CN117633446A - Wind speed prediction method and system based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction - Google Patents
Wind speed prediction method and system based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction Download PDFInfo
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Abstract
The invention discloses a wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combination prediction, which comprises the following steps: acquiring historical wind speed data of a wind power plant, forming a wind speed time sequence, and dividing a training set and a testing set; CEEMD (continuous emission model) decomposition is carried out on the wind speed time sequence to obtain a series of intrinsic mode components and a residual sequence; calculating sample entropy of residual sequences of all eigenvector components and judging complexity of each sequence; carrying out EWT secondary decomposition on the sequence with the highest sample entropy value to obtain a series of subsequences with higher resolution; respectively creating ARIMA models for all the subsequences to obtain predicted values of the subsequences; and superposing the predicted values of all the subsequences to obtain a final wind speed predicted result. The method adopts the combination of CEEMD and EWT decomposition technologies, can effectively reduce the complexity of the sequence, and then carries out ARIMA prediction on the sequence which is relatively stable after two times of decomposition.
Description
Technical Field
The invention relates to the technical field of wind speed prediction, in particular to a wind speed prediction method, a wind speed prediction system, a wind speed prediction computer medium and a wind speed prediction computer based on CEEMD-SE-EWT double decomposition and ARIMA combination prediction.
Background
Wind energy is a pollution-free and renewable energy source, is a reliable way for solving the production and living energy sources, is one of the most mature power generation modes with the lowest cost in the field of new energy sources, and has very wide development space. However, the intermittent and unstable wind speed causes instability of the energy generated, extremely influences the conversion and utilization of wind energy, and jeopardizes the stability and power dispatching of the power system. The accurate wind speed prediction can reduce the risk of wind speed uncertainty on a power system, and has important significance in the aspects of stable power supply, power scheduling, safe operation and the like of a wind farm.
In recent years, researchers at home and abroad adopt various models to predict wind speed, and the prediction mainly comprises single prediction and combined prediction. The commonly used single prediction model is mainly divided into three types of physical methods, statistical methods and machine learning methods according to prediction principles. The physical model is mainly based on weather forecast and is suitable for long-term wind speed forecast in large-scale areas. The machine learning method mainly comprises a support vector machine, a neural network, kalman filtering and the like. Statistical methods include autoregressive, autoregressive moving averages, differential autoregressive moving averages (ARIMA), and the like.
However, since the wind speed has strong volatility and randomness, the prediction result of a single prediction model is greatly affected by the wind characteristics, thereby causing unstable prediction accuracy.
Therefore, a method for predicting wind speed is needed to decompose the time sequence into relatively stable subsequences, and predict the subsequences respectively, so as to obtain a relatively stable prediction result.
Disclosure of Invention
The invention aims to: in order to overcome the defects, the invention aims to provide a wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction so as to improve wind speed prediction precision of a wind power plant.
In order to solve the technical problems, the invention provides a wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction, which comprises the following steps:
step S1: acquiring historical wind speed data of a wind power plant, forming a wind speed time sequence, and dividing a training set and a testing set;
step S2: carrying out complementary set empirical mode decomposition on the data of the wind speed time sequence to obtain at least one intrinsic mode component and a residual sequence;
step S3: calculating sample entropy of residual sequences of all eigenvector components and judging complexity of each sequence;
step S4: performing empirical wavelet decomposition on the sequence with the highest calculated sample entropy value to obtain at least one subsequence with higher resolution;
step S5: performing ARIMA prediction on all subsequences obtained by the two decomposition to obtain predicted values of all subsequences;
step S6: and superposing the predicted values of all the subsequences to obtain a final predicted result of the original wind speed time sequence.
Further, in step S2, the method further comprises the steps of:
step S21: and respectively adding a pair of Gaussian white noise sequences with equal amplitude and opposite directions on the original time sequence to reconstruct a new signal sequence:
S 1 (t)＝X(t)+ε(t)
S 2 (t)＝X(t)-ε(t)
wherein X (t) represents an original time sequence, ε (t) represents a Gaussian white noise sequence, S 1 (t) represents a weightA first signal sequence S 2 (t) represents a reconstructed second signal sequence;
step S22: performing empirical mode decomposition on the reconstructed signal sequence to obtain a limited number of eigenmode function components respectively:
wherein C is ij (t) represents the j-th eigenmode function obtained by empirical mode decomposition with the i-th addition of white noise; r is (r) i (t) residual items obtained after empirical mode decomposition;
step S23: adding different Gaussian white noise sequences, and repeating the step S21 and the step S22 to obtain a plurality of sets of eigenvalue function components and a set of trend items;
step S24: calculating the set average value of all the groups of intrinsic modal components to obtain final modal components:
wherein c j (t) represents the final modal component.
