CN116502163A - Vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning - Google Patents

Vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning Download PDF

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CN116502163A
CN116502163A CN202310427373.6A CN202310427373A CN116502163A CN 116502163 A CN116502163 A CN 116502163A CN 202310427373 A CN202310427373 A CN 202310427373A CN 116502163 A CN116502163 A CN 116502163A
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周文松
张秀林
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Harbin Institute of Technology
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Abstract

Vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning relates to the technical field of structural health monitoring. The invention aims to solve the problems of low efficiency and poor accuracy caused by the fact that the existing automatic detection method for structural abnormal vibration data only considers the abnormal characteristics of historical data in the time domain. According to the invention, the residual sequence and the PSD sequence are respectively extracted from the historical vibration monitoring data to serve as training samples, so that the abnormal characteristic information is enriched, and the size of the model input sample is reduced. Inputting the sample into a convolutional neural network to extract higher-level data features, and fusing the features of the historical data in the time domain and the frequency domain; then learning abnormal features of the fused feature sequence by using a long-short-term memory neural network model; and finally, abnormal detection of vibration monitoring data is realized by using the trained model.

Description

Vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning
Technical Field
The invention belongs to the technical field of structural health monitoring.
Background
Structural health monitoring systems have been widely used in large span bridge structures and continuously produce large amounts of vibration monitoring data. Rapid mining and utilization of these data is an important aspect in the field of structural health monitoring. However, since the structure is in a severe environment for a long time, various faults occur in the sensor or the whole monitoring system, so that various types of anomalies exist in vibration monitoring data, which seriously interfere with analysis and evaluation of the structure. In addition, these anomalies can interfere with the early warning capabilities of structural health monitoring systems when they are mixed with data related to an emergency event such as an earthquake, a ship collision, or a traffic accident. Therefore, identifying and locating anomalous data is an important step in vibration data analysis.
In conventional vibration data anomaly detection, a variety of signal processing techniques are required to manually detect anomalies, but the manual detection process requires expert involvement and is time consuming. In the existing automatic detection method, vibration data is mainly visualized into images in a time domain, and abnormal data is detected by utilizing a computer vision technology. However, according to the method, only abnormal characteristics of the historical data in the time domain are considered, and the single characteristics are difficult to classify the abnormal data more accurately, so that the accuracy of detection results is low, and the detection efficiency is low.
Disclosure of Invention
The invention aims to solve the problems of low efficiency and poor accuracy caused by the fact that the existing automatic detection method for structural anomalies only considers the anomaly characteristics of historical data in the time domain, and provides a vibration monitoring data anomaly detection method based on multi-characteristic fusion and deep learning.
The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning specifically comprises the following steps:
extracting residual sequences from the upper peak envelope and the lower peak envelope of the vibration monitoring data segment to be detected respectively, and extracting power spectrum density sequences with the same length as the residual sequences from the power spectrum density distribution of the vibration monitoring data segment to be detected;
the residual sequence and the power spectrum density sequence are connected in parallel to construct measured data;
and inputting the detected data into a CNN-LSTM detection model for detection, and obtaining a detection result.
Further, the CNN-LSTM detection model comprises an input layer, a convolution layer, a pooling layer, a flattening layer, an LSTM layer and an output layer;
the input layer is used for inputting measured data to the convolution layer;
the convolution layer adopts t convolution kernels m with the size of 3*2 to carry out one-dimensional convolution operation according to a stride 1 and a window vector of each convolution sampling position of measured data, and t feature graphs e are generated;
the pooling layer is used for carrying out maximum pooling operation on t feature graphs e respectively to obtain t feature graphs c;
the flattening layer is used for rearranging t feature graphs c and carrying out feature fusion to obtain a time sequence M;
the LSTM layer is used for capturing long-term correlation of the time sequence M and learning abnormal characteristics;
the output layer is used for classifying abnormal features captured by the LSTM layer by using a softmax activation function to obtain a detection result of the CNN-LSTM detection model.
