CN107292446B - Hybrid wind speed prediction method based on component relevance wavelet decomposition - Google Patents

Abstract

The invention relates to a mixed wind speed prediction method based on wavelet decomposition considering component relevance, which divides original data into a training set and a test set; decomposing the training set into a plurality of subsequences, identifying false subsequences according to correlation coefficients of the subsequences and original data, removing corresponding false subsequences, building a prediction model for the remaining subsequences, and predicting the (n +1) th data through the (1) th to n) th data in the subsequences; superimposing the predicted ones of the respective subsequencesn+1 data 1, to obtain the final prediction result; updating the training set, decomposing the updated training set into a plurality of new subsequences, and establishing an LSSVM model for predictingn+2 data, superimposing the predictions of the individual subsequencesn+2 data to obtain predicted value; and continuing to advance by one step until all predictions are completed. The invention reduces the influence of the false components of the subsequence, and improves the prediction performance, the prediction accuracy and the prediction stability.

Description

Hybrid wind speed prediction method based on component relevance wavelet decomposition

Technical Field

The invention relates to the technical field of wind speed prediction, in particular to a hybrid wind speed prediction method based on component relevance wavelet decomposition.

Background

Due to the characteristics of renewable wind energy, no pollution and abundance, the wind energy plays an important role in reducing emission of greenhouse gases and replacing fossil fuels. The global wind energy commission predicts that the percentage of wind energy in the global electricity supply will reach 12% in 2020 and 22% in 2030. However, due to the randomness, nonlinearity and non-stationarity of the wind speed time sequence, how to completely implement the application of wind power generation to the multi-source energy network still has great difficulty, such as capacity planning, fan maintenance and the like.

In order to improve the accuracy of wind speed prediction, a large number of prediction methods are developed. The method is mainly divided into three categories: physical methods, time series methods and artificial intelligence based methods. The physical method takes into account meteorological factors such as terrain, atmospheric pressure and ambient temperature when predicting wind speed. Numerical Weather Prediction (NWP) is widely used as a representative of physical methods. It is typically used for long-term wind speed predictions and is not suitable for short-term wind speed predictions. The time series method uses historical data to predict wind speed, including Autoregressive models (AR Autoregressive), Autoregressive Moving Average models (Autoregressive Moving Average ARMA), differential Autoregressive Moving Average models (Autoregressive Integrated Moving Average models ARIMA), and Fractional differential Autoregressive Moving Average models (Fractional Autoregressive Moving Average models FARIMA). Although these methods can capture linear relationships in wind speed data well, they do not reveal the non-linear characteristics well. The artificial intelligence based method can reveal nonlinear characteristics in the wind speed time series and establish the nonlinear relation between the input value and the output value. The fuzzy logic method comprises an Artificial Neural Network (Artificial Neural Network ANN), a Support Vector Machine (Support Vector Machine SVM), a Least Square Support Vector Machine (Least Square Support Vector Machine LSSVM) and a fuzzy logic method. Because the wind speed sequence has extremely strong nonlinear characteristics, the prediction accuracy based on artificial intelligence is superior to that of a time sequence method in general. However, the model parameters need more adjustment, and the problems of low efficiency and overfitting exist.

In recent years, hybrid models based on Decomposition have been developed, and typical Decomposition methods include Empirical Mode Decomposition (Empirical Mode Decomposition EMD), Ensemble Empirical Mode Decomposition (emmble EEMD), Fast Ensemble Empirical Mode Decomposition (Fast Empirical Mode Decomposition fed), Discrete Wavelet Transform (Discrete Wavelet Transform DWT) and Wavelet Packet Decomposition (Wavelet Packet Decomposition WPD), and wind speed prediction models such as ARIMA, ANN, SVM, and LSSVM models, which are built for decomposed subsequences. Predicting each subsequence of the EMD decomposed wind speed time series by adopting a recursive ARIMA model; if the FEEMD is applied, the calculation performance of the EEMD in wind speed prediction can be improved; further, three different hybrid models were developed, e.g., combining two decomposition methods (e.g., DWT and WPD) and two prediction methods (time series and ANN). It combines DWT, WPD, EMD and FEEMD with Extreme Learning Machine (ELMS) into four hybrid models. Compared with other hybrid models, the decomposition-based hybrid model can decompose the nonlinear non-stationary wind speed time series into more stable and regular subsequences to optimize the prediction result. Many studies have shown that the decomposition-based mixing method is superior to the method without decomposition.

