Denoising method for multidimensional time series autoencoder of towed sensor array

Abstract

The present invention discloses a method for denoising a multidimensional time series autoencoder of a towed sensor array. The method integrates the traditional time series denoising method into deep learning. Based on the VAE network framework, the convolutional neural network of its generator is replaced with a deep residual shrinkage network to achieve the purpose of removing high and low threshold noise. By introducing the residual shrinkage network, the improved residual shrinkage network is suitable for the situation where the noise content in each sample is different, and is suitable for removing noise signals within the threshold. After that, the image after soft threshold denoising is output through a wavelet transform neural network. The wavelet neural network is used as the basic architecture of the generator. The present invention can be applied to the original signals collected in a variety of scenarios, has a wide range of applications, and its practicality and accuracy are significantly improved.

Description

Technical Field

[0001] The present invention belongs to the field of ocean observation and deep learning technology, and specifically relates to a denoising method for a multidimensional time series autoencoder of a towed sensor array. Background Art

[0002] Time series denoising is an important step in processing collected time series signals. It has broad application prospects in the processing of time series signals collected in various scenarios. In practical applications, due to the complexity of the signal collection environment and the interference of various factors, the collected signals have a lot of noise, which affects the collection and utilization of effective information and poses great challenges to the utilization of signals.

[0003] Time series acquisition equipment has been widely used, such as in many fields such as weather forecasting, security monitoring and underwater detection. However, acquisition equipment is often affected by jitter, moving objects, impurities and noise in the water, resulting in unclean captured photos. Therefore, the research on time series denoising technology has important theoretical and practical application value. The denoised data is helpful for further use and analysis.

[0004] Traditional denoising technology is widely used, but it still has many shortcomings: for example, it removes a lot of useful noise, has low efficiency and limited application scenarios. Therefore, newer denoising methods are needed to help meet actual denoising needs. The development of deep learning provides many ideas and solutions. Summary of the invention

[0005] The purpose of the present invention is to provide a towed sensor array multidimensional time series autoencoder denoising method to make up for the deficiencies of the prior art.

[0006] In order to achieve the above object, the specific technical solution adopted by the present invention is:

[0007] A method for denoising a multidimensional time series autoencoder of a towed sensor array comprises the following steps:

[0008] S1: Build the overall link of the towing system;

[0009] S2: Deployment and recovery of the towed sensor array, collection of three-dimensional profile observation data of the towed sensor array, and obtaining the original signal;

[0010] S3: Use multi-source denoising to initially denoise the original acquired signal to obtain a possible true value reference value;

[0011] S4: The original acquisition signal and the corresponding true value reference are matrixed, and the GAF (Gramian Angular Field) matrix is ​​generated from the one-dimensional time series of the Cartesian coordinate system using polar coordinate encoding;

[0012] S5: Based on the matrixed two-dimensional original acquired signal and the corresponding true value reference as input and ideal output, the training set and test set are constructed;

[0013] S6: Improve the VAE (Variational Auto Encoder) network architecture to form a weighted soft threshold variational auto encoder network, and use the training set to train the network;

[0014] S7: Input the test data into the trained network model, output the VAE integrated denoised image, and convert it into a one-dimensional time series using polar coordinate decoding.

[0015] Furthermore, in S1, the overall link of the towing system is constructed: the towing system consists of a deck unit, a towing chain, a depth-fixing submersible, an electrode, etc.; the total length of the towing cable is L, which includes N s sensor integrated module, assuming the distance from the i-th node to the previous node is L i .

