Self-adaptive denoising method suitable for time series data of power system

Abstract

A self-adaptive denoising method suitable for time series data of an electric power system comprises the following steps: step 1, constructing a self-adaptive variational mode decomposition model, and decomposing an original time series data sequence of the electric power system into subsequences of different energy components by the self-adaptive variational mode decomposition model; 2, selecting a sub-sequence of a high-energy entropy component from the sub-sequences decomposed in the step 1 as a main component and keeping the sub-sequence, and combining the sub-sequences of the other components with the residual decomposed sub-sequences decomposed in the step 1; 3, constructing a self-adaptive time-varying filter empirical mode decomposition model, and decomposing the combined components in the step 2 by taking the minimum residual as a target to obtain a new decomposed sub-component and a residual component; and 4, combining the main components reserved in the step 2 and the sub-components decomposed in the step 3, and removing the residual components in the step 3 to complete denoising of the time sequence data of the power system.

Description

Technical Field

[0001] The present invention relates to the technical field of power systems, in particular to signal analysis and prediction modeling technologies of power systems, and specifically to an adaptive denoising method applicable to power system time series data. Background Art

[0002] In recent years, the rapid development of artificial intelligence (AI) technology has promoted its wide application in power systems, especially in the fields of power load forecasting, photovoltaic power generation forecasting, wind speed and wind power prediction, power quality disturbance identification, etc. Using artificial intelligence models such as neural networks and deep learning, by deeply mining the non-linear dependence ability and excellent pattern recognition ability inside the data, more and more power system time series data are modeled using them.

[0003] Power system time series data usually has complex characteristics such as non-linearity, high volatility, and random noise, which pose challenges to the processing of deep learning models. Although recurrent neural networks (RNNs), long short-term memory networks (LSTMs), and gated recurrent units (GRUs) have been widely used because they can capture the dependencies inside the sequence, their generalization ability and robustness are still insufficient when dealing with complex data. Non-linearity and random volatility increase the difficulty of model learning, resulting in prediction bias and a decline in generalization performance; at the same time, random noise and high-frequency fluctuations interfere with the capture of trends and weaken the stability of the model.

[0004] To address the modeling challenges of complex time series data, researchers have proposed a framework that combines decomposition techniques with deep learning. By decomposing complex non-stationary data into several simple subsequences, decomposition techniques can not only reduce the complexity of the data, enabling deep learning models to focus more on the learning of each subsequence feature, but also remove the noise in the data during the reconstruction process, thus significantly improving the modeling efficiency and recognition accuracy. However, there are still many problems in practical applications, and these limitations directly affect the improvement of model performance.

[0005] There are some decomposition methods that require given parameters. The parameter selection usually depends on experience or exhaustive search methods, lacking scientificity and wide applicability. For example, wavelet transform is highly sensitive to the selection of wavelet bases. Different wavelet bases may lead to significant differences in the decomposition results, and instead, it cannot effectively decompose and denoise. In the variational mode decomposition model, the number of modes and the penalty factor are crucial for the decomposition quality. Different parameter selections directly affect the effects of decomposition and denoising. For some decomposition methods that do not require parameter setting, such as empirical mode decomposition (EMD), it is prone to mode mixing or endpoint effects during the decomposition process. Its variants EEMD and CEEMDAN improve the decomposition effect by introducing methods such as Gaussian white noise, but still do not solve the problem of residual noise in the reconstructed data. And the parameter-free decomposition method also leads to uncontrollability of the decomposition process and results, affecting the effects of decomposition and denoising. Summary of the Invention

[0006] The object of the present invention is to reduce the redundant characteristics of data, remove noise with minimal data loss, thereby maximizing the retention of the effective components of the data, avoiding errors caused by noise interference, providing high-quality trend information support for the medium- and long-term operation and planning of the power system, and laying a solid data foundation for the intelligent management and optimization of the power system. Therefore, an adaptive denoising method applicable to power system time series data is proposed.

[0007] In order to solve the above technical problems, the technical solution adopted by the present invention is as follows:

[0008] An adaptive denoising method applicable to power system time series data includes the following steps:

[0009] Step 1: Construct an adaptive variational mode decomposition model, and decompose the original power system time series data sequence into subsequences of different energy components by the adaptive variational mode decomposition model;

[0010] Step 2: Select the subsequence with high energy entropy component from the subsequences decomposed in Step 1 as the main component and retain it, and merge the remaining sub-sequences and the remaining decomposition after decomposition in Step 1;

[0011] Step 3: Construct an adaptive time-varying filter empirical mode decomposition model, with the minimum residual as the goal, decompose the merged component in Step 2 to obtain new decomposed sub-components and residual components;

[0012] Step 4: Merge the main component retained in Step 2 and the sub-components decomposed in Step 3, remove the residual component in Step 3, and complete the denoising of the power system time series data.

[0013] In Step 1, the expression of the constructed variational mode decomposition model VMD is:

[0014]

[0015] In the formula, the decomposition process of the variational mode decomposition model VMD is defined as f VMD ; x is the set of original sequences; u Res is the residual component after decomposition, and the residual is the noise; K is the number of sub-components; i refers to the index; u i represents the i-th sub-component decomposed currently.

[0016] When constructing the adaptive variational mode decomposition model, the following steps are adopted:

[0017] Step S1.1: Convert the decomposition problem of the variational mode decomposition model VMD into an optimal solution problem of parameters, i.e., (K, α, φ);

[0018] Step S1.2: Select the energy entropy as the final objective function for solving the transformed variational mode decomposition model;

[0019] Step S1.3: Select the optimization algorithm BKA as the optimization tool to complete the construction of the adaptive variational mode decomposition model (optimization algorithm BKA - energy entropy - variational mode decomposition model VMD).

[0020] In step S1.2, when selecting the energy entropy as the objective function for decomposition, the formula adopted is as follows:

[0021] 1) Obtain the components with different center frequencies after decomposition, and determine the marginal spectrum energy E. Then, the relative energy of each frequency component is:

[0022]

[0023] In the formula, E k represents the energy of the k-th component; k is the current frequency component index, and the value range of k is [1, K]; K represents the total number of components obtained after decomposition.

[0024] 2) According to the information entropy theory and the probability distribution p k , for the k-th component, the energy entropy H EE is defined as:

[0025] H EE (k) = -p k lgp k (3)

[0026] In the formula, H EE (k) represents the energy entropy of each frequency component and is used as an element of the vector;

[0027] 3) The characteristic phase T composed of the energy entropy is:

[0028] T = [H EE(1), H EE (2), …, H EE (K)] (4).