Further, in step S3, the calculation formula of the sample entropy value is:
wherein SampEn represents a sample entropy value, m is a dimension, r is a similarity margin, A m (r) probability of matching m+1 points for two sequences, B m (r) is the probability that two sequences match m points with a similar tolerance r.
Further, in step S3, the method further comprises the steps of:
step S31: setting a wind speed time sequence bit: x (i), i=1, 2,3,..n, and defining a sample entropy parameter dimension m and a similarity tolerance r;
step S32: reconstructing m-dimensional vector X m (1)、X m (2)、X m (3)，...，X m And (n-m+1), calculating the distance between each sequence and n-m+1 sequences, wherein the maximum value of the absolute value of the difference value of the corresponding elements of the two vectors is:
where j=1, 2,3,..n, j+.i;
step S33: statistics d [ X ] m (i)，X m (j)]Number < r, and calculating the ratio to the total number n-m:
further calculateAverage B at all i values m (r)：
Step S34: increasing the dimension to m+1, and repeating the steps S32 and S33 to obtain the probability A of matching m+1 points m (r)、B m (r), and further the sample entropy is defined as:
and when N is a finite value, the sample entropy is:
wherein the probability A m (r)、B m (r) is the probability that two sequences match m points with a similar tolerance r.
Further, in step S4, the method further comprises the steps of:
step S41: calculating a fourier transform of the input signal;
step S42: dividing the Fourier spectrum into N continuous segments, determining boundaries by searching local maxima of the spectrum, and arranging the boundary in descending order, wherein, assuming that the number of maxima is M, when M is larger than or equal to N, the first N-1 maxima are reserved, when M is smaller than N, all the maxima are reserved and N is corrected, thereby taking the intermediate frequency between the two local maxima as omega n ；
Step S43: finding a segmentation boundary and segmenting a frequency spectrum;
step S44: and constructing a proper wavelet filter bank to decompose the signals.
Further, in step S44, the method further includes the steps of:
step S441: the empirical wavelet is defined as a bandpass filter over each interval n, and for n > 0, the empirical scale function phi is defined by the following two equation expressions, respectively n (omega) and empirical wavelet ψ n (ω)：
Wherein β (x) =x 4 (35-84x+70x 2 -20x 3 )；
Step S442: defining the empirical wavelet transform by the same method as classical wavelet transform, and detail coefficient [ ]) The inner product of the empirical wavelet and the signal gives:
approximation coefficient [ ]) Given by the empirical scale function and the inner product of the signal:
wherein F [. Cndot.]And F -1 [.]Fourier transform and inverse transform, respectively, whereby the signal f (t) is reconstructed as:
step S443: the signal f (t) is decomposed to obtain an amplitude modulation-frequency modulation single component f with the frequency from low to high through the empirical wavelet transformation processing k (t)(k＝1，2，3，...)：
Further, in step S5, the mathematical expression of the prediction model is:
E(ε t )＝0，Var(ε t )＝σ 2
wherein ε t And x t Respectively representing sample data and white noise, epsilon at time t t The mean value of (2) is 0, and the variance is a constant; b is a hysteresis operator, bx t ＝x t-1 ；Is a difference operator, < >>d represents the number of differences over the non-stationary sequence; phi (B) is an autoregressive coefficient polynomial, < >>p is the order of the autoregressive polynomial; θ (B) is a moving average coefficient polynomial, +.>q is the order of the moving average polynomial.
Further, in step S5, the prediction model is determined by three parameters of p, d and q, and the determining process includes the following steps:
step S51: performing a smoothness test on the sequence and determining a differential order, comprising: verifying the stability of the time sequence, and performing differential operation on the non-stationary sequence to convert the non-stationary sequence into a stationary sequence, wherein the differential order is d;
step S52: determining ARMA model orders p and d, comprising: the autocorrelation function and the partial autocorrelation function are calculated to perform preliminary order determination, and then the order is selected violently through the red pool information criterion and the Bayesian information criterion;
step S53: verifying the model, performing residual error test, comprising: observing whether the residual error of the ARIMA model is normal distribution with an average value of 0 and a variance of constant, and simultaneously observing whether continuous residual errors are relevant or not to ensure that the residual error of the selected model is white noise;
step S54: wind speed predictions are made using the created ARIMA model.
