Att-KAN neural network model-based sound velocity distribution forecasting method

Abstract

The invention discloses a sound velocity distribution forecasting method based on an Att-KAN neural network model, and belongs to the technical field of ocean observation. According to the method, an Att-KAN neural network model is constructed, prediction time resolution, prediction starting time and prediction maximum time length are specified according to a task, prediction iteration times and historical sound velocity distribution reference data corresponding to the prediction starting time are determined, and the prediction time resolution, the prediction starting time and the prediction maximum time length are calculated. And taking four or more integral change cycle data at the moment before the forecast starting time as a training set of the model to obtain a prediction result, and performing normalization processing on the result. According to the method, the problem of prediction of underwater sound velocity profile distribution in the time dimension is solved, sound velocity distribution at future moments can be accurately predicted in real time, and sound velocity distribution at specified time resolution intervals in the future is estimated; the problems of insufficient time resolution of ocean sound velocity distribution estimation and lack of future sound velocity forecasting function are solved, and important guiding significance is provided for ocean scientific research.

Description

Technical Field

[0001] The present invention relates to the field of ocean observation technology, and in particular to a sound speed distribution prediction method of a Kolmogorov-Arnold neural network (Att-KAN) based on an attention mechanism. Background Art

[0002] At present, most of the research on underwater sound speed distribution is based on the spatial dimension, and most of them rely on real-time sonar observation data and related data such as temperature field and salinity field. There are relatively few studies on sound speed field based on the time dimension. Wuhan University proposed a three-dimensional underwater sound speed inversion framework assisted by autonomous underwater vehicles with collaborative ray tracing and artificial intelligence models, which can quickly obtain three-dimensional sound speed distribution. However, due to the need for the assistance of autonomous underwater vehicles, it faces the problems of high system complexity and high R&D costs. Li Qianqian and others from Shandong University of Science and Technology proposed a method for inverting the full-depth water temperature profile based on a small amount of fixed-depth temperature data, and then indirectly estimated the sound speed distribution. This method combines empirical orthogonal function (EOF) decomposition and back propagation (BP) neural network, uses a marine mobile platform to obtain a small amount of fixed-depth temperature data in real time, and efficiently and accurately inverts the full-depth water temperature profile through data processing and model reconstruction, which is then used for sound speed distribution estimation. However, this method still requires real-time underwater temperature data measurement operations, cannot provide large-scale real-time sound speed distribution estimation, and cannot capture the dynamic change characteristics of sound speed distribution.

[0003] The existing underwater sound speed profile distribution estimation method needs to be measured and collected through sonar observation technology, and still relies on the underwater real-time data measurement operation system, making it difficult to achieve real-time estimation and prediction of the sound speed distribution. Summary of the invention

[0004] The present invention proposes a sound speed distribution prediction method based on a Kolmogorov-Arnold neural network assisted by an attention mechanism. The historical sound speed profile data of the spatial area where the task is located is used as a reference, and the historical sound speed profile distribution sorted in chronological order is used to accurately predict the future sound speed distribution of the target area, so as to make up for the shortcomings of the existing technology.

[0005] To achieve the above object, the present invention adopts the following technical solutions: A method for predicting sound velocity distribution based on an Att-KAN neural network model comprises the following steps: S1: Collect spatial historical sound speed data sets as reference data for sound speed profiles; S2: Determine the time resolution according to the sound speed distribution prediction task requirements, and use Indicates; forecast start time, using and the maximum forecast time length, expressed as express; S3: secondary screening of the spatial historical sound speed dataset, and performing standardized interpolation in depth and time dimensions; S4: preprocessing and classification of the sound velocity distribution sample data after screening and standardized interpolation in S3; S5: Construct Att-KAN neural network model: The model includes data input layer, attention mechanism layer, KAN layer, fully connected layer and output layer; take 3 layers of KAN linear layer and 1 layer of fully connected layer as hidden layer, the number of neurons in the hidden layer is N1, N2, N3, N3 respectively; Att-KAN neural network model is a neural network similar to multi-layer perceptron. In addition to using commonly used activation functions, it also adds a B-spline function group. The output of the Att-KAN layer is the sum of the output of the activation function and the output of the B-spline function. At the same time, an attention mechanism layer is added before the KAN layer formed by stacking 3 layers of KAN linear layers; For each depth layer, the Att-KAN network model is constructed, and the prediction result is a length of Output sound speed value time series; S6: The Att-KAN neural network model is trained and verified, and the model processing results are normalized and output; S7: The Att-KAN neural network model performs prediction: according to the task specified forecast time resolution, forecast start time, and forecast maximum time length, the number of forecast iterations and the historical sound speed distribution reference data corresponding to the forecast start time are determined. The prediction result can be obtained by taking the data of 4 or more whole change cycles before the forecast start time as the training set of the model, and the result is normalized by S6 to output the predicted future sound speed distribution data.

