Empirical sound velocity error modeling compensation method based on neural network

Abstract

The invention discloses an empirical sound velocity error modeling compensation method based on a neural network, which belongs to the technical field of ocean observation data processing, is used for sound velocity error modeling compensation, and comprises the following steps: carrying out data alignment on observation data of CTD and SVP; comparing and analyzing the difference between the sound velocity value calculated by the CTD through an empirical formula and the sound velocity value directly measured by the SVP, and evaluating the correlation through a Pearson's correlation coefficient; constructing a nonlinear regression model by adopting a machine learning algorithm, and continuously optimizing model parameters; establishing a model evaluation index to evaluate the compensated sound velocity precision; machine learning setting parameters are fed back and corrected, and the compensation model is continuously optimized. Compared with the prior art, the method has the advantages that the accuracy of CTD sound velocity calculation is improved, and the established mathematical model has universality and expandability and can be adjusted and optimized according to different sea areas and different measurement conditions; the marine observation cost can be reduced, and the utilization efficiency of the marine observation data can be improved.

Description

Technical Field

[0001] The present invention discloses an empirical sound speed error modeling compensation method based on a neural network, belonging to the technical field of marine observation data processing. Background Art

[0002] With the advancement of marine science towards refinement and intelligence, the high-precision measurement and analysis of marine physical parameters have become a research hotspot. Especially in the deep-sea field, the use of submersibles as a support platform is essential for conducting refined investigations, and accurate and reliable navigation and positioning technology is an important prerequisite for ensuring the operation of submersibles. Accurate navigation and positioning require accurate sound speed profile data as a support. In the marine exploration system, CTD and SVP, as basic equipment for obtaining key marine physical parameters, play an irreplaceable role. CTD, with its precise measurement capabilities for seawater conductivity, temperature, and depth, calculates the sound speed based on classical empirical formulas and is widely used in traditional marine research; SVP, on the other hand, uses acoustic principles to directly obtain sound speed data at different depths, providing an intuitive basis for marine acoustic research.

[0003] However, in the face of the challenges of the multi-scale and complex and variable marine environment in current marine observations, the existing CTD sound speed calculation methods have obvious shortcomings. On the one hand, most traditional CTD empirical formulas are fitted based on experimental data under specific sea areas and specific conditions, which are essentially a simplified empirical approximation. When facing extremely complex marine environments such as deep-sea hydrothermal areas and polar ice oceans, the fixed empirical coefficients in the formula are difficult to adapt to the complex and variable seawater characteristics, resulting in a significant increase in the sound speed calculation error. On the other hand, with the penetration of artificial intelligence and big data analysis in the field of marine science, the processing of marine observation data is developing towards real-time, efficient, and intelligent directions, but the existing technology lacks the in-depth fusion and intelligent mining of simultaneously observed CTD and SVP data and is difficult to meet the urgent needs of current marine research for high-precision and refined sound speed data. In addition, in practical application scenarios such as marine resource exploration and underwater vehicle navigation, even a small error in the sound speed data may cause serious consequences. Therefore, it is urgent to develop an innovative sound speed error compensation method based on multi-source data fusion and intelligent modeling. Summary of the Invention

[0004] The purpose of the present invention is to provide an empirical sound speed error modeling compensation method based on a neural network to solve the problem that the application of the CTD empirical formula for calculating the sound speed is limited in complex marine environments in the prior art.

[0005] An empirical sound speed error modeling compensation method based on a neural network includes:

[0006] S1. Obtain and read the observation data of CTD and SVP, align the two sets of data based on the observation time, and match the timestamps so that the CTD and SVP data relationships correspond at the same moment;

[0007] S2. Compare and analyze the difference between the sound speed values calculated by CTD through empirical formulas and the directly measured sound speed values of SVP, and evaluate the linear correlation between the sound speed values calculated from CTD data and the actually measured sound speed values of SVP through the Pearson correlation coefficient;

[0008] S3. Using the temperature, conductivity, depth measured by CTD, the sound speed value calculated by CTD through empirical formulas, and the directly measured sound speed value of SVP as variables, adopt a machine learning algorithm to construct a non - linear regression model. During the model training process, taking the actually measured sound speed of SVP as the target value and the CTD measurement parameters as the input values, continuously optimize the model parameters to minimize the error between the sound speed output by the model and the actually measured sound speed of SVP;

