Continuous missing original data filling method for bottom-supported acoustic wave observation

Abstract

The invention discloses a continuous missing original data filling method for bottom-supported acoustic wave observation, and relates to the technical field of ocean bottom-supported acoustic wave observation, and the method comprises the steps: decomposing an original time sequence into different feature subsequences through a singular spectrum analysis algorithm, and extracting a trend component and a transient change component; a trend component missing part is subjected to fitting through a BP neural network according to existing time sequence data to generate overall trend component data to complete filling of missing data; according to the transient change component, filling of missing data of each part of the data is completed through a GRU-DTW neural network model according to forward and backward complete time sequence data of a transient component missing data period; and after data filling is completed, complete original data are reconstructed and formed and are used for statistical calculation of wave characteristic values. According to the method, the original states of different numbers of continuous missing data are efficiently restored, and the measurement accuracy of the wave height and the wave period is improved.

Description

Technical Field

[0001] The present invention relates to the technical field of bottom-mounted marine acoustic wave observation, and in particular to a method for filling continuous missing original 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 gravitational acceleration type, sea surface radar type, bottom-mounted acoustic type, and pressure type to realize real-time acquisition and processing of wave characteristic data. Currently, it has been widely used in fields such as meteorological forecasting, disaster warning, ecological protection, engineering safety, resource development, and scientific research. At the same time, in order to improve the quality of wave data observation, data quality control and analysis methods based on multi-principle observation technologies have become one of the international research hotspots. In the research of bottom-mounted acoustic wave observation, affected by factors such as the underwater environment and surface operations, it is easy to cause abnormalities or continuous missing measurements in the original wave data obtained by acoustic detection, resulting in inaccurate inversion calculations of wave characteristic data, seriously affecting the data quality and the accuracy of subsequent early warning and forecasting. Therefore, there is an urgent need for a reliable method for filling and generating non-stationary time-series original data with continuous missing measurements during the acoustic detection process to ensure the reliability and accuracy of wave characteristic calculations.

[0003] Currently, data missing value filling methods are mainly divided into three categories: deletion method, single imputation, and multiple imputation. Among them, the deletion method directly deletes samples or variables with missing values, which will lead to a reduction in the sample size and introduce biases; single filling is performed by methods such as mean, median, mode, linear interpolation, spline interpolation, and hot deck imputation, which is suitable for filling small-scale missing values of trend continuous ordered data and has poor effects on non-continuous or mutant data; multiple imputation provides unbiased and effective correlated estimated data based on available information and can solve the problem of filling data types with complex characteristics.

[0004] In recent years, intelligent-driven multiple imputation models based on deep learning have become the focus of research. The non-stationary time-series raw depth data of bottom-mounted acoustic wave measurement belongs to multi-component time-series data with coexisting trends and transient changes. It is necessary to rely on a deep learning network for time series to build an intelligent-driven imputation model for multiple imputations to solve the problem of inaccurate wave height and wave period measurements caused by missing raw data. Most of the intelligent model-driven algorithms for data imputation based on time series are based on long short-term memory networks (LSTM), bidirectional long short-term memory networks (Bi-LSTM), non-linear autoregressive neural networks (NARX), BP neural networks, etc., and cooperate with different learning mechanisms to build data imputation models to achieve data interpolation and analysis. However, the current imputation models for time series data mainly focus on slowly varying feature data or data with traceable transformation rules. There is little research on intelligent imputation models for data with long-term trend terms and rapid transient changes. In the process of analyzing time series data, the changing rules of the obtained raw data are not refined, and targeted imputation strategies are not adopted according to trends and transient changes. 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-mounted acoustic wave observation.

[0006] The technical solution adopted by the present invention to solve its technical problems is: a method for filling continuous missing raw data for bottom-mounted acoustic wave observation, including the following steps: Step 1: Decompose the original time series into different characteristic subsequences through the singular spectrum analysis algorithm, and extract the trend component and the transient change component; Step 2: For the missing part of the trend component obtained in Step 1, the overall trend component data is generated by fitting through a BP neural network according to the existing time series data to complete the filling of the missing data; Step 3: For the transient change component obtained in Step 1, according to the forward and backward complete time series data of the missing data period of the transient component, the missing data of each part of the data is respectively completed through the GRU-DTW neural network model; Step 4: After the data filling in Steps 2 and 3 is completed, a complete original data is reconstructed for statistical calculation of wave characteristic values.

