A Sound Velocity Profile Clustering Method Based on a Deep Embedded Clustering Neural Network

Abstract

The present invention belongs to the technical field of ocean sound velocity profile clustering, and particularly relates to a sound velocity profile clustering method based on a deep embedded clustering neural network. The method includes the following steps: obtaining a sound velocity profile data set by using sound velocity formula conversion; performing standardization processing on the monthly average sound velocity profile data set of the sea area to be clustered as a training data set; building an autoencoder for pre-training; training a deep embedded clustering neural network for clustering by using the sound velocity gradient data set, and visualizing the clustering result. The present invention improves the DEC algorithm and applies it to sound velocity profile clustering, links the sound velocity profile feature extraction step and the clustering step, and simultaneously optimizes the two steps by using deep learning technology to obtain a more reasonable clustering effect; moreover, the optimization process is automatically completed based on a deep learning neural network, and no manual intervention is required during the optimization process, and the operation is simple. It can be widely applied to the sound velocity profile clustering of different sea areas around the world, and has wide applicability.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean sound speed profile clustering, and particularly relates to a sound speed profile clustering method based on a deep embedded clustering neural network. Background Art

[0002] The ocean sound speed profile structure has an important influence on underwater acoustic propagation. Through clustering, ocean sound speed profiles with similar structural characteristics can be divided into the same category. By referring to different types of sound speed profiles, different sea areas can be effectively divided, so that the underwater acoustic characteristics of a specific sea area can be determined quickly and accurately. Traditional clustering methods mainly extract features from sound speed profile data through means such as PCA and EOF. Since machine learning, SOM neural networks and other means have been used for clustering, the clustering methods of ocean sound speed profiles have been more effective. The application of machine learning methods makes clustering more convenient and more operable. However, the feature extraction step and the clustering step are usually separated, and the clustering effect may not be ideal. Summary of the Invention

[0003] The purpose of the present invention is to provide a sound speed profile clustering method based on a deep embedded clustering neural network. This method is based on high-resolution, long-time series sound speed profile data obtained from high-resolution ocean reanalysis products, and realizes a deep embedded clustering neural network in which the encoder feature extraction network in the AE auto-encoder is nested with a soft clustering layer that minimizes the KL divergence (Kullback-Leibler Divergence). The encoder feature extraction network in the trained AE auto-encoder is used to extract the dimensionality-reduced features of the sound speed profile data, and then input into the soft clustering layer for clustering. The KL divergence is used to calculate the loss of the clustering result, and the loss is fed back to the encoder feature extraction network and the soft clustering layer for joint optimization, providing a more effective method for clustering sound speed profiles in different sea areas.

[0004] To achieve the above purpose, the present invention adopts the following technical solutions:

[0005] A sound speed profile clustering method based on a deep embedded clustering neural network, comprising the following steps:

[0006] Step 1, based on the longitude, latitude, sea water temperature, salinity, and water depth data of the target sea area to be clustered provided by high-resolution ocean reanalysis products, use the sound speed formula to convert to obtain the monthly average sound speed profile dataset of the target sea area to be clustered;

[0007] Step 2: Preprocess the monthly average sound speed profile dataset of the target sea area to be clustered, unify the depth interval and maximum depth, and perform standardization processing on the sound speed gradient dataset obtained by conversion using the gradient formula. The standardized sound speed gradient dataset will be used as the dataset for training, validating, and testing the depth-embedded clustering neural network;

[0008] Step 3: Build an AE autoencoder and pre-train the AE autoencoder using the sound speed gradient dataset. After the pre-training is completed, only retain the encoder feature extraction network for the initial mapping from the high-dimensional data space to the low-dimensional feature space;

[0009] Step 4: Embed the soft clustering layer into the encoder feature extraction network to obtain a depth-embedded clustering neural network. Train this network again using the sound speed gradient dataset, calculate the loss of the soft clustering result based on the KL divergence, and feedback the loss to the encoder feature extraction network and the soft clustering layer for dual optimization;

[0010] Step 5: Use the trained depth-embedded clustering neural network to perform sound speed profile clustering, visualize the clustering results, and evaluate the clustering quality using two indicators, the average distortion degree and the silhouette coefficient, in the internal evaluation method.

[0011] The specific steps of Step 1 are as follows:

[0012] Step 1.1: Refer to the grid cell structure of the high-resolution ocean reanalysis product to design the data structure of physical quantities such as seawater temperature, salinity, and pressure in the target sea area to be clustered; use equally spaced grids to divide longitude and latitude within the horizontal range, and use non-equally spaced division in depth; output at equal time intervals in the time dimension; data such as seawater temperature, salinity, and pressure are physical quantities of the ocean water body, and are in a default value state at land and the seabed sediment layer;

[0013] Step 1.2: Use the sound speed formula to convert the seawater temperature, salinity, and pressure data of the high-resolution ocean reanalysis product into a high-resolution sound speed profile dataset. The expression of the sound speed formula is as follows:

[0014] c(s,T,p)=c ω (T,P)+a(T,p)s+b(T,p)s 3 / 2 +d(T,p)s 2 ;

[0015] In the formula: c is the seawater sound speed value, s, T, and p are the seawater salinity, water temperature, and hydrostatic pressure respectively, c ω 、a、b、d are empirical functions related to seawater temperature and hydrostatic pressure, 0≤s≤40, 0°≤T≤40°, 0Pa≤p≤10 8 Pa;

[0016] Step 1.3, referring to the data storage structure of the high-resolution ocean reanalysis product, store the sound speed profile data set obtained by the above conversion according to the same structure; the horizontal spatial resolution, vertical spatial resolution, time resolution, and time span of the storage structure of the sound speed profile data set are the same as those of the referenced high-resolution ocean reanalysis product;

[0017] Since the sound speed profile is mainly affected by temperature, the thermocline has a similar morphological structure to the sound speed profile, and the temporal evolution of the thermocline is mainly reflected on the seasonal scale. Usually, monthly average data is used for research; based on this, the sound speed profile data is averaged monthly, and the time resolution is changed from the original output once every 3 hours to an average of once a month, resulting in a monthly average sound speed profile data set.

