Oil tank wall missing signal recovery method and device based on conditional autoencoder

Abstract

The present invention belongs to the field of fault diagnosis and artificial intelligence, and specifically relates to a method and device for recovering missing signals from the wall of an oil tank based on a conditional autoencoder. The method collects magnetic leakage signals from the wall of a healthy oil tank, preprocesses the collected magnetic leakage signals to obtain a grayscale matrix, converts the preprocessed data into a color image, and then generates training samples based on the grayscale matrix and the color image; constructs a missing signal recovery model for the wall of an oil tank based on a conditional autoencoder; uses training samples to train the missing signal recovery model based on the conditional autoencoder; inputs the signal to contain missing data into the trained missing signal recovery model to recover the missing signal. The addition of missing signal features enhances the purposefulness of the entire network, allowing the network to have a stronger understanding of missing information and a stronger sense of guidance in the signal recovery process, thus solving the problem of large missing signals being difficult to recover.

Description

Technical Field

[0001] The present invention belongs to the field of fault diagnosis and artificial intelligence, and in particular relates to a method for recovering missing signals from the wall of an oil storage tank based on a conditional autoencoder. Background Art

[0002] The national economy and living standards are constantly improving, directly impacting the increasing use of energy. Oil, the most frequently used energy source, is also dangerous. A leak can be extremely harmful to the environment and cause significant economic losses. Therefore, the storage and transportation of oil must adhere to strict regulations. Storage tanks are the most common facilities for oil storage. Storage tanks primarily consist of the tank wall, tank bottom, and tank roof. Over time, the tank wall is susceptible to corrosion defects and even leaks due to its prolonged exposure to oil.

[0003] Magnetic flux leakage (MFL) testing of oil tank walls is a commonly used nondestructive testing method for tank wall corrosion. The integrity of the MFL signal directly impacts the detection of corrosion. However, due to abnormal signals or interference during the testing process, the measured MFL signal often contains significant signal loss. If signal loss occurs at the location of corrosion, it can seriously affect the assessment of tank wall health. Therefore, recovering the missing signal is a critical component of tank wall health testing. Commonly used methods include statistical recovery and model-based recovery.

[0004] Common statistical recovery methods include multiple imputation method, regression imputation method, etc., as follows:

[0005] Multiple interpolation is a method for filling missing data. The steps are as follows: (1) determine the missing data; (2) obtain a data set based on the estimation; (3) perform interpolation and modeling operations on the above data set; (4) integrate the above established models; (5) evaluate the quality of the model; (6) obtain the final complete data set.

[0006] The multiple imputation method has certain limitations, specifically: (1) the amount of calculation is very large; (2) the implementation is very complicated and difficult to fully master; (3) the number of required variables must be large enough to ensure the accuracy of the results; (4) during the implementation process, the interpolation model is not the same as the analysis model.

[0007] Regression interpolation is a method for recovering missing data based on a regression model. The specific steps are as follows: (1) determine the variables of the system and obtain the regression model of the system; (2) calculate the estimated values of each parameter in the above model; (3) obtain the specific expression of the regression equation through the above estimated values; (4) bring the attribute values of each independent variable in the model into the regression equation to obtain the corresponding missing values.

[0008] The regression interpolation method has certain disadvantages, specifically: (1) Although this method is an unbiased estimate, it is very easy to ignore random errors in practice; (2) The greater the amount of information, the more serious the reduction in accuracy of the results caused by ignoring random errors; (3) There is a linear relationship between the variables, and this relationship is difficult to guarantee in actual application problems.

[0009] The model-based recovery method is to restore missing data by modeling normal data according to the characteristics of the missing signal. Common methods include autoencoders, long short-term memory, etc.

[0010] An autoencoder is an artificial neural network with unsupervised learning. The steps are as follows: (1) forward propagation from the network input layer, intermediate layer to the output layer; (2) establishing a relationship between the network input and output, and then realizing reverse transmission; (3) subtracting the network input from the reconstructed result to obtain the error value; (4) minimizing the error value by changing the parameters.

[0011] Autoencoders have certain disadvantages, specifically: (1) the target cannot be obtained as expected; (2) useful information is easily lost; (3) the reconstruction effect is relatively poor.