However, the above conclusions come from decomposing all data at once, including known data (training data) and unknown data (test data). This means that the purpose of wind speed prediction is violated, assuming that the future data is known. To avoid this problem, many studies suggest that the raw data be divided into a training set and a test set, with the training set being decomposed in real time. More specifically, only data in the training set is available, and data in the test set is unknown. The training data is continually updated and resolubilized again each time new data is obtained. The EMD-based hybrid approach does not even predict performance as the undivided approach. Although these studies have raised the recognition of decomposition-based methods, their conclusions are worth extensive review.

Disclosure of Invention

Based on the above problems, the present invention aims to provide a real-time decomposition-based hybrid wind speed prediction method based on wavelet decomposition considering component relevance, which is more excellent in accuracy and stability, and the technical solution is as follows:

a hybrid wind speed prediction method based on wavelet decomposition considering component relevance comprises the following steps:

step 1: the raw data is divided into two parts, including a training set: { x (1), …, x (n); test set { x (N +1), …, x (N + N) };

step 2: the test set is considered unknown, a DWT or EMD model is built to decompose the training set into a plurality of subsequences { c_j(1)，…，c_j(n)}，j＝1…M+1；

And step 3: and performing correlation analysis of the subsequences and the original sequence, and identifying false subsequences according to correlation coefficients of the subsequences and the original data: if the correlation coefficient exceeds the selected threshold, rejecting the corresponding sub-series, otherwise, retaining the corresponding sub-series;

and 4, step 4: establishing an LSSVM or LSSVM-GARCH prediction model for the remaining subsequence, and predicting the (n +1) th data through the 1 st to n th data in the subsequence:

superposing n +1 th data predicted by each subsequence

j ═ 1 … M +1, the final prediction was obtained:

and 5: updating the training set to be { x (2), …, x (n +1) }, and decomposing the updated training set into a plurality of new subsequences ({ c)_j(2)，…，c_j(n +1) }, j ═ 1 … M + 1); establishing an LSSVM model to predict the (n + 2) th data, and superposing the predictions of the subsequences to obtain the (n + 2) th data to obtain a predicted value

Step 6: continuing to advance one-step prediction by following the process of the step 5 until all predictions are finished;

and 7: the prediction error is evaluated.

Further, the specific method for decomposing the training set into a plurality of subsequences according to the DWT model comprises the following steps: the signal { x (t) } is decomposed into frequency band components using DWT on the basis of the specified wavelet basis functions:

where M is the number of component layers, c_j(t) (i ═ 1,2, …, M) denotes the j-th layer detail component, c_M+1(t) represents an approximation component, and the frequency gradually decreases as the number of layers increases.

Furthermore, the specific method for decomposing the training set into a plurality of subsequences according to the EMD model comprises the following steps: the signal x (t) can be decomposed into eigenmode equations and a residual through an iterative screening process:

where M is the number of component layers, c_j(t) (j ═ 1,2, …, M) denotes the eigenmode function of the j-th layer, c_M+1(t) represents the residual amount.

Further, the correlation coefficient between the subsequence and the original sequence in step 3 is expressed as follows:

wherein, x (t), t ═ 1,2 … n are training data points; c. C_j(t) is the jth sub-sequence.

Further, the exceeding of the selected threshold value indicates that the correlation coefficient is less than 1/10 of the absolute value of the maximum correlation coefficient

Furthermore, before the prediction model is established in the step 4, the Lagrange multiplier LM is adopted to test the heteroscedasticity of the error terms

Poor property, i.e.

Wherein r is²Is goodness of fit, H₀Is a null hypothesis, H₁Is an alternative hypothesis; chi shape²(q) is a chi-squared distribution obeying order q; eta₁,η₂…η_qIs a non-negative coefficient; in the formula, the residual error follows a GARCH model of p-order and q-order, and is recorded as GARCH (p, q), p is the order of ARCH item, and q is the order of GARCH item;

if the statistic value of LM is greater than χ²(q), then, the null-dropping assumption adopts an alternative assumption; and (4) representing that the error components have heteroscedasticity, establishing an LSSVM-GARCH prediction model, and otherwise, establishing the LSSVM prediction model.