[0018] The specific steps of Step 2 are as follows:

[0019] Step 2.1, to ensure the refined expression of the sound speed profile, and considering that the changes in the sound speed profile are mainly concentrated above 1500 meters of water depth, and the changes in the sound speed data below 1500 meters of water depth are not significant and have little reference significance for clustering; intercept the sound speed profile data above 1500 meters, and use the Akima interpolation method at a depth interval of 5 meters to interpolate from a depth of 5 meters to 1500 meters, with a total of 300 depth values, to obtain a monthly average sound speed profile data set shallower than 1500 meters with equal depth intervals;

[0020] The Akima interpolation method is defined as interpolating between two points. In addition to the values of these two points, the values of the four points adjacent to these two points are also required. Therefore, a total of 6 points (x i , y i )(i = 1, 2, 3, 4, 5, 6) are involved; among them, the point (x, y) to be interpolated is between the 3rd and 4th points, x3 < x < x4, y3 < y < y4; x represents the sound speed value, with the unit of (m / s); y represents the depth, with the unit of (m), and the interpolation formula is:

[0021] y = a0 + a1(x - x3) + a2(x - x3) 2 + a3(x - x3) 3 ;

[0022] In the formula:

[0023] a0 = y3, a1 = t3,

[0024]

[0025] where t3 and t4 are the slopes of the 3rd and 4th points respectively, and the slope calculation formula is:

[0026]

[0027] where m i =(y i+1 -y i ) / (x i+1 -x i ). Since the above formula does not hold when the denominator is 0, in this case, Akima stipulates that: t i =(m i+1 -m i ) / 2 or t i =m i . After the above interpolation processing, a sound speed profile data set with equal depth intervals is established;

[0028] Step 2.2, represent the monthly average sound speed profile data set with equal depth intervals as a sound speed matrix C. This matrix is an N×D order matrix, where N is the number of samples and D is the number of sound speed sampling points after interpolation in depth. The sound speed values in the matrix are represented as c i,j (i = 1, 2, … N; j = 1, 2, … D). The sound speed profile can be described not only by the sound speed c, but also by the sound speed gradient g. The sound speed gradient can more intuitively reflect the structural changes of the sound speed profile in each layer, which is conducive to extracting low-dimensional feature vectors for soft clustering; representing the sound speed profile by the sound speed gradient, based on the gradient calculation formula, convert the sound speed matrix C to obtain the sound speed gradient matrix G, and the matrix G is still of N×D order; the sound speed gradient calculation formula is:

[0029]

[0030] where the gradient is g, the sound speed is c, the depth is D, and the sound speed gradient value in the matrix G is represented as g i,j (i = 1, 2, … N; j = 1, 2, … D);

[0031] Step 2.3, perform standardization processing on the sound speed gradient data to make the feature vectors of each dimension independently and identically distributed and unify the scales between features, so as to accelerate the speed and accuracy of deep learning; adopt z-score standardization (z-score Normalization), and the standardized sound speed gradient matrix E is still of N×D order, that is, standardize the sound speed values corresponding to each depth value, so that the average value of each type of data is 0 and the standard deviation is 1; the standardized data is represented as e i,j (i = 1, 2, … N; j = 1, 2, … D), is the average value of the sound speed gradient of each variable, that is, each depth layer, and σ j is the standard deviation of the sound speed gradient of each layer. The standardization formula is:

[0032]

[0033] After the above formula conversion, a standardized sound speed gradient dataset is obtained; and the standardized sound speed gradient dataset will be used as the dataset for training, validating, and testing the deep embedded clustering neural network.

[0034] The specific steps of Step 3 are as follows:

[0035] Step 3.1, build an AE autoencoder. As an unsupervised neural network, the autoencoder can be used for data dimensionality reduction and is composed of two parts of neural networks, the encoder and the decoder, connected in sequence; through encoding by the encoder, the hidden low-dimensional features of the input original data are learned, and then the reconstructed data is decoded and output through the decoder; for the D-dimensional sound speed gradient data sample X, when passing through the encoder network, θ1 is the parameter of the encoder feature extraction network, that is, the parameter of the encoder part of the network, and the encoding formula is:

[0036] Z = f(X; θ1);

[0037] The low-dimensional feature vector Z in the feature space is obtained, with a dimension of Fn. This feature vector Z then passes through the decoder network. θ2 is the parameter of the decoder part of the network, and the decoding formula is:

[0038]

[0039] Finally, the reconstructed sound speed gradient data sample is obtained The error of the autoencoder for this sample is:

[0040]

[0041] where X d (d = 1, 2, …, D) is the d-th dimension of the input sample X; in network training, for a batch of M input data samples, the loss function is to minimize the autoencoder error:

[0042]

[0043] where X m (m = 1, 2, …, M) is the m-th of the batch input samples, is the reconstruction of the m-th sample; the model is optimized by backpropagating the loss to minimize the loss function, that is, the input and output data are infinitely close;

[0044] The structure of the AE autoencoder feature extraction network is as follows:

[0045] The first layer is the input layer in the encoder network, where X d(d = 1, 2, …, D) are the input variables of the AE autoencoder network, with a total of D, specifically referring to the sound speed gradient values at each depth in the original sound speed gradient data;

[0046] The second layer is the hidden layer in the encoder network, which is composed of 4 fully connected layers with dimensions of 500, 500, 2000, and 10 connected in sequence. After each fully connected layer, the LeakyReLU function is used as the activation function to avoid neuron "death". The expression of the LeakyReLU function is as follows:

[0047]

[0048] Among them, x represents the variable of the input function, and β = 0.1;

[0049] The third layer is the encoding layer, which is a fully connected layer without an activation function. The input dimension of this layer is 10, and the output dimension is Fn. The output is the feature after data dimensionality reduction, representing the number of feature vectors obtained by compression;

[0050] The fourth layer is the hidden layer in the decoder network, which is composed of 4 fully connected layers with dimensions of 10, 2000, 500, and 500 connected in sequence. After each fully connected layer, the LeakyReLU function is used as the activation function;

[0051] The fifth layer is the output layer in the decoder network, where are the output variables of the AE autoencoder network, with a total of D, specifically referring to the sound speed gradient values at each depth in the reconstructed sound speed gradient data;

[0052] Finally, the Adam optimizer is used to calculate the loss function and the backpropagation loss is used to optimize the network;

[0053] Step 3.2, input the sound speed gradient data set to pre-train the AE autoencoder to obtain the trained encoder feature extraction network; by continuously adjusting the three parameters of the iteration batch size (batch_size), learning rate (learning_rate), and number of iterations (epochs), a better reconstruction effect can be obtained.

[0054] The specific steps of Step 4 are as follows:

[0055] Step 4.1, initialization. By pre-training the AE autoencoder, initialize the encoder feature extraction network parameters θ1 and the decoder part network parameters θ2; represent the low-dimensional feature vector after passing through the encoder feature extraction network as the embedding point Z in the feature space m (m = 1, 2, …, 2048), perform k-means clustering to obtain the initial cluster centers μ k(k = 1, 2, …, K), where the number of batch training samples is defined as M, the number of clusters is defined as K, m represents the m-th sample, and k represents the k-th sound speed profile;

[0056] Step 4.2, calculate the soft assignment. Use the Student's t-distribution to calculate the embedding point Z corresponding to a sample in the feature space after dimensionality reduction m and the cluster center μ k The probability that the sample m belongs to a certain category k cluster is defined as the soft assignment q m,k , that is, the proportion of the similarity of a certain sample in the sum of the similarities of all samples:

[0057]

[0058] where, represents the similarity of a certain sample, Z m = f(X m ; θ), α is the degree of freedom of the Student's t-distribution, α = 1;

[0059] Step 4.3, minimize the KL divergence. Define the auxiliary distribution p m,k as follows:

[0060]