[0006] Furthermore, in S1, the spatial coordinates are specified as longitude M° and latitude N° according to the sound speed distribution prediction task, and the sound speed profile data measured at different historical moments in the spatial region are selected from the global Argo data set to form a spatial historical sound speed data set.

[0007] Furthermore, in S3, according to the time resolution of the sound speed distribution forecast, the spatial historical sound speed data set of S1 is dynamically secondary filtered to form a historical sound speed distribution time standardized data set as training reference data. The training data covers a time range that includes at least 4 complete change cycles of data. For example, when the forecast time resolution unit is "hour", the sample must cover no less than 4 full day cycles, that is, the sample data of no less than 4 days before the forecast moment must be filtered; when the forecast time resolution is "month", the sample must cover no less than 4 full year cycles, that is, the sample data of no less than 4 years before the forecast moment must be filtered. The selected data are sequentially subjected to standardized linear layered interpolation in depth direction and standardized interpolation in time direction; the standardized interpolation method in depth direction is as follows: from 0 to 10 meters, one layer is divided every 5 meters; from 10 to 180 meters, one layer is divided every 10 meters; from 180 to 460 meters, one layer is divided every 20 meters; from 500 to 1250 meters, one layer is divided every 50 meters; from 1300 to 1900 meters, one layer is divided every 100 meters; the depth exceeding 1900 meters is one layer, and a total of 58 layers are divided. The selected data are interpolated in time dimension, and the interpolation time interval is equal to the forecast time resolution.

[0008] Furthermore, in S3: The time-normalized data set of historical sound speed distribution is expressed as: ; in represents the ith sound velocity profile, there are I in total, and the ith sound velocity profile is further expressed as: ; in is the speed of sound, unit: m / s, subscript Expressed as depth layers, " represents the transpose of the vector; in formula (1), the S data set is arranged in time order, and the time interval and time resolution are Consistency; = 0,1,…,J, where is the depth layer index label, and the maximum depth layer of the full ocean depth sound speed distribution is dJ; Formula (1) can be expanded to obtain the sound speed data matrix: ; After the historical sound speed distribution time-normalized data set is collected, it is transferred to S4.

[0009] Further, the S4 includes: S4-1: Divide the training set and validation set The historical sound speed distribution time standardization data set S is a sound speed value data matrix with J rows and I columns. The first IC columns of the historical sound speed distribution time standardization data set S are divided into the training data set T, as shown in formula (4); the last C columns of S are used as the verification data set E, as shown in formula (5), where IC≥4C; S4-2: Data preprocessing: The training data set T is normalized as , the normalization formula is shown in formula (6), where is the normalized data, To normalize the data, is the mean of the sequence data, is the standard deviation of the sequence data; A certain depth From formula (7), we can get: It means to sum the j-th row data of matrix T from the first column to the last column; From formula (8), we get: S4-3: Then normalize the training data set Specifically divided into training input set and training label set ; The training input set X is shown in formula (10), and the training label set Y is shown in formula (11); ; ; ; ; ; ; ; ; S4-4: Split the training input set and training label set again according to the depth layer The training input set and training label set are divided into , ; , They are expressed by formulas (12) and (13) respectively; ; ; It means that for the data of the j-th row of matrix X, each sliding window takes data of size C, and the sliding window step size is 1; It means that for the j-th row of data in matrix Y, each sliding window takes data of size 1, and the sliding window step size is 1; After the sound velocity distribution sample data preprocessing is completed, it goes to S5.