Further, in step S6, the method further comprises the steps of:
step S61: average absolute error is carried out on the predicted sequence and the test set sequence:
wherein Z (t) is the wind speed measured at the moment t, Z' (t) is the predicted wind speed at the moment t, and N is the number of wind speed predictions;
step S62: average absolute percentage error is performed on the predicted sequence and the test set sequence:
step S63: square root error is carried out on the predicted sequence and the test set sequence:
and calculating the determination coefficients of the predicted sequence and the test set sequence:
wherein,representing the sample mean.
The invention also provides a wind speed prediction system based on CEEMD-SE-EWT double decomposition and ARIMA combination prediction, which comprises:
the data processing module is used for acquiring historical wind speed data of the wind power plant, forming a wind speed time sequence and dividing a training set and a testing set;
the double decomposition module is used for carrying out complementary set empirical mode decomposition on the data of the wind speed time sequence to obtain at least one intrinsic mode component and a residual sequence, further calculating sample entropy of the residual sequence of all the intrinsic mode components and judging the complexity of each sequence, and further carrying out empirical wavelet decomposition on the sequence with the highest calculated sample entropy value to obtain at least one subsequence with higher resolution;
and the prediction module is used for performing ARIMA prediction on all the subsequences obtained by the two decomposition to obtain predicted values of all the subsequences, and further superposing the predicted values of all the subsequences to obtain a final predicted result of the original wind speed time sequence.
The invention also provides a computer medium, wherein the computer medium is stored with a computer program, and the computer program is executed by a processor to realize the wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combination prediction.
The invention also provides a computer, comprising the computer medium.
Compared with the prior art, the technical scheme of the invention has the following advantages:
1. the CEEMD-SE-EWT double decomposition technology is adopted, the complexity of the sequence is further reduced on the basis of noise reduction, ARIMA prediction is combined, the non-stationarity of the wind speed sequence is reduced, the prediction precision is improved, and the applicability and the stability are realized;
2. the original sequence is decomposed and evaluated layer by layer through CEEMD-SE-EWT double decomposition technology to obtain a relatively stable time sequence, and then the ARIMA model is utilized to predict the stable subsequence, so that the wind speed prediction accuracy is further improved; therefore, the nonlinear decomposition characteristic of CEEMD-SE-EWT and the statistical modeling advantage of ARIMA are utilized, so that the final wind speed prediction effect is more accurate and reliable.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following description will briefly explain the drawings used in the embodiments or the description of the prior art, and it is obvious that the drawings in the following description are only embodiments of the present invention, and other drawings can be obtained according to the provided drawings without inventive effort for a person skilled in the art.
FIG. 1 is a first flowchart of a wind speed prediction method of the present invention based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction.
FIG. 2 is a second flowchart of a wind speed prediction method of the present invention based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction.
FIG. 3 is a flow chart of a method of performing complementary set empirical mode decomposition in accordance with the present invention.
Fig. 4 is a flowchart of a sample entropy calculation method of the present invention.
FIG. 5 is a short-term prediction of wind speed in wind farm data according to the present invention.
Fig. 6 is a flow chart of a signal decomposition method of the present invention.
FIG. 7 is a flow chart of the ARIMA model wind speed prediction method of the present invention.
Fig. 8 is a flowchart of a method of evaluating a predictive model of the present invention.
FIG. 9 is a graph showing the results of a CEEMD-SE-EWT-ARIMA method of the present invention compared with ARIMA, CEEMD-ARIMA, WT-ARIMA, CEEMD-WT-ARIMA methods.
FIG. 10 is a block diagram of a wind speed prediction system based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction of the present invention.
Description of the specification reference numerals:
101. data processing module 102, double decomposition module 103, prediction module.
Detailed Description
Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein like or similar reference numerals refer to like or similar elements or elements having like or similar functions throughout. The embodiments described below by referring to the drawings are illustrative and intended to explain the present invention and should not be construed as limiting the invention.