[0061] Define the auxiliary distribution p m,k The beneficial effects are: (1) improve the cluster purity; (2) pay more attention to the embedding points with high confidence; (3) contribute to the loss of each cluster center to prevent the hidden feature space from being distorted due to too many clusters; the loss function is defined as the KL divergence between the soft assignment distribution q m,k and the auxiliary distribution p m,k . The loss function is used to measure the difference between the above two distributions. The goal of model training is to minimize the KL divergence between the assignment distribution q m,k and the auxiliary distribution p m,k . The calculation formula of the loss function L is as follows:

[0062]

[0063] Step 4.4, feedback the loss calculated above to the clustering layer and the feature extraction network at the same time. Use the SGD (Stochastic Gradient Descent) optimizer with momentum to optimize the embedding point Z m and the cluster center position μ k . The gradient calculation formulas of the loss function with respect to the embedding point Z m and the cluster center μ k are as follows:

[0064]

[0065]

[0066] Pass it to the encoder feature extraction network, and then use standard backpropagation to calculate the gradient of the encoder feature extraction network parameter θ1 Optimize the encoder feature extraction network parameter θ1; when the changed cluster assignment points between two iterations are less than the set target value, stop training. The set target value is specified manually, generally preferably 0.001, but not limited to 0.001.

[0067] The specific steps of step 5 are as follows:

[0068] Step 5.1, cluster the sound speed gradient dataset by the deep embedded clustering neural network and present it in the form of a scatter plot in the feature space;

[0069] Step 5.2, plot the sound speed profile of the cluster center in each type as the sound speed profile representative of that type;

[0070] Step 5.3, evaluate the quality of the clustering result by calculating the average distortion degree and the silhouette coefficient, and test the optimal number of clusters K. Plot the average distortion degree S1 and the silhouette coefficient S2 of the clustering result as a line chart;

[0071] The average distortion degree S1 is essentially the average of the within-cluster sum of squared deviations. The smaller the sum of the distances from all sample points to the centroid, the more similar the samples in each cluster are considered, and the better the clustering effect. Generally, the inflection point of the average distortion degree S1 line is considered a better number of clusters; the calculation formula for the average distortion degree S1 is as follows:

[0072]

[0073] Divide the N samples in the sound speed gradient dataset into K classes, and use Cluster k (k = 1, 2, …, K) to represent the set of all embedded points Z n (n = 1, 2, …, N) in the k-th class cluster;

[0074] The silhouette coefficient S2 is the average of the silhouette coefficients of all embedded points. For a single embedded point, a is the average distance to other embedded points in the same class, a reflects the within-cluster density, b is the average distance to the embedded points in the nearest different class, b reflects the between-cluster dispersion, the value range of S2 is [0, 1], and the one with the largest value is generally considered a better number of clusters; the calculation formula for the silhouette coefficient S2 is as follows:

[0075]

[0076] The present invention provides a sound velocity profile clustering method based on a deep embedded clustering neural network, and its beneficial effects are as follows:

[0077] 1. In the present invention, an AE autoencoder is introduced for feature extraction of sound velocity profile data, which can significantly compress the data volume. Under normal circumstances, the data compression ratio reaches 250 times, effectively avoiding the problem of excessive consumption of computing resources caused by a large amount of data;

[0078] 2. The present invention uses the sound velocity profile gradient as the clustering basis. The sound velocity gradient can better reflect the contour shape and change trend of the sound velocity profile, and is more reasonable and effective than directly using sound velocity data for clustering;

[0079] 3. The present invention improves the DEC algorithm and applies it to sound velocity profile clustering, links the sound velocity profile feature extraction step and the clustering step, and uses deep learning technology to optimize these two steps simultaneously to obtain a more reasonable clustering effect; and this optimization process is automatically completed based on a deep learning neural network, and no human intervention is required during the optimization process;

[0080] 4. For users of the present invention, in addition to providing sound velocity profile data, only one initialization parameter, that is, the clustering number K, needs to be customized to run the model, and no complex initialization parameters need to be provided, and the operation is simple;

[0081] 5. The deep embedded clustering neural network model proposed by the present invention can be widely applied to sound velocity profile clustering in different seas around the world, and has wide applicability. Brief Description of the Drawings

[0082] Figure 1 is the main step diagram of the embodiment of the present invention;

[0083] Figure 2 is the brief flow chart for realizing sound velocity profile clustering in the embodiment of the present invention;

[0084] Figure 3 is the deep embedded clustering neural network structure diagram of the embodiment of the present invention;

[0085] Figure 4 is the scatter diagram of the sound velocity profile clustering result in the feature space in the embodiment of the present invention;

[0086] Figure 5 is the scatter diagram of the sound velocity profile clustering result after the 0th iteration in the embodiment of the present invention;

[0087] Figure 6 is the scatter diagram of the sound velocity profile clustering result after the 225th iteration in the embodiment of the present invention;

[0088] Figure 7It is a scatter plot of the sound speed profile clustering result after the 450th iteration in the embodiment of the present invention;

[0089] Figure 8 It is a scatter plot of the sound speed profile clustering result after the 900th iteration in the embodiment of the present invention;

[0090] Figure 9 It is a scatter plot of the sound speed profile clustering result after the 1350th iteration in the embodiment of the present invention;

[0091] Figure 10 It is a scatter plot of the sound speed profile clustering result after the 2250th iteration in the embodiment of the present invention;

[0092] Figure 11 It is a scatter plot of the sound speed profile clustering result after the 3150th iteration in the embodiment of the present invention;

[0093] Figure 12 It is a scatter plot of the sound speed profile clustering result after the 4500th iteration in the embodiment of the present invention;

[0094] Figure 13 It is a scatter plot of the sound speed profile clustering result after the last iteration in the embodiment of the present invention;

[0095] Figure 14 It is the sound speed profile of the clustering center in the type 1 sound speed profile clustering cluster in the embodiment of the present invention;

[0096] Figure 15 It is the sound speed profile of the clustering center in the type 2 sound speed profile clustering cluster in the embodiment of the present invention;

[0097] Figure 16 It is the sound speed profile of the clustering center in the type 3 sound speed profile clustering cluster in the embodiment of the present invention;

[0098] Figure 17 It is the sound speed profile of the clustering center in the type 4 sound speed profile clustering cluster in the embodiment of the present invention;

[0099] Figure 18 It is the sound speed profile of the clustering center in the type 5 sound speed profile clustering cluster in the embodiment of the present invention;

[0100] Figure 19 It is the line graph of the average distortion degree and silhouette coefficient of the clustering result in the embodiment of the present invention. Detailed implementation manners

[0101] The following provides a detailed description of the present invention in conjunction with specific embodiments.

[0102] The present invention provides a sound speed profile clustering method based on a deep embedded clustering neural network. By introducing an improved DEC algorithm and building a deep embedded clustering neural network suitable for ocean sound speed profiles, the present invention realizes the joint optimization of the feature extraction step and the clustering step, improving the efficiency of sound speed profile feature extraction and the clustering effect.

