is considered damaged when the damage index of an unknown state sample exceeds three times the standard deviation of the corresponding damage indices in the training and validation sets.

[0085] When issuing warnings for multiple cables, attention should be paid to whether the damage index is positive or negative. Only when the damage index exceeds the damage threshold and is negative will the cable be identified as damaged. When the damage index exceeds the damage threshold and is positive, the cable will be identified as being affected by the surrounding cables due to the redistribution of cable force. The cable itself has not been damaged, but the surrounding cables have been damaged.

[0086] like Figure 4-5 As shown, a cable-stayed bridge has 27 cables. When cable 1 or cables 13-15 suffer 1% damage, it can be seen that the method proposed in this invention can accurately detect the damage.

[0087] After verification, the accuracy rate of the early warning of 1% minor damage in a single or multiple cables is 100%, indicating that the real-time early warning method for cable structures based on Deep-FCSVDD provided by the present invention is feasible.

Claims

1. A real-time early warning method for cable-stayed structures based on Deep-FCSVDD, characterized in that, The steps are as follows: S1. Collect the lateral acceleration response of each cable in the cable structure; The lateral acceleration response of the cable refers to the acceleration response of the cable perpendicular to the direction of traffic flow, and the acceleration response is collected using an accelerometer; S2. Perform independent dataset splitting on the lateral acceleration response of each cable, and preprocess the acceleration response in each generated dataset. Each cable corresponds to a training set, a validation set, and a test set. S2.

1. Perform independent dataset segmentation for the lateral acceleration response of each cable. The collected acceleration responses under healthy and unknown cable conditions were divided into three datasets: a training set, a validation set, and a test set. The training and validation sets were used for training and selecting the Deep-FCSVDD model, respectively. The training and validation sets could only contain data under healthy cable conditions, while the test set contained data under unknown cable conditions and was used to test the algorithm's performance for early warning of cable conditions. Among them, the unknown state includes healthy and damaged; the healthy state refers to the state in which the cable has not been damaged, and the unknown state refers to the state in which the cable has been damaged but has not been discovered and requires further judgment. S2.2 Preprocess the accelerated responses in each dataset generated in S2.

1. Preprocessing includes two steps: data augmentation and frequency domain processing. Data augmentation is used to expand the dataset and improve model accuracy, while frequency domain preprocessing is used to extract effective information from the acceleration response and reduce the learning difficulty of the model. S2.2.1 Data augmentation refers to slicing the time-domain signal of the lateral acceleration response of the cable using a sliding window. First, an initial window of size NT is selected, and the time-domain data points contained in the initial window are taken as a sample. Then, the initial window is moved along the positive direction of the time axis with a specific step size. The data points contained in the window after the movement are taken as a new sample. The window movement is repeated until the window reaches the end of the data. In step S2.2.1, the size of the initial window NT needs to be determined based on the fundamental frequency of the cable, and its calculation method is as follows: Where f represents the fundamental frequency of the cable, and the frequency resolution Δf is required to be no less than 1% of f. s This represents the sampling frequency, taken as 100Hz. f represents rounding down. max f represents the highest frequency of the selected frequency band. min This represents the lowest frequency of the selected frequency band; S2.2.2 Frequency domain preprocessing refers to converting the samples in S2.2.1 to the frequency domain through fast Fourier transform, calculating their power spectral density (PSD), then extracting a frequency band with a high signal-to-noise ratio from the PSD, and finally standardizing the PSD data within the extracted frequency band. S3. Copy all three datasets of Lasso and mix the copied datasets together according to the categories to form an overall training set, an overall validation set and an overall test set. Use the three overall datasets to train and test the fully convolutional one-dimensional convolutional autoencoder 1D-CAE. Finally, save the best weights of the 1D-CAE. The 1D-CAE consists of an encoder and a decoder. The encoder comprises a one-dimensional convolutional layer, a one-dimensional normalization layer, a one-dimensional max pooling layer, and two non-linear activation functions. The detailed architecture is as follows: Input -> One-dimensional convolutional layer -> One-dimensional normalization layer -> LeakyReLU -> One-dimensional max pooling layer -> One-dimensional convolutional layer -> One-dimensional normalization layer -> LeakyReLU -> One-dimensional max pooling layer -> One-dimensional convolutional layer -> One-dimensional normalization layer -> LeakyReLU -> One-dimensional max pooling layer -> One-dimensional convolutional layer ->ReLU->Low-dimensional features; The decoder consists of a one-dimensional transposed convolutional layer, a one-dimensional normalization layer, an upsampling layer, and two non-linear activation functions. The detailed architecture is as follows: Low-dimensional features->One-dimensional transposed convolutional layer->One-dimensional normalization layer->LeakyReLU->Upsampling layer->One-dimensional transposed convolutional layer->One-dimensional normalization layer->LeakyReLU->Upsampling layer->One-dimensional transposed convolutional layer->One-dimensional normalization layer->LeakyReLU->Upsampling layer->One-dimensional convolutional layer->Tanh->Reconstructed input; S4. Build a Deep-FCSVDD model for each cable. The model architecture is the encoder part of 1D-CAE. The initial weights are the optimal weights of 1D-CAE saved in step S3. Input the training set and test set of each cable into the corresponding initialized Deep-FCSVDD model to obtain the features of each sample in the dataset in the low-dimensional feature space. Then, take the average of these low-dimensional features to obtain the center vector. Use the center vector and the output of the Deep-FCSVDD model to define the loss function. S5. Adjust the hyperparameters and input the training set and validation set established for each cable into the corresponding Deep-FCSVDD model for training. S5.1 Setting hyperparameters during training, including initial learning rate, maximum number of training epochs, batch size, model convergence criterion, Momentum, and Weightdecay; S5.2 Determine whether the loss function tends to converge with the increase of iterations during the training process; if convergence is satisfied, proceed to step S5.3; if convergence is not satisfied, return to S5.1, adjust the parameters and continue training. S5.

3. Does the validation set result meet the requirements? If the validation set prediction result meets the requirements, proceed to step S6; if not, return to S5.1, adjust the parameters, and continue training. S6. Complete the training of the Deep-FCSVDD model and save the training weight parameters corresponding to the best results on the validation set. S7. Provide real-time warnings for each cable based on the defined damage indicators and warning thresholds; S7.1 The damage index consists of two parts. The first part is the DI defined based on the autocorrelation function. a The first part is used to detect large damage; the second part is the DI defined according to the cross-correlation function. c Used to detect minor damage; DI a and DI c The calculation method is as follows: DI a (x)=argpeak(R z(x) )-argpeak(R c )(4) IN c (x)=argmax(R z(x),c )(5) Where argpeak represents the x-coordinate of the first peak, argmax represents the x-coordinate of the maximum value, z(x) represents the output of Deep-FCSVDD, and R z(x) R represents the autocorrelation function with respect to z(x). c R represents the autocorrelation function with respect to c. z(x),c This represents the cross-correlation function with respect to z(x) and c; S7.2 The warning threshold refers to the damage index calculated based on the training set and validation set corresponding to each cable, and then the damage threshold is determined by the 3σ principle.

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