The wind speed prediction is performed by adopting a combination of CEEMD-SE-EWT double decomposition technology and ARIMA prediction model, specifically, CEEMD is that white noise is firstly added on an original sequence, a series of eigenvalue components with different frequencies and a residual sequence are obtained through an EMD algorithm, and meanwhile, CEEMD enables noise residues in a reconstructed signal to be smaller. EWT integrates the self-adaptive decomposition concept of the EMD method and the tight support frame theory of the wavelet transformation theory, and can efficiently decompose subsequences with different frequencies. The original sequence is firstly decomposed by CEEMD, the complexity of each subsequence is measured by SE calculation, then the subsequence with higher complexity is further decomposed by EWT, and finally the relatively stable time sequence is obtained. ARIMA is a time sequence model in a statistical method, is suitable for linear and stable time sequences, sub-sequences obtained by decomposing a wind speed sequence twice are stable, and all sub-sequences are predicted by using the ARIMA model, so that a good prediction effect is finally obtained.
Referring to FIGS. 1,2, and 5, in some embodiments, the present invention discloses a wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction, the method comprising the steps of:
step S1: and acquiring historical wind speed data of the wind power plant, forming a wind speed time sequence, and dividing a training set and a testing set.
Further, in step S1, wind speed data is obtained by using a fan of a wind farm, the data length is proportionally divided into a training set and a test set, the training set is used for data input, prediction is performed through a combined model, prediction data is obtained, and the test set is used for comparing with a test result and analyzing a prediction effect.
Step S2: performing complementary set empirical mode decomposition (CEEMD) on the data of the wind speed time sequence to obtain at least one intrinsic mode component and a residual sequence;
specifically, referring to fig. 3, in step S2, the method specifically includes the following sub-steps:
step S21: and respectively adding a pair of Gaussian white noise sequences epsilon (t) with equal amplitude and opposite directions on the original time sequence X (t) to reconstruct a new signal sequence S (t):
S 1 (t)＝X(t)+ε(t)
S 2 (t)＝X(t)-ε(t)
wherein X (t) represents an original time sequence, ε (t) represents a Gaussian white noise sequence, S 1 (t) represents the reconstructed first signal sequence, S 2 (t) represents a reconstructed second signal sequence;
step S22: performing Empirical Mode Decomposition (EMD) on the reconstructed signal sequence S (t) to obtain a limited number of eigenmode function components respectively:
wherein C is ij (t) represents the ith addition of white noise, the jth eigenmode function (IMF) obtained by EMD decomposition; r is (r) i (t) is a residual term obtained after EMD decomposition;
step S23: adding different Gaussian white noise sequences, and repeating the step S21 and the step S22 to obtain a plurality of sets of eigenvalue function components and a set of trend items;
step S24: calculating the average value of the set of all the intrinsic modal components to obtain a final modal component c j (t)：
Wherein c j (t) represents the final modal component.
Step S3: and measuring the complexity of the wind speed time sequence by adopting Sample Entropy (SE), and calculating a sample entropy value for each intrinsic mode component and residual sequence, wherein the calculation formula of the sample entropy value sampEn is as follows:
wherein m is the dimension, r is the similarity tolerance, A m (r) probability of matching m+1 points for two sequences, B m (r) is the probability that two sequences match m points with a similar tolerance r.
Step S4: performing empirical wavelet decomposition on the sequence with the highest calculated sample entropy value to obtain at least one subsequence with higher resolution;
specifically, referring to fig. 4, in step S4, the method specifically includes the following sub-steps:
step S41: calculating a fourier transform of the input signal;
step S42: dividing the Fourier spectrum into N continuous segments, determining boundaries by searching local maxima of the spectrum, and arranging the boundary in descending order, wherein, assuming that the number of maxima is M, when M is larger than or equal to N, the first N-1 maxima are reserved, when M is smaller than N, all the maxima are reserved and N is corrected, thereby taking the intermediate frequency between the two local maxima as omega n ；
Step S43: finding a segmentation boundary and segmenting a frequency spectrum;
step S44: and constructing a proper wavelet filter bank to decompose the signals.
Step S5: performing ARIMA prediction on all subsequences obtained by two times of decomposition to obtain predicted values of all subsequences, wherein the ARIMA prediction model is determined by three parameters of p, d and q, and the mathematical expression is as follows:
E(ε t )＝0，Var(ε t )＝σ 2
specifically, ε t And x t Respectively representing sample data and white noise, epsilon at time t t The mean value of (2) is 0, and the variance is a constant; b is a hysteresis operator, bx t ＝x t-1 ；Is a difference operator, < >>d represents the number of differences over the non-stationary sequence; phi (B) is an autoregressive coefficient polynomial, < >>p is the order of the autoregressive polynomial; θ (B) is a moving average coefficient polynomial, +.>q is the order of the moving average polynomial.
