Deep-sea sound source depth estimation method based on variational auto-encoding network feature selection

Abstract

The present application relates to a kind of deep-sea sound source depth estimation method based on variational auto-encoding network feature selection, to study the η sound velocity profile data of sea area as the sample data of the present application, the sound field ray model based on bellhop is used to calculate the sound field interference stripe under different sound source depth each profile, then using variational convolution auto-encoding network is trained, realize the dimension reduction processing of sound field interference stripe chart, obtain the one-dimensional feature vector corresponding to sound field interference stripe chart. The variance between one-dimensional feature vector under different sound velocity profile is calculated, the variance value of each characteristic value under the condition of sound velocity disturbance can be obtained, the characteristic value corresponding to the larger variance is removed, and the one-dimensional feature vector after feature selection is obtained. Finally, with the aid of one-dimensional residual convolutional neural network, the one-dimensional feature vector after feature selection is trained, so as to realize the estimation of deep-sea sound source depth.

Description

Technical Field

[0001] This invention belongs to the fields of marine physics, marine engineering, and underwater acoustics engineering. It relates to a method for estimating the depth of deep-sea sound sources based on feature selection of variational autoencoder networks, which is applicable to solving the problem of sound source depth estimation under deep-sea sound speed disturbance conditions. Background Technology

[0002] Underwater sound source localization has always been a hot topic in oceanographic research, and sound source depth estimation, as an aspect of underwater sound source localization, has also attracted much attention from scholars. Although various deep-sea sound source depth estimation methods have been applied in engineering practice, such as matching field-based methods, multipath arrival delay-based methods, and interferometric fringe-based methods, sound source depth estimation methods still face significant technical challenges in complex deep-sea areas with severe sound speed disturbances. The main reason for this is that existing sound source depth estimation methods exhibit significant deviations when dealing with areas with severe sound speed disturbances. Sound speed disturbances cause nonlinear interactions and complex model evolutions in the predicted sound field, leading to uncertainties in sound field estimation, and consequently, uncertainties in sound source depth estimation. A detailed analysis follows:

[0003] (1) Matching Field-Based Methods. This method can be broadly divided into two types: copy field matching and modal matching. The copy field matching method requires sampling the distance and depth space within the acoustic field coverage area. At each sampling point, a sound source is assumed to exist, located on a grid node. The distance and depth of the sound source can then be considered known quantities. The sound pressure of the assumed sound source can be calculated using the acoustic field model, forming a copy field. Matching this copy field with the measured field yields the sound source depth. The modal matching method extracts acoustic signals of different modes from the received signal. This signal contains the distance and depth information of the sound source. The sound source depth is obtained by selecting and matching a subset of modes. In complex underwater acoustic environments with significant spatiotemporal variations, such as underwater sound velocity disturbance distances, the matching field method suffers from "environmental mismatch," leading to substantial errors in sound source depth estimation.

[0004] (2) The method based on multipath arrival time delay. This method utilizes the time delay information of the direct wave, primary seabed reflected wave, and primary sea surface reflected wave of the deep-sea sound source signal. The time delay information of the multipath signals is sensitive to the sound source depth, and the sound source depth can be estimated using ray transmission or multipath signal time delay matching methods. Similar to the above methods, when facing sea areas with severe sound speed disturbances, the time delay information of the multipath signals at the same sound source depth has uncertainty, causing deviations in the sound source depth estimation results.

[0005] (3) Interference fringe-based method. This method is based on the fact that, under reliable acoustic path conditions, the target motion generates alternating bright and dark fringes. When the sound source moves horizontally, the array's beam scanning output will present alternating bright and dark fringes on the direct wave angle of arrival curve. These fringes fluctuate at different frequencies with the sound source depth, and the sound source depth can be estimated based on the fringe fluctuation frequency. Similar to the above method, when facing sea areas with severe sound speed disturbances, the changes in interference fringes will produce uncertainties, causing deviations in the sound source depth estimation results.

[0006] In short, methods based on matched fields, multipath arrival delays, and interferometric fringes generally cause deviations in sound source depth estimation results in regions with active ocean dynamic processes, i.e., areas with severe sound speed disturbances. Therefore, it is necessary to seek new principles and technical approaches. Summary of the Invention

[0007] Technical problems to be solved

[0008] To avoid the shortcomings of existing technologies, this invention proposes a deep-sea sound source depth estimation method based on feature selection of variational autoencoder networks, which is particularly suitable for sound source depth estimation under deep-sea sound speed disturbance conditions.

