A method for filling in continuous missing raw data for bottom-based acoustic wave observations

Abstract

The present invention discloses a method for filling continuously missing raw data for bottom-mounted acoustic wave observation, which relates to the technical field of bottom-mounted acoustic wave observation in the ocean. The method comprises decomposing the original time series into different characteristic subsequences through a singular spectrum analysis algorithm, extracting trend components and transient change components; filling missing data of the trend component by generating overall trend component data based on existing time series data through a BP neural network fitting; and filling missing data of the transient change component by using a GRU-DTW neural network model based on the complete time series data in the forward and backward directions of the period when the transient component data is missing. After the data filling is completed, the complete raw data is reconstructed for statistical calculation of wave eigenvalues. The present invention efficiently restores the original state of different amounts of continuously missing data, thereby improving the measurement accuracy of wave height and wave period.

Description

Technical Field

[0001] The present invention relates to the technical field of ocean bottom-mounted acoustic wave observation, and in particular to a method for filling in continuously missing raw data for bottom-mounted acoustic wave observation. Background Art

[0002] Ocean wave observation is a core technology in modern marine science and engineering practice. It mainly uses principles such as gravity acceleration, sea surface radar, bottom acoustics, and pressure to achieve real-time collection and processing of wave characteristic data. It has been widely used in fields such as weather forecasting, disaster warning, ecological protection, engineering safety, resource development, and scientific research. At the same time, to improve the quality of wave data observation, data quality control and analysis methods based on multi-principle observation technology have become one of the international research hotspots. In the study of bottom acoustic wave observation, due to factors such as the underwater environment and surface operations, the original wave data obtained by acoustic detection is easily abnormal or continuously missing, resulting in inaccurate inversion calculation of wave characteristic data, seriously affecting data quality and the accuracy of subsequent warning forecasts. Therefore, a reliable method for filling in the continuously missing non-stationary time series original data in the acoustic detection process is urgently needed to ensure the reliability and accuracy of wave characteristic calculations.

[0003] At present, data missing filling methods are mainly divided into three categories: deletion, single interpolation and multiple interpolation. Among them, the deletion method directly deletes samples or variables with missing values, which will lead to a reduction in sample size and introduce bias; single interpolation uses methods such as mean, median, mode, linear interpolation, spline interpolation, and hot card filling to fill in the missing values. It is suitable for filling small-scale missing values ​​in trend-continuous ordered data, but has poor effect on non-continuous or mutation data; multiple interpolation provides unbiased and effective association estimation data based on available information, which can solve the problem of filling data types with complex characteristics.

[0004] In recent years, intelligently driven multiple imputation models based on deep learning have become a research focus. Non-stationary raw depth data from bottom-based acoustic wave measurements are multi-component time series data with both trends and transient variations. Therefore, it is necessary to build intelligently driven imputation models with multiple imputations based on time series deep learning networks to address the inaccurate measurement of wave height and period caused by missing raw data. Most intelligent model-driven algorithms for data imputation based on time series are based on long short-term memory (LSTM) networks, bidirectional long short-term memory (Bi-LSTM) networks, nonlinear autoregressive neural networks (NARX), and BP neural networks. These algorithms utilize various learning mechanisms to construct data imputation models and implement data interpolation and analysis. However, current imputation models for time series data primarily target data with slowly varying characteristics or data with traceable transformation patterns. Limited research has been conducted on intelligent imputation models for data with long-term trends and rapid transient variations. Furthermore, during the analysis of time series data, the acquired raw data's variation patterns are not refined, and targeted imputation strategies based on trends and transient variations are not implemented. Summary of the Invention

[0005] In order to overcome the above problems existing in the prior art, the present invention proposes a method for filling continuous missing raw data for bottom-based acoustic wave observation.