Further, the method for obtaining the CNN-LSTM detection model comprises the following steps:
l historical data segments with the same step length are collected in continuous historical vibration detection data,
extracting a residual sequence and a power spectrum density sequence of each historical data segment respectively,
the residual sequence and the power spectrum density sequence of the same historical data segment are connected in parallel to form a sample, so that the samples corresponding to all the historical data segments are constructed into a sample set,
marking the types of the samples in the sample set, and dividing the samples in the sample set into a training set and a verification set;
constructing a CNN-LSTM basic model;
training the CNN-LSTM basic model by using a training set;
and verifying the trained CNN-LSTM basic model by using a verification set, judging whether the trained CNN-LSTM basic model is qualified or not, if so, obtaining a CNN-LSTM detection model, otherwise, re-selecting a historical data segment from historical vibration detection data, and training the CNN-LSTM basic model.
Further, the specific method for extracting the residual sequence of the first historical data segment is as follows:
respectively calculating the upper peak envelope curve y of the historical data in the first historical data segment u And lower peak envelope curve y l ，
Dividing the historical data in the first data segment by using the I sampling windows, respectively calculating the average value of the historical data in each sampling window, respectively replacing the abnormal data in the sampling window by using the average value of the historical data in each sampling window to obtain the first non-abnormal data segment,
respectively calculating the upper peak envelope curve x of the historical data in the first constant-free segment u And lower peak envelope curve x l ，
By y u 、y l 、x u And x l Calculating residual sequence r of historical data in time domain in the first historical data segment l ＝[r 1 ,r 2 ,…,r I ]，
Wherein r is i For the residual value of the ith sampling window in the ith historical data segment,i＝1,2,...,I，l＝1,2,...,L，/>and->An upper peak envelope and a lower peak envelope of the historical data in the ith sampling window in the ith historical data segment, respectively,/->And->The upper peak envelope and the lower peak envelope of the historical data in the ith sampling window in the ith constant-free segment are respectively.
Further, in the ith sampling window, when the difference between the value of the historical data x and the average value of the historical data in the ith sampling window is greater than 6σ, the historical data x is abnormal data, and σ is the standard deviation of the historical data in the ith sampling window.
Further, the specific method for extracting the power spectrum density sequence of the first historical data segment is as follows:
carrying out unilateral power spectrum density estimation on the historical data in the first historical data segment to obtain power spectrum density distribution p of the historical data in the first historical data segment in the frequency range of 0-fs 2 1 Wherein fs is the sampling frequency of the history data in the first history data segment;
extracting a power spectral density distribution p 1 The first I values of (a) constitute a characteristic sequence p 2 And for the characteristic sequence p 2 Normalizing the elements in the data segment to obtain a power spectrum density sequence p of the first historical data segment l ：
p l ＝normalize(p 2 )，
Where normal (·) represents the normalization function, I is the number of sampling windows of the residual sequence of the first historical data segment.
Further, the residual sequence rl of the historical data in the first historical data segment in the time domain is compared with the power spectrum density sequence p of the first historical data segment l In parallel, obtain the first sample S l ，
Constructing a sample set S= [ S ] from samples corresponding to L historical data segments 1 ,S 2 ,...,S L ]，l＝1,2,...,L。
Further, the number ratio of the historical data in the training set to the historical data in the verification set is 7:3.
Further, the objective function H expression of the CNN-LSTM detection model is as follows:
wherein,,probability of the prediction class being the nth class for the first sample, < >>Probability of the true class being the nth class for the first sample, +.>Input of softmax activation function in output layer when prediction class for the i sample is N-th class, n=1, 2.
Further, the j-th element e in the feature map e j The expression is:
where f (·) is the activation function and the expression f (α) =max (0, α), α is the variable of the activation function,representing element multiplication, w j A window vector for the jth convolution sampling position, b being a bias term;
the t feature images c are connected in parallel according to column vectors to form a feature matrix
Wherein,,the element of the kth pooled sampling position on the t-th feature map c, k being the total number of pooled sampling positions,
matrix the featuresThe elements of all the rows of a row are arranged in a row, obtaining a time sequence M:
aiming at the problem of low detection efficiency and accuracy of the existing abnormal vibration monitoring data detection method, the method enriches abnormal characteristic information and reduces the input size of the model to improve the calculation efficiency by extracting and fusing the characteristics of the historical data in the time domain and the frequency domain. And establishing a CNN-LSTM model to classify the characteristic sequences, and further finishing abnormal vibration monitoring data detection. Compared with the conventional abnormal data detection method, the method can fully automatically and accurately detect various abnormal data. Compared with the existing computer vision method, the method is more efficient and accurate, and has stronger generalization capability.