[0009] S4. Use the non - linear regression model established in S3 to compensate the sound speed calculated by the CTD empirical formula. Obtain the compensated sound speed value by calculating the sound speed value calculated by CTD through the empirical formula and the predicted sound speed correction value, and establish model evaluation indicators to evaluate the accuracy of the compensated sound speed;

[0010] S5. According to the evaluation of the compensated sound speed accuracy, feedback and correct the machine learning setting parameters, and continuously optimize the compensation model until the evaluation indicators meet the requirements.

[0011] S1 includes S1.1. Assume that the time series of CTD data is i is the i - th CTD data, N CTD is the total number of CTD data samples, t CTD,i is the time of the i - th CTD data; the time series of SVP data is j is the j - th SVP data, N SVP is the total number of SVP data samples, t SVP,j is the time of the j - th SVP data; set the time tolerance as Δt, and establish the corresponding relationship between CTD data and SVP data in time, satisfying |t CTD,i - t SVP,j | < Δt.

[0012] S1 includes S1.2. When there are cases where some time points cannot be precisely matched, use the linear interpolation algorithm to optimize the CTD data and SVP data;

[0013] For the temperature T data of CTD, if there is a k - th SVP data time point t CTD,i and t SVP,j and there is a k - th SVP data time point t SVP,k between them that satisfies tCTD,i <t SVP,k <t CTD,i+1 , calculate the CTD data value corresponding to the moment t using the linear interpolation algorithm, and interpolate to calculate the CTD temperature T SVP,k corresponding to the moment t SVP,k The temperature T of the CTD int erp (t SVP,k ) is as follows:

[0014]

[0015] In the formula, T() is the temperature value corresponding to the time point;

[0016] Interpolate the conductivity, depth, and SVP data of the CTD in the same way as the temperature T data of the CTD.

[0017] S1 includes S1.3. Introduce the dynamic time warping (DTW) algorithm to improve the accuracy of data alignment. By calculating the optimal matching path between two time series, the alignment of time series is achieved. Set the time series feature vector of the CTD data x i is the time eigenvalue vector composed of temperature, conductivity, and depth at the i-th time point, and the time series feature vector of the SVP data y j is the eigenvalue at the j-th time point. Construct an N CTD ×N SVP distance matrix D(i, j) to represent the distance between x i and y j . Calculate using the Euclidean distance:

[0018]

[0019] In the formula, x i1 , x i2 and x i3 are the first, second, and third eigenvalues of the i-th CTD data respectively, and y j1 , y j2 and y j3 are the first, second, and third eigenvalues of the j-th SVP data respectively;

[0020] Find the optimal path P from D(1, 1) to D(N CTD , N SVP ) through the dynamic programming algorithm:

[0021] P = [p1, p2,..., p M ;

[0022] p M = (i m , jm )

[0023] Wherein, p M is a point on the path, M is the path length, i m is the time series eigenvalue of the CTD data of the m-th point on p M , j m is the time series eigenvalue of the SVP data of the m-th point on p M . The preliminarily aligned data is recalibrated through the optimal path to align the CTD and SVP data in the time dimension.

[0024] S2 includes S2.1. The empirical formula for calculating the sound speed by CTD is:

[0025] c CTD = c0 + a1ΔT + a2ΔT 2 + a3ΔT 3 + a4S + a5SΔT + a6SΔT 2 + a7D + a8D 2 + a9DΔT + a 10 DS;

[0026] Wherein, c CTD is the sound speed value calculated by the CTD through the empirical formula, c0 is the reference sound speed, c0 takes the sound speed value under standard conditions, ΔT is the change in temperature relative to the reference temperature, D is the depth, S is the salinity, a f is the empirical coefficient, and f takes values from 1 to 10;

[0027] S2.2. Calculate the deviation Δc between c CTD and the measured sound speed c SVP of SVP as:

[0028] Δc = c SVP - c CTD ;

[0029] S2.3. Use the Pearson correlation coefficient to perform a correlation analysis on c CTD and c SVP . The Pearson correlation coefficient r is:

[0030]

[0031] Wherein, and are respectively the sound speed value calculated by the CTD empirical formula of the i1-th and the measured sound speed value of SVP, and are respectively c CTD and c SVPThe average value, where n is the total number of sound speed values, r ranges from [-1, 1]. When r meets the set correlation coefficient threshold, it is considered that there is a correlation basis between the two sets of data, and S3 is performed.