[0010] Further, the S5 includes: According to the different depth layers, the sound velocity distribution prediction is performed in layers, and an Att-KAN network is constructed for each depth layer. For each Att-KAN network constructed for each depth layer, the prediction result is a length of The output sound speed value time series.

[0011] Take 3 Att-KAN linear layers and 1 fully connected layer as hidden layers, and the number of neurons in the hidden layers are N1, N2, N3, and N3 respectively. Att-KAN is a neural network similar to a multi-layer perceptron. In addition to using the commonly used activation function, it also adds a B-spline function group. The output of the Att-KAN layer is the sum of the output of the activation function and the output of the B-spline function. 'SiLU' and 'B-Spline' represent the SiLU activation function and the B-Spline function group respectively: ; ; Where i is the number of neurons in the current Att-KAN layer, It follows a normal distribution with a mean of 0 and a standard deviation of 0.1. is the B-spline function; The output of each Att-KAN layer is expressed as , yes Additive summation of and B-spline(x): .

[0012] Further, the S6 includes: S6-1: Before model training, determine the learning rate of each depth layer. And the number of iterations is , represents the corresponding depth layer, j=1, 2,…, J; S6-2: During model training, the Att-KAN network model of each depth layer is trained separately. Represents the Att-KAN network of the jth depth layer. The input and output of the model are expressed as: ; in Represents the output matrix of the model, expressed as: ; S6-3: Calculate the mean square error (MSE) between the model output value and the training label set: ; Then use the MSE value to update the model parameters; the same goes for other deep layer training methods; S6-4: Model validation is also performed separately for each depth layer; using the training input set The next cycle data of the last time cycle data is used as the input of the model for prediction to predict the data of a future time resolution, that is, the sequence data of length 1, and then the sliding window (sliding window step size is 1) takes the new value as the input for predicting the next time resolution, until the prediction completes a time cycle, and the remaining depth layers are similar; The prediction result of the first depth layer is a time series of sound velocity values ​​with a length of C, as shown in formula (20): ;

[0013] The same is true for the other depth layers, so the final predicted sound speed data set is , as shown in formula (21): ; Since the training data set was normalized before model training, the predicted sound speed data should be denormalized (the inverse operation of the original normalization operation), that is, the predicted data should be restored to the scale range of the original data to facilitate comparative analysis with the verification data.

[0014] S6-5: The denormalization formula is: ; Prediction results after denormalization : ; in, Represents the predicted sound speed value of the i-th time resolution at the j-th depth layer.

[0015] S6-6: After the denormalization operation is completed, the root mean square error (RMSE) between the actual value and the predicted value is calculated: ; in Represents the RMSE of the predicted i-th time resolution. If the RMSE value is not less than the expected threshold, return to S1, increase the number of iterations of the training model, and continue to train the model until the model converges, that is, the RMSE is less than the expected threshold or has no obvious change.

[0016] Compared with the prior art, the present invention has at least the following beneficial effects: The present invention solves the problem of predicting the underwater sound speed profile distribution in the time dimension, can make real-time and accurate predictions of the sound speed distribution at future moments, and estimate the sound speed distribution at future specified time resolution intervals, solving the problems of insufficient time resolution of ocean sound speed distribution estimation and lack of future sound speed prediction function, and provides important guiding significance for marine scientific research. The present invention can predict the sound speed distribution at future specified time resolution intervals at the predicted location, with relatively high accuracy and prediction efficiency, and provides important guiding significance for marine scientific research. BRIEF DESCRIPTION OF THE DRAWINGS

[0017] Figure 1 It is the overall flow chart of the present invention.

[0018] Figure 2 This is a schematic diagram of the basic structure of the Att-KAN neural network model.

[0019] Figure 3 It is a schematic diagram comparing the predicted full-sea-depth sound speed distribution and the actual full-sea-depth sound speed distribution. DETAILED DESCRIPTION

[0020] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with specific embodiments and with reference to the accompanying drawings.

