A method and system for predicting the time series of sound speed profiles under significant changes in the background field

Abstract

The present invention provides a method and system for predicting the time series of sound speed profiles under significant changes in the background field. The method includes: performing EOF decomposition on the historical sound speed profile data with a long time series to extract the background sound speed profile and the first few orders of EOF basis functions; obtaining the sound speed at a fixed depth in the historical sound speed profile data based on the depth corresponding to the extreme point of the first-order EOF; predicting the sound speed at a fixed depth for a subsequent period of time through an LSTM neural network; establishing a relationship model between the sound speed data at a fixed depth and the first few orders of EOF coefficients; and sequentially inputting the sound speed data at a fixed depth for a subsequent period of time into the relationship model to achieve the time series prediction of the sound speed profile. Based on the negative coupling relationship between the background sound speed profile and the first-order EOF component, this method effectively solves the problem of increased reconstruction error faced by the method of directly predicting the EOF coefficients when the background sound speed profile is not representative, and significantly improves the prediction accuracy of the sound speed profile when the background sound speed field changes significantly.

Description

Technical Field

[0001] The present invention belongs to the technical fields of underwater acoustic engineering, ocean engineering, and sonar technology, and particularly relates to a method and system for predicting the time series of sound speed profiles under significantly changing background fields. Background Art

[0002] The sound speed of seawater is an important parameter affecting the underwater sound propagation characteristics, and affects underwater navigation, acoustic positioning, acoustic detection, etc. However, the existence of internal waves causes severe disturbances in the distribution of seawater sound speed, making the spatio-temporal changes of the sound speed field show complex randomness, and seriously affecting the sound signal propagation process. How to achieve the time series prediction of the sound speed profile in the whole ocean depth has become an important research topic.

[0003] Affected by complex ocean dynamic processes, the temporal variation of the seawater sound speed profile has significant temporal evolution characteristics and non-linear characteristics. Neural networks can effectively capture the spatio-temporal variation characteristics of the sound speed profile. By analyzing and modeling historical sound speed profiles, the changing trend of the sound speed profile within a certain period of time in the future can be predicted. For example, in reference [1] (“A novel sound speed profile prediction method based on the convolutional long-short-term memory network”, published in the 5th issue, volume 10 of Journal of Marine Science and Engineering in April 2022, starting page number is 572), a convolutional neural network (CNN) capable of mining the spatial characteristics of the sound speed distribution is added to the basis of the LSTM neural network, and the sound speed profile of the next 1 month is predicted using 24 months of historical sound speed profiles. In order to simplify the parameters of the sound speed profile prediction, it is usually necessary to reduce the dimension of the sound speed profile. Research shows that the periodic characteristics of the sound speed profile are also reflected in the time series of the empirical orthogonal function (EOF) coefficients. The problem of the temporal prediction of the sound speed profile can be transformed into the temporal prediction of the EOF coefficients. For example, in reference [2] (“Sound speed profile prediction method based on the statistical characteristics of internal waves”, published in the 6th issue, volume 42 of Journal of Harbin Engineering University in June 2021, starting page number is 859), the problem of sound speed profile prediction is simplified to the prediction problem of the first-order EOF coefficient, and the prediction of the second-order EOF coefficient is realized by using the statistical characteristics between the first two-order EOF coefficients when internal waves exist. However, the existence of soliton internal waves causes the sound speed profile to change violently in a short time. If there are large differences between the background sound speed profiles of the training set and the test set, when directly predicting the sound speed profile using the EOF coefficient-based sound speed profile prediction method, the representative error of the background sound speed will lead to a significant reduction in the reconstruction accuracy of the sound speed profile. Summary of the Invention

[0004] The purpose of the present invention is to overcome the defects of the prior art and propose a method for predicting the temporal sequence of the sound speed profile under significant changes in the background field.