[0032] S3 includes S3.1. Design a deep neural network structure with hidden layers. The input layer contains 5 neurons, corresponding to the temperature T, conductivity C, depth D, c CTD and c SVP , the hidden layer is set to 3 layers, and the number of neurons in each layer is 32, 16, and 8 respectively. By gradually reducing the number of neurons, feature extraction and dimensionality reduction processing are performed on the input data. The output layer is 1 neuron, and the predicted sound speed correction value Δc is output. pred ;

[0033] S3.2. Before model training, initialize the weight matrix W(l) and bias vector b(l) of the neural network. The weight matrix W(l) uses the random initialization method and is randomly sampled from a normal distribution with a mean of 0 and a standard deviation of 0.1, so that each neuron has a different weight distribution at the initial time. The bias vector b(l) is initialized to 0 to provide a basic offset for the activation of the neurons.

[0034] S3 includes S3.3. The transfer function between the hidden layer neurons uses the ReLU function f(x), f(x) = max(0, x), where x is the CTD measurement parameter. When the input x is greater than 0, the output is x, enabling the neurons to respond to positive inputs; when the input x is less than or equal to 0, the output is 0, suppressing negative inputs, so that the neural network can learn feature representations.

[0035] S3 includes S3.4. Divide the aligned CTD and SVP data into training set, validation set, and test set, with proportions of 70%, 15%, and 15% respectively. The training set is used to update the model parameters, the validation set is used to monitor the training process of the model, and the test set is used to evaluate the final performance of the model. The backpropagation algorithm is used to calculate the error between the model prediction value and the true value with the mean square error MES:

[0036]

[0037] In the formula, is the i1th predicted sound speed value;

[0038] During the backpropagation process, the weights and biases are updated based on the error gradients, and the Adam optimizer is used to dynamically adjust the learning rate. The initial learning rate is set to 0.001 and adjusted during training according to the loss change on the validation set. If the validation set loss does not decrease for 5 consecutive epochs, the learning rate is reduced to 0.5 times the original value to balance the model's convergence speed and accuracy. After each epoch of training, the model performance is evaluated on the validation set, and the validation set loss and accuracy are recorded. When the validation set loss no longer decreases, the training is stopped and the model parameters are saved;

[0039] S3.5. After training is completed, the mean absolute error and coefficient of determination are introduced, and the model is evaluated using the test set. The mean absolute error MAE is as follows:

[0040]

[0041] Coefficient of determination R 2 is as follows:

[0042]

[0043] In the formula, is the compensated sound speed for the i1-th one.

[0044] S4 includes S4.1. Through Δc pred and c CTD calculate the compensated sound speed value c compensated :

[0045] c compensated = c CTD + Δc pred ;

[0046] S4.2. Use evaluation metrics to evaluate the accuracy of the compensated sound speed. The evaluation metrics include root mean square error, mean absolute error, and mean absolute percentage error. The mean absolute percentage error MAPE is as follows:

[0047]

[0048] In the formula, is the compensated sound speed value for the i1-th one.

[0049] S5 includes feedback correction of the machine learning setting parameters according to the evaluation results of the compensated sound speed accuracy. If the RMSE value is too large, it indicates that the fluctuations of the model prediction values are large, and the learning rate is reduced to make the model more stable during parameter updates;

[0050] If the MAE value is too large, it indicates that the average error of the model is large, and the number of neurons in the hidden layer is increased or the hidden layer structure is adjusted to enhance the model's learning ability for data features and reduce the average error;

[0051] When the MAPE value deviates greatly, it indicates that the relative error of the model for data of different magnitudes is large, and the data is normalized.