[0103] In order to make the technical problems, technical solutions and beneficial effects solved by the present invention more clearly understood, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.

[0104] Appendix Figure 1 is the main step diagram of the embodiment of the present invention. Appendix Figure 2 is the brief flow chart for realizing sound speed profile clustering in the embodiment of the present invention. Specifically, it includes the following steps:

[0105] Step 1: Based on the longitude, latitude, sea water temperature, salinity and water depth data of the target sea area to be clustered provided by the high-resolution ocean reanalysis product, use the sound speed formula to convert to obtain the monthly average sound speed profile data set of the target sea area to be clustered;

[0106] The specific steps of Step 1 are as follows:

[0107] Step 1.1: Obtain the high-resolution ocean reanalysis product data set, design a grid structure for storing sound speed profile data, and select the target sea area to be clustered;

[0108] The high-resolution ocean reanalysis product adopted in this embodiment is the CORA v2.0 (China Ocean Reanalysis) reanalysis product. The data of this product is sourced from the National Marine Data and Information Service, and the data website is http: / / mds.nmdis.org.cn. Download the dataset of physical quantities such as seawater temperature, salinity, and pressure required in the embodiment from this website. The ocean reanalysis product combines historical ocean observation data with an ocean dynamic model using data assimilation technology to reconstruct the historical changes of the complete ocean state field, obtaining a dataset covering the globe and all elements, providing important basic data for ocean environmental data. In the specific implementation process, the high-resolution ocean reanalysis product is not limited to CORA v2.0, but also includes various three-dimensional temperature-salinity-current reanalysis products such as the Estimation of the Circulation and Climate of the Ocean (ECCO) in the United States, Simple Ocean Data Assimilation (SODA), the HYbrid Coordinate Ocean Model (HYCOM) of the US Navy, and the ECMWF ocean reanalysis of the European Centre for Medium-Range Weather Forecasts. In this embodiment, the CORA v2.0 dataset is adopted, but the scope of application of the present invention is not limited to the CORA v2.0 dataset;

[0109] Refer to the grid cell structure of the high - resolution ocean re - analysis product and design a grid structure for storing sound velocity profile data; the grid cell structure of the CORA v2.0 dataset of the high - resolution ocean re - analysis product used in this embodiment is as follows: in the sea area, the longitude and latitude are divided into equally - spaced grids (resolution is 0.1°); the time resolution is 3 hours; the depth is divided non - equally (a total of 50 layers), and the specific layer depths are [-5, -15, -25, -35, -45, -55, -65, -75.004997, -85.025002, -95.095001, -105.31000, -115.87000, -127.15000, -139.74001, -154.47000, -172.39999, -194.73500, -222.71001, -257.47000, -299.92999, -350.67999, -409.92999, -477.47000, -552.71002, -634.73499, -722.40002, -814.46997, -909.73999, -1007.1550, -1105.9050, -1205.5350, -1306.2050, -1409.1500, -1517.0950, -1634.1750, -1765.1350, -1914.1500, -2084.0349, -2276.2251, -2491.2500, -2729.2500, -2990.2500, -3274.2500, -3581.2500, -3911.2500, -4264.2500, -4640.2500, -5039.2500, -5461.2500, -5906.2500], with the unit being (meters); since the element data such as temperature and salinity provided by the high - resolution ocean re - analysis product are physical quantities of ocean water, the values at land and seabed sediment layers are in a null value state (default is NAN).

[0110] Select a certain sea area in the mid - latitude of the Pacific Ocean as the target sea area for clustering, with the longitude range [175.95°E, 179.95°E] and the latitude range [40.95°N, 44.95°N]. The horizontal spatial resolution is 0.1°. At this resolution, the number of sampling points in the target sea area for clustering is 1600, and the calculation formula is as follows:

[0111] (pieces);

[0112] The time span is the whole - year data of 2014, the time resolution is 3 hours, and there are a total of 2920 time scales.

[0113] The above steps determine the grid structure for storing the sound velocity profile data: the longitude and latitude are divided into equally spaced grids (resolution 0.1°); the time resolution is 3 hours; the depth is divided into unequally spaced grids (a total of 50 layers); the longitude range of the target sea area to be clustered is [175.95°E, 179.95°E], and the latitude range is [40.95°N, 44.95°N]; the time span is the annual data in 2014, the time resolution is 3 hours, and there are a total of 2920 time scales.

[0114] Step 1.2, based on the sound velocity formula, convert the seawater temperature, salinity, and pressure datasets of the high-resolution ocean reanalysis product to obtain a high-resolution sound velocity profile dataset;

[0115] Using the sound velocity formula, convert the seawater temperature, salinity, and pressure datasets of the high-resolution ocean reanalysis product to a high-resolution sound velocity profile dataset. The expression of the sound velocity formula is as follows:

[0116] c(s,T,p) = c ω (T,p) + a(T,p)s + b(T,p)s 3 / 2 + d(T,p)s 2 ;

[0117] where: c is the seawater sound velocity value, s, T, and p are the seawater salinity, temperature, and hydrostatic pressure respectively; c ω , a, b, and d are empirical functions related to seawater temperature and hydrostatic pressure. For specific meanings, see "Precise equation of state of seawater for oceanic ranges of salinity, temperature and pressure (CT Chen, FJ Millero. 1977)" ("Precise Equation of State of Seawater for Oceanic Ranges of Salinity, Temperature and Pressure"), "Speed of sound in seawater at high pressures (Chen, Chen-Tung. 1977)" ("Speed of Sound in Seawater at High Pressures"), "Marine Physics (Ye Anle, Li Fengqi. 1992)"; 0 ≤ s ≤ 40, 0° ≤ T ≤ 40°, 0 Pa ≤ p ≤ 10 8 Pa, and the standard deviation of the calculated sound velocity value is 0.19 m / s;

[0118] After conversion by the above formula, a high-resolution sound velocity profile dataset is obtained;

[0119] Step 1.3, average the above high-resolution sound velocity profile dataset by month to obtain a monthly average sound velocity profile dataset;

[0120] The time span of the selected high-resolution ocean reanalysis dataset for the target sea area to be clustered is the whole year of 2014, with a time resolution of 3 hours and a total of 2,920 time scales.

[0121] The high-resolution sound speed profile dataset is averaged monthly, that is, all the sound speed profile data in the same month under the same spatial coordinate points are summed and then averaged, so that the time resolution of the high-resolution sound speed profile dataset is averaged from the original 3 hours to one month, obtaining a monthly averaged sound speed profile dataset; this monthly averaged sound speed profile dataset has a time resolution of 1 month, a total of 12 time scales, the horizontal spatial resolution remains unchanged at 0.1°, the vertical stratification is still 50 layers, and the depth values of each layer remain unchanged.