[0029] In step S1.3, the expression of the constructed adaptive variational mode decomposition model is as follows:

[0030]

[0031] s.t. K ∈ [K min , K max , α ∈ [α min , α max , φ ∈ [φ min , φ max (6)

[0032] In the formula, the value range of the total number of components K obtained after decomposition is between [K min , K max ; α is the penalty factor, and its value range is between [α min , α max ; φ represents the convergence accuracy, and its value range is between [φ min , φ max ; the subscripts min and max represent the corresponding minimum and maximum values; represents minimizing this objective function; f BKA-VMD-EE is the name of the objective function; represents the sub-component under the current energy entropy decomposition index.

[0033] When constructing the adaptive variational mode decomposition model, the following steps are adopted:

[0034] The first step is to input the maximum number of iterations Maxiter, the population size N V , the range of the number of decomposition modes K, the penalty factor α, the convergence accuracy φ, and the input time series x;

[0035] The second step is to initialize the relevant parameters of the BKA and the variational mode decomposition model VMD model to prepare for the subsequent optimization and signal decomposition processes;

[0036] The third step is to set the energy entropy calculation formula, which is used as an important criterion for measuring the decomposition quality to evaluate the energy distribution of each modal component, so as to perform effective performance evaluation during the optimization process;

[0037] The fourth step is to set the iteration variable i = 1 and start entering the iterative optimization process;

[0038] The fifth step is to enter the loop; when i < Maxiter, use the BKA algorithm to update the current optimization process, establish the model and obtain the optimized best parameter values [K *, α * , φ * , then increment the iteration variable i by 1 and continue with the next iteration until the maximum number of iterations is reached;

[0039] Step 6: When i ≥ Maxiter, end the iteration process and output the minimum energy entropy H in the loop EE The corresponding optimized parameters, denoted as [K, α, φ];

[0040] Step 7: Based on the optimized best parameters [K, α, φ], decompose the input time series x and extract each modal component in the signal;

[0041] Step 8: Calculate and extract the finally decomposed modal components, which represent different frequency components in the input time series and have important analysis value;

[0042] Step 9: Calculate the residual signal vector after decomposition. The residual represents the part that cannot be represented by the decomposed modes and usually includes noise or high-frequency components;

[0043] Step 10: Return the finally decomposed modal components, the residual signal, and output the optimized parameters [K, α, φ] to provide complete results for subsequent further analysis or applications.

[0044] The time-varying filter empirical mode decomposition model (TVFEMD) in Step 3 screens by constructing a non-uniform B-spline approximation as a filter, introduces a cut-off frequency rearrangement algorithm, and uses the local narrowband signal as the iteration termination criterion; this method can effectively separate high-frequency and low-frequency components and has good stability at low sampling rates; it not only retains the core advantages of the empirical mode decomposition EMD but also reduces mode mixing and sensitivity to noise, maintaining the time-varying characteristics of the signal. It specifically includes the following steps:

[0045] Step 3.1) Estimate the local cut-off frequency:

[0046] First, perform a Hilbert transform on the input time series y(t) and record the result as Then:

[0047]

[0048] In the formula, A(t) is the instantaneous amplitude of the complex analytic signal; φ(t) is the instantaneous phase; arctan is the arctangent function used to calculate the phase. The corresponding analytic signal h(t) is:

[0049]

[0050] where \(l\) is the imaginary unit; determine the local maximum value sequence \(\{t\)\) of the instantaneous amplitude \(A(t)\) and the local minimum value sequence \(\{t\)\) max \(\}\), for a multi-component signal, its analytic signal \(h(t)\) can also be expressed as the sum of two signal components, that is: min

[0051]

[0052] where \(a\) 1 (t)\) and \(a\) 2 (t)\) represent the amplitudes of the two signal components; based on local extrema and derivative operations, the maximum and minimum values of \(a\) 1 (t)\), \(a\) 2 (t)\) can be calculated; the upper envelope curve \(cur\) 1 (t)\) and the lower envelope curve \(cur\) 2 (t)\) are obtained by interpolation, and then the instantaneous mean value \(\gamma\) 1 (t)\) and the instantaneous envelope \(\gamma\) 2 (t)\) are obtained, that is:

[0053]

[0054] Next, interpolate \(A(t)\) 2 (t\) max )\(\varphi'(t\) max )\) and \(A(t)(t\) min )\(\varphi'(t\) min )\), \(\varphi'(t\) max )\) and \(\varphi'(t\) min )\) represent the derivative of the instantaneous phase, that is, the instantaneous frequency. After interpolation, the interpolation results \(\beta\) 1 (t)\) and \(\beta\) 2 (t)\) are obtained respectively, and the instantaneous frequency components \(\varphi\) 1 '(t)\) and \(\varphi\) 2 '(t)\) are calculated:

[0055]

[0056] Then calculate the local cut-off frequency \(\varphi'\) bis (t)\):

[0057]

[0058] Step 3.2) Obtain the local mean value;

[0059] Obtain the local mean value by processing the signal with a time-varying filter; when an intermittent problem occurs, recalibrate the local cut-off frequency \(\varphi'\) bis (t)\), and the adjusted reconstructed signal is \(\delta(t)=\cos[\int\varphi'\) bis ​(t)d(t)], where δ(t) represents the reconstructed signal. Pole When constructing a time-varying filter as nodes, perform time-varying filtering on y(t) using B-spline to obtain an approximate filtering result of m(t);

[0060] Step 3.3) Determine whether the remaining signal meets the stop criterion;

[0061] Define the stop condition as σ(t), and given a bandwidth threshold r; if σ(t) ≤ r, it is confirmed as a component; if the condition is not met, then y(t) = y(t) - m(t), which is used as the new input signal, and repeat the above steps until it is satisfied; the calculation formula for the proportionality index σ(t) is as follows:

[0062]

[0063] In the formula, B Loughlin (t) is the Loughlin instantaneous bandwidth of the component signal at time point t, and φ avg (t) is the corresponding weighted average of the instantaneous frequency;

[0064] Step 3.4) Obtain the final decomposed modal components;

[0065] Finally, the original input signal y(t) is decomposed into S subsequences {m i (t)|i = 1, 2,..., S}; after simultaneously meeting the decomposition conditions, the formula is as follows:

[0066]

[0067] In the formula: m i (t) is the i-th subsequence, and z(t) is the decomposition residue;

[0068] Step 3.5) Establish a selection model for the optimal values of the key parameters in steps 3.1) to 3.4), including the B-spline order, stop criterion, and number of decomposition modes;