[0007] For the above method for filling continuous missing raw data for bottom-mounted acoustic wave observation, Step 1 specifically includes: Step 1.1: Construct a trajectory matrix: Given a time series {x1, x2,..., x , , ,

[0007] , , , , N , , ,

[0006] , ,

[0005] } of length N, select a window length L, where 1 < L < N / 2, and construct a trajectory matrix X of size L×K according to certain rules for the time series, where K = N - L + 1; Step 1.2, Singular Value Decomposition: Perform singular value decomposition on the trajectory matrix X, and the decomposition formula is: ; where is an L×L left singular orthogonal matrix, and its column vectors are called left singular vectors; is a diagonal matrix of L×K singular values, and the diagonal elements are singular values; is a K×K right singular orthogonal matrix, and its column vectors are called right singular vectors; Step 1.3, Grouping and Reconstruction: According to the magnitudes and characteristics of the singular values, group matrices to decompose a series of subsequences. Group the matrices corresponding to larger singular values into one group to represent the trend component, group the matrices with periodic characteristics into one group to represent the periodic component, i.e., the transient change component, and the remaining ones are grouped as noise components.

[0008] For the above-mentioned method for filling continuous missing original data for bottom-mounted acoustic wave observations, the specific content of Step 2 is as follows: The BP neural network has 1 input layer, m hidden layers, and 1 output layer. Each neuron receives the input from the neurons in the previous layer, and after weighted summation and processing by a non-linear activation function, the output is passed to the next layer. The expression from the input layer to the hidden layer is: ; where 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 j-th neuron in the hidden layer; is the net input of the j-th neuron in the hidden layer; After being processed by the activation function , the output of the j-th neuron in the hidden layer is ; The expression from the hidden layer to the output layer is: ; where is the weight from the j-th neuron in the (m - 1)-th hidden layer to the k-th neuron in the m-th hidden layer; is the bias of the neuron; is the net input of the k-th neuron; After being processed by the activation function , the output of the k-th neuron in the hidden layer is , and the output of the k-th neuron in the output layer is ; Update the weights and biases through backpropagation.

[0009] The above method for filling continuous missing original data for bottom-mounted acoustic wave observation, where the backpropagation uses the LM algorithm, combines the gradient descent method and the Gauss-Newton method, and the update formula is: ; Among them, 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 contributions of the gradient descent method and the Gauss-Newton method. When is very large, it is close to the gradient descent method; when is very small, it is close to the Gauss-Newton method; is the p×p identity matrix.

[0010] The above method for filling continuous missing original data for bottom-mounted acoustic wave observation, specifically, step 3 is as follows: Using the data of the forward non-missing sampling points, the continuous filling time series data of the forward missing points is generated through the GRU gated recurrent unit neural network; Using the data of the backward non-missing sampling points, the continuous filling time series data of the backward missing points is generated through the GRU gated recurrent unit neural network; After sequence reversal, the sequence data consistent with the forward filling data is generated; The optimal matching path between the two time series is found through the DTW dynamic time warping algorithm, so that the two sequences are aligned on the time axis and have the same length as the filling data.

[0011] The above method for filling continuous missing original data for bottom-mounted acoustic wave observation, where the GRU gated recurrent unit neural network controls data update through an update gate and a reset gate, and obtains a new time step by adding or deleting state information , and the calculation formula is: ; , , ; Among them, W is the input weight matrix, R is the recurrent 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 the candidate hidden state, is the reset gate, is the update gate.

[0012] The above method for filling in the missing original data for bottom-mounted acoustic wave observation. The specific process of finding the optimal matching path between two time series by the DTW dynamic time warping algorithm is as follows: Construct a cumulative distance matrix: There are two time series with lengths m and n, 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 , and the derivation formula is: ; Find the optimal path: Starting from the lower right corner of the cumulative distance matrix C, through backtracking, in each step, according to the cumulative distance at the current position, select the adjacent position with the smallest cumulative distance as the previous position until backtracking to the upper left corner . The index pairs corresponding to the points on this path constitute the optimal matching between the two time series.

[0013] The beneficial effects of the present invention are as follows. For the problem of missing original depth data in complex time series with non-stationarity, trends, and transient changes in bottom-mounted acoustic wave measurement, the present invention can efficiently restore the original state of different amounts of continuously missing data, solve the problems such as filling distortion caused by the increase in the continuous missing amount of other time series models, and improve the measurement accuracy of wave height and wave period.

