CN117725378A - Lightning arrester resistive current prediction method based on VMD-ELM-AEFA - Google Patents
Lightning arrester resistive current prediction method based on VMD-ELM-AEFA Download PDFInfo
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Abstract
The invention discloses a lightning arrester resistive current prediction method based on VMD-ELM-AEFA, which comprises the steps of adopting a variation modal decomposition algorithm to decompose an original lightning arrester resistive current in sequence, reducing complexity and nonlinearity of an original sequence, and extracting effective information of the sequence; extracting k decomposed IMF components, carrying out normalization processing on the component data, and dividing corresponding training sets and test sets; optimizing the ELM model by adopting an AEFA algorithm to find the optimal population position, calculating the optimal weight and threshold of the ELM model, and then substituting the optimal weight and threshold into the model again to predict so as to obtain the model prediction result of each component; and superposing the results of the respective components obtained by model prediction to obtain the final resistive current prediction result. The final prediction result shows that the random generation of the weight and the threshold value of the single extreme learning machine is not optimal, so that the fitting goodness of the resistive current is poor, the MAPE value is 1.129, the AEFA algorithm is introduced to optimize ELM internal parameters, the error index of the model is improved to be 0.97, finally, the VMD decomposition model is introduced to remove noise from a nonlinear original resistive current sequence on the basis of the combination model, effective information is extracted and combined, and finally, the MAPE is improved to 0.483, so that the model has higher generalization compared with the single model.
Description
Technical Field
The invention relates to the technical field of lightning arrester resistive current prediction, in particular to a VMD-ELM-AEFA-based lightning arrester resistive current prediction method.
Background
Lightning arresters are an important device for protecting electrical systems and equipment from lightning strikes. In the operation of lightning arresters, resistive current is an important parameter, and the stability of large-scale power systems is critical to the reliability of the power supply. Lightning surge may cause transient faults or blackouts in the power system, and by predicting resistive currents, system operators may be assisted in taking necessary measures to maintain system stability, reducing the risk of faults and blackouts. While one of the main functions of the lightning arrester is to conduct lightning impulse to the ground to protect equipment and lines associated with the power system from damage. The resistive current refers to the magnitude of the current when the lightning arrester directs a lightning impulse. By predicting the resistive current, it is ensured that the arrester is sufficiently powerful to cope with various lightning surges, thereby protecting the safe operation of critical equipment.
At present, a machine learning and neural network method is often adopted to study the resistive current prediction of the lightning arrester, but the resistive current is usually a nonlinear and particularly random sequence, and the accurate prediction of the resistive current can not be achieved only through a single model.
Disclosure of Invention
The invention solves the technical problems that: aiming at the characteristics of nonlinear resistance current and extremely strong randomness, the invention provides a lightning arrester data analysis method based on a VMD-ELM-AEFA algorithm, and the accurate prediction of the resistive current of the lightning arrester is realized through a composite model.
In order to solve the technical problems, the invention provides the following technical scheme:
firstly, the original lightning arrester resistive current is subjected to sequence decomposition, so that complexity and nonlinearity of an original sequence are reduced, and meanwhile effective information of the sequence is extracted. And then extracting k decomposed IMF components, carrying out normalization processing on the component data, and dividing corresponding training sets and test sets. Then initializing AEFA algorithm parameters including charge quantity, upper and lower boundaries, iteration times and the like; the ELM model parameters comprise hidden node numbers, initial weights and thresholds, then the resolved IMF components and residuals are optimized by adopting an AEFA algorithm at the same time to find the optimal population position, and the optimal weights and thresholds of the ELM model are calculated and then are substituted into the model again for prediction, so that model prediction results of all the components are obtained. And finally, superposing the results of the respective components obtained by model prediction to obtain the final resistive current prediction result.