[0052] Compared with the prior art, the present invention has the following beneficial effects: By using the simultaneously observed CTD and SVP data, through the establishment of a neural network mathematical model and an error compensation method, the accuracy of calculating the sound speed by CTD is improved, providing more reliable data support for fields such as marine acoustic research and marine exploration; the established mathematical model has universality and scalability, and can be adjusted and optimized according to different sea areas and different measurement conditions to adapt to diverse marine environments; it helps to reduce the cost of marine observations and improve the utilization efficiency of marine observation data. Description of the Drawings

[0053] Figure 1 is the technical flow chart of the present invention. Detailed Embodiments

[0054] To make the objectives, technical solutions and advantages of the present invention clearer, the technical solutions in the present invention are described clearly and completely below. Obviously, the described embodiments are some but not all of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without making creative efforts fall within the scope of protection of the present invention.

[0055] The technical flow chart of the present invention is as Figure 1 shown. An empirical sound speed error modeling and compensation method based on a neural network includes steps of data acquisition, data preprocessing, data alignment, sound speed calculation and comparison, model construction and training, model evaluation, application of the compensation model, and model optimization and iteration.

[0056] An empirical sound speed error modeling and compensation method based on a neural network includes:

[0057] S1. Obtain and read the observation data of CTD and SVP, align the two sets of data based on the observation time, and make the relationship between the CTD and SVP data correspond at the same moment through timestamp matching;

[0058] S2. Compare and analyze the difference between the sound speed value calculated by CTD through an empirical formula and the sound speed value directly measured by SVP, and evaluate the linear correlation between the sound speed value calculated from the CTD data and the actually measured sound speed value of SVP through the Pearson correlation coefficient;

[0059] S3. Using the temperature, conductivity, depth measured by CTD, the sound speed value calculated by CTD through an empirical formula, and the sound speed value directly measured by SVP as variables, a non-linear regression model is constructed using a machine learning algorithm. During the model training process, with the measured sound speed of SVP as the target value and the CTD measurement parameters as the input values, the model parameters are continuously optimized to minimize the error between the sound speed output by the model and the measured sound speed of SVP;

[0060] S4. Use the non-linear regression model established in S3 to compensate the sound speed calculated by the CTD empirical formula. The compensated sound speed value is obtained by calculating the sound speed value calculated by CTD through the empirical formula and the predicted sound speed correction value, and a model evaluation index is established to evaluate the accuracy of the compensated sound speed;

[0061] S5. According to the evaluation of the compensated sound speed accuracy, feedback and correct the machine learning setting parameters, and continuously optimize the compensation model until the evaluation index meets the requirements.

[0062] S1 includes S1.1. Assume that the time series of CTD data is i is the i-th CTD data, N CTD is the total number of CTD data samples, t CTD,i is the time of the i-th CTD data; the time series of SVP data is j is the j-th SVP data, N SVP is the total number of SVP data samples, t SVP,j is the time of the j-th SVP data; set the time tolerance to Δt, and establish the corresponding relationship between CTD data and SVP data in time, satisfying |t CTD,i -t SVP,j |<Δt.

[0063] S1 includes S1.2. When there is a situation where some time points cannot be precisely matched, the linear interpolation algorithm is used to optimize the CTD data and SVP data;

[0064] For the temperature T data of CTD, if there is a k-th SVP data time point t CTD,i and t SVP,j satisfying t SVP,k <t CTD,i <t SVP,k <t CTD,i+1 , use the linear interpolation algorithm to calculate the CTD data value corresponding to the time point t SVP,k , and interpolate to calculate the CTD temperature T SVP,k corresponding to the time point t int erp (t SVP,k ) is:

[0065]

[0066] Wherein, T() represents the temperature value corresponding to the time point;

[0067] Interpolate the conductivity, depth, and SVP data of the CTD in the same manner as the temperature T data of the CTD.