[0069] The B-spline order (Bsp) is used to regulate the smoothness and local adaptability of the filter. Too low an order will result in insufficient flexibility, and too high an order may lead to overfitting; the instantaneous bandwidth threshold is used as the stop criterion for decomposition (σ), which is used to comprehensively control the termination of decomposition. Loose conditions will lead to over-decomposition, and strict conditions will lead to incomplete decomposition; the number of decomposition modes (K T ) limits the depth of decomposition to avoid modal redundancy or information loss. The filter construction conditions dynamically adjust the bandwidth and center frequency in combination with the local characteristics of the signal, so as to achieve accurate extraction of modal components. The optimal configuration of these parameters is of great significance for improving the adaptability and accuracy of decomposition and reducing modal aliasing; therefore, extract Bsp, K T, the parameters of σ are transformed into the problem of the optimal solution of the parameters;

[0070] S3.6) Establish the objective function of the optimal value parameter selection model;

[0071] Select the minimum decomposition residual as the final objective function for solving the empirical mode decomposition model of the adaptive time-varying filter;

[0072] S3.7) Select the optimization algorithm BKA as the optimization tool for the optimal value parameter selection model, and construct the adaptive decomposition process;

[0073] Select the optimization algorithm BKA as the optimization tool to construct the adaptive decomposition of the empirical mode decomposition model of the adaptive time-varying filter;

[0074] The minimum decomposition residual in step S3.6) is an index to measure the size of the decomposition residual, and it evaluates the effect of the decomposition model by calculating the difference between the decomposed time series and the original series. The minimum decomposition residual E REI is defined by the following formula:

[0075]

[0076] In the formula, represents the summation of all components after decomposition, that is, the reconstruction result of the signal; i represents the index of the current data point; N represents the number of data points in this time; E REI The smaller it is, the smaller the deviation between the decomposed result and the original data, reflecting the better denoising performance or decomposition quality of the model; Select REI as the objective function to minimize the decomposition residual and improve the decomposition accuracy.

[0077] In step S3.7), the construction of the adaptive decomposition process has the following mathematical expression:

[0078]

[0079] s.t.K T ∈[K Tmin ,K Tmax ,B SP ∈[B SPmin ,B SPmax ,σ∈[σ min ,σ max (20)

[0080] In the formula, K T represents the number of decomposition modes; B SP represents the B-spline order; σ represents the stopping criterion; f BKA-TVF-REI is an objective function, and the goal is to minimize this function; min means minimization; Denotes a summation operation, traversing all terms from index i = 1 to i = S; m i REI (t) represents the decomposed sub-component at each index; z Res (t) represents the decomposition residual. K T The value range of is in [K Tmin , K Tmax , K Tmin and K Tmax represent the upper and lower limits of this decision variable; B SPmin and B SPmax represent the upper and lower limits of B SP ; σ min and σ max represent the upper and lower limits of σ.

[0081] The process of constructing the adaptive decomposition in step S3.7) is as follows:

[0082] First step, input the maximum number of iterations Maxiter, population size N T , the range of the number of decomposition modes K T , the range of B-spline order B SP , the range of the stopping criterion σ, and the input time series y(t).

[0083] Second step, based on the input parameters, initialize the relevant parameters of BKA and TVFEMD to prepare for the subsequent optimization and signal decomposition process.

[0084] Third step, set the relative error index (REI) as the key index to measure the convergence of the optimization process and the performance of the model, ensuring that the optimization effect of each iteration can be effectively improved.

[0085] Fourth step, set the iteration variable i = 1 and prepare to enter the iterative optimization process.

[0086] Fifth step, enter the loop. When i < Maxiter, use the BKA algorithm to update the current optimization process, establish the model and obtain the optimal parameter values [K T * , B SP * , σ * , update the iteration variable i, and then continue the next iteration until the maximum number of iterations is reached.

[0087] Sixth step, when i ≥ Maxiter, end the iterative process and output the optimal parameters corresponding to the minimum E REI during the loop process, marked as [K T , B SP , σ].

[0088] Step 7: According to the optimal parameters [K T , B SP , σ] obtained by optimization, decompose the input time series y(t) to extract each modal component in the signal.

[0089] Step 8: Calculate and extract the modal components finally obtained by decomposition. These modal components reflect different frequency components of the input time series and provide a necessary basis for subsequent signal analysis.

[0090] Step 9: Calculate the residual signal vector obtained by decomposition. The residual usually includes the part of the signal that has not been decomposed, and this part of the information may be noise or high-frequency components.

[0091] Step 10: Return the decomposed modal components, residual signal, and output the optimized parameters [K T , B SP , σ] to provide complete results for further applications or analysis.

[0092] Compared with the prior art, the present invention has the following technical effects:

[0093] 1) The present invention can solve problems such as non-linearity, high volatility, and noise interference in power system time series data processing. The method proposes a dual decomposition mechanism, combining decomposition techniques based on different mathematical principles (variational mode decomposition and time-varying filter empirical mode decomposition), overcomes the limitations of a single decomposition algorithm, reduces the redundant characteristics of data, removes noise while minimizing data loss, thereby retaining the effective components of the data to the greatest extent and ensuring the accuracy of the denoised data;

[0094] 2) The present invention designs an adaptive decomposition strategy, uses a dynamic optimization algorithm to achieve the optimal solution of key decomposition parameters (such as the number of modes, bandwidth threshold, convergence accuracy, etc.) under different objective function orientations, and overcomes the problem of high dependence on empirical parameters in traditional decomposition methods. This dynamic optimization mechanism makes the decomposition process more stable and scientific, ensures wide applicability in different power system scenarios, and improves the reliability and interpretability of the decomposition results;

[0095] 3) The present invention realizes the separation and extraction of the main energy components by minimizing the energy entropy of the components, and minimizes the decomposition residual by setting the minimum objective function of the decomposition residual, thereby improving the decomposition accuracy;

[0096] 4) The proposed method can obtain denoised time series data, a main component that reflects the main trend and is smooth, and sub-components that contain different frequency characteristics. By removing irrelevant interference, the denoised data improves data quality and authenticity, and is applicable to abnormal fluctuation detection, new energy power output characteristic analysis, and equipment fault prediction; the main trend and smooth components are suitable for medium- and long-term operation trend monitoring of the power grid, load disturbance assessment, and optimal regulation of energy storage devices; the decomposed high-frequency characteristics are suitable for dynamic characteristic analysis, harmonic interference detection, and short-term power quality assessment;

[0097] 5) By effectively extracting key features from power system time series data and separating the main trend from interference components, this method improves the quality and usability of the data, providing a clear data basis and analysis path for various application scenarios. Through the separation of data features and the improvement of data quality after denoising, it also significantly reduces the modeling burden for complex signals, enhances the feature recognition ability for different data, and lays a solid data foundation and technical guarantee for the intelligent operation and planning of the power system. Brief Description of the Drawings

