A transformer oil gas concentration prediction method based on multi-window step-by-step decomposition

Abstract

The application discloses a transformer oil gas concentration prediction method based on multi-window step-by-step decomposition, adopts a step-by-step decomposition SDS sampling technology, firstly utilizes an HP filter to perform step-by-step decomposition, obtains a long-term trend item and a high-frequency fluctuation component, and utilizes singular spectrum analysis SSA to perform step-by-step decomposition on the high-frequency fluctuation component to obtain a short-period component. Wherein, the optimal decomposition window in the step-by-step decomposition process is determined by a dispersion entropy DE, a fuzzy entropy FE and an HP, SSA combined method, and the extraction effect of the model on time sequence characteristics is improved. Then, a variational mode decomposition VMD is adopted to perform noise reduction processing on the high-frequency item containing noise. Finally, each component obtained through decomposition is input into a long short-term memory network LSTM for prediction, the prediction values of each component are accumulated, and the prediction result of the original gas concentration is obtained. The method can solve the problems of low overall prediction accuracy of a single LSTM network and data leakage in a traditional sequence decomposition method according to the historical operation state data of the transformer.

Description

Technical Field

[0001] This invention relates to the field of power transformer operating status assessment and prediction, specifically to a method for predicting dissolved gas concentration in transformer oil based on multi-window stepwise decomposition. Background Technology

[0002] Currently, transformers, as one of the most critical pieces of equipment in the power system, have a significant impact on the stable operation of the power system. Relying on traditional, periodic manual maintenance for transformer health checks is extremely costly in terms of manpower, resources, and finances. It can also lead to excessive or untimely maintenance, resulting in transformer damage and shortened lifespan. The concentration of dissolved gases in transformer oil is related to latent transformer faults; therefore, predicting the concentration of dissolved gases in the oil can help assess the future condition of the transformer and implement refined management throughout its entire life cycle, effectively improving the reliability of power grid operation.

[0003] Dissolved Gas Analysis (DGA) is an internationally recognized effective method for detecting early-stage faults and defects in transformers. By using historical data of relevant oil condition indicators collected by online oil chromatography monitoring devices, it models and predicts future dissolved gas concentrations in the oil, effectively understanding equipment status and development trends. This has significant technical value for power transformer condition prediction. Currently, methods such as empirical mode decomposition (EMD), ensemble empirical mode decomposition (EEMD), and variational mode decomposition (VMD) have been studied for predicting dissolved gas concentrations in transformer oil. However, these decomposition methods all employ overall decomposition sampling (ODS) to process data samples, i.e., first decomposing the dissolved gas concentration sequence into subsequences, and then dividing them into training and test samples. This assumes that future data is known during the decomposition process, leading to data leakage, and the model training results cannot be used to guide online prediction.

[0004] Therefore, the applicant proposes a method for predicting the concentration of dissolved gases in transformer oil based on multi-window stepwise decomposition. Summary of the Invention

[0005] The purpose of this invention is to provide a method for predicting the concentration of dissolved gases in transformer oil based on multi-window stepwise decomposition, so as to improve the accuracy of predicting the concentration of dissolved gases in transformer oil.

[0006] To solve the above-mentioned technical problems, the present invention proposes the following technical solution:

[0007] A method for predicting transformer oil and gas concentration based on multi-window stepwise decomposition includes the following steps:

[0008] Step 1: Obtain dissolved gas concentration data in the original transformer oil;

[0009] Step 2: The dissolved gas concentration data in the original transformer oil is decomposed and noise reduced step by step to obtain the long-term trend component, short-period fluctuation component and modal component.

[0010] Step 3: Input the components of the gas sequence to be predicted after decomposition into the LSTM network for prediction;

[0011] Step 4: Superimpose and reconstruct the prediction results of each component to obtain the final prediction result of the gas concentration to be predicted.

[0012] In step 1, dissolved gas concentration data in transformer oil are selected, including H2, CH4, C2H4, C2H6, CO, and CO2. Sampling intervals and several sets of sample points are set, and the data is cleaned and normalized. Data cleaning includes: quality verification and correction of the data to ensure its accuracy; checking for missing values ​​and outliers in the data and processing them according to the actual situation. Through these processes, the dissolved gas concentration data in transformer oil can be made consistent and comparable, providing reliable input for subsequent decomposition and prediction steps.