[0068] S1 includes S1.3. Introduce the dynamic time warping (DTW) algorithm to improve the accuracy of data alignment. By calculating the optimal matching path between two time series, the alignment of time series is achieved. Set the time series feature vector of the CTD data x i is the time eigenvalue vector composed of temperature, conductivity, and depth at the i-th time point, and the time series feature vector of the SVP data y j is the eigenvalue at the j-th time point. Construct an N CTD ×N SVP distance matrix D(i, j) to represent the distance between x i and y j . Calculate using the Euclidean distance:

[0069]

[0070] Wherein, x i1 , x i2 and x i3 are the first, second, and third eigenvalues of the i-th CTD data respectively, and y j1 , y j2 and y j3 are the first, second, and third eigenvalues of the j-th SVP data respectively;

[0071] Find the optimal path P from D(1, 1) to D(N CTD , N SVP ) through the dynamic programming algorithm:

[0072] P = [p1, p2,..., p M ;

[0073] p M = (i m , j m );

[0074] Wherein, p M is the point on the path, M is the path length, i m is the time series eigenvalue of the CTD data of the m-th point on p M , and j m is the time series eigenvalue of the SVP data of the m-th point on p MThe time series eigenvalue of the SVP data at the m-th point on is used to re-calibrate the preliminarily aligned data through the optimal path, so that the CTD and SVP data are aligned in the time dimension.

[0075] S2 includes S2.1. The empirical formula for calculating the sound speed by CTD is:

[0076] c CTD = c0 + a1ΔT + a2ΔT 2 + a3ΔT 3 + a4S + a5SΔT + a6SΔT 2 + a7D + a8D 2 + a9DΔT + a 10 DS;

[0077] In the formula, c CTD is the sound speed value calculated by CTD through the empirical formula, c0 is the reference sound speed, c0 takes the sound speed value under standard conditions, ΔT is the change in temperature relative to the reference temperature, D is the depth, S is the salinity, a f is the empirical coefficient, and f takes values from 1 to 10;

[0078] S2.2. Calculate the deviation Δc between c CTD and the measured sound speed c SVP of SVP as:

[0079] Δc = c SVP - c CTD ;

[0080] S2.3. Use the Pearson correlation coefficient to analyze the correlation between c CTD and c SVP . The Pearson correlation coefficient r is:

[0081]

[0082] In the formula, and are respectively the sound speed value calculated by the CTD empirical formula for the i1-th and the measured sound speed value of SVP. and are respectively the average values of c CTD and c SVP . n is the total number of sound speed values. The value range of r is [-1, 1]. When r meets the set correlation coefficient threshold, it is considered that there is a correlation basis between the two groups of data, and S3 is carried out.

[0083] S3 includes S3.1. Design a deep neural network structure with a hidden layer. The input layer contains 5 neurons, corresponding to the temperature T, conductivity C, depth D, c CTD and c SVP, the hidden layer is set to 3 layers, and the number of neurons in each layer is 32, 16, and 8 respectively. By gradually reducing the number of neurons, feature extraction and dimensionality reduction processing are performed on the input data. The output layer has 1 neuron, which outputs the predicted sound speed correction value Δc pred ;

[0084] S3.2. Before model training, the weight matrix W(l) and bias vector b(l) of the neural network are initialized. The weight matrix W(l) is randomly initialized by sampling from a normal distribution with a mean of 0 and a standard deviation of 0.1, so that each neuron has a different weight distribution initially. The bias vector b(l) is initialized to 0 to provide a basic offset for the activation of neurons.

[0085] S3 includes S3.3. The transfer function between hidden layer neurons uses the ReLU function f(x), f(x) = max(0, x), where x is the CTD measurement parameter. When the input x is greater than 0, the output is x, enabling the neuron to respond to positive inputs; when the input x is less than or equal to 0, the output is 0, suppressing negative inputs, so that the neural network can learn feature representations.