[0098] The present invention will be further described below in conjunction with the drawings and embodiments:

[0099] Figure 1 is a flowchart of the method of the present invention;

[0100] Figure 2 is a time series diagram of renewable energy power generation; the figure includes sub-components decomposed by the adaptive variational mode decomposition model, the corresponding amplitude spectrum, power spectrum, and the decomposed noise (residual) component;

[0101] Figure 3 is a time series schematic diagram of the performance of high-voltage measurement equipment; the figure includes sub-components decomposed by the adaptive variational mode decomposition model, the corresponding amplitude spectrum, power spectrum, and the decomposed noise (residual) component;

[0102] Figure 4 is an optimization iteration diagram of the adaptive variational mode decomposition model (left) and the empirical mode decomposition model of the adaptive time-varying filter (right);

[0103] Figure 5 is a schematic diagram of sub-components with different frequency characteristics obtained after decomposition using the method proposed in the present invention; the figure includes the time series of renewable energy power generation; it can be seen that the present invention can clearly decompose different types of time series into smooth main component components and sub-components containing different frequency characteristics, and these components can be used for different application scenarios respectively.

[0104] Figure 6Schematic diagram of sub-components with different frequency characteristics obtained after decomposing using the method proposed in the present invention; the figure includes the time series of the performance of high-voltage measurement equipment; it can be seen that the present invention can clearly decompose different types of time series into smooth main component components and sub-components containing different frequency characteristics, and these components can be used for different application scenarios respectively.

[0105] Figure 7 Schematic diagram for comparing the noise (residual) component after decomposing by the adaptive variational mode decomposition model and the noise (residual) component after final decomposition; the figure includes the time series of the power generation of renewable energy; it can be seen that the unit magnitude of the noise after final decomposition by the present invention is 10 -11 which is much smaller than the magnitude of the noise after decomposing by their respective adaptive variational mode decomposition models,

[0106] indicating that the present invention can minimize the decomposition loss;

[0107] Figure 8 Schematic diagram for comparing the noise (residual) component after decomposing by the adaptive variational mode decomposition model and the noise (residual) component after final decomposition; the figure includes the time series of the performance of high-voltage measurement equipment; it can be seen that the unit magnitude of the noise after final decomposition by the present invention is 10 -17 which is much smaller than the magnitude of the noise after decomposing by their respective adaptive variational mode decomposition models, indicating that the present invention can minimize the decomposition loss. Specific implementation manner

[0108] An adaptive denoising method applicable to time series data of power systems, which reduces the redundant characteristics of the data, removes noise under the condition of minimizing data loss, and thus maximally retains the effective components of the data; specifically includes the following steps:

[0109] Step 1: Construct an adaptive variational mode decomposition model to decompose the original time series data sequence of the power system into subsequences of different energy components.

[0110] Step 2: Select the subsequence of the high energy entropy component as the main component and retain it, and merge the remaining sub-sequence components and the remaining decomposition after decomposition in Step 1.

[0111] Step 3: Construct an empirical mode decomposition model of an adaptive time-varying filter, and decompose the components merged in Step 2 with the goal of minimizing the residual.

[0112] Step 4: Combine the main components retained in Step 2 and the sub-components decomposed in Step 3, and remove the residual components in Step 3 to complete the denoising of the power system time series data. At this time, the denoised power system time series data with the minimum data loss is obtained, which can reflect the main trend of the power system time series data, the smooth main components, and the sub-components with different frequency characteristics after decomposition.

[0113] The variational mode decomposition model (VMD) in Step 1 refers to a non-recursive signal decomposition method. By constructing a variational problem and introducing a penalty factor and a penalty operator, the constrained problem is transformed into an unconstrained problem for iterative solution. The iteration stops when the convergence accuracy condition (less than) is met, and finally the optimal center frequency of each component and the sub-components with finite bandwidth are obtained. Its formula is expressed as follows:

[0114]

[0115] In the formula, the decomposition process of the variational mode decomposition model VMD is defined as f VMD ; x is the set of the original sequence; u Res is the residual component after decomposition, and the residual is the noise; K is the number of sub-components; i refers to the index; u i represents the i-th sub-component currently decomposed.

[0116] The steps to construct the adaptive variational mode decomposition model in Step 1 are as follows:

[0117] S1.1. An appropriate decomposition number K can reduce mode mixing and effectively separate signal modes; the penalty factor α ensures the signal reconstruction accuracy during the decomposition process; the convergence accuracy φ determines the iteration stop condition. Therefore, the decomposition problem of VMD is transformed into an optimal solution problem of parameters, that is, (K, α, φ).

[0118] S1.2. Select energy entropy as the final objective function for the solution of the transformed VMD.

[0119] S1.3. Select the optimization algorithm BKA as the optimization tool to construct the adaptive variational mode decomposition model (optimization algorithm BKA - energy entropy - variational mode decomposition model VMD).

[0120] Energy entropy is an index to measure the uncertainty of data information and is used to reflect the energy distribution characteristics of the signal in the frequency domain. The time series data collected by the power system usually comes from multiple sources, and its signals show different spectral characteristics and energy distributions. Therefore, energy entropy is selected as the objective function for decomposition, and its calculation formula is as follows:

[0121] 1) Obtain the components with different center frequencies after decomposition, determine the marginal spectrum energy E, and then the relative energy of each frequency component is:

[0122]

[0123] Wherein, E k represents the energy of the k-th component; k is the current frequency component index, and the value range of k is [1, K]; K represents the total number of components obtained after decomposition.

[0124] 2) According to the information entropy theory and the probability distribution p k , for the k-th component, the energy entropy H EE is defined as:

[0125] H EE (k) = -p k lgp k (3)

[0126] Wherein, H EE (k) represents the energy entropy of each frequency component and is an element of the vector;

[0127] 3) The characteristic phase T composed of energy entropy is:

[0128] T = [H EE (1), H EE (2), …, H EE (K)] (4).

[0129] The optimization algorithm BKA shows a more robust dynamic search ability by simulating the high adaptability of the black-winged kite to environmental changes and target positions. In the present invention, BKA is selected as the solution algorithm to search for the optimal solution.

[0130] The constructed adaptive VMD decomposition has the following mathematical expression:

[0131]

[0132] s.t. K ∈ [K min , K max , α ∈ [α min , α max , φ ∈ [φ min , φ max (6)

[0133] Wherein, the value range of the total number of components K obtained after decomposition is between [K min , K max ; α is the penalty factor, and its value range is between [α min , α max ; φ represents the convergence accuracy, and its value range is between [φ min , φ max ; the subscripts min and max represent the corresponding minimum and maximum values; represents minimizing the objective function; f BKA-VMD-EE is the name of the objective function; represents the sub-component under the current energy entropy decomposition index.