[0009] Technical solution

[0010] A method for estimating the depth of deep-sea acoustic sources based on feature selection using variational autoencoders (VACs) is characterized by the following steps:

[0011] Step 1: Using η sound velocity profiles from the study area as sample data, calculate the sound field interference fringes G at different sound source depths for each profile using a Bellhop-based sound field ray model. i,d (f,r);

[0012] Step 2: Use sound field interference fringes G under different sound source depths and different sound velocity profiles i,d (f,r) data is used to train the variational autoencoder network;

[0013] The encoder of the trained variational autoencoder network transforms any input acoustic interference fringe data into a one-dimensional feature vector x corresponding to the acoustic interference fringe pattern. i,d where i is the index of the sound speed profile and d is the depth of the sound source:

[0014] x i,d =enconder(G i,d (f,r));

[0015] Step 3: Based on the obtained one-dimensional eigenvectors corresponding to different sound source depths and sound speed profiles, calculate the variance of the one-dimensional eigenvectors as a function of sound speed perturbation at different sound source depths:

[0016]

[0017] Where, mean(x) i,d ) is the mean of the one-dimensional eigenvector perturbation with the speed of sound, w is the length of the one-dimensional eigenvector, and k is the index of the feature of the one-dimensional eigenvector.

[0018] Then, the eigenvalues ​​with larger variances in the one-dimensional eigenvector are removed to form the one-dimensional eigenvector after feature selection.

[0019] Step 4: Use the one-dimensional feature vectors selected from different sound source depth features to train a 50-layer one-dimensional residual convolutional neural network. After training, the 50-layer one-dimensional residual convolutional neural network can estimate the sound source depth.

[0020] The 50-layer one-dimensional residual convolutional neural network consists of 49 convolutional layers and one fully connected layer.

[0021] The one-dimensional feature vector is first transformed into a two-dimensional feature vector with a length of 112 and 64 channels through a convolutional layer. Then, it is transformed into a two-dimensional feature vector with a length of 64 and 64 channels through a pooling layer. Next, it is transformed into a feature vector with a length of 1024 through a residual network consisting of 16 convolutional blocks, followed by a mean pooling layer. Finally, it is transformed into a vector with a length equal to the number of sound source depth categories to be estimated through a linear layer. Each value of the vector represents the probability that the estimated result is the corresponding sound source depth value, thereby realizing the estimation of the sound source depth.

[0022] The sound field interference fringes G under different profiles at different sound source depths i,d (f,r) is: G i,d (f,r)=bellhop(S i ), where f is the preset sound field frequency range, r is the preset sound field distance range, i is the index of the sound velocity profile, d is the sound source depth, and S i Let p be a p×η matrix containing the set of sound speed profiles, where p is the number of layers of the sound speed profile and η is the number of sound speed profiles.

[0023] In step 2, the sound field interference fringe pattern is cropped to a size of (128, 128) before being fed into the variational convolutional autoencoder network for training.

[0024] The variational autoencoder network consists of an encoder and a decoder. The encoder first extracts the interference fringe features through four convolutional layers, followed by two linear layers. The decoder first goes through two linear layers, followed by four deconvolutional layers to reconstruct the interference fringe pattern.

[0025] The loss function in step 2, during the training of the variational autoencoder network, consists of two parts:

[0026] Loss = MSE(G i,d (f,r),G′ i,d (f,r))+KL(p1||p2)

[0027] The first term of the loss function is the mean square error (MSE) between the autoencoder reconstruction result and the original data, and the second term of the loss function is the KL divergence between the distribution returned by the encoder and the standard normal distribution.

[0028] The mean square error of MSE is calculated as follows:

[0029]

[0030] The KL divergence calculation:

[0031]

[0032] Among them, G i,d (f,r) represents the actual acoustic field interference fringes, and G′ i,d (f,r) represents the acoustic interference fringes reconstructed by the variational autoencoder network; p1 represents the data distribution simulated by the variational autoencoder, p2 represents the data distribution simulated by the variational autoencoder, μ1 represents the mean of the data distribution simulated by the variational autoencoder, and δ1 represents the variance of the data distribution simulated by the variational autoencoder.

[0033] In step 4, the feature vector is interpolated to a length of (1, 224) before being fed into the training of a 50-layer one-dimensional residual convolutional neural network.