[0021] Embodiment 1: A sound speed distribution prediction method based on attention-assisted kolmogorov–arnold network (Att-KAN), such as Figure 1 The specific steps are as follows: Step 1: Extract from the sound speed forecast location and spatial historical sound speed dataset According to the sound speed distribution prediction task, the spatial coordinates are specified as longitude M° and latitude N°. The sound speed profile data measured at different historical times in this spatial region are selected from the global Argo data set to form a spatial historical sound speed data set as the sound speed profile reference data.

[0022] Step 2: Determine the time resolution, forecast start time and maximum forecast time length of the sound speed distribution forecast The time resolution is determined according to the sound speed distribution prediction task requirements. Indicates; forecast start time, using and the maximum forecast time length, expressed as express.

[0023] Step 3: Secondary screening of the spatial historical sound speed dataset and standardized interpolation of depth and time dimensions According to the time resolution of the sound speed distribution forecast, the data is dynamically secondary screened from the spatial historical sound speed data set in step 1 to form a time-standardized data set of historical sound speed distribution as training reference data. The training data covers a time range that includes at least 4 complete change cycles. For example, when the forecast time resolution unit is "hour", the sample must cover at least 4 full-day cycles, that is, the sample data of at least 4 days before the forecast time is screened; when the forecast time resolution is "month", the sample must cover at least 4 full-year cycles, that is, the sample data of at least 4 years before the forecast time is screened. The screened data is sequentially subjected to standardized linear hierarchical interpolation in the depth direction and standardized interpolation in the time direction. The standardized interpolation method in the depth direction is as follows: from 0 to 10 meters, one layer is divided every 5 meters; from 10 to 180 meters, one layer is divided every 10 meters; from 180 to 460 meters, one layer is divided every 20 meters; from 500 to 1250 meters, one layer is divided every 50 meters; from 1300 to 1900 meters, one layer is divided every 100 meters; more than 1900 meters depth is one layer, a total of 58 layers. The selected data is interpolated in the time dimension, and the interpolation time interval is equal to the forecast time resolution.

[0024] The time-normalized data set of historical sound speed distribution is expressed as: ; in represents the ith sound velocity profile, there are I in total, and the ith sound velocity profile can be further expressed as: ; in is the sound velocity value, unit: m / s, subscript Expressed as Depth Layer “ ” represents the transpose of the vector. In formula (1), the S data sets are arranged in time order, and the time interval and time resolution are Consistency; = 0,1,…,J, where is the depth layer index label, and the maximum depth layer of the full ocean depth sound speed distribution is dJ.

[0025] The expansion of formula (1) can obtain the sound speed value data matrix: ; After the time-normalized data set of historical sound speed distribution is collected, proceed to step 4.

[0026] Step 4: Preprocess the sound velocity distribution sample data The preprocessing of sound speed distribution sample data is mainly divided into two parts: the division of training set and validation set and the preprocessing of training set.

[0027] (1) Divide the training set and validation set Data change time period Determined by the objective laws of nature. The first IC sound speed distribution data of the time-standardized data set S of the historical sound speed distribution are used as the training data set, and the following C sound speed distribution data are used as the validation data set, where IC≥4C.

[0028] (2) Specific processing of training sets The historical sound speed distribution time standardized data set S is a sound speed value data matrix with J rows and I columns. The first IC columns of the historical sound speed distribution time standardized data set S are divided into the training data set T, as shown in Formula 4; the last C columns of S are used as the verification data set E, as shown in Formula 5. The training data set T is normalized as , the normalization formula is shown in Formula 6, where is the normalized data, To normalize the data, is the mean of the sequence data, is the standard deviation of the sequence data.

[0029] Since the sound speed changes in different ocean depth layers have their own characteristics, the data of each layer needs to be normalized separately during normalization. In addition, for the accuracy and reliability of the experiment, the data of the validation set E cannot be used to obtain the and . A certain depth layer It can be obtained from formula 7, It means to sum the j-th row data of matrix T from the first column to the last column; It can be obtained by formula 8.

[0030] Then the normalized training data set is Specifically divided into training input set and training label set The training input set X is shown in Formula 10, and the training label set Y is shown in Formula 11.