[0014] (1) For the problem of refined extraction of original missing data in non-linear and non-stationary acoustic wave observation, through the singular spectrum analysis (SSA) algorithm, several components with different scales are adaptively extracted from large-scale components to detail components, improving the resolution ability of the filling model for trend components and transient change components.

[0015] (2) For problems such as the filling efficiency and accuracy of missing data in the large-scale trend components extracted by SSA, through the BP neural network fitting function, automatically learn the "reasonable rules" between input and output data, and train to generate a non-linear continuous function adapted to the global situation in the case of local data missing, improving the filling speed and accuracy of missing data in large-scale trend components.

[0016] (3) For problems such as fitting the true distribution of missing data in small-scale transient change components extracted by SSA, using the existing real observation data before and after the missing part, through the non-linear modeling ability of GRU and the dynamic fusion matching ability of DTW, better fit the true distribution of missing data, and improve the distribution goodness of filling missing data in small-scale transient change components. Description of the Drawings

[0017] Figure 1 is the schematic diagram of the process of the present invention; Figure 2 is the schematic diagram of continuous missing data in the embodiment of the present invention; Figure 3 is the schematic diagram of the data after filling in the embodiment of the present invention; Figure 4 is the comparative analysis diagram of wave height characteristic values in the embodiment of the present invention; Figure 5 is the comparative analysis diagram of wave period characteristic values in the embodiment of the present invention. Detailed implementation manners

[0018] To enable those skilled in the art to better understand the technical solution of the present invention, the present invention will be described in detail below with reference to the accompanying drawings and specific implementation manners.

[0019] As Figure 1 shown, this embodiment discloses a method for filling continuous missing original data for bottom-mounted 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 transient change component are extracted. The missing part of the trend component is generated by fitting through a BP network; the missing part of the transient change component is generated by forward and backward prediction through a GRU neural network based on the existing observation data of the front and rear time series to generate two time series filling data, and the two time series data are fused into the optimal matching missing filling data of the transient change component through the dynamic time warping (DTW) algorithm; after the missing data filling of the trend component and the transient change component is completed, they are accumulated to generate complete original data for statistical calculation of wave characteristic values.

[0020] (1) Singular spectrum (SSA) signal decomposition The singular spectrum analysis delimits the decomposition window according to the minute level, constructs a trajectory matrix based on the effective time period of the missing data, and obtains the trend component and transient change component of each effective time period through singular spectrum decomposition, completing the classification and extraction. The singular spectrum analysis (SSA) is an algorithm for time series analysis. It combines the ideas of principal component analysis and time series decomposition. A time series is decomposed into a series of subsequences with different characteristics by constructing a trajectory matrix and then performing singular value decomposition (SVD) on it. Each subsequence represents a different component of the original time series, and it is mainly used for time series decomposition, noise reduction, trend extraction, period analysis, etc.

[0021] The first step is to construct a trajectory matrix: Given a time series {x1, x2,..., x 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) from the time series according to certain rules. The matrix expression is shown in formula (1).

[0022] (1).

[0023] Second step, singular value decomposition (SVD): Perform singular value decomposition on the trajectory matrix X, and the decomposition formula is shown in formula (2).

[0024] (2); where is an L×L left singular orthogonal matrix, and its column vectors are called left singular vectors; is a diagonal matrix of L×K singular values, and the diagonal elements are singular values; is a K×K right singular orthogonal matrix, and its column vectors are called right singular vectors.

[0025] Third step, grouping and reconstruction: According to the magnitudes 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 one group to represent the trend component, group the basic matrices with periodic characteristics into one group to represent the periodic component, and the rest into the noise component, thereby realizing the decomposition and analysis of the original time series.

[0026] (2) Fitting and filling the trend component data with a BP neural network The singular spectrum (SSA) algorithm extracts the missing trend component data, and the BP neural network fits and generates the overall trend component data based on the existing time series data to complete the filling of the missing data. The BP neural network fitting function automatically learns the "reasonable rules" between the input and output data. In the case of local data missing, it trains and generates a non-linear continuous function adapted to the global situation, improving the speed and accuracy of filling the missing data of the large-scale trend component. BP is a multi-layer feedforward neural network, which adjusts the weights of the network through the backpropagation algorithm to minimize the error between the network output and the expected output. Through two simple processes of forward calculation and backpropagation, using the gradient descent method, it gradually updates the parameter matrices in the network, thereby realizing other tasks such as fitting of the function.