[0013] Step 2 includes the following sub-steps:

[0014] Step 2.1: Perform sampling based on stepwise SDS decomposition:

[0015] Let the time series TS = {y t |t=1,...,L+K}, where L+K is the length of the time series TS, y t Let be the concentration of dissolved gases in the transformer oil at time t; use y1 to y L The remaining portion is used as training data and as test data.

[0016] Step 2.2: Perform HP-SSA-VMD decomposition based on stepwise SDS decomposition.

[0017] Step 2.2 includes the following sub-steps:

[0018] Step 2.2.1: Based on the SDS sampling in Step 2.1, HP filtering decomposition is performed on the complex original oil dissolved gas concentration sequence to obtain the long-term trend component and high-frequency fluctuation component with relatively simple features. The genetic algorithm is used to optimize the dispersion entropy value of the long-term trend component under different decomposition windows. Based on the variance of the dispersion entropy value, the window corresponding to the minimum variance is the optimal decomposition window T1.

[0019] Step 2.2.2: Perform SSA decomposition on the high-frequency fluctuation component obtained in Step 2.2.1 to obtain the short-period fluctuation component and the noisy high-frequency term. Use a genetic algorithm to optimize the fuzzy entropy value of the short-period fluctuation component under different decomposition windows. The window corresponding to the minimum fuzzy entropy value is the optimal decomposition window T2.

[0020] Step 2.2.3: Decompose the noisy high-frequency term obtained in Step 2.2.2 using the VMD method to obtain several modal components IMFn and a residual component RES. Calculate the permutation entropy value of each modal component and filter out modal components that are greater than the threshold as noise.

[0021] In step 2.2.1, when performing HP filtering decomposition on the complex dissolved gas concentration sequence in the original oil, the following steps are adopted:

[0022] Suppose time series data X = {x1, x2, ..., x} T The long-term trend sequence G = {g1, g2, ..., g} T} and short-term fluctuation sequence S={s1,s2,...s T} constitutes, i.e., x i =g i +s i Let i = 1, 2, ..., T; define the trend as a minimization problem:

[0023] The solution is given by the formula, where λ is the smoothing parameter; T is the number of samples in the time series X, G, and S; x T g T s T These represent the gas concentration values ​​of time series X, G, and S at time T, respectively.

[0024] Calculate the dispersion entropy value of the long-term trend component for a time series of length N, x = {x1, x2, x3, ..., x...}. N The following steps are adopted:

[0025] 1) First, consider the time series x = {x1, x2, x3, ..., x...} N The values ​​in the sequence {x} are normalized; generally, to reduce the impact of outliers, the normal cumulative distribution function (NCDF) is used to normalize the sequence {x}.i}Mapped to sequence {y i}, y={y1,y2,y3,...,y N}, {y i The value of} is between [0,1]; the specific formula for calculating this normalization is as follows:

[0026]

[0027] In the formula: σ and γ represent the time series {x} i The standard deviation and mean of the time series {x}; N is the time series {x}. i} and {y i The number of samples in}; x N y N They are time series {x i} and {y i The gas concentration value at time N;

[0028] 2) Transform the sequence {y} i The data is categorized into class c, as shown in the following formula:

[0029]

[0030] In the formula: c is the sequence z c Number of classes in z; c It is the sequence after partitioning; It is the sequence z c The i-th data in;

[0031] 3) Construct a sequence with a delay of d and dimension m. The formula is as follows:

[0032]

[0033] In the formula: It is the sequence z c The j-th data in;

[0034] 4) Change the sequence Mapping to discrete modes The formula is as follows:

[0035]

[0036] In the formula: c m It is assigned to each sequence The number of discrete patterns; It is a discrete mode; v i It is the i-th discrete value after being mapped to the discrete pattern, where i = 0, 1, ..., m-1;

[0037] 5) Calculate each c mDiscrete mode relative frequencies:

[0038]

[0039] In the formula: It is each c m The discrete mode relative frequencies; It is each c m Number of times it appears;

[0040] 6) For a sequence {x} with a time length of N, i Its dispersion entropy is:

[0041]

[0042] In the formula: It is each c m The discrete mode relative frequencies;

[0043] In step 2.2.2, when performing SSA decomposition on the high-frequency fluctuation components obtained in step 2.2.1, the following steps are adopted:

[0044] 1) Convert the original time series X = {x1, x2, x3, ..., x...} N Based on the set embedding dimension L (L≤N / 2), it is transformed into a trajectory matrix Y;

[0045]

[0046] In the formula: K = N - L + 1; N is the number of samples in the time series; x N This represents the gas concentration value at time N in the time series.