[0016] Furthermore, in S2, the deployment and recovery of the towed sensor (towed optical, temperature, salinity, pressure sensor) array includes the following steps:

[0017] 1) The deployment and recovery process of the towing chain is implemented by the deck unit winch, A-frame, and module assembly and disassembly device. Assume that the ship speed is v, the towing time is T, and the cable length from the water surface to the i-th node is l i The depth-fixing submersible ensures that the bottom of the towing chain can carry out three-dimensional profile observation within a certain depth, and tests the tension F(t) in real time to ensure that it is within the winch bearing capacity limit F max within;

[0018] 2) Based on the principle of electromagnetic coupling, the towing system realizes contactless power supply and data transmission in the same transmission link. The above-water electric control system converts DC power into high-frequency AC signals, and supplies power to the underwater sensor integrated module and performs data communication. Suppose the absorbance, fluorescence, temperature, conductivity, and pressure time series collected by the i-th sensor integrated module are A and B, respectively. i (t), F i (t), T i (t), C i (t), D i (t), t∈(0,T), i=1, 2,…,N s , the time series set is S i (t),For each sensor, the above five time series signals are processed.

[0019] Furthermore, in S3, traditional denoising methods include wavelet denoising, empirical mode decomposition and singular spectrum analysis.

[0020] Furthermore, the S4 specifically includes the following steps:

[0021] 1) For the time series set S of the i-th sensor i (t)=(s1,s2,…s i ), use the min-max scaler to scale the sequence to [-1,1];

[0022] 2) Then, for the scaled time series, calculate the dot product of each pair and put them into the Gram matrix, where G represents the Gram matrix, as shown below:

[0023]

[0024] 3) Convert the scaled Cartesian coordinate system time series to the polar coordinate system time series, because polar coordinates can preserve the absolute time relationship; suppose the time series consists of V timestamps t, and the value of the time series and its corresponding timestamp are represented by angle and radius respectively. The angle The calculation formula is as follows:

[0025]

[0026] where t∈(0,π);

[0027] 4) Calculate the radius variable r j , j represents the jth timestamp, and the interval [0,1] is divided into V equal parts; thus, V+1 separation points {0,…,1} are obtained; 0 is discarded, and these points are continuously associated with the time series one by one; the calculation formula is as follows:

[0028]

[0029] 5) Use the inner product operation to deal with sparsity. In order to best interpret individual and connection information from two perspectives, another operation of the inner product is defined as follows:

[0030]

[0031] The following Gram-like matrix is ​​obtained:

[0032]

[0033] The diagonal consists of the original values ​​of the scaled time series.

[0034] Furthermore, in S6, the VAE network is improved to obtain a weighted soft threshold variational autoencoder network. The basic architecture of the network mainly includes two parts: an encoder and a generator. The specific design steps are as follows:

[0035] 1) The encoder compresses the input two-dimensional image into a low-rank mapping. In the specific design, the two-dimensional representation data of the time series signal is decoded through a neural network. The original network is designed as an intermediate design with multiple hidden layers. Since the image input is a 64*64 size structure, it is flattened into a fully connected design with 4096 neuron structures. The encoder unit with a 4-layer neural network is input. Considering the mapping relationship between neurons in each layer, the second to fifth layers are designed as fully connected layers with 1000, 500, 250, and 30 neuron structures, respectively. Finally, it is downsampled to a two-dimensional structure, and the standard deviation and variance are output, denoted as α and β, to obtain the data distribution q of the original image. τ (z|x)=N(z;α,β 2 ).

[0036] 2) In the design of the generator, we follow the symmetric structure design with the encoder and use the reparameterization technique to transform N(z; α, β 2 ) distribution to obtain the input z, z of the generator G i =α+β⊙ε,i∈(1,2,3), where ε~N(0,I). Random sampling is performed three times to obtain three different data distributions. As input, the three sampling samples are sent to three generators for training respectively, which are used for denoising different signals collected in various situations;

[0037] Introducing the deep residual shrinkage network, this module is aimed at noisy data and uses the self-attention mechanism to automatically set the threshold to ensure that each sample has its own unique set of thresholds. At the same time, adding an identity path to the model reduces the difficulty of model training. The image after soft threshold denoising is then output through the wavelet transform neural network;

[0038] The network is designed to have a multi-generator structure, and the pixel mean square error (MSE) function is selected as the judgment criterion of the loss function; the two-dimensional image signal of the possible true value reference value is recorded as O t , the output of the previous generator With O t Calculate the error between the two The training cycle is repeated until the error value is less than the set threshold. Similarly, the other two denoising results can be obtained;

[0039] The data set is used for cyclic iterative parameter training until the network is fitted, and the network feature parameters are saved to obtain the network model weighted soft threshold variational autoencoder network.