[0027] First step, network architecture: The BP neural network has 1 input layer, m hidden layers, and 1 output layer. Each neuron receives the input from the neurons in the previous layer, and after weighted summation and processing by the non-linear activation function, it passes the output to the next layer. Step 2, Input layer to hidden layer: Assume that there are n neurons in the input layer, 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 j-th neuron in the hidden layer is , the net input of the j-th neuron in the hidden layer is , after being processed by the activation function , the output of the j-th neuron in the hidden layer is . The expression is shown in formula (3).

[0028] (3).

[0029] Step 3, Hidden layer to output layer: The weight from the j-th neuron in the (m - 1)-th hidden layer to the k-th neuron in the m-th hidden layer is , the bias of the neuron is , the net input of the k-th neuron is , after being processed by the activation function , the output of the k-th neuron in the hidden layer is , and the output of the k-th neuron in the output layer is . The expression is shown in formula (4).

[0030] (4).

[0031] Step 4, Backpropagation: The purpose of backpropagation is to update the weights and biases. The LM algorithm is an improved backpropagation algorithm that combines the advantages of the gradient descent method and the Gauss-Newton method and can converge to the optimal solution faster. The update formula is shown in formula (5): (5); where, is the update amount of the parameter vector V. Assume that the number of weight and bias parameters is p, then V is a p-dimensional vector; J is the Jacobian matrix, and its 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 contributions of the gradient descent method and the Gauss-Newton method. When is very large, it is close to the gradient descent method; when is very small, it is close to the Gauss-Newton method; is the p×p identity matrix.

[0032] (3) GRU-DTW Transient Component Filling ​The transient components extracted by the Singular Spectrum Analysis (SSA) algorithm are filled with missing data for each part of the data through the GRU-DTW neural network model according to the forward and backward complete time series data of the missing data period of the transient components. First, the continuous filled time series data of the forward missing points are generated by GRU using the forward non-missing sampling point data. Secondly, the continuous filled time series data of the backward missing points are generated by GRU using the backward non-missing sampling point data, and the sequence data consistent with the forward filled data are generated after sequence reversal. Finally, the optimal matching path between the two time series is found through (DTW) to ensure that they can be aligned as much as possible on the time axis and have the same length as the filled data. Through the non-linear modeling ability of GRU and the dynamic fusion matching ability of DTW, the true distribution of the missing data is better fitted, and the distribution goodness of filling the missing data of the small-scale transient change components is improved.

[0033] 1) Gated Recurrent Unit (GRU) Neural Network 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, and the matrix multiplication becomes smaller, which improves the training efficiency of the data model, making it easier to converge and form a large model algorithm. 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 correlations in the time series. GRU controls data update through the update gate and the reset gate, adding or deleting state information to obtain a new time step. 。

[0034] The inputs of the reset gate and the update gate are composed of the current time step and the hidden state of the previous time step t - 1. The candidate hidden state is obtained through the update gate , the hidden state . The candidate hidden state is calculated by multiplying the result of the reset gate and the hidden state at time step t - 1, concatenating with the current time step , and passing through the tanh calculation. The calculation formulas are shown in Formulas (6) and (7). Where W is the input weight matrix, R is the recurrent weight matrix, b is the bias matrix, is the sigmoid function; , , represent the reset gate, the update gate, and the candidate state respectively.

[0035] (6); , , (7).

[0036] 2) DTW (Dynamic Time Warping) The DTW (Dynamic Time Warping) algorithm is a classic algorithm for measuring the similarity between two time series. Its core idea is to find the optimal matching path between two time series through dynamic programming, so that they can be aligned as much as possible on the time axis, thereby calculating the similarity measure between them. It allows time series to stretch and distort on the time axis to overcome the problem of time misalignment caused by factors such as speed and rhythm.

[0037] The first step is to construct the cumulative distance matrix: Suppose there are two time series with lengths m and n, denoted as F = [f1, f2,..., f m ] and G = [g1, g2,..., g n ]. First, it is necessary to calculate the Euclidean distance matrix between them . After obtaining the distance matrix D, it is necessary to construct a cumulative distance matrix , and the derivation formula is shown in formula (8).

[0038] (8).