[0005] To achieve the above purpose, the present invention proposes a method for predicting the temporal sequence of the sound speed profile under significant changes in the background field, including:

[0006] Step 1: Perform EOF decomposition on the long-time historical sound speed profile data, and extract the background sound speed profile and the first few-order EOF basis functions;

[0007] Step 2: Based on the depth corresponding to the first-order EOF extreme point, obtain the sound speed at a fixed depth from the historical sound speed profile data;

[0008] Step 3: Predict the sound speed at a fixed depth for a subsequent period of time through an LSTM neural network;

[0009] Step 4: Establish a relationship model between the sound speed data at a fixed depth and the first few orders of EOF coefficients through a BP neural network;

[0010] Step 5: Input the sound speed at a fixed depth for the subsequent period of time obtained in Step 3 into the relationship model in sequence to achieve the time series prediction of the sound speed profile.

[0011] Preferably, the extraction of the background sound speed profile in Step 1 includes:

[0012] Set N sound speed profiles, interpolate each profile into M standard layers to obtain the sound speed matrix C M×N :

[0013]

[0014] In the formula, each column is the value of a sound speed profile at the standard depth, and each row is the sound speed of all sound speed profiles at the same depth;

[0015] Take the average of each layer of the N sound speed profiles to obtain the average sound speed profile That is, the background sound speed profile:

[0016]

[0017] In the formula, T is the transpose, and i represents the i-th sound speed profile, i ∈ [1, N].

[0018] Preferably, the first few orders of EOF basis functions in Step 1 include:

[0019] Expand the background sound speed profile to obtain the background sound speed profile matrix

[0020]

[0021] Subtract the sound speed profile matrix C M×N from the background sound speed profile matrix to obtain the perturbation matrix ΔC of each profile relative to the background field M×N :

[0022] Obtain the covariance matrix R of the perturbation matrix according to the following formula M×M :

[0023]

[0024] Performing eigenvalue decomposition to obtain:

[0025] R M×M V M×M = λ M×M V M×M

[0026] where λ M×M represents the eigenvalue matrix, and V M×M is the EOF basis function;

[0027] Projecting from EOF to the perturbation matrix ΔC according to the following formula M×N , to obtain the EOF coefficient matrix A M×N :

[0028]

[0029] Preferably, in the LSTM neural network in step 3, the input is the sound speed at a fixed depth of the historical sound speed profile data, and the output is the sound speed value at a fixed depth within a subsequent period of time.

[0030] Preferably, the method further includes a training step for the BP neural network, including:

[0031] Setting the number of training rounds, the minimum error of the training target, and the learning rate, and training through the sound speed data at the depth corresponding to the first-order EOF extreme point in the training set C z1 . When the minimum error of the training target or the maximum number of training times is reached, the training of the BP neural network is completed, and the output is the first few orders of EOF coefficients

[0032] Preferably, step 5 includes:

[0033] Sequentially inputting the sound speed at a fixed depth within a subsequent period of time obtained in step 3 into the relationship model established in step 4 to obtain the first few orders of EOF coefficients as the reconstruction coefficient α j , where j represents the order;

[0034] According to the background sound speed profile obtained in step 1 and the EOF basis function v j (z) corresponding to different sea water depths z, using the first few orders of EOF to complete the reconstruction of any sound speed profile to obtain the reconstructed sound speed profile Realizing the time series prediction of the sound speed profile:

[0035]

[0036] On the other hand, the present invention proposes a sound speed profile time series prediction system under significant changes in the background field, including:

[0037] The EOF decomposition module is used to perform EOF decomposition on the historical sound speed profile data with a long time series, and extract the background sound speed profile and the first few orders of EOF basis functions;

[0038] The historical data acquisition module is used to obtain the sound speed at a fixed depth of the historical sound speed profile data based on the depth corresponding to the extreme point of the first-order EOF;

[0039] The prediction module is used to predict the sound speed at a fixed depth within a subsequent period of time through an LSTM neural network;

[0040] The relationship model establishment module is used to establish a relationship model between the sound speed data at a fixed depth and the first few orders of EOF coefficients through a BP neural network;

[0041] The output module is used to input the sound speed at a fixed depth within a subsequent period of time obtained by the prediction module into the relationship model in sequence to realize the time series prediction of the sound speed profile.