[0134] The adaptive VMD decomposition constructed in S1.1 has the following process:

[0135] In the first step, input the maximum number of iterations Maxiter, population size N V , the range of the number of decomposition modes K, penalty factor α, convergence accuracy φ, and the input time series x.

[0136] In the second step, initialize the relevant parameters of the BKA and VMD (Variational Mode Decomposition) models to prepare for the subsequent optimization and signal decomposition processes.

[0137] In the third step, set the energy entropy calculation formula, which is an important criterion for measuring the decomposition quality, used to evaluate the energy distribution of each modal component, so as to conduct effective performance evaluation during the optimization process.

[0138] In the fourth step, set the iteration variable i = 1 and start entering the iterative optimization process.

[0139] In the fifth step, enter the loop. When i < Maxiter, use the BKA algorithm to update the current optimization process, establish the model and obtain the optimized best parameter values [K * , α * , φ * , then increase the iteration variable i by 1 and continue the next iteration until the maximum number of iterations is satisfied.

[0140] In the sixth step, when i ≥ Maxiter, end the iterative process and output the optimized parameters corresponding to the minimum energy entropy H EE , marked as [K, α, φ].

[0141] In the seventh step, based on the optimized best parameters [K, α, φ], decompose the input time series x and extract each modal component in the signal.

[0142] In the eighth step, calculate and extract the finally decomposed modal components, which represent different frequency components in the input time series and have important analysis value.

[0143] In the ninth step, calculate the residual signal vector after decomposition. The residual represents the part that cannot be represented by the decomposed modes and usually includes noise or high-frequency components.

[0144] Step 10: Return the finally decomposed modal components and residual signals, and output the optimized parameters [K, α, φ], providing complete results for subsequent further analysis or applications.

[0145] In Step 3, the time-varying filter empirical mode decomposition (TVFEMD) decomposes by constructing a non-uniform B-spline approximation as a filter for sifting, introducing a cut-off frequency rearrangement algorithm, and using the local narrowband signal as the iteration termination criterion. This method can effectively separate high-frequency and low-frequency components and has good stability at low sampling rates. It not only retains the core advantages of EMD but also reduces mode mixing and sensitivity to noise, maintaining the time-varying characteristics of the signal. The usage steps are as follows:

[0146] Step 3.1) Estimate the local cut-off frequency:

[0147] First, perform the Hilbert transform on the input time series y(t), and record the result as Then:

[0148]

[0149] In the formula, A(t) is the instantaneous amplitude of the complex analytic signal; φ(t) is the instantaneous phase; arctan is the arctangent function used to calculate the phase. The corresponding analytic signal h(t) is:

[0150]

[0151] In the formula, l is the complex unit; determine the local maximum value sequence {t max} and the local minimum value sequence {t min} of the instantaneous amplitude A(t). For a multi-component signal, its analytic signal h(t) can also be expressed as the sum of two signal components, that is:

[0152]

[0153] In the formula, a 1 (t) and a 2 (t) represent the amplitudes of the two signal components; based on local extreme values and derivative operations, the maximum and minimum values of a 1 (t) and a 2 (t) can be calculated; the upper envelope curve cur 1 (t) and the lower envelope curve cur 2 (t) are obtained by interpolation, and then the instantaneous mean value γ 1 (t) and the instantaneous envelope γ 2 (t) are obtained, that is:

[0154]

[0155] Next, interpolate A(t) 2 (t max )φ′(t max ) and A(t)(t min )φ′(t min ) where φ′(t max ) and φ′(t min ) represent the derivative of the instantaneous phase, i.e., the instantaneous frequency. After interpolation, the interpolation results β 1 (t) and β 2 (t) are obtained respectively, and the instantaneous frequency components φ 1 ′(t) and φ 2 ′(t) are calculated:

[0156]

[0157] Then calculate the local cut-off frequency φ′ bis (t):

[0158]

[0159] Step 3.2) Obtain the local mean value;

[0160] Process the signal through constructing a time-varying filter to obtain the local mean value; when an intermittent problem occurs, recalibrate the local cut-off frequency φ′ bis (t), and the adjusted reconstructed signal is δ(t) = cos[∫φ′ bis (t)d(t)], where δ(t) represents the reconstructed signal. The poles are used as nodes to construct a time-varying filter, and B-spline is used to perform time-varying filtering on y(t) to obtain the approximate filtering result as m(t);

[0161] Step 3.3) Determine whether the remaining signal meets the stop criterion;

[0162] Define the stop condition as σ(t), and a bandwidth threshold r is given; if σ(t) ≤ r, it is confirmed as a component; if the condition is not met, then y(t) = y(t) - m(t) is used as the new input signal, and the above steps are repeated until it is satisfied; the calculation formula for the ratio index σ(t) is as follows:

[0163]

[0164] where B Loughlin (t) is the Loughlin instantaneous bandwidth of the component signal at time point t, and φ avg (t) is the corresponding weighted average of the instantaneous frequency;

[0165] Step 3.4) Obtain the final decomposed mode components;

[0166] Finally, the original input signal y(t) is decomposed into S subsequences {m i (t)|i = 1, 2, …, S}; after satisfying the decomposition conditions, the formula is as follows:

[0167]

[0168] In the formula: m i (t) is the i-th subsequence, and z(t) is the decomposition residual;

[0169] Step 3.5) Establish a selection model for the optimal values of the key parameters in Steps 3.1) to 3.4), including the B-spline order, stopping criterion, and number of decomposition modes;

[0170] The B-spline order (Bsp) is used to regulate the smoothness and local adaptability of the filter. Too low an order will result in insufficient flexibility, and too high an order may lead to overfitting; the instantaneous bandwidth threshold, as the decomposition stopping criterion (σ), is used to comprehensively control the termination of decomposition. Loose conditions will lead to over-decomposition, and strict conditions will lead to incomplete decomposition; the number of decomposition modes (K T ) limits the depth of decomposition to avoid modal redundancy or information loss. The filter construction conditions dynamically adjust the bandwidth and center frequency in combination with the local characteristics of the signal, so as to achieve accurate extraction of modal components. The optimal configuration of these parameters is of great significance for improving the adaptability and accuracy of decomposition and reducing modal aliasing; therefore, extracting the parameters of Bsp, K T , σ is transformed into an optimal solution problem of the parameters.