[0040] Furthermore, in S7, the original time series signal to be denoised can be selected, the true reference value can be converted into a two-dimensional image sample, and then input into the generator network of the trained weighted soft threshold variational autoencoder network to obtain the output of three reconstructed samples, which correspond to the denoising results of the three traditional methods respectively, and the loss values ​​m1, m2, and m3 of the MSE of the sequence images denoised by the three generators and the multi-source method are calculated, and each loss is assigned a weight w1, w2, and w3, and the total error value loss is obtained as follows:

[0041] loss=w1m1+w2m2+w3m3 (6)

[0042] To minimize the total error, use each weight to combine the denoised image generated by each generator, output the VAE integrated denoised image, and convert the output GAF image into a one-dimensional time series using polar coordinate decoding to complete the denoising work.

[0043] Advantages and beneficial effects of the present invention:

[0044] Aiming at the problem of time series denoising, the present invention integrates the traditional time series denoising method into deep learning, and replaces the convolutional neural network of its generator with a deep residual shrinkage network based on the VAE network framework to achieve the purpose of removing high and low threshold noise. By introducing the residual shrinkage network, the sensitivity of the soft threshold function in deleting redundant features is improved; the improved residual shrinkage network is suitable for the situation where the noise content in each sample is different, and is suitable for removing noise signals within the threshold. The image after soft threshold denoising is then output via a wavelet transform neural network. Since the original convolutional neural network has a huge number of convolution operations and parameters, the operation speed is slow, and it cannot be directly used for image denoising, and due to the excellent effect of wavelet transform on signal noise removal, the present invention uses a wavelet neural network (WNN) as the basic architecture of the generator.

[0045] The present invention converts one-dimensional time series signals into two-dimensional images through the GAF method, adopts advanced image denoising methods for processing, and combines the advantages of traditional denoising methods with the auxiliary use of multiple traditional denoising methods. One network can solve the denoising problems of three traditional methods. The trained model can be applied to the original signals collected in various scenarios. It has a wide range of applications, and its practicality and accuracy are significantly improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0046] Figure 1 It is a flow chart of the present invention. DETAILED DESCRIPTION

[0047] The present invention is further explained and illustrated below through specific embodiments in conjunction with the accompanying drawings.

[0048] Embodiment 1:

[0049] A method for denoising a multidimensional time series autoencoder of a towed sensor array comprises the following steps (the specific process is as follows Figure 1 shown):

[0050] S1: Build the overall link of the towing system: The towing system consists of a deck unit, a towing chain, a depth-fixing submersible, electrodes, etc.; Assume that the total length of the towing cable is L, which includes N s sensor integrated module, assuming the distance from the i-th node to the previous node is L i ;

[0051] S2: Deployment and recovery of the towed sensor array, collection of three-dimensional profile observation data of the towed sensor array, and obtaining original signals; the towed sensor selects towed optical, temperature, salinity, and pressure sensors, as follows:

[0052] 1) The deployment and recovery process of the towing chain is implemented by the deck unit winch, A-frame, and module assembly and disassembly device. Assume that the ship speed is v, the towing time is T, and the cable length from the water surface to the i-th node is l i The depth-fixing submersible ensures that the bottom of the towing chain can carry out three-dimensional profile observation within a certain depth, and tests the tension F(t) in real time to ensure that it is within the winch bearing capacity limit F max within;