[0006] The technical solution adopted by the present invention to solve the technical problem is: a method for filling continuous missing raw data for bottom-mounted acoustic wave observation, comprising the following steps:

[0007] Step 1: Decompose the original time series into different characteristic subsequences through the singular spectrum analysis algorithm, and extract the trend component and transient change component;

[0008] Step 2: The missing trend component obtained in step 1 is fitted by BP neural network according to the existing time series data to generate the overall trend component data to complete the missing data filling;

[0009] Step 3: For the transient change component obtained in step 1, the GRU-DTW neural network model is used to fill in the missing data of each part of the data according to the complete forward and backward time series data of the period where the transient component is missing data;

[0010] Step 4: After the data filling in steps 2 and 3 is completed, the complete original data is reconstructed for statistical calculation of wave eigenvalues.

[0011] In the above-mentioned method for filling in continuously missing raw data for bottom-based acoustic wave observation, step 1 specifically includes:

[0012] Step 1.1, construct trajectory matrix: given a time series of length N {x1,x2,…,x N, select a window length \(L\), where \(1 < L < N / 2\), and construct a trajectory matrix \(X\) of size \(L\times K\) from the time series according to certain rules, where \(K = N - L+1\);

[0013] Step 1.2, Singular value decomposition: Perform singular value decomposition on the trajectory matrix \(X\), and the decomposition formula is:

[0014] ;

[0015] where, is an \(L\times L\) left singular orthogonal matrix, and its column vectors are called left singular vectors; is a diagonal matrix of \(L\times K\) singular values, and the diagonal elements are singular values; is a \(K\times K\) right singular orthogonal matrix, and its column vectors are called right singular vectors; <​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​​is the weight from the jth neuron in the m-1th hidden layer to the kth neuron in the mth hidden layer; is the bias of the neuron; is the net input of the kth neuron; after the activation function After processing, the output of the kth neuron in the hidden layer is , the output of the kth neuron in the output layer for ;

[0023] Update weights and biases via backpropagation.

[0024] In the above-mentioned method for filling in the continuous missing raw data for bottom-based acoustic wave observation, the back propagation adopts the LM algorithm, combined with the gradient descent method and the Gauss-Newton method, and the update formula is:

[0025] ;

[0026] in, is the update amount of the parameter vector V, the number of weight and bias parameters is p, and V is a p-dimensional vector; J is the Jacobian matrix; is the difference vector between the predicted value and the true value; is an adaptive parameter used to balance the contribution of gradient descent and Gauss-Newton method. When is large, it is close to the gradient descent method; when When it is very small, it is close to the Gauss-Newton method; is the p×p identity matrix.

[0027] The above-mentioned method for filling continuous missing raw data for bottom-based acoustic wave observation, the step 3 is specifically as follows: using the forward non-missing sampling point data to generate continuous filling time series data of the forward missing points through the GRU gated recurrent unit neural network; using the backward non-missing sampling point data to generate continuous filling time series data of the reverse missing points through the GRU gated recurrent unit neural network; after sequence reversal, generating sequence data consistent with the forward filling data; using the DTW dynamic time adjustment algorithm to find the optimal matching path between the two time series, so that the two sequences are aligned on the time axis and have the same length as the filling data.

[0028] The above-mentioned method for filling in the continuous missing raw data for bottom-based acoustic wave observation, the GRU gated recurrent unit neural network controls data update by updating the gate and resetting the gate, adding or deleting state information to obtain a new time step , the calculation formula is:

[0029] ;

[0030] , , ;

[0031] Among them, W is the input weight matrix, R is the cycle weight matrix, b is the bias matrix, is the sigmoid function; is the current time step, is the hidden state of the previous time step, is a candidate hidden state, To reset the gate, For updating the door.