[0047] 2) Calculate matrix YY T eigenvalues ​​λ1, λ2, ..., λ L (λ1≥λ2≥…≥λ L ) and the corresponding eigenvectors U1, U2, ..., U L Let d be the number of non-zero eigenvalues, and define... Where Y T It is the transpose of the trajectory matrix Y; λ i It is a matrix YY T The i-th eigenvalue; the singular value decomposition of the trajectory matrix Y can be written as:

[0048] Y = Y1 + Y2 + ... + Y i i = 1, 2, ..., d (8)

[0049] In the formula: U i and V iLet be the left and right singular vectors corresponding to the i-th singular value of the trajectory matrix Y, and let each matrix Y... i The degree of contribution to the trajectory matrix Y and the eigenvalue λ i The relevant contribution rate η can be defined as:

[0050] η=λ i / ∑λ (9)

[0051] 3) Convert each submatrix Y i Reconstruct the time series of length N; assuming Y is an L×K matrix, let L* = min(L,K), K* = max(L,K), where K = N-L+1, L* is the minimum of L and K, and K* is the maximum of L and K; reconstruct the sequence Z. c =(z c1 ,z c2 ,…,z cn );

[0052] 4) Set the contribution rate threshold η e (generally η is taken) e (≥80%), then reconstruct the subsequence step by step according to the eigenvalues ​​from largest to smallest, and ∑λ i / ∑λ≥η e The sequence is reconstructed into short-period fluctuation components, and the remainder is reconstructed into noisy high-frequency terms. Then the fuzzy entropy value of the short-period fluctuation components is calculated.

[0053] In step 2.2.2, when decomposing the noisy high-frequency term obtained in step 2.2.2 using the VMD method, the following steps are adopted:

[0054] 1) Constructing a constrained variational optimality problem:

[0055]

[0056] In the formula: {u k} represents a set of K IMF components; {w k Let} be the set of K frequency centers; δ(t) be the Dirac function; and f(t) be the initial signal. To find the partial derivative of u with respect to t; k (t) is the Kth mode function; w k The center frequency of the Kth modal function;

[0057] 2) Using the Lagrange multiplier λ and the quadratic penalty factor α, the constrained variational problem is transformed into an unconstrained variational problem:

[0058]

[0059] In the formula: <·> indicates the inner product, and * represents the convolution operation;

[0060] 3) The Alternating Directional Multiplier Iteration Algorithm (ADMM) is used to continuously update each modal component and center frequency to obtain a specified number of VIMF components.

[0061] In step 3, the long-term trend component, short-period fluctuation component, and several modal components of the gas sequence to be predicted are input into the LSTM network for prediction.

[0062] In step 3, the prediction results of each component are superimposed and reconstructed to obtain the final prediction result of the gas concentration to be predicted. To verify the model's prediction effect, the root mean square error (RMSE), mean absolute percentage error (MAE), and mean absolute error (MAPE) are used as model evaluation indicators. The detailed expressions are as follows:

[0063]

[0064]

[0065]

[0066] In the formula, y i , These are the actual value, the average of the actual values, and the predicted value, respectively.

[0067] Compared with the prior art, the present invention has the following technical effects:

[0068] 1) The method provided by this invention, based on SDS sampling technology, can effectively avoid the data leakage problem in traditional ODS sampling technology;

[0069] 2) The method provided by this invention adopts adaptive determination of the optimal window for stepwise decomposition, and the establishment process of the two windows is carried out independently without interference. It has better universality than traditional decomposition methods and can update the window at any time according to different data, thereby decomposing subsequences with relatively obvious features, which is convenient for subsequent model prediction.