[0031] ; ; ; ; ; ; ; ; In order to ensure the interpretability and accuracy of the prediction, the training data set and the validation data set cannot be mixed. Therefore, the last month of the training data set is not involved in the training, and the subscript of the actual training input set ends with IC-1.

[0032] (3) Further specific segmentation of the dataset After normalizing the data set, in order to train the model and make predictions in layers, the training input set and training label set need to be split again according to the depth layer. The training input set and training label set can be split into , . , They are expressed by formulas 12 and 13 respectively: ; ; It means that for the data of the j-th row of matrix X, each sliding window takes data of size C, and the sliding window step size is 1; It means that for the j-th row of data in matrix Y, each sliding window takes data of size 1, and the sliding window step size is 1.

[0033] After the sound velocity distribution sample data preprocessing is completed, go to step 5.

[0034] Step 5: Construct the Att-KAN neural network model for predicting sound velocity distribution According to different depth layers, the sound speed distribution prediction is performed in layers, and an Att-KAN network is constructed for each depth layer.

[0035] For each depth layer of the Att-KAN network, the prediction result is a length of The output sound speed value time series.

[0036] Take 3 Att-KAN linear layers and 1 fully connected layer as hidden layers, and the number of neurons in the hidden layers are N1, N2, N3, and N3 respectively. The Att-KAN neural network model is as follows Figure 2 As shown in Figure 2, Att-KAN is a neural network similar to a multi-layer perceptron. In addition to using the commonly used activation function, it also adds a B-spline function group. The output of the Att-KAN layer is the sum of the output of the activation function and the output of the B-spline function. Figure 2 The '+' in represents the addition operation, 'SiLU' and 'B-spline' represent the SiLU activation function and the B-spline function group respectively: ; ; Where i is the number of neurons in the current Att-KAN layer, It follows a normal distribution with a mean of 0 and a standard deviation of 0.1. is the B-spline function.

[0037] The output of each Att-KAN layer is expressed as , yes Additive summation of and B-spline(x): .

[0038] Step 6: Model Training Before model training, determine the learning rate of each depth layer And the number of iterations is , represents the corresponding depth layer, j=1, 2,…,J.

[0039] (1) Model training When training the model, the Att-KAN network of each depth layer is trained separately. represents the Att-KAN network of the jth depth layer. The input and output of the model are expressed as: ; in Represents the output matrix of the model, expressed as: ; Then find the mean square error (MSE) between the model's output value and the training label set: ; Then use the MSE value to update the model parameters. The same goes for other depth layer training methods.

[0040] (2) Model validation

[0041] Model validation is also performed separately for each depth layer.

[0042] Using the training input set The next cycle data of the last time cycle data is used as the input of the model for prediction, to predict the data of the next time resolution, that is, the sequence data of length 1, and then the sliding window (sliding window step size is 1) takes the new value as the input for predicting the next time resolution until the prediction completes a time cycle. The rest of the depth layers are similar.

[0043] The prediction result of the first depth layer is a time series of sound speed values ​​with a length of C, as shown in Formula 20: ; The same is true for the other depth layers, so the final predicted sound speed data set is , as shown in Formula 21: ; Since the training data set was normalized before model training, the predicted sound speed data should be denormalized (the inverse operation of the original normalization operation), that is, the predicted data should be restored to the scale range of the original data to facilitate comparative analysis with the verification data.

[0044] The denormalization formula is: ; Prediction results after denormalization : ; in, Represents the predicted sound speed value of the i-th time resolution at the j-th depth layer.

[0045] After the denormalization operation is completed, the root mean square error (RMSE) between the actual value and the predicted value is calculated: ; in Represents the RMSE of the predicted i-th time resolution. If the RMSE value is not less than the expected threshold, return to step (1), increase the number of iterations of the training model, and continue to train the model until the model converges, that is, the RMSE is less than the expected threshold or has no significant change.

[0046] Step 7: Model prediction According to the task-specified forecast time resolution, forecast start time, and forecast maximum time length, determine the number of forecast iterations and the historical sound speed distribution reference data corresponding to the forecast start time. Use 4 or more integer change cycle data before the forecast start time as the training set of the model to obtain the prediction result. Perform the denormalization process of step 6 on the result and output the predicted future sound speed distribution data.