Drawings
FIG. 1 is a diagram of a vibration monitoring data anomaly detection framework based on a CNN-LSTM model;
FIG. 2 is a schematic diagram of typical abnormal vibration data and residual sequences and PSD sequences extracted therefrom, wherein (a) represents a normal type, (b) represents an outlier type, (c) represents a single-frequency oscillation type, (d) represents a missing type, and (e) represents a sub-minimum type;
FIG. 3 is a confusion matrix for the detection results of a model on a training set and a validation set, where (a) represents the training set and (b) represents the validation set;
FIG. 4 is a graph of the test results of a model on a test set;
FIG. 5 is a confusion matrix of test results for a model on a test set;
FIG. 6 is a flow chart of a vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning.
Detailed Description
The following description of the embodiments of the present invention will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present invention, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention. It should be noted that, without conflict, the embodiments of the present invention and features of the embodiments may be combined with each other.
Referring to fig. 6, a vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to the present embodiment is specifically described, and specifically includes:
firstly, training a CNN-LSTM detection model, wherein the training process is as follows:
and collecting L historical data segments with the same step length in continuous historical vibration detection data, and then respectively extracting a residual sequence and a power spectrum density sequence of each historical data segment.
Specifically, the specific method for extracting the residual sequence of the first historical data segment is as follows:
calculating the upper peak envelope curve y of the historical data in the first historical data segment respectively by using spline linear interpolation on the local maximum value u And lower peak envelope curve y l 。
And dividing the historical data in the first data segment by using the I sampling windows, and respectively calculating the average value of the historical data in each sampling window. In the ith sampling window, when the difference between the value of the historical data x and the average value of the historical data in the ith sampling window is larger than 6σ, the historical data x is abnormal data, and σ is the standard deviation of the historical data in the ith sampling window. And replacing the abnormal data in the ith sampling window by using the historical data average value in the ith sampling window, and further replacing the abnormal data in all the sampling windows by the average value of the sampling windows to obtain the ith non-abnormal constant segment.
Then, respectively calculating the upper peak envelope curve x of the historical data in the first constant segment without variation by using spline linear interpolation on the local maximum value u And lower peak envelope curve x l 。
By y u 、y l 、x u And x l Calculating residual sequence r of historical data in time domain in the first historical data segment l ＝[r 1 ,r 2 ,…,r I ]。
Wherein r is i For the residual value of the ith sampling window in the ith historical data segment,i＝1,2,...,I，l＝1,2,...,L。/>and->Respectively an upper peak envelope and a lower peak envelope of historical data in an ith sampling window in a first historical data segment; />And->The upper peak envelope and the lower peak envelope of the historical data in the ith sampling window in the ith constant-free segment are respectively.
The specific method for extracting the power spectrum density sequence of the first historical data segment comprises the following steps:
carrying out unilateral power spectrum density estimation on the historical data in the first historical data segment to obtain the historical data in the first historical data segment in the range of 0-fs2 frequency range power spectral density distribution p 1 Where fs is the sampling frequency of the history data in the first history data segment and p 1 ∈R (nfft2)×1 Nfft is the number of discrete fourier transform points used in the single-sided power spectral density estimation process.
In order to make the power spectral density sequence the same length as the residual sequence, the power spectral density distribution p is extracted 1 The first I values of (a) constitute a characteristic sequence p 2 And has
For characteristic sequence p 2 Normalizing the elements in the data segment to obtain a power spectrum density sequence p of the first historical data segment l ：
p l ＝normalize(p 2 )，
Wherein normal (·) represents the normalization function, p l Representing the normalized power spectral density distribution of the historical data over the frequency range of 0 to (Ingft) fs, the value of nfft can be adjusted to ensure that the extracted power spectral density sequence is within the frequency range of interest for the study.