[0171] S3.6) Establish the objective function of the optimal value parameter selection model;

[0172] Select the minimum decomposition residual as the final objective function for solving the empirical mode decomposition model of the adaptive time-varying filter.

[0173] S3.7) Select the optimization algorithm BKA as the optimization tool for the optimal value parameter selection model to construct an adaptive decomposition process;

[0174] Select the optimization algorithm BKA as the optimization tool to construct the adaptive decomposition of the empirical mode decomposition model of the adaptive time-varying filter.

[0175] The minimum decomposition residual in S3.6 is an index to measure the size of the decomposition residual, and it evaluates the effect of the decomposition model by calculating the difference between the decomposed time series and the original series. The minimum decomposition residual E REI is defined by the following formula:

[0176]

[0177] In the formula, Denotes the sum of all components after decomposition, i.e., the reconstruction result of the signal; i represents the index of the current data point; N represents the number of data points in this instance. E REI The smaller it is, the smaller the deviation between the decomposed result and the original data, reflecting better denoising performance or decomposition quality of the model. In this paper, REI is selected as the objective function to minimize the decomposition residual and improve the decomposition accuracy. The construction of the adaptive decomposition process in S3.7 has the following mathematical expression:

[0178]

[0179] s.t. K T ∈ [K Tmin , K Tmax , B SP ∈ [B SPmin , B SPmax , σ ∈ [σ min , σ max (20)

[0180] In the formula, K T represents the number of decomposition modes; B SP represents the B-spline order; σ represents the stopping criterion; f BKA-TVF-REI is an objective function, and the goal is to minimize this function; min means minimization; represents the summation operation, traversing all terms from index i = 1 to i = S; m i REI (t) represents the decomposition sub-component at each index; z Res (t) represents the decomposition residual. K T takes values in the range of [K Tmin , K Tmax , K Tmin and K Tmax represent the upper and lower limits of this decision variable; B SPmin and B SPmax represent the upper and lower limits of B SP ; σ min and σ max represent the upper and lower limits of σ.

[0181] The process of constructing the adaptive decomposition in S3.7 is as follows:

[0182] In the first step, input the maximum number of iterations Maxiter, population size N T , the range of the number of decomposition modes K T , the range of the B-spline order B SP , the range of the stopping criterion σ, and the input time series y(t).

[0183] Step 2: Based on the input parameters, initialize the relevant parameters of BKA and TVFEMD to prepare for the subsequent optimization and signal decomposition processes.

[0184] Step 3: Set the relative error index (REI) as the key index to measure the convergence of the optimization process and the performance of the model, ensuring that the optimization effect of each iteration can be effectively improved.

[0185] Step 4: Set the iteration variable i = 1 and prepare to enter the iterative optimization process.

[0186] Step 5: Enter the loop. When i < Maxiter, use the BKA algorithm to update the current optimization process, establish the model and obtain the optimal parameter values [K T * , B SP * , σ * , and update the iteration variable i, then continue the next iteration until the maximum number of iterations is reached.

[0187] Step 6: When i ≥ Maxiter, end the iterative process and output the optimal parameters corresponding to the minimum E REI marked as [K T , B SP , σ].

[0188] Step 7: According to the optimal parameters [K T , B SP , σ] obtained by optimization, decompose the input time series y(t) to extract each modal component in the signal.

[0189] Step 8: Calculate and extract the finally decomposed modal components, which reflect the different frequency components of the input time series and provide a necessary basis for subsequent signal analysis.

[0190] Step 9: Calculate the residual signal vector obtained by decomposition. The residual usually includes the part of the signal that has not been decomposed, and this part of the information may be noise or high-frequency components.

[0191] Step 10: Return the decomposed modal components, residual signal, and output the optimized parameters [K T , B SP , σ] to provide complete results for further applications or analysis.

[0192] The denoised power system time series data obtained in Step 4 improves the data quality by removing irrelevant data, avoids misjudgment caused by noise interference, helps to accurately identify abnormal fluctuations under equipment failures, and thus enhances the reliability of anomaly detection. At the same time, the denoised data helps to accurately analyze the fluctuation characteristics of the power output of renewable energy (wind power, photovoltaic), and reduces the interference of noise on power generation prediction. Its main function is to reduce the error caused by noise interference and improve the authenticity and reliability of the data.

[0193] The main component that reflects the main trend and is smooth in the power system time series data obtained in Step 4 can be used to monitor the long-term operation trend of the power grid, evaluate the medium- and long-term disturbance degree of the base load curve after the integration of wind power and photovoltaic power generation, identify the seasonal fluctuations of the load, and optimize the control plan of energy storage devices. Its main function is to provide high-quality trend information support for the medium- and long-term operation and planning of the power system by eliminating the interference of short-term fluctuations on trend analysis.

[0194] The sub-components with different frequency characteristics obtained in Step 4 are respectively used for harmonic analysis and dynamic characteristic evaluation. The high-frequency component can capture short-term disturbance characteristics, including identifying harmonic interference, detecting harmonics generated by the operation of industrial equipment (such as frequency converters, electric arc furnaces), and analyzing power quality problems caused by the access of distributed energy. In addition, the high-frequency component can also detect transient abnormal signals such as line short circuits and lightning strikes, reveal the short-term electricity consumption behavior of user equipment (such as the instantaneous power fluctuation of electric vehicle charging), and analyze the short-term fluctuation characteristics of wind speed and light intensity. Its main function is to provide reliable support for dynamic characteristic analysis, harmonic detection, etc., thus laying a solid data foundation for the intelligent management and optimization of the power system.

[0195] The present invention has tested two types of time series data: one is the time series of the performance of high-voltage measurement equipment (i.e., the change of the actual ratio error of the instrument transformer over time), and the other is the time series of renewable energy power generation (i.e., the actual power of wind power generation over time). Among them, the sample size of the time series of the performance of high-voltage measurement equipment is 12644×1, and its data characteristics are as Figure 2 shown in the original signal; the sample size of the time series of renewable energy power generation is 34588×1, and its data characteristics are as Figure 3 shown in the original signal. All tests were performed on a computer equipped with an 11th Gen Core TM i7 processor and 16GB of memory, and Matlab 2023b was used for model processing and analysis.

[0196] Figure 5Schematic diagram of sub-components with different frequency characteristics obtained after decomposition using the method proposed in the present invention; the figure includes the time series of the power generation of renewable energy; it can be seen that the present invention can clearly decompose different types of time series into smooth main component components and sub-components containing different frequency characteristics, and these components can be used for different application scenarios respectively.