[0070] 3) The method proposed in this invention has better prediction performance than a single LSTM prediction model, providing some support and assistance for power transformer condition assessment and remaining life prediction. Attached Figure Description

[0071] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0072] Figure 1 This is a comparison chart of CO2 concentration prediction results between the method of this invention and the traditional method;

[0073] Figure 2 This is a comparison chart of the prediction error MAE between the method of this invention and the traditional method;

[0074] Figure 3 This is a flowchart of the method of the present invention. Detailed Implementation

[0075] A method for predicting transformer oil and gas concentration based on multi-window stepwise decomposition includes the following steps:

[0076] Step 1: Obtain dissolved gas concentration data in the original transformer oil;

[0077] Step 2: The dissolved gas concentration data in the original transformer oil is decomposed and noise reduced step by step to obtain the long-term trend component, short-period fluctuation component and modal component.

[0078] Step 3: Input the components of the gas sequence to be predicted after decomposition into the LSTM network for prediction;

[0079] Step 4: Superimpose and reconstruct the prediction results of each component to obtain the final prediction result of the gas concentration to be predicted.

[0080] In step 1, dissolved gas concentration data in transformer oil are selected, including H2, CH4, C2H4, C2H6, CO, and CO2. Sampling intervals and several sets of sample points are set, and the data is cleaned and normalized. Data cleaning includes: quality verification and correction of the data to ensure its accuracy; checking for missing values ​​and outliers in the data and processing them according to the actual situation. Through these processes, the dissolved gas concentration data in transformer oil can be made consistent and comparable, providing reliable input for subsequent decomposition and prediction steps.

[0081] Step 2 includes the following sub-steps:

[0082] Step 2.1: Perform sampling based on stepwise SDS decomposition:

[0083] Let the time series TS = {y t |t=1,...,L+K}, where L+K is the length of the time series TS, y t Let be the concentration of dissolved gases in the transformer oil at time t; use y1 to y L The remaining portion is used as training data and as test data.

[0084] Step 2.2: Perform HP-SSA-VMD decomposition based on stepwise SDS decomposition.

[0085] Step 2.2 includes the following sub-steps:

[0086] Step 2.2.1: Based on the SDS sampling in Step 2.1, HP filtering decomposition is performed on the complex original oil dissolved gas concentration sequence to obtain the long-term trend component and high-frequency fluctuation component with relatively simple features. The genetic algorithm is used to optimize the dispersion entropy value of the long-term trend component under different decomposition windows. Based on the variance of the dispersion entropy value, the window corresponding to the minimum variance is the optimal decomposition window T1.

[0087] Step 2.2.2: Perform SSA decomposition on the high-frequency fluctuation component obtained in Step 2.2.1 to obtain the short-period fluctuation component and the noisy high-frequency term. Use a genetic algorithm to optimize the fuzzy entropy value of the short-period fluctuation component under different decomposition windows. The window corresponding to the minimum fuzzy entropy value is the optimal decomposition window T2.

[0088] Step 2.2.3: Decompose the noisy high-frequency term obtained in Step 2.2.2 using the VMD method to obtain several modal components IMFn and a residual component RES. Calculate the permutation entropy value of each modal component and filter out modal components that are greater than the threshold as noise.

[0089] In step 2.2.1, when performing HP filtering decomposition on the complex dissolved gas concentration sequence in the original oil, the following steps are adopted:

[0090] Suppose time series data X = {x1, x2, ..., x} T The long-term trend sequence G = {g1, g2, ..., g} T} and short-term fluctuation sequence S={s1,s2,...s T} constitutes, i.e., x i =g i +s i Let i = 1, 2, ..., T; define the trend as a minimization problem:

[0091] The solution is given by the formula, where λ is the smoothing parameter; T is the number of samples in the time series X, G, and S; x T g T s T These represent the gas concentration values ​​of time series X, G, and S at time T, respectively.

[0092] Calculate the dispersion entropy value of the long-term trend component for a time series of length N, x = {x1, x2, x3, ..., x...}. N The following steps are adopted:

[0093] 1) First, consider the time series x = {x1, x2, x3, ..., x...} N The values ​​in the sequence {x} are normalized; generally, to reduce the impact of outliers, the normal cumulative distribution function (NCDF) is used to normalize the sequence {x}.i}Mapped to sequence {y i}, y={y1,y2,y3,...,y N}, {y i The value of} is between [0,1]; the specific formula for calculating this normalization is as follows:

[0094]