[0047] In order to verify the accuracy of the predicted sound speed profile, the predicted full-sea depth sound speed profile data for the sixth month were compared with the actual data and the predicted values ​​of the long short-term memory (LSTM) neural network and the mean prediction method.

[0048] Embodiment 2: This example is based on the method provided in Example 1 for specific experimental verification: Step 1: According to the sound speed distribution prediction task, the spatial coordinates are specified as 168.5° east longitude and 16.5° north latitude. The sound speed profile data measured for 60 months in this space area from 2016 to 2020 are selected from the global Argo dataset to form a spatial historical sound speed dataset as the sound speed profile reference data.

[0049] Step 2: Select the time resolution according to the sound speed distribution prediction task requirements For 1 month, take the forecast start time For January 2020, take the maximum forecast time length For 1 year.

[0050] Step 3: The sound speed profile data measured in this space area from 2016 to 2020 are used as the space historical sound speed data set. The forecast start time is January 2020. Before that, there are 4 full-year cycles of training reference data to meet the training requirements.

[0051] The selected data are sequentially subjected to standardized linear layered interpolation in the depth direction and standardized interpolation in the time direction. The standardized interpolation method in the depth direction is as follows: from 0 to 10 meters, one layer is divided every 5 meters; from 10 to 180 meters, one layer is divided every 10 meters; from 180 to 460 meters, one layer is divided every 20 meters; from 500 to 1250 meters, one layer is divided every 50 meters; from 1300 to 1900 meters, one layer is divided every 100 meters; the depth exceeding 1900 meters is one layer, and a total of 58 layers are divided. The selected data are interpolated in the time dimension, and the interpolation time interval is equal to the forecast time resolution.

[0052] Then the time-normalized data set of historical sound speed distribution is expressed as: ; Where i = 1~60 means 5 years and 60 months from January 2016 to December 2020 are arranged in chronological order. It represents the sound speed distribution data corresponding to the time.

[0053] The i-th sound velocity profile can be further expressed as: = 0,1,…,58; in is the sound velocity value, unit: m / s, subscript Expressed as depth layers, The maximum value is 58, that is, the maximum common depth layer of the full ocean sound velocity distribution is 58 layers. ” stands for the transpose of a vector.

[0054] Expand and write the collected historical sound speed distribution time normalized data set S to be a sound speed value data matrix with 58 rows and 60 columns: ; After the time-normalized data set of historical sound speed distribution is collected, proceed to step 4.

[0055] Step 4: (1) The data change time period is C = 12. The first 48 sound speed distribution data of the historical sound speed distribution time standardization data set S are used as the training data set, and the remaining 12 sound speed distribution data are used as the validation data set.

[0056] (2) Specific processing of training sets The first 48 columns of the historical sound speed distribution time standardized dataset S are divided into the training dataset T, and the last 12 columns of S are used as the verification dataset E.

[0057] Training dataset: ; Validation dataset: ; The training data set T is normalized as : Normalized training set: .

[0058] The normalized training data set Specifically divided into training input set and training label set , a training method with an interval of one cycle is adopted, that is, 12 columns of data are used to predict the 13th column of data (that is, when the data from January to December 2016 is used as the training input, the data from January 2017 is used as the training output; when the data from February 2016 to January 2017 is used as the training input, the data from February 2017 is used as the training output), and so on.

[0059] Training input set: ; Training label set: ; Then X and Y are further divided into , .

[0060] After the sound velocity distribution sample data preprocessing is completed, go to step 5.

[0061] Step 5: In model construction, three Att-KAN linear layers and one fully connected layer are taken as hidden layers, and the number of neurons in the hidden layers are 12, 256, 128, and 128 respectively.

[0062] Step 6: (1) The main parameters of model training are set as: learning rate is 0.0001, and the number of iterations is For 300 times, represents the corresponding depth layer, j=1, 2,…,58.

[0063] Training the first depth layer When building a network, the input of the model is: = , the corresponding model output is = ; Then calculate the MSE value to update the model parameters. The training method of the remaining layers is similar.