[0086] S3 includes S3.4. The aligned CTD and SVP data are divided into a training set, a validation set, and a test set, with proportions of 70%, 15%, and 15% respectively. The training set is used to update model parameters, the validation set is used to monitor the training process of the model, and the test set is used to evaluate the final performance of the model. The backpropagation algorithm is used to calculate the error between the model prediction value and the true value with the mean square error MSE:

[0087]

[0088] In the formula, is the i1-th predicted sound speed value;

[0089] During the backpropagation process, the weights and biases are updated according to the error, and the Adam optimizer is used to dynamically adjust the learning rate. The initial learning rate is set to 0.001 and adjusted according to the loss change on the validation set during training. If the validation set loss does not decrease for 5 consecutive epochs, the learning rate is reduced to 0.5 times the original to balance the convergence speed and accuracy of the model. After each epoch of training, the model performance is evaluated on the validation set, and the validation set loss and accuracy are recorded. When the validation set loss no longer decreases, training is stopped and the model parameters are saved;

[0090] S3.5. After training is completed, the mean absolute error and coefficient of determination are introduced, and the test set is used to evaluate the model. The mean absolute error MSE is:

[0091]

[0092] Coefficient of determination R 2 is as follows:

[0093]

[0094] In the formula, is the i1-th compensated sound velocity.

[0095] S4 includes S4.1. Through Δc pred and c CTD calculate the compensated sound velocity value c compensated :

[0096] c compensated = c CTD + Δc pred ;

[0097] S4.2. Use evaluation indicators to evaluate the accuracy of the compensated sound velocity. The evaluation indicators include root mean square error, mean absolute error, and mean absolute percentage error. The mean absolute percentage error MAPE is as follows:

[0098]

[0099] In the formula, is the i1-th compensated sound velocity value.

[0100] S5 includes making feedback corrections to the machine learning setup parameters according to the evaluation results of the compensated sound velocity accuracy. If the RMSE value is too large, it indicates that the fluctuations of the model prediction values are large, and the learning rate is reduced to make the model more stable during parameter update;

[0101] If the MAE value is too large, it indicates that the average error of the model is large. Increase the number of neurons in the hidden layer or adjust the hidden layer structure to enhance the model's learning ability for data features and reduce the average error;

[0102] When the MAPE value deviates greatly, it indicates that the relative error of the model for data of different magnitudes is large, and the data is normalized.

[0103] To more comprehensively evaluate the deviation situation, indicators such as mean absolute error (MAE) and root mean square error (RMSE) are introduced. The mean absolute error reflects the average absolute value of the sound velocity deviation and can intuitively reflect the average error level. Since the root mean square error squares the errors, RMSE highlights the influence of larger errors and is used to measure the overall dispersion degree of the errors. By analyzing the variation trends of MAE and RMSE with depth or other parameters, the error characteristics of the CTD empirical formula under different conditions can be understood. MAPE shows the proportional difference between the compensated sound velocity and the measured sound velocity from the perspective of relative error, and is especially suitable for error comparison between data of different magnitudes.

[0104] Present the sound speed comparison results in a visual manner and plot the sound speed-depth curve, where the abscissa is the depth and the ordinate is c SVP and c CTD , and distinguish them with different colors or line types. At the same time, plot the variation curve of the deviation Δc with depth in the figure to intuitively observe the difference between the sound speed calculated by CTD and the measured sound speed of SVP at different depths. It is also possible to plot the variation curves of MAE and RMSE with depth to further show the distribution characteristics of errors at different depths, providing intuitive data support for subsequent error compensation and model optimization.

[0105] The above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that: they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements on some or all of the technical features, and these modifications or replacements do not make the essence of the corresponding technical solutions deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. An empirical sound velocity error modeling and compensation method based on a neural network, characterized in that Including: S1. Obtain and read the observation data of CTD and SVP, align the two sets of data based on the observation time, and through timestamp matching, make the data relationship between CTD and SVP correspond at the same moment; S2. Compare and analyze the difference between the sound speed values calculated by CTD through empirical formulas and the directly measured sound speed values of SVP, and evaluate the linear correlation between the sound speed values calculated from CTD data and the actually measured sound speed values of SVP through the Pearson correlation coefficient; S3. Using the temperature, conductivity, depth measured by CTD, the sound speed value calculated by CTD through empirical formulas, and the directly measured sound speed value of SVP as variables, construct a non-linear regression model using machine learning algorithms. During the model training process, taking the actually measured sound speed of SVP as the target value and the CTD measurement parameters as the input values, continuously optimize the model parameters to minimize the error between the sound speed output by the model and the actually measured sound speed of SVP; S4. Use the non-linear regression model established in S3 to compensate the sound speed calculated by the CTD empirical formula. Obtain the compensated sound speed value by calculating the sound speed value calculated by CTD through the empirical formula and the predicted sound speed correction value, and establish a model evaluation index to evaluate the accuracy of the compensated sound speed; S5. According to the evaluation of the compensated sound speed accuracy, feedback and correct the machine learning setting parameters, and continuously optimize the compensation model until the evaluation index meets the requirements.