[0034] Beneficial effects

[0035] This invention proposes a method for estimating the depth of deep-sea sound sources based on feature selection using a variational autoencoder network. Within the study area, η sound velocity profiles are obtained using a sound velocity measurement device as sample data. A Bellhop-based sound field ray model is used to calculate the sound field interference fringes at different sound source depths across each profile. This fringes is a two-dimensional matrix with a defined frequency range and distance range as independent variables and sound field propagation loss as the dependent variable. A variational convolutional autoencoder network is then trained to reduce the dimensionality of the sound field interference fringe pattern, resulting in a one-dimensional feature vector. The variance between the one-dimensional feature vectors at different sound velocity profiles is calculated to obtain the variance of each feature value under sound velocity perturbation. Feature values ​​with large variances are removed, resulting in the selected one-dimensional feature vector. Finally, a one-dimensional residual convolutional neural network is used to train the selected one-dimensional feature vector, thereby estimating the depth of deep-sea sound sources.

[0036] The beneficial effects of this invention are reflected in:

[0037] (1) This invention uses a trained encoder to map the sound field interference fringe pattern into a one-dimensional feature vector. Then, based on the statistical property of variance, it removes the feature values ​​in the one-dimensional feature vector that are drastically affected by sound speed disturbance. Compared with traditional methods, this invention considers the influence of sound speed disturbance on sound source depth estimation, making the sound source depth estimation result more robust.

[0038] (2) This invention utilizes variational autoencoder network and one-dimensional residual convolutional neural network to establish a feature mapping network between sound field interference fringes and sound source depth based on a small amount of data information. Compared with traditional methods, it does not require analysis of arrival structure features of time delay and angle, and is simple to operate.

[0039] (3) The network used in this invention is a lightweight network with few computational parameters, fast operation speed, and simple implementation. Attached Figure Description

[0040] Figure 1 The sound velocity profile samples collected by the sound velocity measurement equipment in the Northwest Pacific Ocean (study area) are the data source used in this patent. 200 sound velocity profiles were selected for plotting in the figure (longitude range of the study area: 124°~142°; latitude range: 0°~20°N).

[0041] Figure 2 Taking a sound source depth of 50m as an example, randomly select Figure 1 Using a sound velocity profile as input data, the Bellhop sound field ray model is used to generate an interference fringe image with a receiving depth of 300m, a sound source frequency range of 50-500Hz, and a distance range of 10-60km.

[0042] Figure 3 (a) The root mean square error (RMSE) of the interference fringe images corresponding to different sound velocity profiles generated using the Bellhop sound field ray model when the sound source depth is 50m; (b) The root mean square error (RMSE) of the interference fringe images corresponding to different sound velocity profiles generated using the Bellhop sound field ray model when the sound source depth is 100m; (c) The root mean square error (RMSE) of the interference fringe images corresponding to different sound velocity profiles generated using the Bellhop sound field ray model when the sound source depth is 250m; (d) The root mean square error (RMSE) of the interference fringe images corresponding to different sound velocity profiles generated using the Bellhop sound field ray model when the sound source depth is 500m; (e) The root mean square error (RMSE) of the interference fringe images corresponding to different sound velocity profiles generated using the Bellhop sound field ray model when the sound source depth is 1000m.

[0043] Figure 4: Structure diagram of variational autoencoder and one-dimensional residual convolutional neural network.

[0044] Figure 5 The sound field interference fringes are converted into a one-dimensional feature vector by a trained encoder. The variance of each feature value in the one-dimensional feature vector under sound speed perturbation is the result of different sound source depths.

[0045] Figure 6 The confusion matrix between the actual sound source depth and the sound source depth predicted by the model established in this patent.

[0046] Figure 7 Without feature selection, i.e. without considering the influence of sound speed perturbation, the accuracy of sound source depth estimation using variational autoencoder network and 50-layer one-dimensional residual neural network model is only 25%. Detailed Implementation

[0047] The present invention will now be further described in conjunction with the embodiments and accompanying drawings:

[0048] A method for estimating the depth of deep-sea sound sources based on feature selection using a variational autoencoder network is characterized by the following steps: Within the study area, η sound velocity profiles are obtained using a sound velocity measurement device as sample data. A Bellhop-based sound field ray model is used to calculate the sound field interference fringes at different sound source depths across each profile. This fringes is a two-dimensional matrix with a set frequency range and a distance range as independent variables and sound field propagation loss as the dependent variable. A variational convolutional autoencoder network is then trained to reduce the dimensionality of the sound field interference fringe pattern, resulting in a one-dimensional feature vector. The variance between the one-dimensional feature vectors at different sound velocity profiles is calculated to obtain the variance of each feature value under sound velocity perturbation. Feature values ​​with large variances are removed, resulting in the selected one-dimensional feature vector. Finally, a one-dimensional residual convolutional neural network is used to train the selected one-dimensional feature vector, thereby estimating the depth of the deep-sea sound source. The process consists of the following four steps.