[0095] In the formula: σ and γ represent the time series {x} i The standard deviation and mean of the time series {x}; N is the time series {x}. i} and {y i The number of samples in}; x N y N They are time series {x i} and {y i The gas concentration value at time N;

[0096] 2) Transform the sequence {y} i The data is categorized into class c, as shown in the following formula:

[0097]

[0098] In the formula: c is the sequence z c Number of classes in z; c It is the sequence after partitioning; It is the sequence z c The i-th data in;

[0099] 3) Construct a sequence with a delay of d and dimension m. The formula is as follows:

[0100]

[0101] In the formula: It is the sequence z c The j-th data in;

[0102] 4) Change the sequence Mapping to discrete modes The formula is as follows:

[0103]

[0104] In the formula: c m It is assigned to each sequence The number of discrete patterns; It is a discrete mode; v i It is the i-th discrete value after being mapped to the discrete pattern, where i = 0, 1, ..., m-1;

[0105] 5) Calculate each c mDiscrete mode relative frequencies:

[0106]

[0107] In the formula: It is each c m The discrete mode relative frequencies; It is each c m Number of times it appears;

[0108] 6) For a sequence {x} with a time length of N, i Its dispersion entropy is:

[0109]

[0110] In the formula: It is each c m The discrete mode relative frequencies;

[0111] In step 2.2.2, when performing SSA decomposition on the high-frequency fluctuation components obtained in step 2.2.1, the following steps are adopted:

[0112] 1) Transform the original time series X = {x1, x2, x3, ..., x...} N Based on the set embedding dimension L (L≤N / 2), it is transformed into a trajectory matrix Y;

[0113]

[0114] In the formula: K = N - L + 1; N is the number of samples in the time series; x N This represents the gas concentration value at time N in the time series.

[0115] 2) Calculate matrix YY T eigenvalues ​​λ1, λ2, ..., λ L (λ1≥λ2≥…≥λ L ) and the corresponding eigenvectors U1, U2, ..., U L Let d be the number of non-zero eigenvalues, and define... Where Y T It is the transpose of the trajectory matrix Y; λ i It is a matrix YY T The i-th eigenvalue; the singular value decomposition of the trajectory matrix Y can be written as:

[0116] Y = Y1 + Y2 + ... + Y i i = 1, 2, ..., d (22)

[0117] In the formula: U i and V iLet be the left and right singular vectors corresponding to the i-th singular value of the trajectory matrix Y, and let each matrix Y... i The degree of contribution to the trajectory matrix Y and the eigenvalue λ i The relevant contribution rate η can be defined as:

[0118] η=λ i / ∑λ (23)

[0119] 3) Convert each submatrix Y i Reconstruct the time series of length N; assuming Y is a matrix of shape L×K, let L*×min(L,K) and K*×max(L,K), where K×N-L+1, L* is the minimum value of L and K, and K* is the maximum value of L and K; reconstruct the sequence Z. c =(z c1 ,z c2 ,…,z cn );

[0120] 4) Set the contribution rate threshold η e (generally η is taken) e (≥80%), then reconstruct the subsequence step by step according to the eigenvalues ​​from largest to smallest, and ∑λ i / ∑λ≤η e The sequence is reconstructed into short-period fluctuation components, and the remainder is reconstructed into noisy high-frequency terms. Then the fuzzy entropy value of the short-period fluctuation components is calculated.

[0121] In step 2.2.2, when decomposing the noisy high-frequency term obtained in step 2.2.2 using the VMD method, the following steps are adopted:

[0122] 1) Constructing a constrained variational optimality problem:

[0123]

[0124] In the formula: {u k} represents a set of K IMF components; {w k Let} be the set of K frequency centers; δ(t) be the Dirac function; and f(t) be the initial signal. To find the partial derivative of u with respect to t; k (t) is the Kth mode function; w k The center frequency of the Kth modal function;

[0125] 2) Using the Lagrange multiplier λ and the quadratic penalty factor α, the constrained variational problem is transformed into an unconstrained variational problem:

[0126]

[0127] In the formula: <·> indicates the inner product, and * represents the convolution operation;

[0128] 3) The Alternating Directional Multiplier Iteration Algorithm (ADMM) is used to continuously update each modal component and center frequency to obtain a specified number of VIMF components.

[0129] In step 3, the long-term trend component, short-period fluctuation component, and several modal components of the gas sequence to be predicted are input into the LSTM network for prediction.