[0053] 2) Based on the principle of electromagnetic coupling, the towing system realizes contactless power supply and data transmission in the same transmission link. The above-water electric control system converts DC power into high-frequency AC signals, and supplies power to the underwater sensor integrated module and performs data communication. Suppose the absorbance, fluorescence, temperature, conductivity, and pressure time series collected by the i-th sensor integrated module are A and B, respectively. i (t), F i (t), T i (t), C i (t), D i (t), t∈(0,T), i=1, 2,…,N s , the time series set is S i (t), for each sensor, the above five time series signals are processed

[0054] S3: Use traditional denoising methods to denoise the original signal and obtain the real signal;

[0055] S4: The original signal and the real signal are matrix processed: the one-dimensional time series in the Cartesian coordinate system is converted into a polar coordinate system, and then a GAF matrix is ​​generated using a trigonometric function;

[0056] 1) For the time series set S of N sensorsi (t), use the min-max scaler to scale the sequence to [-1,1].

[0057] 2) Then, for the scaled time series, calculate the dot product of each pair and put them into the Gram matrix, where G represents the Gram matrix, as shown below:

[0058]

[0059] 3) Convert the scaled Cartesian coordinate system time series to polar coordinate system time series, because polar coordinates can preserve the absolute time relationship. Assume that the time series consists of V timestamps t, and the value of the time series and its corresponding timestamp are represented by angle and radius respectively. The angle The calculation formula is as follows:

[0060]

[0061] where t∈(0,π).

[0062] 4) Calculate the radius variable r j , j represents the jth timestamp, and the interval [0,1] is divided into V equal parts. Therefore, V+1 separation points {0,…,1} are obtained. 0 is discarded, and these points are continuously associated with the time series one by one. The calculation formula is as follows:

[0063]

[0064] 5) Use the inner product operation to deal with sparsity. In order to best interpret individual and connection information from two perspectives, another operation of the inner product is defined as follows:

[0065]

[0066] The following Gram-like matrix is ​​obtained:

[0067]

[0068] The diagonal consists of the original values ​​of the scaled time series;

[0069] S5: Based on the matrixed two-dimensional original acquired signal and the corresponding true value reference as input and ideal output, the training set and test set are constructed;

[0070] S6: Improve the VAE (Variational Auto Encoder) network architecture to form a weighted soft threshold variational auto encoder network, and use the training set to train the network;

[0071] S7: Input the test data into the trained network model, output the VAE integrated denoised image, and convert it into a one-dimensional time series using polar coordinate decoding.

[0072] Among them, based on the above three different denoising methods of original signals (of course, other existing denoising methods can also be adopted), the true reference value is converted into a two-bit signal image sample as a label value for reconstructing the denoised image;

[0073] At the encoder output N(z; α, β 2 ) distribution, the input z of the generator G is sampled three times continuously, and z is obtained respectively. i =α+β⊙ε,i∈(1,2,3). Among them ε~N(0,I);

[0074] Then it is input into the generator network of three weighted soft threshold variational autoencoder networks to obtain the output of three reconstructed samples, which correspond to the denoising results of three traditional methods respectively. The loss function is calculated respectively to evaluate the reconstruction performance, and multiple iterations are performed until the network model fits the output.

[0075] In S3, the traditional denoising method includes the following parts:

[0076] 1) Wavelet denoising method

[0077] Assume a noisy signal f(t), which can be expressed by the following formula:

[0078] f(t)=s(t)+e(t) (6)

[0079] Where s(t) represents the real signal and e(t) represents the noise signal.

[0080] Wavelet transform is applied to both sides of the above equation, and then an orthogonal wavelet and decomposition layer number l are selected to perform l-layer wavelet decomposition on the signal f(t).

[0081] The wavelet transform coefficients of the measured signal are processed by nonlinear threshold. The high-frequency coefficients of each layer from the 1st to the lth layer are processed by the soft threshold function, and the low-frequency coefficients of each layer are not processed. The soft threshold function is as follows:

[0082]

[0083] Where ω is the wavelet coefficient, λ is the selected threshold, σ is the variance, and sgn(w) is the sign function, i.e., it is 1 when w>0 and -1 when w<0).