[0049] Step 1: The set of sound velocity profiles is S, which is a p×η matrix, where p is the number of sound velocity profile layers and η is the number of sound velocity profiles. The sound field interference fringes G at different sound source depths are calculated using a Bellhop-based sound field ray model for each profile. i,d (f,r).

[0050] G i,d (f,r)=bellhop(S i (1)

[0051] Where f is the preset sound field frequency range, r is the preset sound field distance range, i is the index of the sound velocity profile, d is the sound source depth, and S i This is the sound velocity profile.

[0052] Figure 1 The data source used in this patent is given, namely the sound velocity profile sample image. The sound field interference fringe pattern corresponding to each sound velocity profile can be calculated using the Bellhop sound field ray model.

[0053] Figure 2 Interference fringe images are given for a sound source depth of 50m, a receiving depth of 300m, a sound source frequency range of 50-500Hz, and a distance range of 10-60km. Similarly, the Bellhop sound field ray model can be used to obtain sound field interference fringe images for all sound source depths and all sound velocity profiles.

[0054] Figure 3 The mean square error pseudo-color images of the sound field interference fringes corresponding to different sound velocity profiles at various sound source depths are presented. From the images (a)-(e), it can be concluded that the greater the sound source depth, the greater the degree of change of the sound field interference fringes due to sound velocity disturbance.

[0055] Step 2: Use the obtained sound field interference fringe data under different sound source depths and different sound speed profiles to complete the training of the variational autoencoder network. Before feeding the sound field interference fringe pattern into the network, crop it to a size of (128, 128).

[0056] The variational autoencoder network consists of an encoder and a decoder. The encoder first extracts interference fringe features through four convolutional layers, followed by two linear layers. The decoder first goes through two linear layers, followed by four deconvolutional layers to reconstruct the interference fringe pattern (to be combined later). Figure 4 (Further explanation of the parameter settings for each layer of the network). During training, the loss function is divided into two parts, as shown in Equation (2). The first term of the loss function is the mean square error (MSE) between the autoencoder reconstruction result and the original data. The second term of the loss function is the KL divergence between the distribution returned by the encoder and the standard normal distribution. The specific calculation formula for the MSE is shown in Equation (3), and the specific calculation formula for the KL divergence is shown in Equation (4).

[0057] Loss = MSE(G i,d (f,r),G′ i,d (f,r))+KL(p1||p2) (2)

[0058]

[0059]

[0060] Among them, G i,d (f,r) represents the actual acoustic field interference fringes, and G′ i,d (f,r) represents the acoustic interference fringes reconstructed by the variational autoencoder network. p1 represents the data distribution simulated by the variational autoencoder, p2 represents the data distribution simulated by the variational autoencoder, μ1 represents the mean of the data distribution simulated by the variational autoencoder, and δ1 represents the variance of the data distribution simulated by the variational autoencoder.

[0061] A well-trained variational autoencoder network can use its encoder (encoder) to transform arbitrary input acoustic field interference fringe data into a one-dimensional feature vector x. i,d , where i is the index of the sound velocity profile and d is the depth of the sound source.

[0062] x i,d =enconder(G i,d (f,r)) (5)

[0063] Step 3: Based on the one-dimensional eigenvectors corresponding to different sound source depths and sound speed profiles, calculate the variance of the one-dimensional eigenvectors with sound speed perturbation at different sound source depths, as shown in Equation (6):

[0064]

[0065] Where, mean(x) i,d Let be the mean of the one-dimensional eigenvector perturbed by the speed of sound, and w be the length of the one-dimensional eigenvector. Then, the eigenvalues ​​with larger variances in the one-dimensional eigenvector are removed, resulting in the selected one-dimensional eigenvector.

[0066] Step 4: Use the one-dimensional feature vectors selected from the depth features of different sound sources to complete the training of a 50-layer one-dimensional residual convolutional neural network. Before feeding the feature vectors into the network, interpolate them to a length of (1, 224).