[0197] Figure 6 Schematic diagram of sub-components with different frequency characteristics obtained after decomposition using the method proposed in the present invention; the figure includes the time series of the performance of high-voltage measurement equipment; it can be seen that the present invention can clearly decompose different types of time series into smooth main component components and sub-components containing different frequency characteristics, and these components can be used for different application scenarios respectively.

[0198] Figure 7 Schematic diagram for comparing the noise (residual) component after decomposition by the adaptive variational mode decomposition model and the noise (residual) component after final decomposition; the figure includes the time series of the power generation of renewable energy; it can be seen that the unit magnitude of the noise after final decomposition by the present invention is 10 -11 which is much smaller than the size of the noise after decomposition by their respective adaptive variational mode decomposition models, indicating that the present invention can minimize the decomposition loss;

[0199] Figure 8 Schematic diagram for comparing the noise (residual) component after decomposition by the adaptive variational mode decomposition model and the noise (residual) component after final decomposition, and the figure includes the time series of the performance of high-voltage measurement equipment; it can be seen that the unit magnitude of the noise after final decomposition by the present invention is 10 -17 , which is much smaller than the size of the noise after decomposition by their respective adaptive variational mode decomposition models, indicating that the present invention can minimize the decomposition loss.

Claims

1. An adaptive denoising method for power system time series data, characterized in that: The following steps are involved: Step 1: construct an adaptive variational mode decomposition model, and use the adaptive variational mode decomposition model to decompose the original power system time series data sequence into subsequences of different energy components; Step 2: Select the subsequence of high energy entropy component from the subsequences decomposed in step 1 as the main component and retain it, and merge the remaining component subsequences with the decomposition remaining after step 1; Step 3: Construct an adaptive time-varying filter empirical mode decomposition model, take the minimum residual as the goal, decompose the combined components in step 2, and obtain new decomposition sub-components and residual components; Step 4: Merge the main components retained in step 2 and the subcomponents decomposed in step 3, remove the residual components in step 3, and complete the denoising of the power system time series data.

2. The method according to claim 1, characterized in that In step 1, the expression of the constructed variational mode decomposition model VMD is: In the formula, the decomposition process of the variational mode decomposition model VMD is defined as f VMD ; x is the set of original sequences; u Res is the residual component after decomposition, the residual is the noise; K is the number of subcomponents; i refers to the index; u i Represents the i-th subcomponent currently decomposed.

3. The method according to claim 1 or 2, characterized in that: When building the adaptive variational mode decomposition model, the following steps are taken: Step S1.1: Convert the decomposition problem of the variational mode decomposition model VMD into the optimal solution problem of parameters, i.e. (K, α, φ); Step S1.2: Select energy entropy as the final objective function for solving the transformed variational mode decomposition model; Step S1.3: Select the optimization algorithm BKA as the optimization tool to complete the construction of the adaptive variational mode decomposition model.

4. The method according to claim 3, characterized in that In step S1.2, energy entropy is selected as the objective function of decomposition, and the formula used is as follows: 1) Obtain the components of different center frequencies after decomposition and determine the marginal spectrum energy E. The relative energy of each frequency component is: In the formula, E k Represents the energy of the kth component; k is the current frequency component index, and the value range of k is [1, K]; K represents the total number of components obtained after decomposition; 2) According to information entropy theory and probability distribution p k , for the kth component, the energy entropy H EE Defined as: H EE (k)=-p k air k (3) In the formula, H EE (k) represents the energy entropy of each frequency component as an element of a vector; 3) The characteristic phase T of energy entropy composition is: T=[H EE (1),H EE (2),…,H EE (K)] (4)。 5. The method according to claim 3, characterized in that: In step S1.3, the adaptive variational mode decomposition model expression is constructed as follows: stK∈[K min ,K max ],α∈[α min ,a max ],φ∈[φ min ,f max ] (6) In the formula, the total number of components K obtained after decomposition ranges from [K min ,K max ]; α is the penalty factor, and its value range is [α min ,α max ]; φ represents the convergence accuracy, and its value range is [φ min ,φ max ]; the subscripts min and max represent the corresponding minimum and maximum values; represents minimizing the objective function; f BKA-VMD-EE is the name of the objective function; Represents the subcomponent under the current energy entropy decomposition index.

6. The method according to claim 5, characterized in that When building an adaptive variational mode decomposition model, the following steps are taken: The first step is to enter the maximum number of iterations Maxiter and the population size N V , the range of the decomposition mode number K, the penalty factor α, the convergence accuracy φ, and the input time series x; The second step is to initialize the relevant parameters of the BKA and variational mode decomposition model VMD model to prepare for the subsequent optimization and signal decomposition process; The third step is to set the energy entropy calculation formula as an important criterion for measuring the decomposition quality, which is used to evaluate the energy distribution of each modal component, so as to conduct effective performance evaluation in the optimization process; Step 4: Set the iteration variable i=1 and start the iterative optimization process; Step 5, enter the loop; when i < Maxiter, use the BKA algorithm to update the current optimization process, establish a model and obtain the optimized best parameter values [K * , α * , φ * , then increment the iteration variable i by 1 and continue with the next iteration until the maximum number of iterations is reached; Step 6: When i ≥ Maxiter, the iteration process ends and the minimum energy entropy H in the loop is output. EE The corresponding optimization parameters are marked as [K, α, φ]; Step 7: Based on the optimal parameters [K, α, φ] obtained through optimization, the input time series x is decomposed to extract the modal components in the signal. Step 8: Calculate and extract the modal components obtained by the final decomposition. These modal components represent the different frequency components in the input time series and have important analytical value. The ninth step is to calculate the residual signal vector after decomposition. The residual represents the part that cannot be represented by the decomposed mode, usually including noise or high-frequency components. In the tenth step, the modal components and residual signals obtained by the final decomposition are returned, and the optimized parameters [K, α, φ] are output to provide complete results for subsequent further analysis or application.