[0122] Step 2: Preprocess the monthly averaged sound speed profile dataset of the target sea area to be clustered, unify the depth interval and the maximum depth, and perform standardization processing on the sound speed gradient dataset obtained by using the gradient formula. The standardized sound speed gradient dataset will be used as the dataset for training, validating, and testing the depth-embedded clustering neural network. The specific steps are as follows:

[0123] Step 2.1: Interpolate the above monthly averaged sound speed profile dataset to obtain a monthly averaged sound speed profile dataset with equal depth intervals.

[0124] Intercept the monthly averaged sound speed profile dataset above 1500 meters, and use the Akima interpolation method at a depth interval of 5 meters to interpolate from a depth of 5 meters to 1500 meters, with a total of 300 depth values, obtaining a monthly averaged sound speed profile dataset with equal depth intervals above 1500 meters.

[0125] Step 2.2: Use the sound speed gradient calculation formula to convert the monthly averaged sound speed profile dataset with equal depth intervals into a monthly averaged sound speed profile gradient dataset with equal depth intervals, simply referred to as the sound speed gradient dataset.

[0126] The monthly averaged sound speed profile dataset with equal depth intervals is represented as a sound speed matrix C, which is a 19,200×300 matrix; N = 1600×12 = 19,200, indicating that there are 1600 sampling points in the dataset, and each sampling point contains 12 monthly averaged sound speed profiles, multiplying to obtain a total of 19,200 sound speed profile samples; D = 300 indicates that there are 300 depth values after interpolation in depth, and the sound speed values in the matrix are represented as c i,j (i = 1, 2, … 19,200; j = 1, 2, … 300); the sound speed gradient calculation formula is as follows:

[0127]

[0128] Using the sound speed profile gradient data as the clustering basis can effectively distinguish different types of sound speed profile data and improve the clustering effect of the sound speed profile; the sound speed gradient value, that is, the rate of change of the sound speed in the vertical direction, can not only truly reflect the shape characteristics of the sound speed profile, but also reflect the trend of the sound speed profile changing with depth in the vertical direction; and the shape and the trend of change with depth of the sound speed profile are the key elements for distinguishing different types of sound speed profiles, which is more reasonable and effective than directly using the sound speed data for clustering.

[0129] Through the above gradient calculation formula, the sound speed matrix C is converted to obtain the sound speed gradient matrix G, that is, the monthly average sound speed profile gradient data set at equal depth intervals, simply referred to as the sound speed gradient data set; the matrix G is still of order 19200×300, and the sound speed gradient value in the matrix is denoted as g i,j (i = 1, 2, …, 19200; j = 1, 2, …, 300);

[0130] Step 2.3, perform standardization processing on the above sound speed gradient data set to obtain a standardized sound speed gradient data set;

[0131] Perform z-score standardization processing on the sound speed gradient data set so that the average value of each type of data is 0 and the standard deviation is 1; the standardized sound speed gradient matrix E is still of order 19200×300, and the data in the matrix E is denoted as e i,j (i = 1, 2, …, 19200; j = 1, 2, …, 300), is the average value of the sound speed gradient of each variable, that is, at each depth layer, and σ j is the standard deviation of the sound speed gradient of each layer, and the standardization formula is:

[0132]

[0133] Through the above formula conversion, a standardized sound speed gradient data set is obtained; and the standardized sound speed gradient data set will be used as the data set for training, validating, and testing the deep embedded clustering neural network.

[0134] Step 3, build an AE autoencoder, and use the sound speed gradient data set to pre-train the AE autoencoder. After the pre-training is completed, only retain the encoder feature extraction network for the initial mapping from the high-dimensional data space to the low-dimensional feature space; the specific steps are as follows:

[0135] Step 3.1, build an AE autoencoder network, input the standardized sound speed gradient data set, and obtain the reconstructed sound speed gradient data set at the output of the decoding layer;

[0136] The autoencoder network consists of an encoder network and a decoder network connected in sequence; through encoding by the encoder, the low-dimensional features implicit in the input original data are learned, and then through decoding by the decoder, the reconstructed data is output; for the D-dimensional sound speed gradient data sample X, when passing through the encoder network, θ1 is the parameter of the encoder feature extraction network, that is, the parameter of the encoder part of the network, and the encoding formula is:

[0137] Z = f(X; θ1);

[0138] The low-dimensional feature vector Z in the feature space is obtained, with the dimension of Fn. This feature vector Z then passes through the decoder network. θ2 is the parameter of the decoder part of the network, and the decoding formula is:

[0139]

[0140] Finally, the reconstructed sound speed gradient data sample is obtained The error of the autoencoder for this sample is:

[0141]

[0142] where: X d (d = 1, 2, …, D) is the d-th dimension of the input sample X; in network training, for a batch of M input data samples, the loss function is to minimize the autoencoder error:

[0143]

[0144] where, X m (m = 1, 2, …, M) is the m-th of the batch input samples, is the reconstruction of the m-th sample; the model is optimized by backpropagating the loss to minimize the loss function, that is, the input and output data are infinitely close;

[0145] The construction and pre-training of the AE autoencoder are implemented through programming; the specific structure of the AE autoencoder network constructed in this example is shown in the appendix Figure 3 ; this network is trained end-to-end in an unsupervised manner, and all activation layers use the LeakyReLU activation function (β = 0.1); according to the reconstruction effect of the sound speed gradient data, the learning rate is determined to be 0.001, the iterative batch size M is set to 2048, and the number of model iterative training times is set to 500 times; the Glorot normal distribution initializer (also known as the Xavier normal distribution initializer) is used to randomly initialize the weights of each layer of the network, the optimizer is Adam, and the loss function is the MSE mean square error; the dimension D of the input sample data is 300, and the dimension Fn of the output reduced-dimensional features is initially set to 2; the model converges after approximately 400 training epochs;

[0146] The specific network hierarchy is as follows:

[0147] The first layer is the input layer in the encoder network, where X d (d = 1, 2, …, 300) are the input variables of the AE autoencoder network, a total of 300, specifically referring to the sound speed gradient values at each depth in the standardized sound speed gradient data;

[0148] The second layer is the hidden layer in the encoder network, which is composed of 4 fully connected layers with dimensions of 500, 500, 2000, and 10 connected in sequence. After each fully connected layer, the LeakyReLU function is used as the activation function to avoid neuron "death". The expression of the LeakyReLU function is as follows, x represents the variable of the input function, and β = 0.1:

[0149]

[0150] The third layer is the encoding layer, which is a fully connected layer without an activation function. The input dimension of this layer is 10, and the output dimension is initialized to Fn = 2. The output is the feature after data dimensionality reduction, representing the number of feature vectors obtained by compression;

[0151] The fourth layer is the hidden layer in the decoder network, which is composed of 4 fully connected layers with dimensions of 10, 2000, 500, and 500 connected in sequence. After each fully connected layer, the LeakyReLU function is used as the activation function;

[0152] The fifth layer is the output layer in the decoder network, where are the output variables of the AE autoencoder network, a total of 300, specifically referring to the sound speed gradient values at each depth in the reconstructed sound speed gradient data; Through the decoder network, the extracted 2D feature vector can be restored to the original 300D sound speed profile data;

[0153] Build the AE autoencoder network according to the above structure;

[0154] Step 3.2, input the standardized sound speed gradient data set into the AE autoencoder network for pre-training to obtain the pre-trained AE autoencoder network; The purpose of pre-training this network is to enable the network to accurately extract the features of the standardized sound speed gradient data set; The following Table 1 shows the values of the feature vectors of the first 20 sound speed profile samples after dimensionality reduction feature extraction of 19,200 sound speed profile samples;

[0155] Before feature extraction, the sound speed profile data has 300 dimensions, that is, a sound speed profile requires 300 values to represent. After feature extraction by the AE autoencoder, the sound speed profile data only has 2 dimensions, that is, only 2 values can represent a sound speed profile that previously required 300 values. It can not only extract low-dimensional feature vectors, but also significantly compress the data volume. The data compression ratio reaches 250 times, effectively avoiding the problem of high consumption of computing resources due to large data volume.