[0042] Compared with the prior art, the advantages of the present invention are as follows:

[0043] By deeply studying the negative coupling relationship between the background field and the first-order EOF component, the method of the present invention constructs a sound speed profile prediction method combining LSTM and BP neural networks, which can realize the time series prediction of the sound speed profile in the scenario where the background field changes significantly. Compared with the traditional method of directly predicting the EOF coefficients of the sound speed profile of the test set, this method can effectively solve the problem of reduced reconstruction accuracy of the sound speed profile caused by the non-representative background sound speed profile. Brief Description of the Drawings

[0044] Figure 1 is a flowchart of the sound speed profile time series prediction method under the significant change of the background field of the present invention;

[0045] Figure 2(a) is the background sound speed profile extracted from the training set and the test set in the embodiment of the present invention;

[0046] Figure 2(b) is the first-order EOF basis function extracted from the training set and the test set in the embodiment of the present invention;

[0047] Figure 2(c) is the second-order EOF basis function extracted from the training set and the test set in the embodiment of the present invention;

[0048] Figure 3(a) is a scatter plot and a fitting line of the sound speed at a fixed depth and the first-order EOF coefficient in the embodiment of the present invention;

[0049] Figure 3(b) is a scatter plot and a fitting curve of the sound speed at a fixed depth and the second-order EOF coefficient in the embodiment of the present invention;

[0050] Figure 4 is the prediction result of the sound speed at a fixed depth in the embodiment of the present invention;

[0051] Figure 5(a) shows the prediction result of the first-order EOF coefficient in the embodiment of the present invention;

[0052] Figure 5(b) shows the prediction result of the second-order EOF coefficient in the embodiment of the present invention;

[0053] Figure 6 is the prediction error of the sound speed profile in the embodiment of the present invention. Detailed implementation manners

[0054] The present invention proposes a method for predicting the time series of the sound speed profile under significant changes in the background field, including:

[0055] Step 1: Perform EOF decomposition on the long-time series historical sound speed profile data, and extract the background sound speed profile and the first few orders of EOF basis functions;

[0056] Step 2: Based on the depth corresponding to the extreme point of the first-order EOF, obtain the sound speed at a fixed depth in the historical sound speed profile data;

[0057] Step 3: Predict the sound speed at a fixed depth within a subsequent period of time through an LSTM neural network;

[0058] Step 4: Establish a relationship model between the sound speed data at a fixed depth and the first few orders of EOF coefficients through a BP neural network;

[0059] Step 5: Input the sound speed at a fixed depth within a subsequent period of time obtained in Step 3 into the relationship model to realize the prediction of the time series of the sound speed profile.

[0060] The technical solution of the present invention will be described in detail below with reference to the accompanying drawings and embodiments.

[0061] Embodiment 1

[0062] Embodiment 1 of the present invention proposes a method for predicting the time series of the sound speed profile under significant changes in the background field. First, use the memory function of the LSTM network to construct a prediction model for the sound speed at a fixed depth to realize the prediction of the time series of the sound speed at a fixed depth, and then combine the non-linear mapping ability of the BP neural network to construct a relationship model between the sound speed at a fixed depth and the EOF coefficient to realize the prediction of the sound speed profile at all depths of the sea.

[0063] The implementation process is divided into the following steps, as Figure 1 shown:

[0064] Step 1: Perform EOF decomposition on the historical sound speed profile, and determine the depth of the extreme point of the first-order EOF of the historical sound speed profile data set and the corresponding sound speed.

[0065] In this embodiment, the temperature chain data obtained from a fixed-point sound propagation experiment in a certain South China Sea area is taken as an example, and the sampling interval is 30 s. Due to the existence of internal solitary waves, the sound speed profile changes violently in a short time. Here, the 2-h sound speed profile data is used as the training set to demonstrate the time series prediction method of the sound speed profile.