[0067] The 50-layer one-dimensional residual convolutional neural network consists of 49 convolutional layers and one fully connected layer. The one-dimensional feature vector first passes through a convolutional layer to become a two-dimensional feature vector of length 112 and number of channels 64. Then, it passes through a pooling layer to become a two-dimensional feature vector of length 64 and number of channels 64. Next, it passes through a residual network composed of 16 convolutional blocks, followed by an average pooling layer to form a feature vector of length 1024. Finally, it passes through a linear layer to transform it into a vector of length equal to the depth category of the sound source to be estimated. Each value in the vector represents the probability that the estimated result is the corresponding sound source depth value, thus achieving the estimation of the sound source depth (to be combined later). Figure 4 (Further explanation of the parameter settings for each layer of the network).

[0068] Figure 4The variational autoencoder and one-dimensional residual convolutional neural network model established in this patent are presented. The neural network model is mainly divided into four parts: (1) Figure 4 The upper left part is the encoder of the variational autoencoder network, which converts the input sound field interference fringe image into a one-dimensional feature vector. It consists of 4 convolutional layers and 2 linear layers. In {conv2d(1,8,3) / 2}, conv2d represents the convolutional layer, 1 represents the number of input channels, 8 represents the number of output channels, 3 represents the size of the convolutional block, and / 2 represents the stride of the convolutional block during feature extraction, which is 2, that is, the convolutional block feature extraction operation is performed every 2 data points in rows and columns to achieve the downsampling function; in {Linear(1280,224)}, Linear represents the linear layer, 1280 is the number of input features, and 224 is the number of output features; in {(128,128,1)}, the two 128s represent the length and width of the input image matrix, and 1 represents the number of channels of the input image; the others are similar. (2) Figure 4 The upper right part is the decoder of the variational autoencoder network, which reconstructs the image by restoring the one-dimensional feature vector into a two-dimensional acoustic field interference fringe image. It consists of four deconvolutional layers and two linear layers. (3) Figure 4 The middle part of the upper half represents the transformation of the acoustic field interference fringes into a one-dimensional feature vector by the trained variational autoencoder, followed by feature selection based on the statistical property of variance, generating a one-dimensional vector after feature selection, which is then fed into a one-dimensional residual convolutional neural network. (4) Figure 4 The lower part is a one-dimensional residual convolutional neural network structure, which is used to extract features from a one-dimensional feature vector to estimate the depth of the sound source.

[0069] Figure 5 The variance values ​​of each eigenvalue in the one-dimensional eigenvector under sound speed perturbation are given for different sound source depths. Eigenvalues ​​with larger variances can be removed based on the magnitude of the variance, thus achieving the removal of eigenvalues ​​significantly affected by sound speed perturbation.

[0070] Figure 6 The confusion matrix between the actual sound source depth and the sound source depth predicted by the model established in this patent is presented. The test sample size was 100, and the sound source depth estimation of the model established in this patent was correct in 97 cases. This shows that the correct sound source depth estimation rate of this patent is 97%.

[0071] Traditional sound source depth estimation methods can be broadly categorized into the three types mentioned in the background section. This patent, "Deep-Sea Sound Source Depth Estimation Method Based on Variational Autoencoder Network Feature Selection," primarily utilizes the third type of method. It proposes a novel deep learning-based neural network structure, combining it with the characteristic of sound field interference fringes, to solve the sound source depth estimation problem. There are many traditional methods that combine deep learning-based neural network structures with sound field interference fringes for sound source depth estimation. Compared to these traditional methods, this patent considers an important additional factor: the continuous variation of sound speed in the marine environment. Because the marine environment is dynamic, changes in sound speed can significantly alter the characteristic of sound field interference fringes corresponding to different sound source depths. The method and network structure proposed in this patent can effectively suppress the impact of sound speed disturbances on sound source depth estimation, improving the accuracy and robustness of sound source depth estimation.

[0072] like Figure 7 The results provided are for sound source depth estimation using a variational autoencoder network and a 50-layer one-dimensional residual neural network model without feature selection, i.e., without considering the influence of sound speed perturbation. The accuracy is only 25%. Figure 6 The study presents a method for estimating sound source depth using a 50-layer one-dimensional residual neural network. This method involves feature selection after extracting a one-dimensional feature map of the sound field interference fringes from a variational autoencoder neural network (VAN). Feature selection removes features significantly affected by sound speed perturbations based on their statistical properties, effectively suppressing the impact of sound speed perturbations on sound source depth estimation. The resulting sound source depth estimation achieves an accuracy of 97%. A significant benefit is that considering sound speed perturbations significantly improves the accuracy of the neural network model for sound source depth estimation, demonstrating that sound speed perturbations are a non-negligible factor.