Further, the method for establishing the LSSVM-GARCH prediction model comprises the following steps:

in the LSSVM model, the truth expression at time i is:

wherein y is_i，

And xi_iTrue value, predicted value and i moment residual error are respectively;

if xi_iThe influence of the change with time on the prediction result cannot be ignored, and the structure of the GARCH model is as follows:

wherein upsilon is_iIs a white noise sequence with a mean of 0 and a variance of 1, eta_lAnd

is a non-negative coefficient; h is_iFor the time i the conditional variance is,

is a coefficient of h_i-kIs the conditional variance at time i-k; xi_i-lIs the i-l time residual.

The invention has the beneficial effects that: according to the invention, the false sequence is identified and removed according to the correlation between the subsequence and the original sequence, so that the influence of false components of the subsequence is reduced, and the prediction performance is improved; by establishing a GARCH model to simulate the fluctuation of the subsequence, the accuracy and the stability of prediction are greatly improved.

Drawings

FIG. 1 is a flow chart of the method.

FIG. 2 is a flow chart of a decomposition-based prediction method.

FIG. 3a is a flow chart of a prediction method based on a one-time decomposition preprocessing.

FIG. 3b is a flow chart of a prediction method based on real-time decomposition preprocessing.

Fig. 4 is a wind speed data sample 1.

FIG. 5 shows the MAE and RMSE for different decomposition level number error terms in look-ahead one-step prediction.

FIG. 6 is a sub-sequence of decomposition of all values and the first 225 values of raw wind speed data.

FIG. 7 is a real-time decomposition of wind speed data 1-225 and wind speed data 2-226 based on two consecutive training sets.

FIG. 8 is a graph of residuals c obtained from a continuous training set₁₀The variation of (2).

FIG. 9 shows the difference between the 224 th data point at one-time decomposition and real-time decomposition.

Fig. 10 is a subsequence of one-time decomposition and real-time decomposition.

Fig. 11 shows the prediction results of data sample 1 using the method and LSSVM.

Fig. 12 is a wind speed sample 2.

Fig. 13 shows the prediction results of data sample 2 using the method and LSSVM.

Detailed Description

The invention is further described in detail below with reference to the figures and the specific embodiments. The process of the method is shown in the figure 1, and the specific process is as follows:

step 1: the raw data is divided into two parts, including a training set ({ x (1), …, x (N) }) and a testing set ({ x (N +1), …, x (N + N) }).

Step 2: assuming that the prediction part is unknown, a Discrete Wavelet Transform (DWT) model is established to decompose a training set into a plurality of subsequences (c)_j(1)，...，c_j(n)},j＝1…M+1)。

And step 3: and (4) performing correlation analysis, and identifying false subsequences according to the correlation coefficients of the subsequences and the original data. If some of the correlation coefficients are less than the selected threshold, 1/10, which is the absolute value of the largest correlation coefficient, the corresponding sub-series are rejected, otherwise the corresponding sub-series should be retained.

And 4, step 4: and testing the heteroscedasticity of the LSSVM residual error by using a Lagrange Multiplier (LM) for the residual subsequence. Building LSSVM or LSSVM-GARCH model for the rest subsequences based on the test result, predicting the (n +1) th data according to the (1) th to the (n) th data,

and 5: superimposing the predicted values of the subsequences (

j-1 … M +1) to obtain a final prediction result,

step 6: the training set is updated with the actual data. If the training set is updated to { x (2), …, x (n +1) }, repeating the steps 2-5 to obtain the corresponding prediction result,

and continuing to advance by one step until the prediction is finished.

And 7: and (5) carrying out error analysis and evaluating the prediction error.

The basic theory involved in the present invention is as follows:

1) DWT/EMD-based mixing method

Discrete Wavelet Transform (DWT) and Empirical Mode Decomposition (EMD) are used as time-frequency domain analysis means, a group of time series can be decomposed into a plurality of subseries arranged from high frequency to low frequency, and the method is generally applied to processing non-stationary nonlinear data. Wherein DWT decomposes the signal { x (t) } into frequency band components on the basis of a specified wavelet basis function,

where M is the number of component layers, c_j(t) (j ═ 1,2, …, M) denotes the j-th level detail component, c_M+1(t) represents an approximation component, and the frequency gradually decreases as the number of layers increases. Currently some DWT variants, such as EWT and WPD, are also applied in wind speed prediction. In the invention, Daubechies 10 is taken as a wavelet basis function.