[0012] Long-term short-term memory is a time-recurrent neural network with the following specific steps: (1) forgetting process, which selectively forgets the input and is achieved through forget gating; (2) selective memory process, which only remembers the important ones and is controlled by gating signals; (3) outputting the desired state.

[0013] Long-term short-term memory mainly reconstructs or predicts signals by extracting their temporal features. For signals with spatial continuity, it does not have the ability to extract spatial features.

[0014] This method uses a conditional autoencoder to recover missing signals. It first adds missing signal information to a conventional autoencoder, fuses features extracted from the missing signal with those of the original signal, and finally decodes the fused features. The inclusion of missing signal features enhances the network's purposefulness, giving it a stronger understanding of missing information and greater guidance during signal recovery, thus resolving the difficulty of recovering large amounts of missing signal.

[0015] An autoencoder is a classic signal recovery model. It uses an unsupervised approach to decode and encode, continuously approximating the input to the output, making it widely used by researchers for signal recovery. However, if the amount of missing signal is too large, the autoencoder's recovery capabilities become limited. A variational autoencoder, a generative model, is used for missing data recovery. Sample data is normalized and fed into the model to obtain the model's mean and variance. Based on a normal distribution, the random variables are reparameterized to obtain the corresponding latent variables. A loss function is established for the model, and an optimizer is applied to update the parameters of the encoder and decoder networks to minimize error. The trained model is then saved and the output of the model decoder represents the data reconstruction. This algorithm learns the latent state representation corresponding to the input data, resulting in very low reconstruction error, effectively reducing the probability of overfitting and requiring fewer iterations, making it suitable for recovering multi-dimensional missing signals. For large amounts of missing data, combining a generative model with a recovery model can significantly improve signal recovery accuracy. Summary of the Invention

[0016] To address the problems of insufficient missing signal samples and low signal recovery accuracy in the prior art, the present invention proposes a method and device for recovering missing signals from the oil tank wall based on a conditional autoencoder. This method focuses on recovering the missing signal portion based on overall signal reconstruction.

[0017] The present invention adopts the following scheme:

[0018] A method for recovering missing signals from the wall of an oil storage tank based on a conditional autoencoder comprises the following steps:

[0019] Step 1: Collect the magnetic flux leakage signal from the healthy oil tank wall;

[0020] Step 2: Preprocess the collected magnetic flux leakage signal, including signal normalization and data conversion into images;

[0021] Step 3: Generate training samples;

[0022] Step 4: Construct a tank wall missing signal recovery model based on conditional autoencoder;

[0023] Step 5: Train the missing signal recovery model based on the conditional autoencoder;

[0024] Step 6: Input the signal containing missing data into the trained model to recover the missing signal.

[0025] Preferably, the step 2 comprises the following steps:

[0026] Step 2.1: Normalize the signal as follows:

[0027]

[0028] Among them, x represents the input sample data, x min 、x max Respectively represent the minimum and maximum values in the input sample data, Indicates the value after normalization;

[0029] Step 2.2: To increase the weight of missing information when training the network, convert the training samples into color images to add missing information. The formula is as follows:

[0030]

[0031] Among them, represents the value of the matrix after conversion into a color image.

[0032] Preferably, step 3 comprises the following steps:

[0033] Step 3.1: Grayscale image segmentation; use a sliding window of size a×b to segment the grayscale image matrix Segmentation is performed, the sliding window moves with a step size of v, and the grayscale image training samples obtained by segmentation are D = {d1, d2, ..., d n}.

[0034] Step 3.2: Color image segmentation; Use a sliding window of size a×b to segment the grayscale image matrix Segmentation is performed, the sliding window moves with a step size of v, and the color image training samples obtained by segmentation are C = {c1, c2, ..., c n}.

[0035] Step 3.3: Randomly add missing data matrix blocks to the segmented color image sample C to obtain the missing color image training sample

[0036] Step 3.4: Each input is a sample pair, and the training sample pair obtained is

[0037] Preferably, step 4 comprises the following steps:

[0038] Step 4.1: Place the sample Input into the network;

[0039] Step 4.2: The grayscale image encoding part consists of α convolutional layers, each of which contains an activation function and is followed by a pooling layer. The grayscale image encoding part is used to extract the grayscale image features f, and the output features are λ-dimensional.