Claims

1.A deep-sea sound source depth estimation method based on variational auto-encoding network feature selection, characterized by The steps are as follows: Step 1: η sound speed profile data of the study sea area are used as sample data, and the sound field interference fringes G of each profile under different sound source depths are calculated using the bellhop-based sound field ray model i,d (f,r); Step 2: Acoustic field interference fringes G using different sound source depths and different sound speed profiles i,d (f, r) data pairs train the variational auto-encoding network; The trained encoder of the variational auto-encoding network transforms any input acoustic field interference fringe data into a one-dimensional feature vector x corresponding to the acoustic field interference fringe pattern i,d where i is the index of the sound velocity profile and d is the depth of the sound source: x i,d = enconder(G i,d (f,r)); Step 3: According to the obtained one-dimensional feature vectors corresponding to different sound source depths and sound velocity profiles, the variance values of the one-dimensional feature vectors with respect to the sound velocity perturbation at different sound source depths are calculated: where mean(x i,d ) is the mean value of the one-dimensional feature vector with the sound speed disturbance, w is the length of the one-dimensional feature vector, and k is the index of the one-dimensional feature vector characteristics. Then the feature values corresponding to the larger variance values in the one-dimensional feature vectors are removed to form the one-dimensional feature vectors after feature selection; Step 4: The one-dimensional residual convolutional neural network of 50 layers is trained using the one-dimensional feature vectors after feature selection at different sound source depths, and the trained one-dimensional residual convolutional neural network of 50 layers realizes the estimation of the sound source depth; The one-dimensional residual convolutional neural network of 50 layers is composed of 49 convolutional layers and one fully connected layer; The one-dimensional feature vector is first converted into a two-dimensional feature with a length of 112 and a channel number of 64 through a convolutional layer, then converted into a two-dimensional feature with a length of 64 and a channel number of 64 through a pooling layer, then passed through 16 residual networks composed of convolutional blocks, then passed through a mean pooling layer to form a feature vector with a length of 1024, and finally converted into a vector with a length of the number of sound source depth categories to be estimated through a linear layer, each value of the vector representing the probability of the estimated result being the corresponding sound source depth value, thereby realizing the estimation of the sound source depth. 2.The deep-sea sound source depth estimation method based on the feature selection of the variational auto-encoding network according to claim 1, wherein: the sound field interference fringes G under the different sound source depth individual profiles i,d (f,r) is: G i,d (f,r) = bellhop(S i ), where f is a pre-set sound field frequency range, r is a pre-set sound field distance range, i is an index of the sound speed profile, d is a sound source depth, S i is a set of sound speed profiles is a p x η matrix, where p is a number of layers of sound speed profiles, and η is a number of sound speed profiles. 3.The deep-sea sound source depth estimation method based on the feature selection of the variational auto-encoding network according to claim 1, wherein: The step 2 crops the sound field interference fringe pattern to a size of (128, 128) before inputting it into the variational convolutional auto-encoding network for training. 4.The deep-sea sound source depth estimation method based on the feature selection of the variational auto-encoding network according to claim 1, wherein: The variational auto-encoding network is composed of an encoder and a decoder, the encoder first passes through 4 convolutional layers to extract interference fringe features, and then connects 2 linear layers, the decoder first passes through 2 linear layers, and then passes through 4 deconvolutional layers to realize the reconstruction of the interference fringe pattern. 5.The deep-sea sound source depth estimation method based on the feature selection of the variational auto-encoding network according to claim 1, wherein: The loss function in the training of the variational auto-encoding network in step 2 is divided into two parts: Loss = MSE(G i,d (f,r), G′ i,d (f,r)) + KL(p1||p2) The first term of the loss function is the mean square error (MSE) between the reconstruction result of the auto-encoder and the original data, and the second term of the loss function is the KL divergence between the distribution returned by the encoder and the standard normal distribution; The MSE mean square error is calculated as: The KL divergence is calculated as: where G i,d (f,r) is the actual sound field interference fringe, G′ i,d (f,r) is the sound field interference fringe reconstructed by the variational autoencoder; p1 is the data distribution simulated by the variational autoencoder, p2 is the data distribution simulated by the variational autoencoder, μ1 is the mean of the data distribution simulated by the variational autoencoder, and δ1 is the variance of the data distribution simulated by the variational autoencoder. 6.The deep-sea sound source depth estimation method based on the feature selection of the variational auto-encoding network according to claim 1, wherein: The feature vector is interpolated to a length of (1, 224) before being input into the one-dimensional residual convolutional neural network of 50 layers for training in step 4.

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