The EMD algorithm differs from the DWT algorithm in that there are no basis functions and the decomposed results are data-oriented and adaptive. Which decomposes the signal x (t) into eigenmode equations (IMFs) and a residue through an iterative screening process. The result of the decomposition is in equation (1), where c_j(t) (j ═ 1,2, …, M) denotes IMF of the j-th layer, c_M+1(t) represents the residual amount. In addition, EMD has also developed several variant models, such as EEMD, FEEMD and multivariate EMD (memd).

And after the wind speed sequence is decomposed into different subsequences by DWT or EMD, establishing a prediction model for each subsequence by adopting LSSVM. Compared with SVMs, LSSVMs can ensure sufficient accuracy while reducing the computation time of the model. The LSSVM model will be briefly reviewed here.

Assuming that each subsequence of the training set consists of an n-m dimensional sequence of numbers, (x)₁，y₁)，(x₂，y₂)，…，(x_n-m，y_n-m)，x_i∈R^m(R represents a real number) is an input vector, y_i∈R^mIs the output vector, i.e.,

wherein m is x_iAnd dimension, the value of which is obtained by the output value of the training set, and the root mean square error is satisfied and is the minimum value.

Based on SVM theory, a nonlinear mapping function phi (x) is adopted_i) X is to be_iMapping into a linear feature space G of higher dimension. The recursive function is:

y＝w^Tφ(x_i)+b,w∈G,b∈R ⑶

wherein y is the fit value; w represents the weight vector, b is the deviation, calculated by optimizing the following function:

where γ is a normalization parameter used to balance the complexity and accuracy of the model; xi_iIs the residual of the sample point i true value and the fitted value.

To solve the problem of optimization in equation (4), a lagrangian function is established:

wherein alpha is_i(i ═ 1,2, …, n-m) is the lagrange multiplier.

The solution of equation (5) is obtained by taking the partial derivatives for w, b, xi, and α, respectively, for L (w, b, xi, α). The resulting function is:

wherein

Is a predicted value; x is the latest input vector (x ∈ R)^m)；

K(x,x_i)＝φ(x)^T×φ(x_i) (i-1, 2, …, n-m) is a kernel density function satisfying the Mercer condition

The detailed flow of the conventional decomposition-based prediction method is shown in fig. 2. The method mainly comprises the following three steps: establishing DWT or EMD model decomposition wind speed data; establishing an LSSVM model for the decomposed subsequences for prediction; and overlapping the subsequences obtained by prediction to obtain a final prediction result. Similarly, EEMD, FEEMD and WPD models can be built to decompose the original wind speed sequence, and ARIMA, ANN and SVM models can be built to predict the wind speed.

2) Data preprocessing scheme

There are currently two data preprocessing schemes: disposable decomposition and real-time decomposition. Where the one-time decomposition assumes that future data is known, the entire original sequence is decomposed at one time. And dividing the decomposed subsequence into a training set and a test set, and establishing a prediction model for the training set and the test set. While in practice wind speed prediction is performed, the future data is unknown, so this assumption is not reasonable. A flowchart based on a one-time decomposition pretreatment scheme is shown in fig. 3a, and the specific steps are as follows:

step 1: building a DWT or EMD model decomposes the original wind speed sequence into several subsequences.

Step 2: dividing each subsequence into a training set and a test set, wherein the training set and the test set are respectively ({ c)_j(1)，...，c_j(n) }) and ({ c)_j(n+1)，…，c_j(n+N)},j＝1…M+1)。

And step 3: establishing an LSSVM model, predicting the (n +1) th data through the 1 st to the n th data in the subsequence,

superposing the (n +1) th data of each subsequence to obtain a predicted value

And 4, step 4: with new data c_j(n +1), j is 1 … M +1 and updates the training set, establishes an LSSVM model for the updated training set, and predicts the (n + 2) th data through the (2) th to the (n) th data

Superposing the n +2 th data of each subsequence to obtain a predicted value

And 5: the process continues with one-step look ahead prediction following the step 4 procedure until all predictions are completed.

Step 6: the prediction error is evaluated.

In fact future data is unknown. The raw data must first be divided into a training set and a test set. And decomposing the data of the training set into a plurality of subsequences. And after the new data updating training set is obtained, decomposing the updated training set again. The flow chart of the scheme based on the real-time decomposition pretreatment is shown in fig. 3b, and the specific steps are as follows:

step 1: raw data were taken as a training set ({ x (1), …, x (N) }) and a test set ({ x (N +1), …, x (N + N) }).