[0040] Step 4.3: The encoding part of the color image with missing information contains β convolutional layers, each convolutional layer contains an activation function, and each convolutional layer is followed by a pooling layer. The encoding part of the color image with missing information is used to extract the features of the missing information. The output features are λ-dimensional;

[0041] Step 4.4: Get the features f and Perform feature fusion and obtain:

[0042]

[0043] Among them, ξ is the fused feature, ε is the sampling value obtained from the data of the standard Gaussian distribution, that is, ε~N(0,1);

[0044] Step 4.5: Combine the fused features ξ with the features of missing information splicing;

[0045] Step 4.6: The decoding part of signal reconstruction consists of γ deconvolution layers, each of which contains an activation function. The role of the decoding part is to reconstruct the fused features to restore the missing signal.

[0046] Preferably, the step 5 comprises the following steps:

[0047] Step 5.1: Input into the network, and undergo α and β convolution and pooling operations respectively to obtain features f and

[0048] Step 5.2: Combine the features f and Perform feature fusion to obtain the fused feature ξ;

[0049] Step 5.3: Combine the fused features ξ with the features of missing information Splicing to obtain mixed features The dimension is 2λ;

[0050] Step 5.4: Input to the decoder, and after γ deconvolution operations, the output image b is obtained i ;

[0051] Step 5.5: The loss function is:

[0052]

[0053] in, is the KL divergence, is a sparse parameter, η is a hyperparameter;

[0054] Step 5.6: Use the gradient descent method to minimize the loss function, continuously update the network parameters, and complete the network training.

[0055] The device for recovering missing signals of oil tank wall based on conditional autoencoder includes:

[0056] Acquisition module, used to collect magnetic flux leakage signals from the walls of healthy oil storage tanks;

[0057] The preprocessing module is used to preprocess the collected magnetic flux leakage signal to obtain a grayscale image matrix and convert the preprocessed data into a color image;

[0058] A generation module is used to generate training samples based on the grayscale image matrix and the color image;

[0059] A framework module for building a tank wall missing signal recovery model based on conditional autoencoders;

[0060] A training module, used for training a missing signal recovery model based on a conditional autoencoder using training samples;

[0061] The recovery module is used to input the signal to be included in the missing data into the trained missing signal recovery model to recover the missing signal.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] (1) The proposed method adopts an unsupervised training method, and the training samples do not require actual missing signals, which solves the problem of insufficient missing signal samples.

[0064] (2) The proposed method refers to the idea of generative model and adds the missing signal information to the normal signal information, so that the model focuses on the missing part of the information and improves the accuracy of missing signal recovery. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] The accompanying drawings, which constitute part of the present invention, are intended to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are intended to explain the present invention and do not constitute an undue limitation of the present invention. In the accompanying drawings:

[0066] Figure 1 This is a diagram of the network structure based on conditional autoencoder.

[0067] Figure 2 Schematic diagram of the oil tank wall missing signal recovery device based on conditional autoencoder. DETAILED DESCRIPTION

[0068] The present invention will be described in detail below with reference to the accompanying drawings and in combination with embodiments. It should be noted that, unless there is a conflict, the embodiments and features of the embodiments of the present invention may be combined with each other.

[0069] The following detailed description is for illustrative purposes only and is intended to provide further details of the present invention. Unless otherwise specified, all technical terms used in the present invention have the same meaning as those generally understood by those skilled in the art to which the present invention belongs. The terms used in the present invention are only for describing specific embodiments and are not intended to limit the exemplary embodiments according to the present invention.

[0070] Example 1:

[0071] The method for restoring missing signals of oil tank wall based on conditional autoencoder is shown in the attached figure. Figure 1 As shown, the following steps are included:

[0072] Step 1: Collect the magnetic flux leakage signal of the healthy oil storage tank wall as training data.

[0073] Step 2: Preprocess the collected magnetic flux leakage signal, including signal normalization and data conversion into images.

[0074] Step 2.1: Normalize the signal as shown in formula (1).