[0064] (2) Model validation For the training input set The last time period data sliding window is used to obtain new data in one step, that is The model uses the data as input to predict the data of the next time resolution, that is, the sequence data of length 1, and then takes a new value in one step of sliding window to predict the next time resolution, until the prediction completes a time period. The rest of the depth layers are similar.

[0065] The prediction result of the first depth layer is a time series of sound speed values ​​with a length of 12: ; The same is true for the other depth layers, so the final predicted sound speed data set is : ; The predicted sound velocity data set is denormalized using the inverse operation of the original normalization operation, that is, the predicted data is restored to the scale range of the original data to facilitate comparative analysis with the verification data.

[0066] Prediction results after denormalization As shown below: ; After the denormalization operation is completed, the root mean square error is calculated. If the RMSE value is not less than the expected threshold, return to step (1), increase the number of iterations of the training model, and continue to train the model until the model converges, that is, the RMSE is less than the expected threshold or has no obvious change.

[0067] The root mean square error between the predicted data of the full-sea-depth sound velocity distribution and the actual data of the full-sea-depth sound velocity distribution after multiple model verifications is within 1 m / s, with an average of about 0.55 m / s. Figure 3As shown in the figure, it can be seen that the predicted sound speed distribution and the actual sound speed distribution are highly matched, that is, this method can accurately predict the future sound speed distribution.

[0068] The present invention solves the problem of predicting the underwater sound velocity profile distribution in the time dimension, and can accurately estimate and predict the sound velocity distribution at a certain moment in real time, solving the problem of insufficient time resolution of ocean sound velocity distribution estimation and lack of future sound velocity prediction function. With the development of underwater sound velocity field measurement and construction technology, it can be widely used in many fields such as underwater communication, positioning, and navigation.

[0069] The specific embodiments described above further illustrate the purpose, technical solutions and beneficial effects disclosed in the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for predicting sound velocity distribution based on the Att-KAN neural network model, characterized in that: The steps include: S1: Collect spatial historical sound speed data sets as reference data for sound speed profiles; S2: Determine the time resolution according to the sound speed distribution prediction task requirements, and use Indicates; forecast start time, using express; and the maximum forecast time length, using express; S3: secondary screening of the spatial historical sound speed dataset, and performing standardized interpolation in depth and time dimensions; S4: preprocessing and classification of the sound velocity distribution sample data after screening and standardized interpolation in S3; S5: Constructing the Att-KAN neural network model: The model includes a data input layer, an attention mechanism layer, a KAN layer, a fully connected layer, and an output layer; three layers of KAN linear layers and one layer of fully connected layer are taken as hidden layers; a B-spline function group is added to the Att-KAN neural network model, and the output of the Att-KAN layer is the sum of the output of the activation function and the output of the B-spline function. At the same time, an attention mechanism layer is added before the KAN layer formed by stacking three layers of KAN linear layers; for each depth layer, the Att-KAN network model is constructed, and the prediction result is a length of Output sound speed value time series; S6: The Att-KAN neural network model is trained and verified, and the model processing results are normalized and output; S7: The Att-KAN neural network model performs prediction: according to the task specified forecast time resolution, forecast start time, and forecast maximum time length, the number of forecast iterations and the historical sound speed distribution reference data corresponding to the forecast start time are determined. The prediction result can be obtained by taking the data of 4 or more whole change cycles before the forecast start time as the training set of the model, and the result is normalized by S6 to output the predicted future sound speed distribution data.

2. The method for predicting sound velocity distribution according to claim 1, characterized in that: In S1, the spatial coordinates are specified as longitude M° and latitude N° according to the sound speed distribution prediction task, and the sound speed profile data measured at different historical moments in the spatial region are selected from the global Argo data set to form a spatial historical sound speed data set.

3. The method for predicting sound velocity distribution according to claim 1, characterized in that: In S3, according to the time resolution of the sound speed distribution forecast, the spatial historical sound speed data set of S1 is dynamically secondary screened to form a historical sound speed distribution time standardized data set as training reference data, and the training data covers a time range that includes at least 4 complete change cycles of data; the screened data are sequentially subjected to standardized linear layered interpolation in the depth direction and standardized interpolation in the time direction; the screened data are interpolated in the time dimension, and the interpolation time interval is equal to the forecast time resolution.