Step 2: the test set is considered unknown, and the DWT or EMD model established for the training set is decomposed into a plurality of subsequences ({ c)_j(1)，…，c_j(n)},j＝1…M+1)。

And step 3: establishing an LSSVM model, predicting the (n +1) th data through the 1 st to the n th data in the subsequence,

superposing the (n +1) th data of each subsequence to obtain a predicted value

And 4, step 4: updating the training set to be { x (2), …, x (n +1) }, and decomposing the updated training set into a plurality of new subsequences ({ c)_j(2)，…，c_j(n +1) }, j ═ 1 … M + 1). Establishing an LSSVM model to predict the (n + 2) th data,

superposing the n +2 th data of each subsequence to obtain a predicted value

And 5: the process continues with one-step look ahead prediction following the step 4 procedure until all predictions are completed.

Step 6: the prediction error is evaluated.

3) Subsequence and original sequence correlation analysis

DWT is widely used to analyze non-stationary nonlinear data, however its resulting spurious components [31] may affect prediction accuracy. In order to reduce the influence of spurious components, correlation coefficients of the subsequences and the original data are introduced. The expression of the correlation coefficient between the subsequence and the original data is as follows:

where x (t), t ═ 1,2 … n are training data points; c. C_j(t) is the jth sub-sequence.

The wind speed sample 1 is also used to illustrate the method. The partial decomposition results for the initial training set (data 1-225) are shown in FIG. 5. Table 2 summarizes the initial training set and the correlation coefficients for each subsequence. The maximum absolute value is 0.600 (initial training set and c)₄Correlation coefficient between) and the threshold value is 0.600. Thus c₄It is removed for spurious components. And establishing an LSSVM or LSSVM-GARCH model for the rest subsequences based on the heteroscedasticity test of the residual errors.

4) GARCH model

The GARCH model was used to simulate and evaluate fluctuations. In the LSSVM model, the truth expression at time i is:

wherein y is_i，

And xi_iTrue, predicted and i time residuals, respectively.

If xi_iThe influence of the change with time on the prediction result cannot be ignored, and the structure of the GARCH model is as follows:

wherein upsilon is_tIs a white noise sequence with a mean of 0 and a variance of 1, eta_lAnd

is a non-negative coefficient. The residuals follow a GARCH model of order p and q in equation (11), denoted GARCH (p, q), where p is the order of the ARCH term and q is the order of the GARCH term. That is to say the current conditional variance depends on the conditional variance of the previous one. If the last is an error of order q, ξ_tThe process of following a q-order autoregressive conditional variance is denoted as arch (q). Specifically, when p and q are both equal to 1, the GARCH (1,1) is a standard GARCH model, and the GARCH (1,1) model is used in the present invention.

Before the GARCH model is built, it should be checked whether the error term has ARCH effect (i.e., heteroscedasticity). The heteroscedasticity of the error terms is typically examined using the Lagrangian Multiplier (LM) [32], i.e.:

wherein r is²Is goodness of fit, H₀Is a null hypothesis, H₁Is an alternative assumption. If the statistic value of LM is greater than χ²(q), the null-dropping assumption employs an alternative assumption, which means that there is an error component heteroscedasticity and a GARCH model should be established.

In order to illustrate the effectiveness and stability of the method, four prediction models are established, including LSSVM, DWT-LSSVM, DWT-LSSVM-GARCH and the models in the invention. First, data sample 1 is used to demonstrate the predictive performance of the method. Another set of wind speed data samples is then used to further illustrate the predicted performance of the method.

Example 1:

a set of wind speed data (data sample 1) measured from the state of minnesota (including 300 sample points) in the united states was used to test the validity and reliability of the hybrid model. FIG. 4 is a sample of wind speed data 1, which is slightly non-stationary. In the prediction method based on one-time decomposition, the subsequence generated by decomposition is divided into two parts: the first 225 samples are the training set and the remaining 75 samples are the test set. In real-time decomposition prediction, the original wind speed sequence is divided into two parts: the 1 st to 225 th data of the sampling points are training sets, and the 226 th to 300 th data are test sets. The training set is used to build a prediction model, and the test set is used to verify the model performance. Real-time decomposition produces an end-point effect, but its effect is difficult to completely suppress.