[0066] There are a large number of optimization estimation parameters required for inverting the seawater sound speed profile. Therefore, it is often necessary to first perform dimensionality reduction processing on the sound speed profile matrix. The EOF method, also known as principal component analysis, realizes data dimensionality reduction by concentrating the main information of the sample data on several main components. Research shows that the sound speed profile can be reconstructed more accurately using the first few orthogonal basis functions, thereby significantly reducing the complexity of data processing while maintaining the integrity of information. Suppose there are N sound speed profiles, and each profile is interpolated into M standard layers to obtain the sound speed matrix:

[0067]

[0068] In the formula, each column represents the value of a sound speed profile at the standard depth, and each row represents the sound speed of all sound speed profiles at the same depth.

[0069] The average of each layer of the N sound speed profiles is taken to obtain the average sound speed profile (T is the transpose), that is, the background sound speed profile:

[0070]

[0071] The background sound speed profile is extended to obtain the background sound speed profile matrix (each column of the matrix is equal):

[0072]

[0073] The sound speed profile matrix is subtracted from the background sound speed profile matrix to obtain the perturbation matrix ΔC of each profile relative to the background field M×N :

[0074]

[0075] The covariance matrix of the perturbation matrix is:

[0076]

[0077] Eigenvalue decomposition gives:

[0078] R M×M V M×M =λ M×M V M×M (6)

[0079] where λ M×MDenote the eigenvalue matrix. Since the magnitude of the eigenvalue corresponds to the richness of information when reconstructing the sound speed profile, the eigenvalues are arranged in descending order; V M×M is the eigenvector matrix corresponding to the eigenvalues, that is, the EOF basis function.

[0080] The EOF coefficient matrix A M×N is obtained by projecting EOF onto the sound speed perturbation:

[0081]

[0082] The eigenvalue corresponding to each eigenvector represents the weight of this eigenvector. The cumulative variance contribution rate of the first k orders is:

[0083]

[0084] When Q ≥ 0.95, it can be considered that the first k-order EOF numbers can represent the main characteristics of the sound speed profile in the current sea area. Therefore, the reconstruction of any sound speed profile in the survey area can be completed using the first k-order EOF:

[0085]

[0086] In the formula, is the reconstructed sound speed profile, is the background sound speed profile, z is the depth of each layer of seawater, α j is the reconstruction coefficient, v j (z) is the EOF basis function.

[0087] Research shows that the first-order EOF plays a dominant role in the process of reconstructing the sound speed profile, and the first-order EOF coefficient represents the vertical displacement of the thermocline. Moreover, the sound speed at the depth corresponding to the extreme point of the first-order EOF of each profile has a strong correlation with the first-order EOF coefficient. Therefore, it can be considered that the sound speed at the depth corresponding to the extreme point of the first-order EOF also has rich information and can largely reflect the overall shape of the sound speed profile. Perform EOF decomposition on the sound speed profiles in the training set. The contribution rate of the first two orders is 98.3%. Figure 2(a) plots the background sound speed profiles extracted from the training set and the test set. Figure 2(b) is the first-order EOF basis function, and Figure 2(c) is the second-order EOF basis function;

[0088] It can be seen that there are significant differences in the position of the thermocline between the two background sound speed profiles, and the maximum difference reaches 4.42 m / s. The depth corresponding to the extreme point of the first-order EOF in the training set is z1 = 56.5 m. The sound speeds at the fixed depth of z1 in the training set and the test set are respectively and

[0089] Step 2: Based on the depth corresponding to the extreme point of the first-order EOF, obtain the sound velocity of the historical sound velocity profile data at a fixed depth.

[0090] A relationship model between constant-depth sound velocity and the first two-order EOF coefficients is constructed to explore the negative coupling relationship between the background sound velocity profile and the first-order EOF component.