[0032] The above-mentioned method for filling the continuous missing raw data for bottom-based acoustic wave observations, the DTW dynamic time adjustment algorithm finds the optimal matching path between two time series. The specific process is as follows: Construct a cumulative distance matrix: There are two time series of length m and n, respectively, denoted as F=[f1, f2, ..., f m ] and G=[g1, g2, ..., g n ]; calculate the Euclidean distance matrix between them After obtaining the distance matrix D, construct a cumulative distance matrix , the derivation formula is:

[0033] ;

[0034] Find the optimal path: From the lower right corner of the cumulative distance matrix C At the beginning, by backtracking, in each step, according to the cumulative distance of the current position, the adjacent position with the smallest cumulative distance is selected as the position of the previous step until backtracking to the upper left corner , the index pair corresponding to the point on this path This constitutes the optimal match between the two time series.

[0035] The beneficial effect of the present invention is that, facing the problem of missing original depth data in complex time series with non-stationary, trend and transient changes in bottom-based acoustic wave measurement, the present invention can efficiently restore the original state of different numbers of continuous missing data, solve the problem of filling distortion caused by the increase in the amount of continuous missing data in other time series models, and improve the measurement accuracy of wave height and wave period.

[0036] (1) Aiming at the problem of fine-grained extraction of original missing data from nonlinear and non-stationary acoustic wave observations, the singular spectrum analysis (SSA) algorithm is used to adaptively extract several components with different scales, from large-scale components to detail components, thereby improving the ability of the filling model to distinguish trend components and transient change components.

[0037] (2) To address the issues of efficiency and accuracy in filling missing data of large-scale trend components extracted by SSA, the BP neural network fitting function is used to automatically learn the "reasonable rules" between input and output data. In the case of local data missing, a nonlinear continuous function that adapts to the global situation is trained and generated, thereby improving the speed and accuracy of filling missing data of large-scale trend components.

[0038] (3) In order to solve the problem of fitting the real distribution of missing data of small-scale transient change components extracted by SSA, the real observation data before and after the missing part are used to better fit the real distribution of missing data through the GRU nonlinear modeling capability and DTW dynamic fusion matching capability, thereby improving the distribution quality of filling the missing data of small-scale transient change components. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] Figure 1 It is a schematic flow chart of the present invention;

[0040] Figure 2 2. Schematic diagram of continuous missing data in an embodiment of the present invention;

[0041] Figure 3 is a schematic diagram of data after filling in an embodiment of the present invention;

[0042] Figure 4 This is a comparative analysis diagram of wave height characteristic values ​​in an embodiment of the present invention;

[0043] Figure 5 3 is a comparative analysis diagram of wave period characteristic values ​​in an embodiment of the present invention. DETAILED DESCRIPTION

[0044] In order to enable those skilled in the art to better understand the technical solution of the present invention, the present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0045] like Figure 1 As shown, this embodiment discloses a method for filling continuous missing original data for bottom-based acoustic wave observation. First, the original time series is decomposed into subsequences with different characteristics through the singular spectrum analysis (SSA) algorithm, and the trend component and the transient change component are extracted, wherein the missing part of the trend component is generated by BP network fitting; the missing part of the transient change component is generated by forward and reverse prediction of the GRU neural network based on the existing observation data of the previous and next time series to generate two time series filling data, and the two time series data are fused into the optimal matching transient change component missing filling data through the dynamic time warping algorithm (DTW); after the missing data of the trend component and the transient change component are filled, the complete original data are accumulated to generate for the statistical calculation of the wave characteristic value.

[0046] (1) Singular spectrum (SSA) signal decomposition

[0047] Singular spectrum analysis divides the decomposition window on a minute-by-minute basis, constructs a trajectory matrix based on the effective period of missing data, and obtains the trend component and transient change component of each effective period through singular spectrum decomposition to complete classification and extraction. Singular spectrum analysis (SSA) is an algorithm for time series analysis. It combines the ideas of principal component analysis and time series decomposition. By constructing a trajectory matrix for a time series and then performing singular value decomposition (SVD) on it, the original time series is decomposed into a series of subsequences with different characteristics. Each subsequence represents a different component of the original time series and is mainly used for time series decomposition, noise reduction, trend extraction, periodic analysis, etc.