[0075]

[0076] Among them, x represents the input sample data, x min 、x max Respectively represent the minimum and maximum values in the input sample data, Indicates the normalized value.

[0077] Step 2.2: In order to enhance the proportion of missing information when training the network, the training samples are converted into color images to add missing information, as shown in formula (2).

[0078]

[0079] in, Represents the value of the matrix after conversion to a color map.

[0080] Step 3: Generate training samples.

[0081] Step 3.1: Grayscale image segmentation. Use a sliding window of size a×b to segment the grayscale image matrix Segmentation is performed, the sliding window moves with a step size of v, and the grayscale image training samples obtained by segmentation are D = {d1, d2, ..., d n}.

[0082] Step 3.2: Color image segmentation. Use a sliding window of size a×b to segment the grayscale image matrix. Segmentation is performed, the sliding window moves with a step size of v, and the color image training samples obtained by segmentation are C = {c1, c2, ..., c n}.

[0083] Step 3.3: Randomly add missing data matrix blocks to the segmented color image sample C to obtain the missing color image training sample

[0084] Step 3.4: Each input is a sample pair, and the training sample pair obtained is

[0085] Step 4: Construct a tank wall missing signal recovery model based on conditional autoencoder (such as Figure 1 ).

[0086] Step 4.1: Place the sample Input to the network.

[0087] Step 4.2: The grayscale image encoding consists of three convolutional layers, each with an activation function and followed by a pooling layer. The grayscale image encoding is used to extract features f of the grayscale image, and the output features are 10-dimensional.

[0088] Step 4.3: The encoding part of the color image with missing information contains 3 convolutional layers, each of which contains an activation function and is followed by a pooling layer. The encoding part of the color image with missing information is used to extract the features of the missing information. The output features are 10-dimensional.

[0089] Step 4.4: Get the features f and Perform feature fusion as shown in formula (3).

[0090]

[0091] Among them, ξ is the fused feature, and ε is the sampling value obtained from the data of the standard Gaussian distribution, that is, ε~N(0,1).

[0092] Step 4.5: Combine the fused features ξ with the features of missing information Splicing.

[0093] Step 4.6: The decoding part of the signal reconstruction consists of three deconvolution layers, each of which contains an activation function. The decoding part is responsible for reconstructing the fused features and recovering the missing signal.

[0094] Step 5: Train the missing signal recovery model based on the conditional autoencoder.

[0095] Step 5.1: Input into the network, and undergo three convolution and pooling operations to obtain the features f and The convolution operation is shown in formula (4).

[0096]

[0097] Where: σ is the activation function ReLU, is the convolution operation, The size of the convolution kernel is .

[0098] Step 5.2: Combine the features f and Perform feature fusion according to formula (3) to obtain the fused feature ξ.

[0099] Step 5.3: Combine the fused features ξ with the features of missing information Splicing to obtain mixed features The dimension is 20.

[0100] Step 5.4: Input into the decoder, and after 3 deconvolution operations, the output image b is obtained i The deconvolution operation is shown in formula (5).

[0101]

[0102] Where: σ is the activation function ReLU, □ is the deconvolution operation, is the deconvolution kernel size.

[0103] Step 5.5: The loss function is shown in formula (6).

[0104]

[0105] in, is the KL divergence, is a sparse parameter and η is a hyperparameter.

[0106] Step 5.6: Use the gradient descent method to minimize the loss function, continuously update the network parameters, and complete the network training.

[0107] Step 6: Input the signal containing missing data into the trained model to recover the missing signal.

[0108] Example 2:

[0109] like Figure 2The oil tank wall missing signal recovery device based on conditional autoencoder shown includes an acquisition module, a preprocessing module, a generation module, a framework module, a training module and a recovery module.

[0110] In the acquisition module, the magnetic leakage signal of the healthy oil storage tank wall is collected; the collected magnetic leakage signal is transmitted to the preprocessing module to obtain a grayscale image matrix, and the processed data is converted into a color image in the preprocessing module; the generation module generates training samples based on the grayscale image matrix and color image.

[0111] In the construction module, a missing signal recovery model for the oil tank wall based on the conditional autoencoder is constructed; the model constructed in the construction module and the training samples obtained in the generation module are transferred to the training module to complete the training of the missing signal recovery model for the oil tank wall based on the conditional autoencoder.