2. The empirical sound velocity error modeling compensation method based on a neural network according to claim 1, wherein S1 includes S1.

1. Assume that the time series of CTD data is i is the i-th CTD data, N CTD is the total number of CTD data samples, t CTD,i is the time of the i-th CTD data; The time series of SVP data is $j$ is the $j$-th SVP data, and $N$ SVP is the total number of SVP data samples, and $t$ SVP,j is the time of the $j$-th SVP data; Set the time tolerance as Δt, and establish the temporal correspondence between CTD data and SVP data, satisfying |t CTD,i - t SVP,j | < Δt.

3. The empirical sound velocity error modeling compensation method based on a neural network according to claim 2, characterized in that S1 includes S1.

2. When there is a situation where precise matching cannot be achieved at some time points, use the linear interpolation algorithm to optimize the CTD data and SVP data; For the temperature T data of the CTD, if there is a k-th SVP data time point t CTD,i and t SVP,j such that the time point t SVP,k satisfies t CTD,i <t SVP,k <t CTD,i+1 , use the linear interpolation algorithm to calculate the CTD data value corresponding to the time point t SVP,k . Interpolate to calculate the CTD temperature T SVP,k at the time point t int erp (t SVP,k ) as follows: In the formula, T() is the temperature value corresponding to the time point; Interpolate the conductivity and depth of CTD and SVP data in the same way as the temperature T data of CTD.

4. The empirical sound velocity error modeling compensation method based on a neural network according to claim 3, characterized in that, S1 includes S1.

3. Introduce the dynamic time warping (DTW) algorithm to improve the accuracy of data alignment. By calculating the optimal matching path between two time series, the alignment of time series is achieved, and the time series feature vector of CTD data is set x i is the time eigenvalue quantity composed of temperature, conductivity and depth at the i-th time point, and the time series feature vector of SVP data y j is the eigenvalue at the j-th time point. Construct an N CTD ×N SVP distance matrix D(i, j), representing x i and y j The distance between them is calculated using the Euclidean distance: where x i1 , x i2 and x i3 are the 1st, 2nd, and 3rd eigenvalues of the i-th CTD data respectively, and y j1 , y j2 and y j3 are the 1st, 2nd, and 3rd eigenvalues of the j-th SVP data respectively; Finding the optimal path P from D(1,1) to D(N CTD ,N SVP ) by the dynamic programming algorithm: P = [p1, p2,..., p M ; p M = (i m , j m ); Where p M is a point on the path, M is the path length, i m is the time series eigenvalue of the CTD data of the m-th point on p M , j m is the time series eigenvalue of the SVP data of the m-th point on p M . The initially aligned data is recalibrated through the optimal path to align the CTD and SVP data in the time dimension.

5. The empirical sound velocity error modeling compensation method based on a neural network according to claim 4, wherein, S2 includes S2.

1. The empirical formula for CTD to calculate sound speed is: c CTD = c0 + a1ΔT + a2ΔT 2 + a3ΔT 3 + a4S + a5SΔT + a6SΔT 2 + a7D + a8D 2 + a9DΔT + a 10 DS; where c CTD is the sound velocity value calculated by the CTD through the empirical formula, c0 is the reference sound velocity, c0 takes the sound velocity value under standard conditions, ΔT is the change in temperature relative to the reference temperature, D is the depth, S is the salinity, a f is the empirical coefficient, and f ranges from 1 to 10; S2.

2. Calculate c CTD The deviation Δc from the actually measured sound velocity c of SVP SVP is: Δc = c SVP -c CTD ; S2.

3. Use the Pearson correlation coefficient for c CTD and c SVP to conduct a correlation analysis. The Pearson correlation coefficient r is as follows: Wherein, and are the sound speed values calculated by the i1-th CTD empirical formula and the measured sound speed values of SVP respectively, and are the average values of c CTD and c SVP respectively, n is the total number of sound speed values, the value range of r is [-1, 1]. When r meets the set correlation coefficient threshold, it is considered that there is a correlation basis between the two groups of data, and S3 is performed.