[0130] In step 3, the prediction results of each component are superimposed and reconstructed to obtain the final prediction result of the gas concentration to be predicted. To verify the model's prediction effect, the root mean square error (RMSE), mean absolute percentage error (MAE), and mean absolute error (MAPE) are used as model evaluation indicators. The detailed expressions are as follows:

[0131]

[0132]

[0133]

[0134] In the formula, y i , These are the actual value, the average of the actual values, and the predicted value, respectively.

[0135] Example:

[0136] A method for predicting dissolved gas concentration in transformer oil based on multi-window stepwise decomposition sampling (SDS) is proposed. First, a Hodrick-Prescott (HP) filter is used for stepwise decomposition to obtain long-term trend terms and high-frequency fluctuation components. Then, singular spectrum analysis (SSA) is used to further decompose the high-frequency fluctuation components to obtain short-period components. Specifically, the optimal decomposition window in the stepwise decomposition process is determined by combining dispersion entropy (DE) and fuzzy entropy (FE) with HP and SSA, respectively, to improve the model's extraction of time-series features. Next, variational mode decomposition (VMD) is used to denoise the noisy high-frequency terms. Finally, the decomposed components are input into a long short-term memory (LSTM) network for prediction, and the predicted values ​​of each component are accumulated to obtain the predicted gas concentration. The method of this invention can solve the problems of low overall prediction accuracy of a single LSTM network and data leakage in traditional sequence decomposition methods by using the collected historical operating status data of transformers.

[0137] Specifically, the following steps are included:

[0138] Step 1: Obtain dissolved gas concentration data in the original transformer oil; Select dissolved gas concentration data in the oil of a certain 500kV transformer, with the time series starting and ending from April 11, 2011 to January 5, 2014, including H2, CH4, C2H4, CO, and CO2, with a sampling interval of 1 day. 1000 sample points were obtained for the 5 gases. The data from the first 800 days were selected as the training set, and the data from the last 200 days were selected as the test set. The statistical characteristics of CO2 data are shown in Table 1.

[0139] Table 1 Dataset Characteristics

[0140] Table 1 Collection characteristics

[0141]

[0142] Step 2: Based on a stepwise decomposition sampling strategy, three different decomposition methods—HP, SSA, and VMD—are used to stepwise decompose and denoise the dissolved gas concentration data in the original transformer oil, obtaining long-term trend components, short-period fluctuation components, and modal components with lower complexity. Specific measures are as follows:

[0143] First, the gas sequence is subjected to stepwise HP decomposition to obtain the long-term trend term and high-frequency fluctuation components. The variance of the dispersion entropy value of the long-term trend term obtained under different HP decomposition windows is calculated, and a genetic algorithm (or other optimization algorithm) is used to optimize it. The window corresponding to the minimum variance is the optimal trend feature decomposition window T1. Second, the high-frequency fluctuation components are stepwise decomposed using SSA to obtain short-period fluctuation components and noisy high-frequency terms. The fuzzy entropy value of the stationary periodic components obtained under different SSA stepwise decomposition windows is optimized using a genetic algorithm. The window corresponding to the minimum fuzzy entropy value is the optimal periodic term decomposition window T2. The initial population size for both GA optimization algorithms is set to 80, and the number of iterations is 150. Then, VMD is used to decompose the noisy high-frequency terms. Furthermore, to effectively separate low-frequency signals and high-frequency noise, the MPE value of each IMF component is calculated. The closer the MPE value is to 1, the greater the random volatility and the higher the irregularity of the time series. The MPE threshold is generally set to 0.6. IMF components greater than 0.6 are considered noise components, and those less than 0.6 are considered low-frequency signal components. The MPE values ​​of each IMF component after VMD decomposition are shown in Table 2. As can be seen from Table 2, the low-frequency components are mainly concentrated in the first two modes, the random fluctuation of the sequence is getting bigger and bigger, and the noise component is gradually increasing.

[0144] Table 2. Average MPE values ​​for each IMF component.