[0091] The sound velocity profile reconstruction error ΔC is divided into three parts: background sound velocity profile error ΔC background , first-order EOF error ΔC1 and second-order EOF error ΔC2:

[0092]

[0093] in, and are the background sound velocity profiles of the training set and the test set, respectively; are the predicted first-order and second-order EOF coefficients; v 1_train 、v 2_train are the first-order and second-order EOF basis functions extracted from the training set; α 1_test , α 2_test are the first-order and second-order EOF coefficients extracted from the test set; v 1_test 、v 2_test are the first-order and second-order EOF basis functions extracted from the test set.

[0094] Figure 3(a) plots the scatter plot of the fixed-depth sound velocity and the first-order EOF coefficient of the training set and the test set. The horizontal axis is the sound velocity of the sound velocity profile of the training set and the test set at the depth z1, and the vertical axis is the corresponding first-order EOF coefficient. It can be seen that the fixed-depth sound velocity and the first-order EOF coefficient show a strong linear relationship. This method uses the BP neural network to construct the relationship between the fixed-depth sound velocity and the EOF coefficient. Here, it is fitted into a linear relationship for the convenience of discussion:

[0095]

[0096] in is the input data of the training set model and the test set model, that is, the sound velocity of each profile at the depth of z1, They are the output data of the training set model and the test set model, that is, the predicted first-order EOF coefficient of the test set.

[0097] Since the basis functions of the training set and the test set are basically the same, ΔC1 in equation (10) can be written as:

[0098]

[0099] Figure 3(b) is a scatter plot of the depth-fixed sound speed and the second-order EOF coefficient for the training set and the test set. The abscissa is the sound speed at the z1 depth of the sound speed profiles of the training set and the test set, and the ordinate is the corresponding second-order EOF coefficient. It can be seen that the depth-fixed sound speed and the second-order EOF coefficient show an approximately parabolic correlation:

[0100]

[0101] where are the output data of the training set model and the test set model respectively, that is, the predicted second-order EOF coefficient of the test set.

[0102] Then ΔC2 in Equation (10) can be written as:

[0103]

[0104] As can be seen from Figure 3, the value range of the depth-fixed sound speed is between 1527 m / s and 1542 m / s. After calculation by Equation (12), it can be obtained that ΔC1 < 0 within this range. As can be seen from Figure 2(a), the background sound speed profile value of the training set between the thermoclines is greater than that of the test set, that is, ΔC background > 0. The signs of the two are opposite, and the errors cancel each other out to a certain extent after superposition. Using Equation (14) to calculate the error ΔC2 of each profile at different depths within the value range of the depth-fixed sound speed, the minimum root mean square error is close to 0 m / s, the maximum root mean square error is 0.43 m / s, and the average root mean square error is 0.21 m / s, which has little impact on the reconstruction accuracy of the sound speed profile.

[0105] Deeply analyze the reason why the signs of ΔC background and ΔC1 are opposite. Since the contribution rate of the first-order EOF of the training set and the test set exceeds 90%, which dominates in the sound speed profile reconstruction, while the contribution rate of the second-order is less than 5%, and the influence of the second-order on the sound speed profile reconstruction is very small, so it is temporarily ignored. Therefore, a sound speed profile can be expressed as the sum of the background sound speed profile and the first-order EOF component, that is, the two show a negative coupling relationship. As can be seen from Figure 2(a), the background sound speed profile value of the training set at the thermocline depth is greater than that of the test set, that is, ΔC background > 0. And because the first-order EOF basis functions of the training set and the test set are basically the same and positive, after projecting a profile into the EOF basis function spaces of the training set and the test set respectively, the corresponding first-order EOF coefficient of the training set is less than that of the test set. Therefore, at the same depth-fixed sound speed, the corresponding coefficients in the training set are generally smaller, while those in the test set are larger. When using the relationship model between the depth-fixed sound speed constructed by the training set and the first-order EOF coefficient to predict the coefficient of the test set, there will be a phenomenon that the predicted coefficient is smaller than the true value. Therefore, the error of the first-order EOF component ΔC1 < 0. And from the above analysis, it is known that ΔC background> 0, that is, the error signs of the two parts are opposite, and the total error ΔC decreases after superposition.