[0156] Table 1 Feature vector values after dimensionality reduction feature extraction of the first 20 sound speed profiles (total 19200)

[0157] Sound velocity profile number Eigenvector 1 Eigenvector 2 1 3.12202 -6.95317 2 -5.1228 11.0592 3 -4.91443 9.6285 4 -4.87327 9.86102 5 -5.46049 10.9081 6 -0.251961 1.47404 7 -0.127697 1.57891 8 -0.034207 1.82652 9 -0.253772 1.94541 10 -0.225033 1.75613 11 -0.12776 1.79942 12 -5.22599 10.6126 13 3.05997 -6.90735 14 -4.28671 9.99263 15 -5.55465 10.8544 16 -4.85537 9.90921 17 -5.60756 11.1432 18 -0.165948 1.42155 19 -0.176164 1.62464 20 -0.10884 1.87431

[0158] Step 4: Embed the soft clustering layer into the encoder feature extraction network to obtain a deep embedded clustering neural network. Train this network again using the sound speed gradient data set, calculate the loss of the soft clustering result based on the KL divergence, and feedback the loss to the encoder feature extraction network and the soft clustering layer for dual optimization. Implement the construction and training optimization of the deep embedded clustering neural network through programming; The specific structure of the deep embedded clustering neural network built in this example is shown in the appendix Figure 3 ; Use the Glorot normal distribution initializer, the optimizer is SGD, the learning rate is 0.01, the momentum is 0.9, and the loss function is the KL divergence; The batch size M is 2048, the maximum number of iterations is 20000, and the compatibility threshold tol is 0.001, which is used as the threshold when training stops; The t-distribution degree of freedom α of the soft assignment is defaulted to 1, the custom number of clusters K is 5, the input sample data dimension D is 300, and the dimension Fn of the output dimensionality reduction feature vector is 2; After 980 training epochs, the number of changed cluster assignment points between two iterations is lower than the compatibility threshold of 0.001, and the training is completed; The specific steps are as follows:

[0159] Step 4.1: Pre-train the AE autoencoder to obtain the initial encoder feature extraction network parameters θ; Represent the low-dimensional feature vector after passing through the encoder feature extraction network as the embedding point Z in the feature space m (m = 1, 2, …, 2048), perform k-means clustering to obtain the initial cluster centers μ k (k = 1, 2, …, 5);

[0160] Step 4.2: Calculate the soft assignment, use the Student's t-distribution to calculate the similarity between the embedding point Z corresponding to a sample in the dimensionality reduction feature space m and the cluster center μ k , and define the probability that sample m belongs to a certain category k cluster as the soft assignment q m,k , that is, the proportion of the similarity of a certain sample in the sum of the similarities of all samples:

[0161]

[0162] Among them, represents the similarity of a certain sample, Z m = f(X m ; 1), where α is the degree of freedom of the student's t-distribution, α = 1;

[0163] Step 4.3, calculate the KL divergence between the soft assignment q m,k and the auxiliary distribution p m,k as the loss function L;

[0164] Define the auxiliary distribution p m,k as:

[0165]

[0166] Define the purpose of the auxiliary distribution p m,k as follows: (1) Improve cluster purity; (2) Pay more attention to the embedding points with high confidence; (3) Contribute to the cluster center loss of each cluster to prevent the hidden feature space from being distorted due to too many clusters; The loss function is defined as the KL divergence between the soft assignment distribution q m,k and the auxiliary distribution p m,k . The loss function is used to measure the difference degree between the above two distributions. The goal of model training is to minimize the KL divergence between the assignment distribution q m,k and the auxiliary distribution p m,k . The calculation formula of the loss function L is as follows:

[0167]

[0168] Step 4.4, feedback the calculated loss function obtained above to both the clustering layer and the feature extraction network at the same time, and use the SGD optimizer with momentum-based stochastic gradient descent to optimize the embedding point Z m and the clustering center position μ k respectively. The gradient calculation formulas of the loss function with respect to the embedding point Z m and the clustering center μ k are as follows:

[0169]

[0170]

[0171] Pass to the encoder feature extraction network, and then use the standard backpropagation to calculate the gradient of the encoder feature extraction network parameter θ1 Optimize the encoder feature extraction network parameter θ1; stop training when the number of changed cluster assignment points between two iterations is less than 0.001;

[0172] The above steps improve the DEC algorithm, making it applicable to sound speed profile clustering, linking the sound speed profile feature extraction step with the clustering step, and using deep learning technology to optimize these two steps simultaneously. The quality of the clustering result can not only be fed back to the clustering layer but also to the feature extraction network, thus realizing the "dual optimization" of the clustering layer and the feature extraction network. This not only enables the feature extraction network to extract high-quality low-dimensional feature vectors to represent high-dimensional sound speed profile data but also continuously adjusts the distribution of the moving feature vectors in the feature space during iterative training, making the embedded points of the same type of sound speed profile in the feature space gather together and the embedded points of different types of sound speed profiles move further away, so as to obtain a more reasonable clustering effect, and the clustering result has the best performance in the clustering evaluation index. At the same time, this optimization process can be very conveniently completed automatically based on a deep learning neural network, and no human intervention is required during the optimization process;

[0173] Build and train a deep embedded clustering neural network according to the above steps to obtain a deep embedded clustering neural network that can be directly used for sound speed profile clustering.