6. The empirical sound velocity error modeling compensation method based on a neural network according to claim 5, wherein S3 includes S3.

1. Design a deep neural network structure with hidden layers. The input layer contains 5 neurons, corresponding to the temperature T, conductivity C, depth D, c CTD and c SVP measured by CTD respectively. The hidden layer is set to 3 layers, and the number of neurons in each layer is 32, 16, and 8 respectively. By gradually reducing the number of neurons, feature extraction and dimensionality reduction processing are performed on the input data. The output layer is 1 neuron, and the output is the predicted sound speed correction value Δc pred ; S3.

2. Before model training, initialize the weight matrix W(l) and bias vector b(l) of the neural network. The weight matrix W(l) is randomly initialized by sampling from a normal distribution with a mean of 0 and a standard deviation of 0.1, so that each neuron has a different weight distribution at the beginning. The bias vector b(l) is initialized to 0 to provide a basic offset for the activation of the neuron.

7. A method for modeling and compensating the empirical sound speed error based on a neural network according to claim 6, characterized in that S3 includes S3.

3. The transfer function between the neurons in the hidden layer adopts the ReLU function f(x), f(x)=max(0,x), where x is the CTD measurement parameter. When the input x is greater than 0, the output is x, enabling the neuron to respond to positive inputs; when the input x is less than or equal to 0, the output is 0, suppressing negative inputs, so that the neural network can learn feature representations.

8. A method for modeling and compensating the empirical sound speed error based on a neural network according to claim 7, characterized in that S3 includes S3.

4. Divide the aligned CTD and SVP data into a training set, a validation set, and a test set, with proportions of 70%, 15%, and 15% respectively. The training set is used for updating model parameters, the validation set is used for monitoring the training process of the model, and the test set is used for evaluating the final performance of the model. Adopt the backpropagation algorithm to calculate the error between the model prediction value and the true value using the mean squared error MES: In the formula, is the i1-th predicted sound velocity value; During the backpropagation process, the gradients of the weights and biases are updated according to the error, and the Adam optimizer is used to dynamically adjust the learning rate. The initial learning rate is set to 0.001 and adjusted during the training process according to the loss change on the validation set. If the validation set loss does not decrease for 5 consecutive epochs, the learning rate is reduced to 0.5 times the original value to balance the convergence speed and accuracy of the model. After each epoch of training, the model performance is evaluated on the validation set, and the validation set loss and accuracy are recorded. When the validation set loss no longer decreases, the training is stopped and the model parameters are saved; S3.

5. After the training is completed, the mean absolute error and the coefficient of determination are introduced, and the model is evaluated using the test set. The mean absolute error MAE is as follows: Coefficient of determination R 2 is as follows: In the formula, is the i1-th compensated sound velocity.

9. A method for modeling and compensating the empirical sound speed error based on a neural network according to claim 8, characterized in that S4 includes S4.

1. By Δc pred and c CTD calculate the compensated sound speed value c compensated : c compensated = c CTD + Δc pred ; S4.

2. The compensated sound speed accuracy is evaluated using evaluation metrics, including the root mean square error, mean absolute error, and mean absolute percentage error. The mean absolute percentage error MAPE is as follows: In the formula, is the compensated sound velocity value of the i1-th.

10. A method for modeling and compensating the empirical sound velocity error based on a neural network according to claim 9, characterized in that S5 includes feedback correction of the machine learning setting parameters according to the evaluation results of the compensated sound speed accuracy. If the RMSE value is too large, it indicates that the fluctuation of the model prediction value is large, and the learning rate is reduced to make the model more stable during parameter update; If the MAE value is too large, it indicates that the average error of the model is large. Increase the number of neurons in the hidden layer or adjust the hidden layer structure to enhance the model's learning ability for data features and reduce the average error; When the MAPE value deviates greatly, it indicates that the relative error of the model on data of different magnitudes is large, and the data is normalized.

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