[0039] The second step is to find the optimal path: Starting from the lower right corner of the cumulative distance matrix C , find the optimal path through backtracking. At each step, according to the cumulative distance at the current position, select the adjacent position with the smallest cumulative distance as the previous position until backtracking to the upper left corner . The index pairs corresponding to the points on this path constitute the optimal matching between the two time series.

[0040] (4) After the trend component and the dynamic component are filled, a complete depth data is reconstructed. According to the wave statistics calculation method, the filled original depth data is converted into wave height and wave period. For different numbers of consecutive missing data (such as in the cases of 60 steps, 100 steps, and 261 steps of consecutive missing data at the same time), this technology has good filling effects, and the filling data of each missing data segment efficiently restores the distribution state of the original depth data, solving the problems such as inaccurate wave height and wave period caused by the missing of original data.

[0041] This embodiment uses Figure 2Taking the missing data as an example, the sampling point ranges of continuous missing data are selected in three parts. The first part is from point 300 to point 360, the second part is from point 700 to point 960, and the third part is from point 1361 to point 1460. Through the filling method disclosed in this embodiment, after reconstructing the three filled trend components and dynamic components, the final estimated depth data is formed, as Figure 3 shown. According to the wave statistical calculation method, the filled original depth data is converted into wave height and wave period, and a numerical difference comparison analysis is carried out with the actual wave height and wave period. The comparison parameters mainly include the maximum wave height (Hmax) and the corresponding period (Tmax), the one-tenth wave height (H1 / 10) and the corresponding period (T1 / 10), the one-third wave height (H1 / 3) and the corresponding period (T1 / 3), and the average wave height (Have) and the corresponding period (Tave). The comparison analysis is as Figures 4-5 shown.

[0042] It can be seen from the wave characteristic values obtained statistically that compared with the real data, the wave height and wave period characteristic values of the missing data are generally smaller, and the mean absolute errors are 0.03 m and 0.825 s respectively. Compared with the real data, the wave height characteristic data of the BPNN and NARX filled data are generally higher. The mean absolute errors of the wave height are 0.29 m and 0.11 m respectively, and the mean absolute errors of the wave period are 0.773 s and 0.57 s respectively. Compared with the statistical error before filling, the error of the wave height characteristic value increases, and although the wave period characteristic value has improved, the advantage is not obvious. Compared with the real data, the wave height and wave period characteristic values of the LSTM and BiLSTM filled data have good similarity. The mean absolute errors of the wave height are 0.013 m and 0.005 m respectively, and the mean absolute errors of the wave period are 0.41 s and 0.28 s respectively. Compared with the statistical error before filling, the mean absolute errors of the wave height are reduced by 56.7% and 83.3% respectively, and the mean absolute errors of the wave period are reduced by 50.3% and 66.1% respectively. Compared with the real data, the overall data consistency of the wave height and wave period of the filling data by the method of this embodiment is the strongest. The mean absolute error of the wave height is 0.0025 m, and the mean absolute error of the wave period is 0.055 s. Compared with the statistical error before filling, the mean absolute error of the wave height is reduced by 91.7%, and the mean absolute error of the wave period is reduced by 93.3%.

[0043] Under the comprehensive consideration of the overall mean absolute error of the wave characteristic values, the methods of this embodiment, LSTM and BiLSTM have obvious advantages in filling the trend and instantaneous dynamic continuous missing data compared with the BPNN and NARX methods. Compared with the statistical error before filling, this technology has more advantages in the filling accuracy than LSTM and BiLSTM. The overall accuracy of the wave height is improved by 35 percentage points and 8.4 percentage points respectively, and the overall accuracy of the wave period is improved by 40 percentage points and 27.2 percentage points respectively.

[0044] The above embodiments are only exemplary embodiments of the present invention and are not used to limit the present invention. Those skilled in the art can make various modifications or equivalent substitutions to the present invention within the essence and protection scope of the present invention, and such modifications or equivalent substitutions should also be regarded as falling within the protection scope of the present invention.

Claims

1. A method for filling in continuously missing original data for bottom-mounted acoustic wave observation, characterized in that It includes the following steps: Step 1: Decompose the original time series into different eigen subsequences by the singular spectrum analysis algorithm, and extract the trend component and the transient change component; Step 2: For the missing part of the trend component obtained in Step 1, use the BP neural network to fit and generate the overall trend component data based on the existing time series data to complete the filling of the missing data; Step 3: For the transient change component obtained in Step 1, according to the forward and backward complete time series data of the missing data period of the transient component, use the GRU-DTW neural network model to complete the filling of the missing data for each part of the data respectively; Step 4: After the data filling in Step 2 and Step 3 is completed, reconstruct the complete original data for the statistical calculation of wave characteristic values.