[0174] Step 5, use the trained deep embedded clustering neural network to perform sound speed profile clustering, visualize the clustering result, and use two indicators, the average distortion degree and the silhouette coefficient, in the internal evaluation method to evaluate the clustering quality. The specific steps are as follows:

[0175] Step 5.1, use the trained deep embedded clustering neural network, customize the number of clusters K as 5, and then the standardized sound speed gradient data set can be clustered. The final clustering result is plotted in the form of a scatter plot in the feature space to obtain the result as shown in the appendix Figure 4 as shown;

[0176] Plot the clustering results of 9 typical stages in the model iterative training process as scatter plots to obtain the appendix Figures 5 to 13 , from the appendix Figures 5 to 13 it can be seen that as the model is continuously iteratively trained, the interval between the embedded points of different categories becomes more and more obvious, and the embedded points of the same category become more and more concentrated. The final clustering result obviously obtains the 5 pre-customized clustering clusters;

[0177] For users, after providing the sound speed profile data of the sea area to be clustered to the model, only need to input one parameter, that is, the number of clusters K, the total number of sound speed profile categories, and then the model can be run to obtain the sound speed profile clustering result. Compared with other deep learning neural networks, the model parameter setting based on the foregoing structure is simple and the operation is convenient, which is conducive to further improving the operation efficiency;

[0178] Step 5.2, draw the sound velocity profiles of the cluster centers in each type as the representative sound velocity profiles of that type, and obtain 5 types of sound velocity profiles as shown in the appendix Figures 14 to 18 ;

[0179] Step 5.3, evaluate the quality of the clustering results by calculating the average distortion degree and the silhouette coefficient, and test the optimal number of clusters K. Plot the average distortion degree S1 and the silhouette coefficient S2 of the clustering results as a line graph, as shown in the appendix Figure 19 ;

[0180] The average distortion degree S1 is essentially the average of the within-cluster sum of squared deviations. The smaller the sum of the distances from all sample points to the centroid, the more similar the samples in each cluster are considered to be, and the better the clustering effect. Generally, the inflection point of the S1 line of the average distortion degree is considered to be a better number of clusters. The calculation formula for the average distortion degree S1 is as follows:

[0181]

[0182] K is initially defined as 5. Divide the N samples in the sound velocity gradient dataset into 5 classes, and use Cluster k (k = 1, 2, …, 5) to represent the set of all embedded points Z n (n = 1, 2, …, N) in the k-th class;

[0183] The silhouette coefficient S2 is the average of the silhouette coefficients of all embedded points. For a single embedded point, a is the average distance to other embedded points in the same class, a reflects the within-cluster density, b is the average distance to the embedded points in the nearest different class, b reflects the between-cluster dispersion, and the value range of S2 is [0, 1]. The larger the silhouette coefficient S2, the better the clustering number at this time. The calculation formula for the silhouette coefficient S2 is as follows:

[0184]

[0185] Because the inflection point of the S1 line of the average distortion degree is a better number of clusters, and the larger the silhouette coefficient S2, the better the clustering number at this time. It can be seen that when the custom number of clusters is 5, it happens to be the inflection point of the average distortion degree line, and the silhouette coefficient is the largest at this time, indicating that the clustering method of the present invention achieves a better clustering effect;

[0186] In the present invention, the sound velocity profile clustering network model based on a deep embedded neural network obtained through sufficient training can not only directly use the fast obtained sound velocity profile clustering results, but also, like other deep learning neural network models, has good generalization ability and can be widely promoted and applied. That is, it can input the sound velocity profile data of different seas around the world for training, and obtain multiple sound velocity profile clustering models applicable to different seas around the world, which are widely used for the sound velocity profile clustering of different seas around the world, and have good generalization ability and promotability.

[0187] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit the protection scope of the present invention. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical solutions of the present invention can be modified or equivalently replaced without departing from the essence and scope of the technical solutions of the present invention.

Claims

1. A sound velocity profile clustering method based on a deep embedded clustering neural network, characterized in that, It includes the following steps: Step 1: Based on the longitude, latitude, seawater temperature, salinity, and water depth data of the target sea area to be clustered provided by the high-resolution ocean reanalysis product, use the sound speed formula to convert and obtain the monthly average sound speed profile dataset of the target sea area to be clustered; Step 2: Preprocess the monthly average sound speed profile dataset of the target sea area to be clustered, unify the depth interval and the maximum depth, and perform standardization processing on the sound speed gradient dataset obtained by using the gradient formula. The standardized sound speed gradient dataset will be used as the dataset for training, validating, and testing the depth-embedded clustering neural network; Step 3: Build an AE autoencoder, which is composed of an encoder feature extraction network and a decoder neural network connected in sequence; use the sound speed gradient dataset to pre-train the AE autoencoder. After the pre-training is completed, only retain the encoder feature extraction network for the initial mapping from the high-dimensional data space to the low-dimensional feature space; Step 4: Embed the soft clustering layer into the encoder feature extraction network to obtain a depth-embedded clustering neural network. Use the sound speed gradient dataset to train the network again, calculate the loss of the soft clustering result based on the KL divergence, and feedback the loss to the encoder feature extraction network and the soft clustering layer for dual optimization; Step 5: Use the trained depth-embedded clustering neural network to perform sound speed profile clustering, visualize the clustering result, and use two indicators, the average distortion degree and the silhouette coefficient, in the internal evaluation method to evaluate the clustering quality.

2. The method for clustering sound velocity profiles based on a deep embedded clustering neural network according to claim 1, wherein The specific steps of Step 1 are as follows: Step 1.1: Refer to the grid cell structure of the high-resolution ocean reanalysis product and design the data structure of the physical quantities of the target sea area to be clustered; use equally spaced grids to divide the longitude and latitude within the horizontal range, and use non-equally spaced division in the depth; output at equal time intervals in the time dimension; the values at the land and seabed sediment layers are in the default state; Step 1.2: Use the sound speed formula to convert the seawater temperature, salinity, and pressure data of the high-resolution ocean reanalysis product into a high-resolution sound speed profile dataset. The expression of the sound speed formula is as follows: ； where: c is the sound speed value of seawater, s, T, and p are the salinity, water temperature, and hydrostatic pressure of seawater, is an empirical function related to seawater temperature and hydrostatic pressure, , , , and the standard deviation of the calculated sound speed value is 0.19 m / s; Step 1.3: Store the sound speed profile data units of the high-resolution and long-time series of the sea area as floating-point types; refer to the data storage structure of the high-resolution ocean reanalysis product and store the above-converted sound speed profile dataset in the same structure; the horizontal spatial resolution, vertical spatial resolution, time resolution, and time span of the storage structure of the sound speed profile dataset are consistent with the referenced high-resolution ocean reanalysis product; Perform monthly averaging on the sound speed profile data and output the time resolution averaged once a month to obtain the monthly average sound speed profile dataset.

3. According to the method for sound speed profile clustering based on a depth-embedded clustering neural network described in claim 1, wherein The specific steps of Step 2 are as follows: Step 2.