Step S6: and superposing the predicted values of all the subsequences to obtain a final predicted result of the original wind speed time sequence.
In some embodiments, in step S3, the complexity of the wind speed time series is calculated by using sample entropy, where the sample entropy can measure the complexity of the time series and the size of the probability of generating a new pattern by using the time series of dimension change, the higher the probability of generating a new pattern, the higher the complexity of the sequence, the larger the entropy value, which can be represented by SampEn (m, r, n), where the dimensions are m and m+1, r is a similarity tolerance, n is a data length, and the sample entropy defining process is:
step S31: setting a wind speed time sequence bit: x (i), i=1, 2,3,..n, and defining a sample entropy parameter dimension m and a similarity tolerance r;
step S32: reconstructing m-dimensional vector X m (1)、X m (2)、X m (3)，...，X m And (n-m+1), calculating the distance between each sequence and n-m+1 sequences, wherein the maximum value of the absolute value of the difference value of the corresponding elements of the two vectors is:
where j=1, 2,3,..n, j+.i;
step S33: statistics d [ X ] m (i)，X m (j)]Number < r, and calculating the ratio to the total number n-m:
and then calculateAverage B at all i values m (r)：
Step S34: increasing the dimension to m+1, and repeating the steps S32 and S33 to obtain the probability A of matching m+1 points m (r)、B m (r) is the probability that two sequences match m points with a similar tolerance r, and the sample entropy is defined as:
and when N is a finite value, the sample entropy is:
specifically, in the practical application process, the parameter m is generally 1 or 2, the similarity margin r is generally 0.1-0.25 times of the standard deviation of the original data, and m is 2 and r is 0.25 times of the standard deviation.
In some embodiments, referring to FIG. 6, in step S44, an empirical wavelet is defined as a bandpass filter over each interval n, designed using the idea of constructing Littlewood-Paley and Meyer wavelets, for n > 0, an empirical scale function φ is defined by the following two equation expressions, respectively n (omega) and empirical wavelet ψ n (ω)：
Wherein β (x) =x 4 (35-84x+70x 2 -20x 3 )；
Step S441: defining an Empirical Wavelet Transform (EWT) in the same way as a classical Wavelet Transform (WT), detail coefficientsThe inner product of the empirical wavelet and the signal gives:
approximation coefficientGiven by the empirical scale function and the inner product of the signal:
wherein F [. Cndot.]And F -1 [·]Fourier transform and inverse transform, respectively, whereby the signal f (t) is reconstructed as:
step S442: the signal f (t) is decomposed to obtain an amplitude modulation-frequency modulation single component f with the frequency from low to high through the empirical wavelet transformation processing k (t)(k＝1，2，3，...)：
In some embodiments, referring to fig. 7, in step S44, in step S5, the prediction model is determined by three parameters p, d, q, where the determining process includes at least the following steps:
step S51: the sequences were subjected to a smoothness test and differential order was determined, namely: firstly, verifying the stability of a time sequence, and performing differential operation on a non-stationary sequence to convert the non-stationary sequence into a stationary sequence, wherein the differential order is d;
step S52: determining ARMA model orders p and d, namely: firstly, calculating an autocorrelation function (ACF) and a partial autocorrelation function (PACF) to perform preliminary order determination, and then, violently selecting orders through a red pool information criterion (AIC) and a Bayesian Information Criterion (BIC);
step S53: and (3) verifying a model, and performing residual error test, namely: observing whether the residual error of the ARIMA model is normal distribution (obeying zero mean, normal distribution with unchanged variance) with the average value of 0 and the variance of 0, and simultaneously observing whether continuous residual errors are (auto) correlated, so as to ensure that the residual error of the selected model is white noise;
step S54: wind speed predictions are made using the created ARIMA model.
In some embodiments, in step S6 of the present invention, the predicted values of all the subsequences are reconstructed to obtain a final predicted result, and the final predicted result is compared with the test set, so that the prediction accuracy and the prediction effect can be evaluated.
Illustratively, the method for predicting and comparing wind speed data measured by a fan of a wind farm in a certain place comprises the following steps:
in step S1, wind farm historical wind speed data is acquired, forming a wind speed time series, for example: the wind speed time sequence is selected from continuous 7-day data measured by a fan in 2 months of 2017, and the total of 1008 data, wherein the first 720 data are training sets, and the last 288 data are test sets.