Residual sequence r of historical data in the first historical data segment in time domain l Power spectral density sequence p with the first historical data segment l Performing column-vector parallel connection to obtain the first sample S l . Sample set s= [ S ] of sample construction corresponding to L pieces of history data 1 ,S 2 ,...,S L ]。
The types of the samples in the sample set are marked, wherein the marking types comprise a normal type and an abnormal type, and the abnormal type comprises an outlier type, a single-frequency oscillation type, a deletion type and a sub-small value type. The samples in the sample set are divided into a training set and a verification set, and the quantity ratio of the historical data in the training set to the historical data in the verification set is 7:3.
And constructing a CNN-LSTM basic model, wherein the CNN-LSTM basic model comprises an input layer, a convolution layer, a pooling layer, a flattening layer, an LSTM layer and an output layer.
The input layer is used for inputting the measured sample data to the convolution layer.
The convolution layer adopts t convolution kernels m with the size of 3*2 to carry out one-dimensional convolution operation according to a stride 1 and a window vector of each convolution sampling position of measured data, and t feature graphs e are generated. The j-th element e in the characteristic diagram e j The expression is:
where f (·) is the activation function and the expression f (α) =max (0, α), α is the variable of the activation function,representing element multiplication, w j And b is a bias term, and is a window vector of the j-th convolution sampling position.
The pooling layer is used for carrying out maximum pooling operation on t feature graphs e respectively to obtain t feature graphs c. The size of the pooling core in the maximum pooling operation is 2 x 2, and the step length is 2.
The flattening layer connects t feature images c in parallel according to column vectors to form a feature matrix
Wherein,,the element of the kth pooled sampling position on the t-th feature map c, k being the total number of pooled sampling positions.
Then the feature matrixThe elements of all the rows of a row are arranged in a row, obtaining a time sequence M:
the LSTM layer is used to capture long-term correlations of the time series M and learn anomaly characteristics.
The output layer is used for classifying the abnormal features captured by the LSTM layer by using a softmax activation function to obtain a detection result.
The cross entropy loss function is applied to update network parameters, and the objective function H expression of the network model is as follows:
wherein,,probability of the prediction class being the nth class for the first sample, < >>Probability of the true class being the nth class for the first sample, +.>Input of softmax activation function in output layer when prediction class for the i sample is N-th class, n=1, 2.
And training the CNN-LSTM basic model by using a training set, verifying the trained CNN-LSTM basic model by using a verification set, judging whether the trained CNN-LSTM basic model is qualified, if so, obtaining a CNN-LSTM detection model, otherwise, re-selecting a historical data segment from historical vibration detection data to train the CNN-LSTM basic model until the qualified CNN-LSTM detection model is obtained.
After the qualified CNN-LSTM detection model is obtained, detection can be started, and the specific detection process is as follows:
and extracting residual sequences from the upper peak envelope and the lower peak envelope of the vibration monitoring data segment to be detected respectively, and extracting power spectrum density sequences with the same length as the residual sequences from the power spectrum density distribution of the vibration monitoring data segment to be detected.
And connecting the residual sequence and the power spectrum density sequence in parallel to construct measured data.
And inputting the detected data into a CNN-LSTM detection model for detection, and obtaining a detection result.
According to the vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning, residual sequences and PSD sequences are respectively extracted from historical vibration monitoring data to serve as training samples, abnormal feature information is enriched, and the size of a model input sample is reduced. Inputting the samples into a Convolutional Neural Network (CNN) to extract higher-level data features, and fusing the features of the historical data in the time domain and the frequency domain; then learning abnormal features of the fused feature sequence by using a long-short-term memory neural network (LSTM) model; and finally, abnormal detection of vibration monitoring data is realized by using the trained model.
DETAILED DESCRIPTION OF EMBODIMENT (S) OF INVENTION
In a first step, acceleration data from an actual suspension bridge structural health monitoring system is used to construct a data set. Continuous historical monitoring data within one month was divided at intervals of 10 minutes, the sampling frequency was 50Hz, and the size of individual samples was 1 x 30000. To avoid the effect of data set imbalance on recognition accuracy, the final data set is constructed as: the normal type, the outlier type, the single-frequency oscillation type, the missing type and the sub-small value type respectively account for 20 percent, the total sample number is 18000, and the ratio is 7: the scale of 3 is divided into training and validation sets.