[0048] The first step is to construct the trajectory matrix: Given a time series {x1, x2, …, x N (where the length is N), select a window length L (1 < L < N / 2), and construct a trajectory matrix X of size L×K (where K = N - L + 1) for the time series according to certain rules. The matrix expression is shown in formula (1).

[0049] (1).

[0050] The second step is singular value decomposition (SVD): Perform singular value decomposition on the trajectory matrix X, and the decomposition formula is shown in formula (2).

[0051] (2);

[0052] where is the left singular orthogonal matrix of L×L, and its column vectors are called left singular vectors; is the diagonal matrix of L×K singular values, and the diagonal elements are singular values; is the right singular orthogonal matrix of K×K, and its column vectors are called right singular vectors.

[0053] The third step is grouping and reconstruction: According to the size and characteristics of the singular values, group the basic matrices to decompose a series of subsequences. Group the basic matrices corresponding to larger singular values into a group to represent the trend component, group the basic matrices with periodic characteristics into a group to represent the periodic component, and the rest into the noise component, so as to achieve the decomposition and analysis of the original time series.

[0054] (2) Fitting and filling the trend component data with a BP neural network

[0055] The singular spectrum analysis (SSA) algorithm extracts missing trend component data and uses the BP neural network to fit the existing time series data to generate overall trend component data to complete the missing data filling. The BP neural network fitting function automatically learns the "reasonable rules" between input and output data. In the case of local data missing, it trains and generates a nonlinear continuous function that adapts to the global situation, improving the speed and accuracy of filling data missing large-scale trend components. BP is a multi-layer feedforward neural network that uses a backpropagation algorithm to adjust the network weights to minimize the error between the network output and the expected output. Through two simple processes of forward calculation and backpropagation, the gradient descent method is used to gradually update the parameter matrix in the network, thereby achieving other tasks such as function fitting.

[0056] The first step is network architecture: BP neural network has 1 input layer, m hidden layers and 1 output layer. Each neuron receives input from the neurons in the previous layer, and after weighted summation and nonlinear activation function processing, it passes the output to the next layer.

[0057] The second step is from input layer to hidden layer: Assume that the input layer has n neurons and the input vector λ=[λ1,λ2,……,λ n ] T , the weight from the i-th neuron in the input layer to the j-th neuron in the first hidden layer is , the bias of the jth neuron in the hidden layer is , the net input of the jth neuron in the hidden layer is , after the activation function After processing, the output of the jth neuron in the hidden layer is The expression is shown in formula (3).

[0058] (3).

[0059] Step 3, from hidden layer to output layer: The weight from the jth neuron in the m-1th hidden layer to the kth neuron in the mth hidden layer is , the bias of the neuron is , the net input of the kth neuron is , after the activation function After processing, the output of the kth neuron in the hidden layer is , the output of the kth neuron in the output layer for The expression is shown in formula (4).

[0060] (4).

[0061] Step 4, back propagation: The purpose of back propagation is to update weights and biases. The LM algorithm is an improved back propagation algorithm that combines the advantages of gradient descent and Gauss-Newton methods and can converge to the optimal solution faster. The update formula is shown in formula (5):

[0062] (5);

[0063] in, is the update amount of the parameter vector V. Assuming that the number of weight and bias parameters is p, V is a p-dimensional vector; J is the Jacobian matrix, whose elements are the partial derivatives of the loss function with respect to the weights; is the difference vector between the predicted value and the true value; is an adaptive parameter used to balance the contribution of gradient descent and Gauss-Newton methods. When is large, it is close to the gradient descent method; when When it is very small, it is close to the Gauss-Newton method; is the p×p identity matrix.