[0106] Step 3: Use the LSTM neural network to realize the time series prediction of the depth-fixed sound speed.

[0107] Taking as the input, the depth-fixed sound speed prediction model is trained through multiple iterations. Input the test set data into the trained LSTM neural network model to obtain the predicted depth-fixed sound speed values of the test set As Figure 4 shown, the prediction results are in good agreement with the true values.

[0108] Step 4: Build a BP neural network model.

[0109] Based on the non-linear mapping ability of the BP neural network, build a relationship model between the sound speed C train_z corresponding to the first-order EOF extreme point of the training set and the EOF coefficient α train at the corresponding depth.

[0110] Through the sound speed data at the depth corresponding to the first-order EOF extreme point in the training set for training. The network structure includes an input layer, multiple hidden layers, and an output layer. The parameter settings are as follows:

[0111] Table 1 Training parameters

[0112] Training rounds 1000 Learning rate 0.01 Minimum error of training target 0.00001

[0113] When the training target of the minimum error or the maximum number of training times is reached, the BP neural network training is completed. The trained BP neural network takes the depth-fixed sound speed predicted in Step 3 as the input, and the output is the first few orders of EOF coefficients

[0114] Step 5: Use the depth-fixed sound speed in Step 3 as the input data and input it into the BP neural network training model in Step 4 to invert the full-depth sound speed profile.

[0115] Use the predicted depth-fixed sound speed as the input of the trained BP neural network model to obtain the predicted first two orders of EOF coefficients of the test set The results are shown in Figure 5. Figure 5(a) is the prediction result of the first-order EOF coefficient; Figure 5(b) is the prediction result of the second-order EOF coefficient;

[0116] It can be seen that the prediction results of the first-order EOF coefficient are generally smaller than the true values, and this result is consistent with the analysis result in Step 2. Use the reconstruction formula to obtain the sound speed profile of the test set, and the error is as Figure 6As shown, the average root mean square error is 0.64 m / s and the maximum root mean square error is 1.68 m / s.

[0117] The verification results of the embodiments show that the method of the present invention can effectively solve the problem of significant errors generated during the reconstruction of the sound speed profile caused by the lack of representativeness of the background sound speed profile, and realize the time series prediction of the sound speed profile under significant changes in the background field.

[0118] Embodiment 2

[0119] Embodiment 2 of the present invention provides a sound speed profile time series prediction system under significant changes in the background field, which is implemented based on the method of Embodiment 1 and includes:

[0120] The EOF decomposition module is used to perform EOF decomposition on the long-time series historical sound speed profile data to extract the background sound speed profile and the first few order EOF basis functions;

[0121] The historical data acquisition module is used to obtain the sound speed at a fixed depth of the historical sound speed profile data based on the depth corresponding to the extreme point of the first order EOF;

[0122] The prediction module is used to predict the sound speed at a fixed depth within a subsequent period of time through an LSTM neural network;

[0123] The relationship model establishment module is used to establish a relationship model between the sound speed data at a fixed depth and the first few order EOF coefficients through a BP neural network;

[0124] The output module is used to input the sound speed at a fixed depth within a subsequent period of time obtained by the prediction module into the relationship model to realize the time series prediction of the sound speed profile.

[0125] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to the embodiments, those of ordinary skill in the art should understand that any modification or equivalent replacement of the technical solutions of the present invention does not depart from the spirit and scope of the technical solutions of the present invention, and they should all be covered within the scope of the claims of the present invention.