[0112] After that, the signal containing missing data can be input into the trained oil tank wall missing signal recovery model based on conditional autoencoder to recover the missing signal.

[0113] It is understood from common technical knowledge that the present invention may be implemented by other embodiments that do not depart from its spirit or essential features. Therefore, the embodiments disclosed above are, in all respects, merely illustrative and not exclusive. All modifications within the scope of the present invention or equivalent to the scope of the present invention are intended to be encompassed by the present invention.

[0114] It will be understood by those skilled in the art that embodiments of the present invention may be provided as methods, systems, or computer program products. Thus, the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware. Furthermore, the present invention may take the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to magnetic disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0115] The present invention is described with reference to flowcharts and / or block diagrams of methods, devices (systems), and computer program products according to embodiments of the present invention. It should be understood that each process and / or block in the flowcharts and / or block diagrams, as well as combinations of processes and / or blocks in the flowcharts and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowcharts and / or block diagrams. Figure 1 a process or multiple processes and / or boxes Figure 1A device that provides the functions specified in a block or multiple blocks.

[0116] These computer program instructions may also be stored in a computer readable memory that can direct a computer or other programmable data processing device to work in a specific manner, so that the instructions stored in the computer readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 a process or multiple processes and / or boxes Figure 1 The function specified in one or more boxes.

[0117] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operational steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing the instructions executed on the computer or other programmable device for implementing the process. Figure 1 a process or multiple processes and / or boxes Figure 1 A step that specifies a function in one or more boxes.

[0118] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, ordinary technicians in the field should understand that the specific implementation methods of the present invention can still be modified or replaced by equivalents. Any modification or equivalent replacement that does not depart from the spirit and scope of the present invention should be covered by the scope of protection of the claims of the present invention.

Claims

1. A method for recovering missing signals from the wall of an oil storage tank based on a conditional autoencoder, characterized in that: The following steps are involved: Step 1: Collect the magnetic flux leakage signal from the healthy oil tank wall; Step 2: Preprocess the collected magnetic flux leakage signal to obtain a grayscale image matrix, and convert the preprocessed data into a color image; Step 3: Generate training samples based on the grayscale image matrix and color image; Step 4: Construct a tank wall missing signal recovery model based on conditional autoencoder; Step 5: Use the training samples to train the missing signal recovery model based on the conditional autoencoder; Step 6: Input the signal containing missing data into the trained missing signal recovery model to recover the missing signal; The step 3 comprises the following steps: Step 3.1: Grayscale image segmentation; using dimensions The sliding window of the grayscale image matrix Segmentation is performed, and the grayscale image training samples obtained by segmentation are ; The sliding window moving step is ; Step 3.2: Color image segmentation; use size The sliding window of the grayscale image matrix Segmentation is performed, and the color image training sample obtained by segmentation is ; The sliding window moving step is ; Step 3.3: Sample of the segmented color image Randomly add missing data matrix blocks to obtain missing color map training samples ; Step 3.4: Each input is a sample pair, and the training sample pair obtained is ; The step 4 comprises the following steps: Step 4.1: Place the sample Input into the network; Step 4.2: The encoding part of the grayscale image contains Convolutional layers, each of which contains an activation function, and each convolutional layer is followed by a pooling layer; the encoding part of the grayscale image is used to extract the features of the grayscale image , the output features are dimension; Step 4.3: The coded portion of the color map containing missing information contains Convolutional layers, each of which contains an activation function, and each convolutional layer is followed by a pooling layer; the encoding part of the color image containing missing information is used to extract the features of the missing information , the output features are dimension; Step 4.4: Get the features and Perform feature fusion and obtain: in, is the fused feature, is the sample value obtained from the standard Gaussian distribution data, ; Step 4.5: Combine the fused features Characteristics with missing information splicing; Step 4.6: The decoding part of signal reconstruction includes deconvolution layers, each of which contains an activation function to complete the construction of the missing signal recovery model; The step 5 comprises the following steps: Step 5.1: Input into the constructed missing signal recovery model, respectively through Sub-convolution and pooling operations to obtain features and ; The convolution operation formula is: in: is the activation function ReLU, is the convolution operation, is the convolution kernel size; Step 5.2: Add features and Perform feature fusion to obtain the fused features ; Step 5.3: Combine the fused features Characteristics with missing information Splicing to obtain mixed features , the dimension is ; Step 5.4: Input to the decoder, after The output image is obtained by the deconvolution operation ; The deconvolution operation is shown below: in: is the activation function ReLU, is the deconvolution operation, is the deconvolution kernel size; Step 5.5: Calculate the loss function; the loss function is: in, is the KL divergence, is a sparse parameter, is a hyperparameter; Step 5.6: Minimize the loss function, update the network parameters, and complete the training of the missing signal recovery model.