[0064] (3) GRU-DTW transient component filling

[0065] The transient components extracted using the singular spectrum analysis (SSA) algorithm are then used to fill in missing data in each part of the data using the GRU-DTW neural network model, using the complete forward and backward time series data for the period of missing transient components. First, the forward non-missing sampling point data is used to generate continuous time series data for the forward missing points through the GRU. Second, the backward non-missing sampling point data is used to generate continuous time series data for the reverse missing points through the GRU. After sequence inversion, the generated sequence data is consistent with the forward filled data. Finally, the DTW algorithm is used to find the optimal matching path between the two time series, ensuring that they are aligned as much as possible on the time axis and have the same length as the filled data. The nonlinear modeling capabilities of the GRU and the dynamic fusion matching capabilities of the DTW algorithm better fit the true distribution of the missing data, improving the distribution quality of the missing data filling of small-scale transient change components.

[0066] 1) GRU Gated Recurrent Unit Neural Network

[0067] GRU is a recurrent neural network with a simpler structure than the Long Short-Term Memory (LSTM) neural network. Compared with LSTM, it has one less gate, which reduces matrix multiplication, improves the efficiency of data model training, and makes it easier to converge and build large model algorithms. The GRU structure consists of an update gate and a reset gate. The update gate helps capture the long-term dependencies of the time series, and the reset gate helps capture the short-term dependencies in the time series. GRU controls data updates through the update gate and reset gate, adding or deleting state information to obtain new time steps. .

[0068] The inputs of the reset gate and update gate are determined by the current time step and the hidden state at the previous time step t-1 composition. Through the update gate , hidden state and candidate hidden states Get candidate hidden states By reset gate and the hidden state at time step t-1 The multiplication result and the current time step The connection is calculated by tanh. The calculation formula is shown in formulas (6) and (7). Where W is the input weight matrix, R is the cycle weight matrix, b is the bias matrix, is the sigmoid function; , , Represent the reset gate, update gate and candidate state respectively.

[0069] (6);

[0070] , , (7).

[0071] 2) DTW Dynamic Time Warping

[0072] The DTW (Dynamic Time Warping) algorithm is a classic method for measuring the similarity between two time series. Its core concept is to find the optimal matching path between two time series through dynamic programming, aligning them as closely as possible along the time axis, and then calculating a similarity measure between them. It allows time series to be stretched and warped along the time axis to overcome time misalignment caused by factors such as speed and rhythm.

[0073] The first step is to construct a cumulative distance matrix: Assume that there are two time series with lengths of m and n, respectively, recorded as F=[f1, f2, ..., f m ] and G=[g1, g2, ..., g n ]. First, we need to calculate the Euclidean distance matrix between them After obtaining the distance matrix D, we need to construct a cumulative distance matrix , the derived formula is shown in formula (8).

[0074] (8).

[0075] The second step is to find the optimal path: from the lower right corner of the cumulative distance matrix C At the beginning, the optimal path is found by backtracking. In each step, according to the cumulative distance of the current position, the adjacent position with the smallest cumulative distance is selected as the position of the previous step until backtracking to the upper left corner , the index pair corresponding to the point on this path This constitutes the optimal match between the two time series.

[0076] (4) After the trend and dynamic components are filled, the complete depth data is reconstructed. According to the wave statistical calculation method, the filled depth original data is converted into wave height and wave period. This technology has a good filling effect for different consecutive missing data (such as 60 steps, 100 steps, and 261 steps). The filled data of each missing data segment effectively restores the distribution state of the original depth data, solving the problem of inaccurate wave height and wave period caused by missing original data.

[0077] This embodiment uses Figure 2 Taking the missing data in the example, the sampling point range of the continuous missing data is selected into three parts, the first part is from 300 to 360 points, the second part is from 700 to 960 points, and the third part is from 1361 to 1460 points. Through the filling method disclosed in this embodiment, the three segments of trend components and dynamic components are reconstructed to form the final estimated depth data, such as Figure 3 As shown. According to the wave statistical calculation method, the original depth data after filling is converted into wave height and wave period, and the numerical difference is compared and analyzed with the actual wave height and wave period. The comparison parameters mainly include the maximum wave height (Hmax) and the corresponding period (Tmax), one-tenth wave height (H1 / 10) and the corresponding period (T1 / 10), one-third wave height (H1 / 3) and the corresponding period (T1 / 3) and the average wave height (Have) and the corresponding period (Tave). The comparative analysis is as follows Figure 4-5 shown.