[0084] The specific threshold selection rule is: for a discrete time series signal s(n), let f(n) = s 2 (n), the threshold is calculated as follows:

[0085]

[0086] Reconstruct the processed wavelet coefficients. k The low-frequency coefficients of the layer and the processed 1st to lth layers k The high-frequency coefficients of the layer are used to reconstruct the signal, thereby obtaining an estimated value S′1(t) of the original signal.

[0087] 2) The empirical mode decomposition (EMD) method is used to denoise the original time series signal.

[0088] First, find the average envelope: for the original signal s(t), find all the extreme points of s(t), fit the extreme points of s(t) by cubic spline interpolation method, and the fitting curve of the maximum points constitutes the upper envelope U(t), and the fitting curve of the minimum points constitutes the lower envelope D(t). Calculate the mean of U(t) and D(t), which is recorded as the average envelope m(t).

[0089]

[0090] Then subtract s(t) from m(t) to get the new sequence f1(t):

[0091] f1(t)=s(t)-m(t) (10)

[0092] The intrinsic mode function (IMF) criterion is applied to f1(t), and the IMF component standard is:

[0093] The number of zero points and extreme value points in the signal is equal or differs by at most 1; the mean of the maximum envelope and the minimum envelope is equal and is 0.

[0094] If f1(t) does not satisfy the above IMF criterion, replace s(t) with f1(t) and repeat formulas (11) and (12) to obtain new sequences f2(t) and m1(t):

[0095] f2(t)=f1(t)-m1(t) (11)

[0096] According to the IMF criterion, until f in equation (12) k (t) (k represents the number of times) meets the IMF condition for the first time, recorded as imf1(t); subtract it from s(t) to obtain the residual signal r1(t):

[0097] r1(t)=s(t)-imf1(t) (12)

[0098] Substituting r1(t) for s(t) and repeating the above steps, we can obtain multiple IMF components and the last inseparable sequence, which is recorded as the trend term r k (t). The EMD algorithm expression can be expressed as:

[0099]

[0100] That is, we get the estimated value of the real signal, recorded as S'2(t)

[0101] 3) Use singular spectrum analysis (SSA) method to denoise time series signals.

[0102] First, for the collected time series array S i (t), select a suitable window length H to lag the original time series and obtain the trajectory matrix:

[0103]

[0104] Let L<N / 2H. Let K=N-H+1K, then the trajectory matrix S is a matrix of H×K:

[0105]

[0106] Perform singular value decomposition (SVD) on the trajectory matrix and decompose S into the following form:

[0107] S=U∑V T (16)

[0108] Where U is an H×H matrix, ∑ is an H×K matrix with all elements 0 except the elements on the main diagonal, and V is a K×K matrix.

[0109] Further grouping is done based on SVD, dividing the original time series into multiple non-overlapping groups and dividing the original data into multiple sequences according to their importance.

[0110] Finally, the first ε main components are selected to reconstruct into a new time series, that is, the estimated value of the true signal is obtained, which is recorded as S'3(t).

[0111] In S6, a VAE network is used as the basis to remove signal noise. VAE uses a neural network to estimate the variational distribution q(z; φ). The input of the inference network is x, and the output is the variational distribution q(z|x; φ). The input of the generation network is z, and the output is the probability distribution p(z|x; θ).

[0112] After initializing the VAE network, an isotropic multivariate Gaussian distribution N(0,I) is selected as the prior p(z) of the latent variable, and the encoder output distribution maps the visible variable x to the latent variable z approximating the prior p(z). The inference model E outputs two separate variables α and β;

[0113] Use the reparameterization technique to transform N(z; α, β 2 ) to sample the input z of the generator G from the distribution: z i =α+β⊙ε,i∈(1,2,3), where ε~N(0,I), the reconstructed samples are obtained after cyclic training The two-dimensional image signal of the possible true value reference value is denoted as O t .