In step S2, the wind speed time series is decomposed by CEEMD to obtain 8 eigen mode components and a residual sequence.
In step S3, the sample entropy value of each subsequence obtained by CEEMD decomposition is calculated, and IMF1 with the maximum sample entropy value is obtained, and the result is shown in the following table:
in step S4, the IMF1 is subjected to EWT decomposition to obtain 8 components, the sample entropy value of the subsequence obtained by the secondary decomposition is calculated again, and the stability of the components of the secondary decomposition is compared and verified, and the result is shown in the following table:
in step S5, all components obtained by twice decomposition of CEEMD and EWT are ARIMA predicted, and the ARIMA prediction model is created as follows: first, the sequences are subjected to a smoothness test and the differential order is determined. Firstly, verifying the stability of a time sequence, and performing differential operation on a non-stationary sequence to convert the non-stationary sequence into a stationary sequence, wherein the differential order is d; then, determining ARMA model orders p and d; firstly, calculating an autocorrelation function (ACF) and a partial autocorrelation function (PACF) to perform preliminary order determination, and then, violently selecting orders through the criteria of a red pool information criterion (AIC), a Bayesian Information Criterion (BIC) and the like; secondly, verifying a model, and performing residual error detection; observing whether the residual error of the ARIMA model is normal distribution (obeying zero mean, normal distribution with unchanged variance) with the average value of 0 and the variance of 0, and also observing whether continuous residual errors are (auto) correlated or not to ensure that the residual error of the selected model is white noise; and finally, predicting the test set data by using the created ARIMA model.
In step S6, referring to fig. 8, the predicted values of all the sub-sequences are reconstructed to obtain a final wind speed predicted result, and the predicted effect is compared and analyzed; the prediction model is evaluated and compared with other models by comparing the prediction sequence with the test set sequence for Mean Absolute Error (MAE), mean Absolute Percent Error (MAPE), root Mean Square Error (RMSE), and determination coefficient (R2). The evaluation index calculation formula is as follows:
/>
wherein Z (t) is the wind speed measured at time t, Z' (t) is the predicted wind speed at time t,and (5) representing a sample mean value, wherein N is the number of wind speed predictions.
Comparing the CEEMD-SE-EWT-ARIMA method of the invention with the predicted results of ARIMA, CEEMD-ARIMA, WT-ARIMA, CEEMD-WT-ARIMA methods, the predicted values being shown in FIG. 9, the MAE, MAPE, RMSE and R2 results of each method are shown in the following table:
from the table, the evaluation indexes of the four prediction results MAE, MAPE, RMSE and R2 of the CEEMD-SE-EWT-ARIMA method are optimal, which shows that the combined prediction of the CEEMD-SE-EWT double decomposition and the ARIMA model has higher prediction precision and stable prediction effect.
In some embodiments, referring to FIG. 10, the present invention further provides a wind speed prediction system based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction, the wind speed prediction system performing wind speed prediction by using a wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction, comprising:
the data processing module 101 is used for acquiring historical wind speed data of the wind power plant, forming a wind speed time sequence, and dividing a training set and a testing set;
the double decomposition module 102 is configured to perform complementary set empirical mode decomposition on data of the wind speed time sequence to obtain at least one eigenmode component and a residual sequence, further calculate sample entropy of the residual sequence of all eigenmode components and the residual sequence, determine complexity of each sequence, and further perform empirical wavelet decomposition on a sequence with a highest calculated sample entropy value to obtain at least one subsequence with higher resolution;
and the prediction module 103 is used for performing ARIMA prediction on all the subsequences obtained by the two decomposition to obtain predicted values of all the subsequences, and further superposing the predicted values of all the subsequences to obtain a final predicted result of the original wind speed time sequence.
In some embodiments, the present invention also provides a computer medium having a computer program stored thereon, the computer program being executed by a processor to implement the above-described wind speed prediction method based on CEEMD-SE-EWT double decomposition and ARIMA combination prediction.
In some embodiments, the present invention also provides a computer, including the one computer medium.
In the description of the present specification, a description referring to terms "one embodiment," "some embodiments," "examples," "specific examples," or "some examples," etc., means that a particular feature, structure, material, or characteristic described in connection with the embodiment or example is included in at least one embodiment or example of the present invention. In this specification, schematic representations of the above terms are not necessarily directed to the same embodiment or example. Furthermore, the particular features, structures, materials, or characteristics described may be combined in any suitable manner in any one or more embodiments or examples. Furthermore, the different embodiments or examples described in this specification and the features of the different embodiments or examples may be combined and combined by those skilled in the art without contradiction.