To quantify the accuracy and stability of the prediction models involved, four criteria are employed here. Mean Absolute Error (MAE), Mean Relative Percentage Error (MRPE), Root Mean Square Error (RMSE), Root Mean Square Relative Error (RMSRE), respectively, i.e.:

wherein { x (t) } and

respectively representing the measured data and the predicted data at the time t; n 'represents the number of data evaluated (for one step ahead prediction, N' equals the number of test set data N).

i) Selection of the number of decomposition layers

Research shows that the number of decomposition layers has great influence on prediction accuracy. Too many levels of decomposition distort the information in the original data, causing spurious components in the subsequence. If the number of decomposition layers is too small, the non-stationarity and non-linearity in the original data cannot be effectively reduced, and the prediction difficulty may be increased, resulting in reduction of prediction accuracy.

The DWT model is adopted in view of its ability to specify the number of decomposition levels. In order to select a proper decomposition layer number, 25 experiments of advanced one-step prediction based on DWT-LSSVM real-time decomposition are carried out, wherein the 1 st to 225 th experiments are divided into a training set and a test set, wherein the first 200 data are the training set, and the remaining 25 data are the test set. FIG. 5 shows the results of MAE and RMSE at different numbers of decomposition layers (3-10). In this study, data sample 1 was taken to have 9 decomposition layers.

ii) decomposition results of two existing decomposition schemes

This section demonstrates the distinction between one-time decomposition and real-time decomposition through the study of data sample 1, and analyzes the shortages of one-time decomposition and the difficulties of real-time decomposition.

Based on DWT decomposition result

The decomposition results of the two methods are given in FIG. 6 (c)₆-c₁₀). The black line represents the subsequence obtained by decomposing 300 wind speed sample points, and the blue line represents the subsequence obtained by decomposing 225 training data before decomposition. As shown in fig. 6, the blue line is significantly deviated from the black line. This means that when new data is obtained, the new decomposed resulting sub-sequence is significantly different from the original sub-sequence.

In the real-time decomposition prediction, the training set needs to be updated and decomposed again after new data is acquired, that is, the latest 225 data are always decomposed into a plurality of subsequences as the training set. The c resulting from the decomposition of two different sets of data points is shown in FIG. 7₁-c₄And c₁₀. The blue line represents the subsequence resulting from decomposing the 1 st through 225 th original data points, and the red line represents the subsequence resulting from decomposing the 2 nd through 226 th original data points. This shows that even a single sample point in the training set will cause significant changes in the sub-sequence. FIG. 8 is a diagram illustrating the same approximation component c generated by updating four consecutive sample points in the training set₁₀The above conclusion is also confirmed by the obvious change.

In FIG. 9, the red line indicates the subsequence c₁-c₃，c₈And c₁₀Is in the case of 75 real-time decompositions. It can be seen from the figure that the same data point has a significant change in the value in the decomposed subsequence generated after the training set is updated. It can be seen from the red line in fig. 9 that the trend (marked with blue line) of the data near the left end point of each sub-sequence is significantly different from the trend of the remaining sub-sequences, which may be caused by the end point effect. The black line in fig. 8 is the result of the decomposition of the 224 th data point in the one-time decomposition (i.e., the total original data decomposition is only one time). It can be seen that this point is constant in the decomposed sub-sequence and the end-point effect is not significant, which makes the one-time decomposition result smoother than the real-time decomposition.

Fig. 10 further illustrates the difference between the one-time decomposition and the real-time decomposition. The black line represents the result of the original data in a one-time decomposition. The red line represents the results of the 226 th to 300 th data points in the real-time decomposition. The first data (226 th) of the red line is obtained by decomposing the 2 nd to 225 th training data plus a new data (i.e. 2 nd to 226 th). Similarly, the second data for each subsequence is obtained by decomposing the 3 rd to 225 th training data plus two new data (i.e., 3 rd to 227 th). Following this procedure, the red line full data can be obtained. By comparing the black and red lines, the red line is very different from the black line, and particularly the low frequency component red line fluctuates more significantly than the black line.

Based on the above results, while one-time decomposition results are smoother than real-time decomposition, it is unreasonable for one-time decomposition to assume that future data is known. In practice, future data in real-time decomposition is also unknown.

Difficulties faced in real-time decomposition: (i) with the new data acquired, the training set should be updated, and the new sub-sequence generated by decomposition may be greatly different from the previous sub-sequence; (ii) compared with one-time decomposition, the end point effect of each subsequence in real-time decomposition and the fluctuation influence of data are enhanced.