[0078] Statistically obtained wave eigenvalues ​​show that compared with the true data, the wave height and wave period eigenvalues ​​of the missing data are generally smaller, with mean absolute errors of 0.03 meters and 0.825 seconds, respectively. Compared with the true data, the wave height eigenvalues ​​of the BPNN and NARX imputed data are generally higher, with mean absolute errors of 0.29 meters and 0.11 meters for wave height, and 0.773 seconds and 0.57 seconds for wave period, respectively. Compared with the pre-implantation statistical errors, the error of the wave height eigenvalues ​​increases, while the wave period eigenvalues ​​improve somewhat, but the advantage is not significant. Compared with the true data, the wave height and wave period eigenvalues ​​of the LSTM and BiLSTM imputed data are similar, with mean absolute errors of 0.013 meters and 0.005 meters for wave height, and 0.41 seconds and 0.28 seconds for wave period, respectively. Compared with the pre-implantation statistical errors, the mean absolute errors of wave height decrease by 56.7% and 83.3%, and the mean absolute errors of wave period decrease by 50.3% and 66.1%, respectively. Compared with the real data, the data filled by the method in this embodiment has the strongest overall consistency in wave height and wave period. The average absolute error of wave height is 0.0025 meters, and the average absolute error of wave period is 0.055 seconds. Compared with the statistical error before filling, the average absolute error of wave height is reduced by 91.7%, and the average absolute error of wave period is reduced by 93.3%.

[0079] Under comprehensive consideration of the overall mean absolute error of wave characteristic values, the method of this embodiment, LSTM and BiLSTM have obvious advantages over BPNN and NARX methods in filling in continuous missing data containing trends and instantaneous dynamics. Compared with the statistical error before filling, this technology has more advantages than LSTM and BiLSTM in filling accuracy. The overall accuracy of wave height is improved by 35 percentage points and 8.4 percentage points respectively, and the overall accuracy of wave period is improved by 40 percentage points and 27.2 percentage points respectively.

[0080] The above embodiments are merely exemplary embodiments of the present invention and are not intended to limit the present invention. Those skilled in the art may make various modifications or equivalent substitutions to the present invention within the spirit and scope of protection of the present invention, and such modifications or equivalent substitutions shall also be deemed to fall within the scope of protection of the present invention.

Claims

1. A method for filling in missing raw data for bottom-based acoustic wave observations, characterized in that: The steps include: Step 1: Decompose the original time series into different characteristic subsequences through the singular spectrum analysis algorithm, and extract the trend component and transient change component; Step 2: The missing trend component obtained in step 1 is fitted by BP neural network according to the existing time series data to generate the overall trend component data to complete the missing data filling; Step 3: For the transient change component obtained in step 1, the GRU-DTW neural network model is used to fill in the missing data of each part of the data according to the complete forward and backward time series data of the period where the transient component is missing data; Step 4: After the data filling in steps 2 and 3 is completed, the complete original data is reconstructed for statistical calculation of wave eigenvalues; The step 2 is specifically as follows: the BP neural network has 1 input layer, m hidden layers and 1 output layer. Each neuron receives input from the neurons in the previous layer, and after weighted summation and nonlinear activation function processing, passes the output to the next layer. The expression from the input layer to the hidden layer is: in, is the weight from the i-th neuron in the input layer to the j-th neuron in the first hidden layer; is the bias of the jth neuron in the hidden layer; is the net input of the jth neuron in the hidden layer; after the activation function After processing, the output of the jth neuron in the hidden layer is ; The expression from hidden layer to output layer is: in, is the weight from the jth neuron in the m-1th hidden layer to the kth neuron in the mth hidden layer; is the bias of the neuron; is the net input of the kth neuron; after the activation function After processing, the output of the kth neuron in the hidden layer is , the output of the kth neuron in the output layer for ; Update weights and biases via backpropagation; The back propagation adopts the LM algorithm, combined with the gradient descent method and the Gauss-Newton method, and the update formula is: in, is the update amount of the parameter vector V, the number of weight and bias parameters is p, and V is a p-dimensional vector; J is the Jacobian matrix; is the difference vector between the predicted value and the true value; is an adaptive parameter used to balance the contribution of gradient descent and Gauss-Newton method. When is large, it is close to the gradient descent method; when When it is very small, it is close to the Gauss-Newton method; is the p×p identity matrix.