While embodiments of the present invention have been shown and described above, it will be understood that the above embodiments are illustrative and not to be construed as limiting the invention, and that variations, modifications, alternatives and variations may be made to the above embodiments by one of ordinary skill in the art within the scope of the invention.
Claims (10)
1. A method of wind speed prediction based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction, the method comprising the steps of:
s1: acquiring historical wind speed data of a wind power plant, forming a wind speed time sequence, and dividing a training set and a testing set;
s2: carrying out complementary set empirical mode decomposition on the data of the wind speed time sequence to obtain at least one intrinsic mode component and a residual sequence;
s3: calculating sample entropy of residual sequences of all eigenvector components and judging complexity of each sequence;
s4: performing empirical wavelet decomposition on the sequence with the highest calculated sample entropy value to obtain at least one subsequence with higher resolution;
s5: performing ARIMA prediction on all subsequences obtained by the two decomposition to obtain predicted values of all subsequences;
s6: and superposing the predicted values of all the subsequences to obtain a final predicted result of the original wind speed time sequence.
2. A method of predicting wind speed according to claim 1, wherein in step S2 the method further comprises the steps of:
s21: and respectively adding a pair of Gaussian white noise sequences with equal amplitude and opposite directions on the original time sequence to reconstruct a new signal sequence:
S 1 (t)＝X(t)+ε(t)
s 2 (t)＝X(t)-ε(t)
wherein X (t) represents an original time sequence, ε (t) represents a Gaussian white noise sequence, ε 1 (t) represents the reconstructed first signal sequence, S 2 (t) represents a reconstructed second signal sequence;
s22: performing empirical mode decomposition on the reconstructed signal sequence to obtain a limited number of eigenmode function components respectively:
wherein C is ij (t) represents the j-th eigenmode function obtained by empirical mode decomposition with the i-th addition of white noise; r is (r) i (t) residual items obtained after empirical mode decomposition;
s23: adding different Gaussian white noise sequences, and repeating the step S21 and the step S22 to obtain a plurality of sets of eigenvalue function components and a set of trend items;
s24: calculating the set average value of all the groups of intrinsic modal components to obtain final modal components:
wherein c j (t) represents the final modal component.
3. The method according to claim 1, wherein in step S3, the sample entropy value is calculated as:
wherein SampEn represents a sample entropy value, m is a dimension, r is a similarity margin, A m (r) probability of matching m+1 points for two sequences, B m (r) is the probability that two sequences match m points with a similar tolerance r.
4. A method of predicting wind speed according to claim 3, wherein in step S3 the method further comprises the steps of:
s31: setting a wind speed time sequence bit: x (i), i=1, 2,3,..n, and defining a sample entropy parameter dimension m and a similarity tolerance r;
s32: reconstructing m-dimensional vector X m (1)、X m (2)、X m (3)，…，X m And (n-m+1), calculating the distance between each sequence and n-m+1 sequences, wherein the maximum value of the absolute value of the difference value of the corresponding elements of the two vectors is:
where j=1, 2,3, …, n, j+.i;
s33: statistics d [ X ] m (i),X m (j)]<r, and calculating the ratio of the number of r to the total number of n-m:
and then calculateAverage B at all i values m (r)：
S34: increasing the dimension to m+1, and repeating the steps S32 and S33 to obtain the probability A of matching m+1 points m (r)、B m (r), and further the sample entropy is defined as:
and when N is a finite value, the sample entropy is:
wherein the probability A m (r)、B m (r) is the probability that two sequences match m points with a similar tolerance r.
5. The wind speed prediction method according to claim 1, characterized in that in step S4, the method further comprises the steps of:
s41: calculating a fourier transform of the input signal;
s42: dividing the Fourier spectrum into N successive segments, determining boundaries by searching local maxima of the spectrum, and arranging them in descending order, wherein, assuming the number of maxima is M, when M is greater than or equal to N, the first N-1 maxima are reserved, when M is greater than or equal to N<N is corrected by keeping all maxima, and the intermediate frequency between two local maxima is taken as omega n ；
S43: finding a segmentation boundary and segmenting a frequency spectrum;
s44: and constructing a proper wavelet filter bank to decompose the signals.