[0114] The pixel mean square error (MSE) function is selected as the criterion for the loss function; and O t Calculation error between The calculation formula is as follows:

[0115]

[0116] Among them, M o is the dimension of the original data, and F represents the norm.

[0117] Improve the above VAE network to obtain a weighted soft threshold variational autoencoder network. The steps are as follows:

[0118] 1) The encoder compresses the input two-dimensional image into a low-rank mapping, and decodes the two-dimensional representation data of the time series signal through a neural network. The original network is designed as an intermediate design with multiple hidden layers. The image input is a 64*64 size structure, which is flattened into a fully connected design with 4096 neuron structures. The encoder unit with a 4-layer neural network is input. According to the mapping relationship between neurons in each layer, the second to fifth layers are designed as fully connected layers with 1000, 500, 250, and 30 neuron structures, respectively. Finally, it is downsampled to a two-dimensional structure, and the standard deviation and variance are output, denoted as α and β, to obtain the data distribution q of the original image. τ (z|x)=N(z;α,β 2 ).

[0119] 2) The generator follows a symmetric structure design with the encoder, using the reparameterization technique from N(z; α, β 2 ) distribution to obtain the input z, z of the generator G i=α+β⊙ε,i∈(1,2,3), where ε~N(0,I). Random sampling is performed three times to obtain three different data distributions. As input, the three sampling samples are sent to three generators for training respectively, which are used for denoising different signals collected in various situations;

[0120] In the generator, a deep residual shrinkage network is introduced. This module is oriented to noisy data. It replaces "feature weighting" with "soft thresholding" and uses a self-attention mechanism to automatically set the threshold to ensure that each sample has its own unique set of thresholds. Therefore, the improved residual shrinkage network is suitable for situations where the noise content in each sample is different, and is suitable for removing noise signals within the threshold. At the same time, an identical path is added to the model to reduce the difficulty of model training.

[0121] The network is designed to have a multi-generator structure, and the pixel mean square error (MSE) function is selected as the judgment criterion of the loss function; the two-dimensional image signal of the possible true value reference value is recorded as O t , the output of the previous generator With O t Calculate the error between the two The training cycle is repeated until the error value is less than the set threshold. Similarly, the other two denoising results can be obtained;

[0122] The data set is used for cyclic iterative parameter training until the network is fitted, and the network feature parameters are saved to obtain the network model weighted soft threshold variational autoencoder network.

[0123] The model calculates the MSE losses m1, m2, and m3 through the three generators and the sequence images of possible true reference values ​​obtained by multi-source denoising, and assigns weights w1, w2, and w3 to each loss to obtain the total error value loss, so that the total error is minimized. Each weight is combined with the denoised image generated by each generator to form a fused denoised sequence image, and the denoised result is obtained through the wavelet neural network.

[0124] On the basis of the above embodiments, the present invention continues to describe in detail the technical features involved therein and the functions and roles played by the technical features in the present invention, so as to help technicians in this field fully understand the technical solution of the present invention and reproduce it.