In the second step, the sample is subjected to feature extraction, and firstly, the residual sequence of the historical data on the time domain and the PSD sequence on the frequency domain are obtained, and various typical vibration data types, and schematic diagrams of the residual sequence and the PSD sequence are shown in fig. 2. It can be seen that the different types of vibration data have a large difference in the time and frequency domains, and finally all the input samples are constructed.
Third, build an improved CNN-LSTM model architecture with GPU acceleration, built from Python scientific suite, tensorFlow and Keras. 12600 training samples consisting of the obtained residual sequence and PSD sequence are input into a CNN-LSTM model, the front CNN model is used for extracting and fusing the time domain features and the frequency domain features of the input samples, and then the LSTM model is used for further learning the long-term correlation and the abnormal data features of the fused feature time sequence. The model was trained by minimizing cross entropy error, using Adam optimizer, with 64 samples per batch, and a conjugate rate of 0.5. The experiment was repeated to optimize the model parameters. When the error of the validation set continuously grows over 10 cycles, it is indicated that the over-fitting has occurred and the training is aborted in advance. Fig. 3 (a) and (b) are confusion matrices of the classification results of the final model on the training set and the verification set, respectively, wherein the diagonal is the number of correctly classified samples, the bracket is the recall of the corresponding type, and it can be seen that the classification results on the training set and the verification set have high accuracy.
And fourthly, testing the trained model by using monitoring data except the data set of the suspension bridge, wherein fig. 4 is the distribution of the detection results of the data of the test set. Obviously, these anomaly data have a certain distribution rule in space and time. To verify the reliability of the proposed method, all data are manually detected and marked for comparison with the detection results of the proposed method. Fig. 5 shows a confusion matrix of the detection result of the proposed method and the actual manual detection result, and it can be seen that the method also has a high accuracy on the test set.
Although the invention herein has been described with reference to particular embodiments, it is to be understood that these embodiments are merely illustrative of the principles and applications of the present invention. It is therefore to be understood that numerous modifications may be made to the illustrative embodiments and that other arrangements may be devised without departing from the spirit and scope of the present invention as defined by the appended claims. It should be understood that the different dependent claims and the features described herein may be combined in ways other than as described in the history claims. It is also to be understood that features described in connection with separate embodiments may be used in other described embodiments.

Claims (10)

1. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning is characterized in that,
extracting residual sequences from the upper peak envelope and the lower peak envelope of the vibration monitoring data segment to be detected respectively, and extracting power spectrum density sequences with the same length as the residual sequences from the power spectrum density distribution of the vibration monitoring data segment to be detected;
the residual sequence and the power spectrum density sequence are connected in parallel to construct measured data;
and inputting the detected data into a CNN-LSTM detection model for detection, and obtaining a detection result.
2. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning of claim 1, wherein the CNN-LSTM detection model comprises an input layer, a convolution layer, a pooling layer, a flattening layer, an LSTM layer, and an output layer;
the input layer is used for inputting measured data to the convolution layer;
the convolution layer adopts t convolution kernels m with the size of 3*2 to carry out one-dimensional convolution operation according to a stride 1 and a window vector of each convolution sampling position of measured data, and t feature graphs e are generated;
the pooling layer is used for carrying out maximum pooling operation on t feature graphs e respectively to obtain t feature graphs c;
the flattening layer is used for rearranging t feature graphs c and carrying out feature fusion to obtain a time sequence M;
the LSTM layer is used for capturing long-term correlation of the time sequence M and learning abnormal characteristics;
the output layer is used for classifying abnormal features captured by the LSTM layer by using a softmax activation function to obtain a detection result of the CNN-LSTM detection model.
3. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 1 or 2, wherein the method for obtaining the CNN-LSTM detection model is as follows:
l historical data segments with the same step length are collected in continuous historical vibration detection data,
extracting a residual sequence and a power spectrum density sequence of each historical data segment respectively,
the residual sequence and the power spectrum density sequence of the same historical data segment are connected in parallel to form a sample, so that the samples corresponding to all the historical data segments are constructed into a sample set,
marking the types of the samples in the sample set, and dividing the samples in the sample set into a training set and a verification set;
constructing a CNN-LSTM basic model;
training the CNN-LSTM basic model by using a training set;
and verifying the trained CNN-LSTM basic model by using a verification set, judging whether the trained CNN-LSTM basic model is qualified or not, if so, obtaining a CNN-LSTM detection model, otherwise, re-selecting a historical data segment from historical vibration detection data, and training the CNN-LSTM basic model.
4. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 3, wherein the specific method for extracting the residual sequence of the first historical data segment is as follows:
respectively calculating the upper peak envelope curve y of the historical data in the first historical data segment u And lower peak envelope curve y l ，
Dividing the historical data in the first data segment by using the I sampling windows, respectively calculating the average value of the historical data in each sampling window, respectively replacing the abnormal data in the sampling window by using the average value of the historical data in each sampling window to obtain the first non-abnormal data segment,
respectively calculating the upper peak envelope curve x of the historical data in the first constant-free segment u And lower peak envelope curve x l ，
By y u 、y l 、x u And x l Calculating residual sequence r of historical data in time domain in the first historical data segment l ＝[r 1 ,r 2 ,…,r I ]，
Wherein r is i For the residual value of the ith sampling window in the ith historical data segment,i＝1,2,...,I，l＝1,2,...,L，/>and->An upper peak envelope and a lower peak envelope of the historical data in the ith sampling window in the ith historical data segment, respectively,/->And->The upper peak envelope and the lower peak envelope of the historical data in the ith sampling window in the ith constant-free segment are respectively.
5. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 4, wherein in the ith sampling window, when the difference between the value of the historical data x and the average value of the historical data in the ith sampling window is greater than 6σ, the historical data x is anomaly data, and σ is the standard deviation of the historical data in the ith sampling window.
6. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 3, wherein the specific method for extracting the power spectral density sequence of the first historical data segment is as follows:
carrying out unilateral power spectrum density estimation on the historical data in the first historical data segment to obtain power spectrum density distribution p of the historical data in the first historical data segment in the frequency range of 0-fs/2 1 Wherein fs is the sampling frequency of the history data in the first history data segment;
extracting a power spectral density distribution p 1 The first I values of (a) constitute a characteristic sequence p 2 And for the characteristic sequence p 2 Normalizing the elements in the data segment to obtain a power spectrum density sequence p of the first historical data segment l ：
p l ＝normalize(p 2 )，
Where normal (·) represents the normalization function, I is the number of sampling windows of the residual sequence of the first historical data segment.
7. A vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 3, wherein the residual sequence r of the historical data in the first historical data segment in the time domain is l Power spectral density sequence p with the first historical data segment l In parallel, obtain the first sample S l ，
Constructing a sample set S= [ S ] from samples corresponding to L historical data segments 1 ,S 2 ,...,S L ]，l＝1,2,...,L。
8. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning of claim 3, wherein the number ratio of the historical data in the training set and the verification set is 7:3.
9. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 3, wherein the objective function H expression of the CNN-LSTM detection model is:
wherein,,probability of the prediction class being the nth class for the first sample, < >>Probability of the true class being the nth class for the first sample, +.>Input of softmax activation function in output layer when prediction class for the i sample is N-th class, n=1, 2.
10. The vibration monitoring data anomaly detection method based on multi-feature fusion and deep learning according to claim 2, wherein the j-th element e in the feature map e j The expression is:
where f (·) is the activation function and the expression f (α) =max (0, α), α is the variable of the activation function,representing element multiplication, w j A window vector for the jth convolution sampling position, b being a bias term;
the t feature images c are connected in parallel according to column vectors to form a feature matrix
Wherein,,the element of the kth pooled sampling position on the t-th feature map c, k being the total number of pooled sampling positions,
matrix the featuresThe elements of all the rows of a row are arranged in a row, obtaining a time sequence M:
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* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117708643A (en) * 2023-11-07 2024-03-15 中交公路长大桥建设国家工程研究中心有限公司 Bridge monitoring abnormal data identification method and system based on fusion sequence characteristics

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN117708643A (en) * 2023-11-07 2024-03-15 中交公路长大桥建设国家工程研究中心有限公司 Bridge monitoring abnormal data identification method and system based on fusion sequence characteristics

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