Claims

1. A method for predicting the time series of sound speed profiles under significant changes in the background field, comprising: Step 1: Perform EOF decomposition on the long-time series of historical sound speed profile data, and extract the background sound speed profile and the first few EOF basis functions; Step 2: Based on the depth corresponding to the extreme point of the first-order EOF, obtain the sound speed at a fixed depth in the historical sound speed profile data; Step 3: Predict the sound speed at a fixed depth within a subsequent period of time through an LSTM neural network; Step 4: Establish a relationship model between the sound speed data at a fixed depth and the first few EOF coefficients through a BP neural network; Step 5: Input the sound speed at a fixed depth within a subsequent period of time obtained in Step 3 into the relationship model in sequence to achieve the prediction of the time series of the sound speed profile; In the LSTM neural network in Step 3, the input is the sound speed at a fixed depth in the historical sound speed profile data, and the output is the sound speed value at a fixed depth within a subsequent period of time.

2. The method for predicting the time series of the sound speed profile under significant changes in the background field according to claim 1, wherein The extraction of the background sound speed profile in Step 1 includes: There are N sound velocity profiles set, and each profile is interpolated into M standard layers to obtain the sound velocity matrix C M×N : In the formula, each column represents the value of a sound speed profile at the standard depth, and each row represents the sound speed of all sound speed profiles at the same depth; Average each layer of the N sound velocity profiles to obtain the average sound velocity profile That is, the background sound velocity profile: In the formula, T is the transpose, and i represents the i-th sound speed profile, where i ∈ [1, N].

3. The method for predicting the time series of the sound speed profile under significant changes in the background field according to claim 2, characterized in that, The first few EOF basis functions in Step 1 include: Expand the background sound speed profile to obtain the background sound speed profile matrix Subtract the sound speed profile matrix C M×N from the background sound speed profile matrix to obtain the perturbation matrix ΔC of each profile relative to the background field M×N : The covariance matrix R of the perturbation matrix is obtained according to the following formula M×M :[[]]END]] Obtain through eigenvalue decomposition: R M×M V M×M = λ M×M V M×M where λ M×M represents the eigenvalue matrix, and V M×M is the EOF basis function; Project from EOF to the perturbation matrix ΔC according to the following formula M×N to obtain the EOF coefficient matrix A M×N as follows:

4. The method for predicting the time series of the sound speed profile under significant changes in the background field according to claim 1, wherein The method further includes the training steps of the BP neural network, including: Set the number of training rounds, the minimum error of the training target, and the learning rate, and train using the sound speed data at the depth corresponding to the first-order EOF extreme point in the training set When the minimum error of the training target is reached or the maximum number of training times is reached, complete the BP neural network training, and the output is the first few orders of EOF coefficients 5. The method for predicting the time series of the sound speed profile under the significant change of the background field according to claim 4, wherein Step 5 includes: Input the depth - constant sound speed in the subsequent period obtained in step 3 into the relationship model established in step 4 to obtain the first few EOF coefficients as the reconstruction coefficient α j , where j represents the order; The background sound speed profile obtained according to Step 1 and the EOF basis function v j (z) corresponding to different depths z of seawater layers. Using the first few orders of EOF to complete the reconstruction of any sound speed profile, the reconstructed sound speed profile Realize the time series prediction of the sound speed profile:

6. A system for the method of predicting the time series of sound speed profiles under significant changes in the background field according to claim 1, characterized in that, Includes: An EOF decomposition module for performing EOF decomposition on the long-time series of historical sound speed profile data and extracting the background sound speed profile and the first few EOF basis functions; A historical data acquisition module for obtaining the sound speed at a fixed depth in the historical sound speed profile data based on the depth corresponding to the extreme point of the first-order EOF; A prediction module for predicting the sound speed at a fixed depth within a subsequent period of time through an LSTM neural network; A relationship model establishment module for establishing a relationship model between the sound speed data at a fixed depth and the first few EOF coefficients through a BP neural network; and An output module for inputting the sound speed at a fixed depth within a subsequent period of time obtained by the prediction module into the relationship model in sequence to achieve the prediction of the time series of the sound speed profile.

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