2. The method for filling in continuously missing original data for bottom-mounted acoustic wave observation according to claim 1, wherein The specific content of Step 1 includes: Step 1.1, construct a trajectory matrix: Given a time series {x1, x2, …, x N} of length N, select a window length L, where 1 < L < N / 2, and construct a trajectory matrix X of size L×K according to certain rules for the time series, where K = N - L + 1; Step 1.2: Singular value decomposition: Perform singular value decomposition on the trajectory matrix X, and the decomposition formula is: ; Among them, is an L×L left singular orthogonal matrix, and its column vectors are called left singular vectors; is a diagonal matrix of L×K singular values, and the diagonal elements are singular values; is a K×K right singular orthogonal matrix, and its column vectors are called right singular vectors; Step 1.3, grouping and reconstruction: According to the magnitude and characteristics of the singular values, matrices are grouped, a series of subsequences are decomposed, the matrices corresponding to the larger singular values are grouped into one group to represent the trend component, i.e., the trend component, and the matrices with periodic characteristics are grouped into one group to represent the periodic component, i.e., the transient change component.

3. The method for filling in continuously missing original data for bottom-mounted acoustic wave observation according to claim 1, wherein The specific content of Step 2 is: The BP neural network has 1 input layer, m hidden layers and 1 output layer. Each neuron receives the input from the neurons of the previous layer. After weighted summation and processing by the non-linear activation function, the output is passed to the next layer. The expression from the input layer to the hidden layer is: ; Among them, 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 j-th neuron in the hidden layer; is the net input of the j-th neuron in the hidden layer; after being processed by the activation function the output of the j-th neuron in the hidden layer is ; The expression from the hidden layer to the output layer is: ; Among them, is the weight from the j-th neuron in the (m - 1)-th hidden layer to the k-th neuron in the m-th hidden layer; is the bias of the neuron; is the net input of the k-th neuron; after being processed by the activation function the output of the k-th neuron in the hidden layer is , and the output of the k-th neuron in the output layer is ; Update the weights and biases through backpropagation.

4. The method for filling in continuously missing original data for bottom-mounted acoustic wave observation according to claim 3, characterized in that, The backpropagation adopts the LM algorithm, combining the gradient descent method and the Gauss-Newton method, and the update formula is: ； Among them, 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 contributions of the gradient descent method and the Gauss-Newton method. When is very large, it is close to the gradient descent method; when is very small, it is close to the Gauss-Newton method; is the p×p identity matrix.

5. The method for filling continuous missing original data for bottom-mounted acoustic wave observation according to claim 1, characterized in that The specific content of Step 3 is: Use the data of the forward non-missing sampling points to generate the continuous filling time series data of the forward missing points through the GRU gated recurrent unit neural network; use the data of the backward non-missing sampling points to generate the continuous filling time series data of the backward missing points through the GRU gated recurrent unit neural network; generate the sequence data consistent with the forward filling data after sequence reversal; find the optimal matching path between the two time series through the DTW dynamic time warping algorithm, so that the two sequences are aligned on the time axis and have the same length as the filling data.

6. The method for filling in continuously missing original data for bottom-mounted acoustic wave observation according to claim 5, characterized in that The GRU (Gated Recurrent Unit) neural network controls data update through an update gate and a reset gate, and obtains a new time step by adding or deleting state information , and the calculation formula is as follows: ; , , ; where, W is the input weight matrix, R is the recurrent weight matrix, and b is the bias matrix, is the sigmoid function; is the current time step, is the hidden state at the previous time step, is the candidate hidden state, is the reset gate, is the update gate.

7. The method for filling in continuously missing original data for bottom-mounted acoustic wave observation according to claim 5, characterized in that The specific process of the DTW (Dynamic Time Warping) algorithm to find the optimal matching path between two time series is as follows: Construct a cumulative distance matrix: There are two time series with lengths 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 , and the derivation formula is: ； Finding the optimal path: starting from the lower right corner of the cumulative distance matrix C and, through backtracking, at each step, according to the cumulative distance at the current position, select the adjacent position with the minimum cumulative distance as the previous position until backtracking to the upper left corner , the index pairs corresponding to the points on this path constitute the optimal match between the two time series.

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