4) Discussion of predictive results

In order to demonstrate the performance of the decomposition-based prediction method, five prediction models are established: the one-time decomposition model based on DWT-LSSVM and EMD-LSSVM is based on a DWT-LSSVM and EMD-LSSVM real-time decomposition model and an independent LSSVM model. The advanced one-step prediction is performed based on the five models, and the evaluation results are shown in table 1. From table 1 it can be observed that:

(1) any one-time decomposition based hybrid model has better performance than either a single or real-time decomposition based model. However, the one-time decomposition method is not reasonable because they assume that future data is known. And therefore only focus on prediction methods based on real-time decomposition.

(2) Compared with a single LSSVM model, the prediction performance of the method based on EMD is worse, and the overall prediction performance of the method based on DWT is slightly reduced. The above-described hybrid method is therefore ineffective in view of the accuracy of prediction and calculation time. One reason for this may be that real-time decomposition may increase the volatility of each sub-sequence, although the non-stationarity of the original data is significantly reduced. Another reason may be that the decomposition produces spurious components.

(3) The performance of the DWT-based hybrid model is greatly superior to that of the EMD-based hybrid model. The prediction accuracy of the DWT-based method is improved by about 30 percent compared with that of the EMD-based method. The reasons for this are firstly the modal aliasing that is present in EMD and secondly the possibility that EMD based methods are affected by a constantly changing number of decomposition layers. Therefore, the study adopted a DWT-based approach.

Table 1 evaluation results of five models

It should be noted that although the prediction error for each sub-series is relatively small, the final prediction result may have a large error. In contrast, a particular sub-series has a large prediction error, and the total error may not be large. The final prediction should be focused on rather than the prediction for each sub-sequence.

In order to improve the prediction performance of DWT-LSSVM, the wind speed prediction method provided by the invention combines the correlation analysis of the subsequence and the original data, reduces the false components in the subsequence, and simulates the fluctuation of the subsequence by using a GARCH model.

TABLE 2 correlation coefficient of 1 st-225 th original data and its subsequences

Data sample 1 was used to test the predictive performance of the method. The predicted performance of the 4 models is given in table 3. The percentage improvement in predicted performance of the method compared to the other 3 models is shown in table 4. FIG. 11 shows the results of the prediction of the 226 th data based on the present method and the LSSVM model alone. As can be seen from tables 4-5 and FIG. 11:

(1) compared with the LSSVM model alone, the DWT-LSSVM model has poorer prediction performance.

(2) Comparing DWT-LSSVM-GARCH with DWT-LSSVM, the GARCH model is effective in improving prediction accuracy. The reason is that the GARCH model helps to simulate and predict data fluctuations.

(3) However, the single GARCH model cannot improve the prediction performance well. The DWT-LSSVM-GARCH model performance is only slightly improved compared with the single LSSVM model.

(4) The method of the invention has higher prediction performance than the other three methods. For example, compared with DWT-LSSVM-GARCH, the MAE, RMSE, MRPE and RMSE are respectively improved by 11.724%, 18.231%, 8.562% and 8.223%. The reason may be that the method reduces the interference of spurious components in the subsequence. The same comparison was made for LSSVM and the present method. It can be seen that the prediction accuracy can be effectively improved no matter the GARCH model or the false components are removed.

TABLE 3 Performance of four predictive models

TABLE 4 degree of improvement of the process of the invention

Example 2:

another case (data sample 2) was used to further explore the predictive performance of the method. Wind speed data sample 2 from louisiana, usa is shown in fig. 12. It is apparent that data sample 2 is more non-stationary than data sample 1. In order to improve the prediction accuracy, the number of decomposition layers of the sample 2 is selected to be 8. The evaluation results are shown in tables 5 to 6, and the prediction results are shown in FIG. 13. This set of data is strongly non-stationary and therefore the conclusion is slightly different from the previous set.

As can be seen from table 6 and fig. 13:

(1) contrary to the conclusions of data sample 1, data sample 2 predicted a significant improvement in performance over DWT-based methods. The reason may be that although the real-time decomposition may slightly reduce the accuracy of the prediction, the non-stationarity in the original data can be effectively reduced, so that the accuracy of the prediction is significantly improved.

(2) The GARCH model is valid as data sample 1.

(3) The method is superior to LSSVM, DWT-LSSVM and DWT-LSSVM-GARCH.

In addition, it is worth mentioning that the present method may be ineffective when the number of decomposition layers is too small. It is clear that spurious components may not be present when the number of decomposed layers is too small or moderate.