4. The method for predicting sound velocity distribution according to claim 1, characterized in that: In the S3: The time-normalized data set of historical sound speed distribution is expressed as: ； in represents the ith sound velocity profile, there are I in total, and the ith sound velocity profile is further expressed as: ； in is the sound velocity value, unit: m / s, subscript Expressed as depth layers, " " represents the transpose of the vector; in formula (1), the S data set is arranged in time order, and the time interval and time resolution are Consistency; = 0,1,…,J, where is the depth layer index label, and the maximum depth layer of the full ocean depth sound speed distribution is dJ; Formula (1) is expanded to obtain the sound speed data matrix: 。 5. The method for predicting sound velocity distribution according to claim 1, characterized in that: The S4 includes: S4-1: Divide the training set and validation set: The historical sound speed distribution time standardization data set S is a sound speed value data matrix with J rows and I columns. The first IC columns of the historical sound speed distribution time standardization data set S are divided into the training data set T, as shown in formula (4); the last C columns of S are used as the verification data set E, as shown in formula (5), where IC≥4C; S4-2: Data preprocessing: The training data set T is normalized as , the normalization formula is shown in formula (6), where is the normalized data, To normalize the data, is the mean of the sequence data, is the standard deviation of the sequence data; A certain depth From formula (7), we can get: It means to sum the j-th row data of matrix T from the first column to the last column; From formula (8), we get: S4-3: Then normalize the training data set Specifically divided into training input set and training label set ; The training input set X is shown in formula (10), and the training label set Y is shown in formula (11); ； ； ； ； ； ； ； ； S4-4: Split the training input set and training label set again according to the depth layer: The training input set and training label set are divided into , ; , They are expressed by formulas (12) and (13) respectively; ； ； It means that for the data of the j-th row of matrix X, each sliding window takes data of size C, and the sliding window step size is 1; It means that for the j-th row of data in matrix Y, each sliding window takes data of size 1, and the sliding window step size is 1.

6. The method for predicting sound velocity distribution according to claim 1, characterized in that: The S5 includes: According to the different depth layers, the sound velocity distribution prediction is performed in layers, and an Att-KAN network is constructed for each depth layer. For each Att-KAN network constructed for each depth layer, the prediction result is a length of The output of the Att-KAN layer is the sum of the output of the activation function and the output of the B-spline function; 'SiLU' and 'B-Spline' represent the SiLU activation function and the B-Spline function group respectively: ； ； Where i is the number of neurons in the current Att-KAN layer, It follows a normal distribution with a mean of 0 and a standard deviation of 0.

1. is the B-spline function; The output of each Att-KAN layer is expressed as , yes Additive summation of and B-spline(x): 。 7. The method for predicting sound velocity distribution according to claim 1, characterized in that: The S6 includes: S6-1: Before model training, determine the learning rate of each depth layer. And the number of iterations is , represents the corresponding depth layer, j=1, 2,…, J; S6-2: During model training, the Att-KAN network model of each depth layer is trained separately. Represents the Att-KAN network of the jth depth layer. The input and output of the model are expressed as: ； in Represents the output matrix of the model, expressed as: ； S6-3: Calculate the mean square error (MSE) between the model output value and the training label set: ； Then use the MSE value to update the model parameters; S6-4: Model validation is performed separately for each depth layer; using the training input set The next cycle data of the last time cycle data is used as the input of the model to predict the data of a future time resolution until the prediction completes a time cycle; The prediction result of the first depth layer is a time series of sound velocity values ​​with a length of C, as shown in formula (20): ； The final predicted sound speed data set is , as shown in formula (21): ； S6-5: The denormalization formula is: ； Prediction results after denormalization : ； in, represents the sound velocity value predicted at the i-th time resolution of the j-th depth layer; S6-6: After the denormalization operation is completed, the root mean square error between the actual value and the predicted value is calculated: ； in Represents the RMSE of the predicted i-th time resolution; if the RMSE value is not less than the expected threshold, return to S1, increase the number of iterations of the training model, and continue to train the model until the model converges.

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