As a preferable scheme of the lightning arrester data analysis method based on the VMD-ELM-AEFA algorithm, the invention comprises the following steps: the decomposition of the variation modal algorithm is completed by establishing a constraint model, the original constraint problem is converted into the non-constraint problem by introducing a Lagrange factor and a secondary penalty factor, and then the bandwidth and the center frequency of each decomposition component are continuously updated by a certain method, so that the optimal solution is searched, and the decomposition of the original signal is completed.
As a preferable scheme of the lightning arrester data analysis method based on the VMD-ELM-AEFA algorithm, the invention comprises the following steps: assume that there are N training samples (x i ，t i ) The number of hidden layer nodes through the network is L, and the output of each node of the neural network output layer is as follows:
wherein f (x) is an activation function, ω i ＝[ω 1 ,ω 2 ,…ω n ]To input weights, beta i To output weights b i Is the bias value between the input layer and the hidden layer.
When the output can approximate any N samples with zero error, namely:
the above formula can be expressed as:
equation (2) can be converted into a specific matrix form:
H·β＝T (4)
wherein T is expressed as a desired output, H is the output of the hidden layer node after being activated by the activation function, and beta is the weight between the hidden layer and the output layer.
As a preferable scheme of the lightning arrester data analysis method based on the VMD-ELM-AEFA algorithm, the invention comprises the following steps: in order to make the sample have better beta, the training error is required to be minimum, and the predicted result of H beta and the real result T can be solved to minimize the square difference to be used as a fitness function, so that the solution with the minimum objective function is the optimal solution. Namely, the weight beta for connecting the hidden layer and the output layer is calculated by a method of minimizing the approximate square difference, and the fitness function is as follows:
min‖Hβ-T‖ 2 (6)
the optimal solution score of (5) can be derived as:
β＝H -1 ·T (7)
as a preferable scheme of the lightning arrester data analysis method based on the VMD-ELM-AEFA algorithm, the invention comprises the following steps: assuming that the population number of charged particles is N, in the search area of d dimension, the ith particle can be expressed as:
wherein,is the position of the ith population in d-dimensional space.
In d-dimensional space, the position update of the population at time t is as follows:
wherein,represents the position of the ith charged particle in d-dimensional space, f (P i ) F (X) i ) Is the objective function value.
The specific power that particle j acts on example i at the current time t is expressed as:
wherein Q is i (t) and Q j (t) represents the charge of the ith and jth particles at t-time, respectively, and K (t) represents the coulomb constant at t-time, which can be expressed as:
wherein K is 0 And α represents a constant and an initial time value, respectively; item and maxiter represent the current iteration number and the maximum iteration number respectively; r is R ij (t) represents the Euclidean distance between particles.
Meanwhile, the electric power formula of other particles acting on the ith particle is calculated as follows:
wherein rand is a random number within the range of 0-1, N is the number of particles, F i Is the resultant force on the ith particle. At the t moment, the formula of the i-th particle electric field describes the formula as follows:
as a preferable scheme of the lightning arrester data analysis method based on the VMD-ELM-AEFA algorithm, the invention comprises the following steps: acceleration of the ith particle at time t according to Newton's second lawCan be expressed as:
wherein M is i (t) represents the unit mass of the ith particle at time t.
Updating the charge particles according to a speed and position updating formula, wherein the specific expression form is as follows:
as a preferable scheme of the lightning arrester data analysis method based on the VMD-ELM-AEFA algorithm, the invention comprises the following steps: and superposing the results of the respective components obtained by the model prediction to obtain the final resistive current prediction result.
Compared with the prior art, the invention has the beneficial effects that: MOA cracking trend is judged based on a lightning arrester resistive current prediction model combined with VMD-ELM-AEFA, the inherent trend of resistive current can be effectively extracted by Variable Modal Decomposition (VMD), the sequence nonlinearity is reduced, in the actual and model prediction results of the resistive current, compared with a single model and an undegraded combined model, the actual fitting goodness and the error index RMSE, MAE, MAPE of the model are obviously improved, and the accurate prediction of the resistive current can be effectively realized.