2. The method for recovering missing signals from the oil tank wall based on conditional autoencoder according to claim 1 is characterized in that: The preprocessing in step 2 is specifically normalization; The leakage magnetic signal is normalized, and the formula is as follows: in, Indicates the input magnetic leakage signal, 、 Respectively represent the minimum and maximum values in the magnetic flux leakage signal, Represents the value of the grayscale image matrix after normalization; The preprocessed data is converted into an image using the following formula: in, Represents the value of the grayscale image matrix after conversion to a color image.

3. The method for recovering missing signals from the oil tank wall based on conditional autoencoder according to claim 1 is characterized in that: = =3， =10， =3。 4. The method for recovering missing signals from the oil tank wall based on conditional autoencoder according to claim 1 is characterized in that: In step 5.6, the gradient descent method is used to continuously minimize the loss function, update the network parameters, and complete the training of the missing signal recovery model.

5. The oil tank wall missing signal recovery device based on conditional autoencoder is characterized by: include: Acquisition module, used to collect magnetic flux leakage signals from the walls of healthy oil storage tanks; The preprocessing module is used to preprocess the collected magnetic flux leakage signal to obtain a grayscale image matrix and convert the preprocessed data into a color image; A generation module is used to generate training samples based on the grayscale image matrix and the color image; Grayscale image segmentation, using size The sliding window of the grayscale image matrix Segmentation is performed, and the grayscale image training samples obtained by segmentation are , the sliding window moving step is ; Color image segmentation, using size The sliding window of the grayscale image matrix Segmentation is performed, and the color image training sample obtained by segmentation is , the sliding window moving step is ; For the color image sample after segmentation Randomly add missing data matrix blocks to obtain missing color map training samples ; Each input is a sample pair, and the training sample pair obtained is ; The framework module is used to build a tank wall missing signal recovery model based on conditional autoencoder; the sample pairs Input to the network; the encoded part of the grayscale image contains Convolutional layers, each of which contains an activation function, and each convolutional layer is followed by a pooling layer; the encoding part of the grayscale image is used to extract the features of the grayscale image , the output features are dimension; the coded portion of the color map containing missing information contains Convolutional layers, each of which contains an activation function, and each convolutional layer is followed by a pooling layer; The coded part of the color map containing missing information is used to extract the features of the missing information , the output features are dimension; for the features obtained and Perform feature fusion to obtain ,in, is the fused feature, is the sample value obtained from the standard Gaussian distribution data, ; The fused features Characteristics with missing information Splicing; the decoding part of signal reconstruction includes deconvolution layers, each of which contains an activation function to complete the construction of the missing signal recovery model; The training module is used to train the missing signal recovery model based on the conditional autoencoder using training samples; Input into the constructed missing signal recovery model, respectively through Sub-convolution and pooling operations to obtain features and , the convolution operation formula is ,in: is the activation function ReLU, is the convolution operation, is the convolution kernel size; the feature and Perform feature fusion to obtain the fused features ; The fused features Characteristics with missing information Splicing to obtain mixed features , the dimension is ;Will Input to the decoder, after The output image is obtained by the deconvolution operation , the deconvolution operation is ,in: is the activation function ReLU, is the deconvolution operation, is the deconvolution kernel size; calculate the loss function, the loss function is ,in, is the KL divergence, is a sparse parameter, is a hyperparameter; minimize the loss function, update the network parameters, and complete the training of the missing signal recovery model; The recovery module is used to input the signal containing missing data into the trained missing signal recovery model to recover the missing signal.

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