TABLE 5 Performance of four predictive models

TABLE 6 degree of improvement of the process of the invention

Claims (7)

1. A hybrid wind speed prediction method based on wavelet decomposition considering component relevance is characterized by comprising the following steps of:

step 1: dividing the measured original wind speed data sample into two parts, including a training set: { x (1), …, x (n); test set { x (N +1), …, x (N + N) };

step 2: the test set is considered unknown, a DWT or EMD model is built to decompose the training set into a plurality of subsequences { c_j(1)，…，c_j(n)}，j＝1…M+1；

And step 3: and performing correlation analysis of the subsequences and the original sequence, and identifying false subsequences according to correlation coefficients of the subsequences and the original data: if the correlation coefficient exceeds the selected threshold, rejecting the corresponding sub-series, otherwise, retaining the corresponding sub-series;

and 4, step 4: establishing an LSSVM or LSSVM-GARCH prediction model for the remaining subsequence, and predicting the (n +1) th data through the 1 st to n th data in the subsequence:

superposing n +1 th data predicted by each subsequence

j ═ 1 … M +1, the final prediction was obtained:

and 5: updating the training set to be { x (2), …, x (n +1) }, and decomposing the updated training set into a plurality of new subsequences ({ c)_j(2)，…，c_j(n +1) }, j ═ 1 … M + 1); establishing an LSSVM model to predict the (n + 2) th data, and superposing the predictions of the subsequences to obtain the (n + 2) th data to obtain a predicted value

Step 6: continuing to advance one-step prediction by following the process of the step 5 until all predictions are finished;

and 7: the prediction error is evaluated.

2. The hybrid wind speed prediction method based on the consideration of the component relevance wavelet decomposition according to claim 1, wherein the specific method for decomposing the training set into a plurality of subsequences according to the DWT model comprises: the signal { x (t) } is decomposed into frequency band components using DWT on the basis of the specified wavelet basis functions:

where M is the number of component layers, c_j(t) (i ═ 1,2, …, M) denotes the j-th layer detail component, c_M+1(t) represents an approximation component, and the frequency gradually decreases as the number of layers increases.

3. The hybrid wind speed prediction method based on the consideration of the component relevance wavelet decomposition according to claim 1, wherein the specific method for decomposing the training set into a plurality of subsequences according to the EMD model comprises: the signal x (t) can be decomposed into eigenmode equations and a residual through an iterative screening process:

where M is the number of component layers, c_j(t) (j ═ 1,2, …, M) denotes the eigenmode function of the j-th layer, c_M+1(t) represents the residual amount.

4. The hybrid wind speed prediction method based on the consideration of the wavelet decomposition of component correlation according to claim 1, wherein the correlation coefficient of the subsequence and the original sequence in step 3 is expressed as follows:

wherein, x (t), t ═ 1,2 … n are training data points; c. C_j(t) is the jth sub-sequence.

5. The method of claim 1, wherein the exceeding of the selected threshold value indicates that the correlation coefficient is less than 1/10 of the absolute value of the largest correlation coefficient.

6. The method as claimed in claim 1, wherein the heteroscedasticity of error terms is tested by using Lagrangian multiplier LM before the prediction model is built in step 4, that is, the heteroscedasticity of error terms is tested

Wherein r is²Is goodness of fit, H₀Is a null hypothesis, H₁Is an alternative hypothesis; chi shape²(q) is a chi-squared distribution obeying order q; eta₁,η₂…η_qIs a non-negative coefficient; in the formula, the residual error follows a GARCH model of p-order and q-order, and is recorded as GARCH (p, q), p is the order of ARCH item, and q is the order of GARCH item;

if the statistic value of LM is greater than χ²(q), then, the null-dropping assumption adopts an alternative assumption; and (4) representing that the error components have heteroscedasticity, establishing an LSSVM-GARCH prediction model, and otherwise, establishing the LSSVM prediction model.

7. The hybrid wind speed prediction method based on consideration of component relevance wavelet decomposition according to claim 6, wherein the LSSVM-GARCH prediction model establishing method comprises:

in the LSSVM model, the truth expression at time i is:

wherein y is_i，

And xi_iAre respectively trueValue, predicted value and i moment residual error;

if xi_iThe influence of the change with time on the prediction result cannot be ignored, and the structure of the GARCH model is as follows:

wherein upsilon is_iIs a white noise sequence with a mean of 0 and a variance of 1, eta_lAnd

is a non-negative coefficient; h is_iFor the time i the conditional variance is,

is a coefficient of h_i-kIs the conditional variance at time i-k; xi_i-lIs the i-l time residual.

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