7. The method according to claim 1, characterized in that The time-varying filter empirical mode decomposition model TVFEMD in step 3 constructs a non-uniform B-spline approximation as a filter for screening, introduces a cutoff frequency rearrangement algorithm, and uses the local narrowband signal as the iteration termination criterion; this method can effectively separate high-frequency and low-frequency components and has good stability at low sampling rates; It not only retains the core advantages of EMD, but also reduces modal confusion and sensitivity to noise, and maintains the time-varying characteristics of the signal. Specifically, it includes the following steps: Step 3.1) Estimate the local cutoff frequency: First, perform Hilbert transform on the input time series y(t) and record the result as but: Where A(t) is the instantaneous amplitude of the complex analytic signal; φ(t) is the instantaneous phase; arctan is the inverse tangent function used to calculate the phase; the corresponding analytic signal h(t) is: Where l is a complex unit; determine the local maximum sequence of instantaneous amplitude A(t) {t max } and the local minimum sequence {t min }, for multi-component signals, its analytical signal h(t) can also be expressed as the sum of two signal components, that is: In the formula, a1(t) and a2(t) represent the amplitudes of the two signal components. Based on local extreme values ​​and derivative operations, the maximum and minimum values ​​of a1(t) and a2(t) can be calculated. The upper envelope curve cur1(t) and the lower envelope curve cur2(t) are obtained by interpolation, and then the instantaneous mean γ1(t) and the instantaneous envelope γ2(t) are obtained, that is: Next, interpolate A(t) 2 (t max )φ′(t max ) and A(t)(t min )φ′(t min ),φ′(t max ) and φ′(t min ) represents the derivative of the instantaneous phase, that is, the instantaneous frequency; after interpolation, the interpolation results β1(t) and β2(t) are obtained respectively, and the instantaneous frequency components φ′1(t) and φ′2(t) are calculated: Then calculate the local cutoff frequency φ′ bis (t): Step 3.2) Obtain the local mean; The local mean is obtained by constructing a time-varying filter to process the signal; when intermittent problems occur, the local cutoff frequency φ′ is recalibrated bis (t), the adjusted reconstructed signal is δ(t) = cos[∫φ′ bis (t)d(t)], δ(t) represents the reconstructed signal; the pole As a node to construct a time-varying filter, use B-spline to perform time-varying filtering on y(t), and get the approximate filtering result m(t); Step 3.3) Determine whether the remaining signal meets the stopping criteria; The stopping condition is defined as σ(t), and the bandwidth threshold r is given; if σ(t)≤r, it is confirmed as a component; if the condition is not met, y(t)=y(t)-m(t) is used as the new input signal, and the above steps are repeated until it is met; the proportional index σ(t) is calculated as follows: In the formula, B Loughlin (t) is the Loughlin instantaneous bandwidth of the component signal at time point t, φ avg (t) is the corresponding instantaneous frequency-weighted average; Step 3.4) obtain the final decomposed modal components; Finally, the original input signal y(t) is decomposed into S subsequences {m i (t)|i=1,2,…,S}; when the decomposition conditions are met at the same time, the formula is as follows: Where: m i (t) is the i-th subsequence, z(t) is the decomposition residual; Step 3.5) establishing a selection model for optimal value parameters for key parameters in steps 3.1) to 3.4) including B-spline order, stop criterion, and decomposition mode number; The B-spline order Bsp is used to control the smoothness and local adaptability of the filter. A low order will lead to insufficient flexibility, while a high order may lead to overfitting. The instantaneous bandwidth threshold is used as the stopping criterion (σ) of decomposition, which is used to comprehensively control the termination of decomposition. Loose conditions will lead to over-decomposition, while strict conditions will lead to incomplete decomposition. The decomposition mode number (K T ) limits the depth of decomposition to avoid modal redundancy or information loss; the filter construction conditions dynamically adjust the bandwidth and center frequency in combination with the local characteristics of the signal, thereby achieving accurate extraction of modal components; the optimal configuration of these parameters is of great significance to improving the adaptability and accuracy of decomposition and reducing modal aliasing; therefore, extracting Bsp, K T , the parameters of σ are transformed into the optimal solution problem of parameters; S3.6) establishing an objective function of the optimal parameter selection model; Selecting the minimum decomposition residual as the final objective function for solving the empirical mode decomposition model of the adaptive time-varying filter; S3.7) Selecting the optimization algorithm BKA as the optimization tool for the optimal value parameter selection model and constructing an adaptive decomposition process; The optimization algorithm BKA is selected as the optimization tool to construct the adaptive decomposition of the empirical mode decomposition model of the adaptive time-varying filter; The minimum decomposition residual in step S3.6) is an indicator to measure the size of the decomposition residual. The effect of the decomposition model is evaluated by calculating the difference between the decomposed time series and the original series. The minimum decomposition residual E REI The formula definition is as follows: In the formula, represents the sum of all components after decomposition, that is, the reconstruction result of the signal; i represents the index of the current data point; N represents the data point of this time; E REI The smaller it is, the smaller the deviation between the decomposed result and the original data is, reflecting the model's better denoising performance or decomposition quality. Selecting REI as the objective function aims to minimize the decomposition residual and improve the decomposition accuracy. The adaptive decomposition process in step S3.7) is mathematically expressed as follows: In the formula, K T represents the decomposition mode number; B SP represents the B-spline order; σ represents the stopping criterion; f BKA-TVF-REI is an objective function, the goal is to minimize this function; min means minimization; represents a sum operation, traversing all items from index i=1 to i=S; m i REI (t) represents the decomposed subcomponent under each index; z Res (t) represents the decomposition residual; K T The value range is between, and Represents the upper and lower limits of this decision variable; B SPmin and B SPmax Representative B SP The upper and lower limits of σ min and σ max Represents the upper and lower limits of σ.

8. The method according to claim 7, characterized in that The process of constructing the adaptive decomposition process in step S3.7) is as follows: The first step is to enter the maximum number of iterations Maxiter and the population size N T , decomposition mode number K T The range of B-spline order B SP The range of , the range of the stopping criterion σ, and the input time series y(t); In the second step, based on the input parameters, the relevant parameters of BKA and TVFEMD are initialized to prepare for the subsequent optimization and signal decomposition process; The third step is to set the relative error index REI as a key indicator to measure the convergence of the optimization process and the performance of the model, to ensure that the optimization effect of each iteration can be effectively improved; Step 4: Set the iteration variable i=1 and prepare to enter the iterative optimization process; Step 5, enter the loop; when i < Maxiter, update the current optimization process using the BKA algorithm, build the model and obtain the optimal parameter values [K T * ,B SP * ,σ * , and update the iteration variable i, then continue with the next iteration until the maximum number of iterations is reached; Step 6: When i ≥ Maxiter, end the iteration process and output the minimum E in the loop process. REI The corresponding optimization parameters are marked as [K T ,B SP ,σ]; Step 7: According to the optimal parameters obtained by optimization [K T ,B SP ,σ], decompose the input time series y(t) and extract the various modal components in the signal; Step 8: Calculate and extract the modal components obtained by the final decomposition. These modal components reflect the different frequency components of the input time series and provide the necessary basis for subsequent signal analysis. The ninth step is to calculate the residual signal vector obtained by decomposition. The residual usually includes the part of the signal that has not been decomposed, which may be noise or high-frequency components. The tenth step is to return the decomposed modal components and residual signals, and output the optimized parameters [K T ,B SP ,σ], providing complete results for further application or analysis.

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