1. To ensure a refined representation of the sound speed profile, considering that the variation of the sound speed profile is mainly concentrated above a water depth of 1500 m and the change in sound speed data below 1500 m is small and of little reference significance for clustering; intercept the sound speed profile data above 1500 m and use the Akima interpolation method at a depth interval of 5 m to interpolate from a depth of 5 m to 1500 m, with a total of 300 depth values, to obtain a monthly average sound speed profile dataset within 1500 m with equal depth intervals. The described Akima interpolation method is defined to perform interpolation between two points. In addition to the values of these two points, the values at the four points adjacent to these two points are also required. Therefore, a total of 6 points are involved. Among them, the point where interpolation is to be performed is between the 3rd and 4th points. , ; represents the speed of sound value, with the unit of meters per second; represents the depth, with the unit of meters, and the interpolation formula is: ； Where: ； where and are the slopes of the 3rd and 4th points respectively, and the slope calculation formula is: ； where , since the above equation does not hold when the denominator is 0, in this case, Akima stipulates that: or ; After the above interpolation process, a sound speed profile data set with equal depth intervals is established; Step 2.2, represent the monthly average sound speed profile dataset with equal depth intervals as a sound speed matrix C, which is a -order matrix, where N is the number of samples and D is the number of sound speed sampling points after interpolation in depth. The sound speed values in the matrix are represented as ; represent the sound speed profile using the sound speed gradient, and convert the sound speed matrix C to obtain the sound speed gradient matrix G based on the gradient calculation formula. The matrix G is still -order; the sound speed gradient calculation formula is: ； where the gradient is g, the sound speed is c, the depth is D, and the sound speed gradient value in the matrix G is expressed as ; Step 2.3, perform standardization processing on the sound velocity gradient data. Use z-score standardization to standardize the sound velocity values corresponding to each depth value layer, so that the average value of each type of data is 0 and the standard deviation is 1; the standardized data is expressed as , is the average value of each variable, that is, the sound velocity gradient of each depth layer, is the standard deviation of the sound velocity gradient of each layer, and the standardization formula is: ； After the above formula conversion, a standardized sound speed gradient dataset is obtained; and the standardized sound speed gradient dataset will be used as the dataset for training, validating, and testing the depth-embedded clustering neural network.

4. The sound speed profile clustering method based on a depth-embedded clustering neural network according to claim 1, characterized in that Step 3.1, build an AE autoencoder. The encoder learns the low-dimensional features hidden in the input raw data, and the decoder decodes and outputs the reconstructed data. For the D-dimensional sound speed gradient data sample X, when passing through the encoder network, is the parameter of the encoder feature extraction network, that is, the parameter of the network in the encoder part. The encoding formula is: ； Obtain the low-dimensional feature vector Z in the feature space, with a dimension of Fn. This feature vector Z then passes through the decoder network. are the parameters of the network in the decoder part, and the decoding formula is: ； Finally, the reconstructed sound speed gradient data sample is obtained. , and the error of the AE autoencoder for this sample is: ； wherein, is the d-th dimension of the input sample X; during network training, for a batch of M input data samples, the loss function is to minimize the autoencoder error: ； Among them, is the m-th of the batch input samples, is the reconstruction of the m-th sample; the model is optimized by backpropagation loss to minimize the loss function; Step 3.

2. Input the sound speed gradient dataset to pre-train the AE autoencoder to obtain a trained encoder feature extraction network; further adjust the iteration batch size, learning rate, and number of iterations to optimize the reconstruction effect.

5. The method for clustering sound velocity profiles based on a deep embedded clustering neural network according to claim 4, characterized in that, The structure of the encoder feature extraction network is as follows: The first layer is the input layer in the encoder network, where are the input variables of the AE autoencoder network, with a total of D, specifically referring to the sound speed gradient values at each depth in the rapid gradient data; The second layer is the hidden layer in the encoder network, which is sequentially connected by 4 fully connected layers with dimensions of 500, 500, 2000, and 10. After each fully connected layer, the LeakyReLU function is used as the activation function. The expression of the LeakyReLU function is as follows: ； In this formula, represents the variable of the input function, ; The third layer is the encoding layer, which is a fully connected layer without an activation function. The input dimension of this layer is 10, and the output dimension is Fn. The output is the feature after data dimensionality reduction, representing the number of feature vectors obtained by compression. The fourth layer is the hidden layer in the decoder network, which is sequentially connected by 4 fully connected layers with dimensions of 10, 2000, 500, and 500. After each fully connected layer, the LeakyReLU function is used as the activation function. The fifth layer is the output layer in the decoder network, where are the output variables of the AE autoencoder network, with a total of D. Specifically, they refer to the sound speed gradient values at each depth in the reconstructed sound speed gradient data; Finally, the Adam optimizer is used to calculate the loss function and use the backpropagation loss to optimize the network.

6. The method for clustering sound velocity profiles based on a deep embedded clustering neural network according to claim 1, wherein The specific steps of step 4 include: Step 4.1, Initialization: By pre-training the AE autoencoder, initialize the network parameters of the encoder feature extraction network , and the network parameters of the decoder part ; Represent the low-dimensional feature vector after passing through the encoder feature extraction network as an embedding point in the feature space , and perform k-means clustering to obtain the initial cluster centers , where the batch training sample number is defined as M, the number of clusters is defined as K, m represents the m-th sample, and k represents the k-th sound speed profile Step 4.2, calculate the soft assignment, and use the t-distribution to calculate the embedding point corresponding to a certain sample in the feature space after dimensionality reduction and the cluster center The probability that sample m belongs to a certain category k cluster is defined as the soft assignment , which represents the proportion of the similarity of a certain sample in the sum of the similarities of all samples, and ; Among them, represents the similarity of a certain sample, , is the degree of freedom of the t-distribution of the student ; Step 4.3, minimize the KL divergence and define the auxiliary distribution as follows: ； The loss function is defined as the KL divergence between the soft assignment distribution and the auxiliary distribution The loss function is used to measure the difference between the above two distributions. The goal of model training is to minimize the KL divergence between the assignment distribution and the auxiliary distribution The calculation formula of the loss function L is as follows: ； Step 4.4, feedback the calculated loss above to both the clustering layer and the encoder feature extraction network, and use the SGD optimizer with momentum-based stochastic gradient descent to optimize the embedding points and the positions of the cluster centers , the gradient calculation formulas of the loss function with respect to the embedding points and the cluster centers are as follows: ， ； Then use standard backpropagation to calculate the gradients of the encoder feature extraction network parameters and optimize the encoder feature extraction network parameters ; when the number of changed cluster assignment points between two iterations is less than the set target value, stop the training. ​ 7. The method for clustering sound velocity profiles based on a deep embedded clustering neural network according to claim 1, wherein The specific steps of step 5 include: Step 5.

1. Cluster the sound speed gradient dataset using the depth-embedded clustering neural network and present it in the form of a scatter plot in the feature space. Step 5.

2. Plot the sound speed profile of the clustering center in each type as the representative sound speed profile of that type. Step 5.

3. Evaluate the quality of the clustering result by calculating the average distortion degree and the silhouette coefficient, and test the optimal number of clusters K. Plot the average distortion degree S1 and the silhouette coefficient S2 of the clustering result as a line graph. Among them, the average distortion degree refers to the average of the within-cluster sum of squared deviations. The average distortion degree is calculated as follows: ； Divide N samples in the sound speed gradient dataset into K classes, and use to represent the set of all embedded points in the cluster of the k-th class ; Silhouette coefficient is the average of the silhouette coefficients of all the embedded points, and the silhouette coefficient is calculated as follows: ； a is the average distance of other embedded points in the same category; b is the average distance of the embedded point in the different category with the closest distance to it.

Images