Drawings
Fig. 1 is a flowchart of a method for predicting resistive current of a lightning arrester based on VMD-ELM-AEFA according to the present invention.
FIG. 2 is a topology of an ELM model of the present invention.
FIG. 3 is a diagram of the original resistive current sequence of the present invention.
Fig. 4 is an exploded view of the VMD of the present invention.
FIG. 5 is a comparison of the combined model.
Fig. 6 is a taylor diagram of the present invention.
Detailed Description
In order that the above-recited objects, features and advantages of the present invention will become more readily apparent, a more particular description of the invention will be rendered by reference to specific embodiments thereof which are illustrated in the appended drawings.
A lightning arrester resistive current prediction method based on VMD-ELM-AEFA specifically comprises the following steps:
s1, adopting a variation modal decomposition algorithm to decompose the original lightning arrester resistive current in sequence, reducing complexity and nonlinearity of the original sequence, extracting effective information of the sequence, and completing algorithm decomposition by establishing a constraint model. Firstly, converting the original constraint problem into the non-constraint problem by introducing Lagrangian factor and secondary penalty factor, and then continuously updating the bandwidth and center frequency of each decomposition component by a certain method to search the optimal solution so as to complete the decomposition of the original signal
S2: assume that there are N training samples (x i ，t i ) The number of hidden layer nodes through the network is L, and the output of each node of the neural network output layer is as follows:
wherein f (x) is an activation function, ω i ＝[ω 1 ,ω 2 ,…ω n ]To input weights, beta i To output weights b i Is the bias value between the input layer and the hidden layer.
When the output can approximate any N samples with zero error, namely:
the above formula can be expressed as:
equation (2) can be converted into a specific matrix form:
H·β＝T (4)
wherein T is expressed as a desired output, H is the output of the hidden layer node after being activated by the activation function, and beta is the weight between the hidden layer and the output layer.
In order to make the sample have better beta, the training error is required to be minimum, and the predicted result of H beta and the real result T can be solved to minimize the square difference to be used as a fitness function, so that the solution with the minimum objective function is the optimal solution. Namely, the weight beta for connecting the hidden layer and the output layer is calculated by a method of minimizing the approximate square difference, and the fitness function is as follows:
min‖Hβ-T‖ 2 (6)
the optimal solution score of (5) can be derived as:
β＝H -1 ·T (7)
s3: and extracting k decomposed IMF components, carrying out normalization processing on the component data, and dividing corresponding training sets and test sets.
S4: initializing AEFA algorithm parameters including charge quantity, upper and lower boundaries, iteration times and the like; the ELM model parameters comprise hidden node numbers, initial weights and thresholds, then the resolved IMF components and residuals are optimized by adopting an AEFA algorithm at the same time to find the optimal population position, and the optimal weights and thresholds of the ELM model are calculated and then are substituted into the model again for prediction, so that model prediction results of all the components are obtained.
Assuming that the population number of charged particles is N, in the search area of d dimension, the ith particle can be expressed as:
wherein,is the position of the ith population in d-dimensional space.
In d-dimensional space, the position update of the population at time t is as follows:
wherein,represents the position of the ith charged particle in d-dimensional space, f (P i ) F (X) i ) Is the objective function value.
The specific power that particle j acts on example i at the current time t is expressed as:
wherein Q is i (t) and Q j (t) represents the charge of the ith and jth particles at t-time, respectively, and K (t) represents the coulomb constant at t-time, which can be expressed as:
wherein K is 0 And α represents a constant and an initial time value, respectively; item and maxiter represent the current iteration number and the maximum iteration number respectively; r is R ij (t) represents particles and granulesEuclidean distance between the children.