2. The method for filling continuous missing raw data for bottom-based acoustic wave observation according to claim 1 is characterized in that: The step 1 specifically includes: Step 1.1, construct a trajectory matrix: Given a time series {x1, x2, …, x N} with length N, select a window length L, where 1 < L < N / 2, and construct a trajectory matrix X of size L×K from the time series according to certain rules, where K = N−L + 1; Step 1.2, singular value decomposition: perform singular value decomposition on the trajectory matrix X, the decomposition formula is: in, is an L×L left singular orthogonal matrix whose column vector is called the left singular vector; is a diagonal matrix of L×K singular values, with the diagonal elements is a singular value; is a K×K right singular orthogonal matrix whose column vector is called the right singular vector; Step 1.3, grouping and reconstruction: According to the size and characteristics of the singular values, matrices Grouping is performed and a series of subsequences are decomposed. The matrices corresponding to larger singular values ​​are grouped into a group representing trend components, namely trend components, and the matrices with periodic characteristics are grouped into a group representing periodic components, namely transient change components.

3. The method for filling continuous missing raw data for bottom-based acoustic wave observation according to claim 1 is characterized in that: The step 3 specifically comprises: using the forward non-missing sampling point data to generate continuous filling time series data of the forward missing points through the GRU gated recurrent unit neural network; using the backward non-missing sampling point data to generate continuous filling time series data of the reverse missing points through the GRU gated recurrent unit neural network; generating sequence data consistent with the forward filling data after sequence reversal; and finding the optimal matching path between the two time series through the DTW dynamic time adjustment algorithm, so that the two sequences are aligned on the time axis and have the same length as the filling data.

4. The method for filling in continuously missing raw data for bottom-based acoustic wave observation according to claim 3 is characterized in that: The GRU gated recurrent unit neural network updates the data by updating the gate and resetting the gate control, adding or deleting state information to obtain a new time step , the calculation formula is: , , Among them, W is the input weight matrix, R is the cycle weight matrix, b is the bias matrix, is the sigmoid function; is the current time step, is the hidden state of the previous time step, is a candidate hidden state, To reset the gate, For updating the door.

5. The method for filling in continuously missing raw data for bottom-based acoustic wave observation according to claim 3 is characterized in that: The DTW dynamic time adjustment algorithm finds the optimal matching path between two time series. The specific process is as follows: Construct a cumulative distance matrix: There are two time series with lengths of m and n, respectively, denoted as F=[f1, f2, ..., f m ] and G=[g1, g2, ..., g n ]; calculate the Euclidean distance matrix between them After obtaining the distance matrix D, construct a cumulative distance matrix , the derivation formula is: ； Find the optimal path: From the lower right corner of the cumulative distance matrix C At the beginning, by backtracking, in each step, according to the cumulative distance of the current position, the adjacent position with the smallest cumulative distance is selected as the position of the previous step until backtracking to the upper left corner , the index pair corresponding to the point on this path This constitutes the optimal match between the two time series.

Images