[0145]

[0146]

[0147] Step 3: Input the long-term trend component, short-period fluctuation component, and low-frequency mode component obtained after decomposing the gas sequence to be predicted into the LSTM network for prediction. The LSTM network uses the cross-entropy loss function and the Adam optimization algorithm, with 96 neurons, 64 epochs, and 32 batch sizes. Divide the dataset into training, validation, and test sets, and use the training set data to train the model. The calculation formulas for each part of the LSTM network are as follows:

[0148] E f =δ(W f *[h t-1 ,x t ]+b f (29)

[0149] E i =δ(W i *[h t-1 ,x t ]+b i (30)

[0150]

[0151]

[0152] E o =δ(W o *[h t-1 ,x t ]+b o (33)

[0153] h t =E o *tanh(C t (34)

[0154] In the formula: E f E i and E o Let C be the outputs of the forget gate, input gate, and output gate at time t; t and Let x be the element state and intermediate element state at time t; t h is the input to the hidden layer at time t; t-1 and h t W represents the output of the hidden layer at time t-1 and time t. f W i W c W o b f b i b c and b o δ represents the weights and biases of the forget gate, input gate, output gate, and intermediate unit states; δ is the Sigmoid function.

[0155] Step 4: The prediction results of each component are superimposed and reconstructed to obtain the final prediction result of the gas concentration to be predicted. Table 3 shows the error indices of the five gas-related test sets.

[0156] Table 3. Prediction Error Indicators for Five Gases

[0157]

[0158] As shown in Table 3, the overall prediction performance of the prediction model based on multi-window stepwise decomposition proposed in this paper is relatively lower than that of the traditional single LSTM model, demonstrating better short-term prediction performance.

Claims

1. A method for predicting transformer oil and gas concentration based on multi-window stepwise decomposition, characterized in that, Includes the following steps: Step 1: Obtain dissolved gas concentration data in the original transformer oil; Step 2: The dissolved gas concentration data in the original transformer oil is decomposed and noise reduced step by step to obtain the long-term trend component, short-period fluctuation component and modal component. Step 3: Input the components of the gas sequence to be predicted after decomposition into the LSTM network for prediction; Step 4: Superimpose and reconstruct the prediction results of each component to obtain the final prediction result of the gas concentration to be predicted; Step 2 includes the following sub-steps: Step 2.1: Perform sampling based on stepwise SDS decomposition: Let time series ,in, It is the length of the time series TS. for t Constantly monitor the dissolved gas concentration in the transformer oil; use y 1 to y L The remaining portion is used as training data and as test data. Step 2.2: Perform HP-SSA-VMD decomposition based on stepwise SDS decomposition; Step 2.2 includes the following sub-steps: Step 2.2.1: Based on the SDS sampling in Step 2.1, HP filtering decomposition is performed on the complex original oil dissolved gas concentration sequence to obtain the long-term trend component and high-frequency fluctuation component with relatively simple features. The genetic algorithm is used to optimize the dispersion entropy value of the long-term trend component under different decomposition windows. Based on the variance of the dispersion entropy value, the window corresponding to the minimum variance is the optimal decomposition window T1. Step 2.2.2: Perform SSA decomposition on the high-frequency fluctuation component obtained in Step 2.2.1 to obtain the short-period fluctuation component and the noisy high-frequency term. Use a genetic algorithm to optimize the fuzzy entropy value of the short-period fluctuation component under different decomposition windows. The window corresponding to the minimum fuzzy entropy value is the optimal decomposition window T2. Step 2.2.3: Decompose the noisy high-frequency term obtained in Step 2.2.2 using the VMD method to obtain several modal components IMFn and a residual component RES. Calculate the permutation entropy value of each modal component and filter out modal components that are greater than the threshold as noise.

2. The method according to claim 1, characterized in that, In step 1, dissolved gas concentration data in transformer oil are selected, including H2, CH4, C2H4, C2H6, CO, and CO2. Sampling intervals and several sets of sample points are set, and the data is cleaned and normalized. Data cleaning includes: quality verification and correction of the data to ensure its accuracy; checking for missing and outlier values ​​in the data and processing them according to the actual situation. Through these processes, the dissolved gas concentration data in transformer oil becomes consistent and comparable, providing reliable input for subsequent decomposition and prediction steps.