Meanwhile, the electric power formula of other particles acting on the ith particle is calculated as follows:
wherein rand is a random number within the range of 0-1, N is the number of particles, F i Is the resultant force on the ith particle. At the t moment, the formula of the i-th particle electric field describes the formula as follows:
acceleration of the ith particle at time t according to Newton's second lawCan be expressed as:
wherein M is i (t) represents the unit mass of the ith particle at time t.
Updating the charge particles according to a speed and position updating formula, wherein the specific expression form is as follows:
finally finding the optimal position through each iteration of AEFA algorithmThen, the result is substituted into the ELM model to calculate the best in (4)And (3) omega and b values and predicting to obtain a component result.
S5: and superposing the results of the respective components obtained by model prediction to obtain the final resistive current prediction result.
Experimental data and parameter settings:
according to the invention, experimental data are selected from 110kv lightning arrester detection data of a 220kv transformer substation in North China for supporting. The experimental software platform is operated in Matlab2021a version environment. The raw arrester resistive current data is shown in fig. 3.
Experimental results and analysis:
compared with the traditional decomposition method, the VMD decomposition model can effectively solve the problem of modal aliasing, thereby providing a good foundation for the accurate prediction of the subsequent prediction model; in the VMD decomposition process, the mode number K needs to be set manually, and too large or too small can have great influence on the decomposition result. A specific analytical discussion of the modal number k values is therefore provided.
TABLE 1 phase relationship table of adjacent imf components
In order to better extract the original characteristic information of the resistive current, the correlation coefficients of the components of the VMD decomposition are subjected to correlation analysis by using the spearman level correlation coefficients, and the selection of a final modulus value K is determined by the final correlation coefficients. In order to avoid missing the original sequence characteristic information, the first 6 modes are firstly analyzed, further observation is carried out, when the K is 7 and 8, the correlation coefficient obtained by decomposing the low-frequency component is larger and exceeds 0.18, the experimental simulation shows that when the correlation coefficient is larger than 0.18, the model aliasing phenomenon can occur in the decomposition to cause excessive decomposition, and therefore the number K of layers of the decomposition is finally determined to be 5.
Setting the population number of the AEFA algorithm as 20, the maximum iteration number as 100, selecting an fitness function as an RMSE value, optimizing the weight and the threshold of the ELM model, and obtaining the hidden layer node number of the ELM for multiple times according to experiments, wherein the hidden layer node number is selected as 15. The data samples total 498 groups, the first 70% of resistive current samples were used as training set, and the last 30% were used as test set to verify the model. The comparison results of the single ELM model, the AEFA-ELM model, and the decomposed VMD-AEFA-ELM model were compared, and the comparison results of the partial test set samples are shown in Table 2.
Table 2 comparison of the results of different models
Fig. 5 is a comparison graph of the combined model to the lightning arrester resistive current prediction, and it can be seen from the graph that the VMD-AEFA-ELM combined model prediction effect proposed herein is optimal, because the VMD decomposition model effectively processes the modal aliasing problem of the original resistive current in the early data processing stage, and meanwhile, the optimal extreme learning machine parameters are found through the artificial electric field algorithm in the optimization stage, so that the prediction accuracy of the model after combination is greatly improved compared with other models. It can also be seen from table 3 that the model presented herein is minimal for all error indicators.
Table 3 error index comparison
Fig. 6 is a taylor diagram between actual values and predicted values of each model, wherein the taylor diagram comprises fitting coefficients, standard deviations and root mean square errors among 3 prediction models, the distance between an origin and each model represents the standard deviation ratio of a reference point, the closer the numerical value is to 1, the better the fitting goodness of the model is, and the model proposed herein is closest to the reference point and the prediction effect is most excellent as can be seen from fig. 6.
It should be noted that the above embodiments are only for illustrating the technical solution of the present invention and not for limiting the same, and although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that the technical solution of the present invention may be modified or substituted without departing from the spirit and scope of the technical solution of the present invention, which is intended to be covered in the scope of the claims of the present invention.