6. The wind speed prediction method according to claim 1, characterized in that in step S44, the method further comprises the steps of:
s441: an empirical wavelet is defined as a bandpass filter over each interval Λn for Λn>0, the empirical scale function phi is defined by the following two equation expressions, respectively n (omega) and empirical wavelet ψ n (ω)：
Wherein β (x) =x 4 (35-84x+70x 2 -20x 3 )；
S442: defining an empirical wavelet transform in the same way as a classical wavelet transform, detailsCoefficients ofThe inner product of the empirical wavelet and the signal gives:
approximation coefficientGiven by the empirical scale function and the inner product of the signal:
wherein F [. Cndot.]And F -1 [·]Fourier transform and inverse transform, respectively, whereby the signal f (t) is reconstructed as:
s443: the signal f (t) is decomposed to obtain an amplitude modulation-frequency modulation single component f with the frequency from low to high through the empirical wavelet transformation processing k (t)(k＝1,2,3,...)：
7. The method according to claim 1, wherein in step S5, the mathematical expression of the prediction model is:
E(ε t )＝0，Var(ε t )＝σ 2
wherein ε t And x t Respectively representing sample data and white noise, epsilon at time t t The mean value of (2) is 0, and the variance is a constant; b is a hysteresis operator, bx t ＝x t-1 ；Is a difference operator, < >>d represents the number of differences over the non-stationary sequence; phi (B) is an autoregressive coefficient polynomial, < >>p is the order of the autoregressive polynomial; θ (B) is a moving average coefficient polynomial, +.>q is the order of the moving average polynomial.
8. The method according to claim 7, wherein in step S5, the prediction model is determined by three parameters p, d, q, and the determination process includes the steps of:
s51: performing a smoothness test on the sequence and determining a differential order, comprising: verifying the stability of the time sequence, and performing differential operation on the non-stationary sequence to convert the non-stationary sequence into a stationary sequence, wherein the differential order is d;
s52: determining ARMA model orders p and d, comprising: the autocorrelation function and the partial autocorrelation function are calculated to perform preliminary order determination, and then the order is selected violently through the red pool information criterion and the Bayesian information criterion;
s53: verifying the model, performing residual error test, comprising: observing whether the residual error of the ARIMA model is normal distribution with an average value of 0 and a variance of constant, and simultaneously observing whether continuous residual errors are relevant or not to ensure that the residual error of the selected model is white noise;
s54: wind speed predictions are made using the created ARIMA model.
9. The wind speed prediction method according to claim 1, characterized in that in step S6, the method further comprises the steps of:
s61: average absolute error is carried out on the predicted sequence and the test set sequence:
wherein Z (t) is the wind speed measured at the moment t, Z' (t) is the predicted wind speed at the moment t, and N is the number of wind speed predictions;
s62: average absolute percentage error is performed on the predicted sequence and the test set sequence:
s63: square root error is carried out on the predicted sequence and the test set sequence:
and calculating the determination coefficients of the predicted sequence and the test set sequence:
wherein,representing the sample mean.
10. A wind speed prediction system based on CEEMD-SE-EWT double decomposition and ARIMA combined prediction, comprising:
the data processing module is used for acquiring historical wind speed data of the wind power plant, forming a wind speed time sequence and dividing a training set and a testing set;
the double decomposition module is used for carrying out complementary set empirical mode decomposition on the data of the wind speed time sequence to obtain at least one intrinsic mode component and a residual sequence, further calculating sample entropy of the residual sequence of all the intrinsic mode components and judging the complexity of each sequence, and further carrying out empirical wavelet decomposition on the sequence with the highest calculated sample entropy value to obtain at least one subsequence with higher resolution;
and the prediction module is used for performing ARIMA prediction on all the subsequences obtained by the two decomposition to obtain predicted values of all the subsequences, and further superposing the predicted values of all the subsequences to obtain a final predicted result of the original wind speed time sequence.
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| CN118013236A (en) * | 2024-04-08 | 2024-05-10 | 西安热工研究院有限公司 | Energy storage auxiliary black start wind speed prediction method and system based on error compensation method |
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| CN117972363B (en) * | 2024-03-29 | 2024-06-07 | 西安热工研究院有限公司 | Wind speed prediction method and system for energy storage auxiliary black start based on stability |
| CN118013236A (en) * | 2024-04-08 | 2024-05-10 | 西安热工研究院有限公司 | Energy storage auxiliary black start wind speed prediction method and system based on error compensation method |
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