3. The method according to claim 1, characterized in that, In step 2.2.1, when performing HP filtering decomposition on the complex dissolved gas concentration sequence in the original oil, the following steps are adopted: Assuming time series data From long-term trend series and short-term fluctuation sequence Composition, that is , ; Define the trend as the solution to the minimization problem: ； In the formula: Here, T is the smoothing parameter; T is the time series. X, G, S The number of samples; , , Time series X, G, S exist T The gas concentration value at that moment; Calculate the dispersion entropy value of the long-term trend component, for a length of... N time series The following steps are adopted: 1) First, the time series The values ​​in the sequence are normalized; to reduce the influence of outliers, the normal cumulative distribution function (NCDF) is used to normalize the sequence. Mapping to sequence , , The value is between [0,1]; the specific formula for this normalization is as follows: ； In the formula: and Time series The standard deviation and mean; N Time series and The number of samples; , Time series and exist N The gas concentration value at that moment; 2) Change the sequence Classified into category c, the formula is as follows: ； In the formula: c is the sequence Number of classes in; It is the sequence after partitioning; It is a sequence The first in i One data point; 3) Construct a delay d Dimension m sequence The formula is as follows: ； In the formula: It is a sequence The first in j One data point; 4) Change the sequence Mapping to discrete modes The formula is as follows: ； In the formula: It is assigned to each sequence The number of discrete patterns; It is a discrete mode; It is the first corresponding to the discrete pattern after mapping. i A discrete value i =0,1,…, m -1; 5) Calculate each Discrete mode relative frequencies: ； In the formula: It is each The discrete modal relative frequencies; It is each Number of times it appears; 6) For time lengths of N sequence Its dispersion entropy is: ； In the formula: It is each The discrete mode relative frequencies.

4. The method according to claim 1 or 3, characterized in that, In step 2.2.2, when performing SSA decomposition on the high-frequency fluctuation components obtained in step 2.2.1, the following steps are adopted: 1) Convert the original time series Based on the set embedding dimension L, where L≤N / 2, it is transformed into a trajectory matrix. ; ； In the formula: ; N This represents the number of samples in the time series. For time series in N The gas concentration value at that moment; 2) Calculate the matrix eigenvalues and the corresponding feature vector Let d be the number of non-zero eigenvalues, and define... ,in It is a trajectory matrix The transpose of the matrix; It is a matrix The i eigenvalues; trajectory matrix The singular value decomposition can be written as: ； In the formula: , and Trajectory matrices The i Each singular value corresponds to a left and a right singular vector, and each matrix For trajectory matrix Contribution level and eigenvalue Related, its contribution rate Defined as: ； 3) Divide each submatrix Restore to a length of N Time series; assuming for L×K A matrix of shapes, let , ,in , yes L and K The minimum value, yes L and K The maximum value; reconstructed sequence ; 4) Set contribution rate threshold Then, the subsequences are reconstructed step by step according to the eigenvalues ​​from largest to smallest. The sequence is reconstructed into short-period fluctuation components, and the remainder is reconstructed into noisy high-frequency terms. Then, the fuzzy entropy value of the short-period fluctuation components is calculated.

5. The method according to claim 4, characterized in that, In step 2.2.2, when decomposing the noisy high-frequency term obtained in step 2.2.2 using the VMD method, the following steps are adopted: 1) Constructing a constrained variational optimality problem: ； In the formula: { u k }for K One IMF component set; { w k }for K A set of frequency centers; δ ( t ) is the Dirac function; f ( t () is the initial signal; To t Find the partial derivatives; For the first K One modal function; w k For the first K The center frequency of each modal function; 2) Using Lagrange multipliers λ and secondary penalty factor α This transforms the constrained variational problem into an unconstrained variational problem: ； In the formula: This indicates the inner product. This is a convolution operation; 3) The Alternating Directional Multiplier Iteration Algorithm (ADMM) is used to continuously update each modal component and center frequency to obtain a specified number of VIMF components.

6. The method according to claim 1, characterized in that, In step 3, the long-term trend component, short-period fluctuation component, and several modal components of the gas sequence to be predicted are input into the LSTM network for prediction.

7. The method according to claim 1, characterized in that, In step 3, the prediction results of each component are superimposed and reconstructed to obtain the final prediction result of the gas concentration to be predicted; to verify the prediction effect of the model, the root mean square error is used. Mean absolute percentage error and mean absolute error As a model evaluation metric; the detailed expression is as follows: ； ； ； In the formula, , , These are the actual value, the average of the actual values, and the predicted value, respectively.

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