Claims

1. A method for denoising a multidimensional time series autoencoder of a towed sensor array, characterized in that: The denoising method includes the following steps: S1: Build the overall link of the towing system; S2: deploying and recovering the towed sensor array, collecting the three-dimensional profile observation data of the towed sensor array, and obtaining the original acquisition signal; S3: Use multi-source denoising to initially denoise the original acquired signal to obtain a possible true value reference value; S4: The original acquisition signal and the corresponding true value reference are matrixed, and the GAF matrix is ​​generated from the one-dimensional time series of the Cartesian coordinate system using polar coordinate encoding; S5: Based on the matrixed two-dimensional original acquired signal and the corresponding true value reference as input and ideal output, the training set and test set are constructed; S6: Improve the autoencoder VAE network architecture, form a weighted soft threshold variational autoencoder network, and use the training set to train the network; the network infrastructure consists of two parts: the encoder and the generator. The specific design steps are as follows: 1) The encoder compresses the input two-dimensional image into a low-rank mapping. In the specific design, the two-dimensional representation data of the time series signal is decoded by the neural network and input into the encoder unit of the neural network. Considering the mapping relationship between neurons in each layer, the second to fifth layers are designed as fully connected layers with 1000, 500, 250, and 30 neuron structures, respectively. Finally, it is downsampled to a two-dimensional structure, and the standard deviation and variance are output, denoted as α and β, to obtain the data distribution q of the original image. τ (z|x)=N(z;α,β 2 ); 2) In the design of the generator, we follow the symmetric structure design with the encoder and use the reparameterization technique to transform N(z; α, β 2 ) distribution to obtain the input z, z of the generator G i =α+β⊙ε,i∈(1,2,3), where ε~N(0,I); Random sampling is performed three times to obtain three different data distributions. As input, the three sampling samples are sent to three generators for training respectively, which are used for denoising the original collected signals in various situations; 3) Introducing a deep residual shrinkage network, which uses a self-attention mechanism to automatically set thresholds for noisy data, ensuring that each sample has its own unique set of thresholds. At the same time, an identity path is added to the model to reduce the difficulty of model training. After that, the soft threshold denoised image is output through the wavelet transform neural network; 4) The network is designed to have a multi-generator structure, and the pixel mean square error function is selected as the judgment criterion of the loss function; the two-dimensional image signal of the possible true value reference value is recorded as O t , the output of the previous generator With O t Calculate the error between the two The training cycle is repeated until the error value is less than the set threshold. Similarly, the other two denoising results are obtained. 5) Use the data set to iterate parameter training until the network is fitted, and save the network feature parameters to obtain the network model weighted soft threshold variational autoencoder network; S7: Input the test data into the trained network model, output the VAE integrated denoised image, and convert it into a one-dimensional time series using polar coordinate decoding.

2. The denoising method according to claim 1, characterized in that: In S3, the multi-source denoising method includes wavelet transform, empirical mode decomposition and singular spectrum analysis.

3. The denoising method according to claim 1, characterized in that: The S4 specifically comprises the following steps: 1) For the time series set S of N sensors i (t)=(s1,s2,…s i ), use the min-max scaler to scale the sequence to [-1,1]; 2) Then, for the scaled time series, calculate the dot product of each pair and put it into the Gram matrix, where G represents the Gram matrix, as shown below: 3) Convert the scaled Cartesian coordinate system time series to the polar coordinate system time series; suppose the time series consists of V timestamps t, and the value of the time series and its corresponding timestamp are represented by angle and radius respectively. The calculation formula is as follows: where t∈(0,π); 4) Calculate the radius variable r j , j represents the jth timestamp, and the interval [0,1] is divided into V equal parts; thus, V+1 separation points {0,…,1} are obtained; 0 is discarded, and these points are continuously associated with the time series one by one; the calculation formula is as follows: 5) Use the inner product operation to handle sparsity. The inner product is defined as follows: The following Gram-like matrix is ​​obtained: The diagonal consists of the original values ​​of the scaled time series.

4. The denoising method according to claim 2, characterized in that: In S7, the original time series signal to be denoised is selected, the denoised signal is converted into a two-dimensional image sample, and then input into the generator network of the trained weighted soft threshold variational autoencoder network to obtain the output of three reconstructed samples, which correspond to the three true reference values ​​after multi-source denoising, respectively. The loss values ​​m1, m2, and m3 of the sequence images denoised by the three generators and the multi-source method are calculated, and each loss is assigned a weight w1, w2, and w3, and the total error value loss is obtained as follows: loss=w1m1+w2m2+w3m3(6) minimizes the total error, uses each weight to combine the denoised image generated by each generator, outputs the VAE integrated denoised image, and converts the denoised GAF ​​image into a one-dimensional time series using polar coordinate decoding to complete the denoising work.

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