Claims (4)
1. A lightning arrester resistive current prediction method based on VMD-ELM-AEFA is characterized in that:
carrying out sequential decomposition on the original lightning arrester resistive current by adopting a variable-decomposition mode decomposition method;
extracting k decomposed IMF components, carrying out normalization processing on the component data, and dividing corresponding training sets and test sets;
initializing AEFA algorithm parameters including charge quantity, upper and lower boundaries and iteration times; the ELM model parameters comprise hidden node numbers, initial weights and thresholds, then the resolved IMF components and the residuals are optimized by adopting an AEFA algorithm at the same time to find the optimal population position, and the optimal weights and thresholds of the ELM model are calculated and then are substituted into the model again for prediction, so that model prediction results of all the components are obtained;
and superposing the results of the components obtained by the model prediction to obtain the lightning arrester resistive current prediction result.
2. The VMD-ELM-AEFA-based arrester resistive current prediction method of claim 1, wherein: the original lightning arrester resistive current is subjected to sequential decomposition by using a variation modal decomposition method, and the method specifically comprises the following steps: firstly, a Lagrangian factor and a secondary punishment factor are introduced to convert the original constraint problem into an unconstrained problem, then the bandwidth and the center frequency of each decomposition component are continuously updated, an optimal solution is found, and the sequence decomposition of the original signal is completed.
3. The VMD-ELM-AEFA-based arrester resistive current prediction method of claim 2, wherein:
let N training samples (x i ，t i ) The number of hidden layer nodes through the network is L, and the output of each node of the neural network output layer is as follows:
wherein f (x) is an activation function, ω i ＝[ω 1 ,ω 2 ,…ω n ]To input weights, beta i To output weights b i A bias value between the input layer and the hidden layer;
when the output can approximate any N samples with zero error, namely:
the above formula can be expressed as:
equation (2) can be converted into a specific matrix form:
H·β＝T (4)
wherein T is expressed as expected output, H is the output of hidden layer nodes after being activated by an activation function, and beta is the weight between the hidden layer and the output layer;
the weight beta connecting the hidden layer and the output layer is calculated by a method of minimizing the approximate square error, and the fitness function is as follows:
min‖Hβ-T‖ 2 (6)
deriving an optimal solution of (5) as:
β＝H -1 ·T (7)
4. the VMD-ELM-AEFA-based lightning arrester resistive current prediction method of claim 1, wherein: initializing AEFA algorithm parameters, wherein the parameters comprise charge quantity, upper and lower boundaries and iteration times; the ELM model parameters comprise hidden node numbers, initial weights and thresholds, then the resolved IMF components and margins are optimized for the ELM model by adopting an AEFA algorithm, the optimal population position is found, the optimal weights and thresholds of the ELM model are calculated and then are substituted into the model again for prediction, and the model prediction results of the components are obtained, wherein the model prediction results are specifically as follows:
assuming that the population number of charged particles is N, in the search area of d dimension, the ith particle can be expressed as:
wherein, the method comprises the steps of,is the position of the ith population in d-dimensional space.
In d-dimensional space, the position update of the population at time t is as follows:
wherein,represents the position of the ith charged particle in d-dimensional space, f (P i ) F (X) i ) Is the objective function value.
The specific power that particle j acts on example i at the current time t is expressed as:
wherein Q is i (t) and Q j (t) represents the charge of the ith and jth particles at t-time, respectively, and K (t) represents the coulomb constant at t-time, expressed as:
wherein K is 0 And α represents a constant and an initial time value, respectively; item and maxiter represent the current iteration number and the maximum iteration number respectively; r is R ij (t) represents the Euclidean distance between particles;
meanwhile, the electric power formula of other particles acting on the ith particle is calculated as follows:
wherein rand is a random number within the range of 0-1, N is the number of particles, F i Is the resultant force on the ith particle. At the t moment, the formula of the i-th particle electric field describes the formula as follows:
updating the charge particles according to a speed and position updating formula, wherein the specific expression form is as follows:
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