CN110083864A - A kind of short-term wind speed forecasting method based on empirical mode decomposition - Google Patents
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Abstract
The invention discloses a kind of short-term wind speed forecasting method based on empirical mode decomposition, this method carries out the pretreatment of missing values and exceptional value to original wind series first, then decomposes pretreated wind series, obtains wind speed subsequence；For each wind speed subsequence, first primarily determine that wind speed subsequence carries out the required order of ARMA modeling, then the order setup parameter section primarily determined is utilized, function, which is calculated, using information coefficient determines optimal factor, and carrying out ARMA modeling using the optimal factor, then the corresponding model prediction result of all subsequences is final forecasting wind speed result.It is verified through embodiment, excessively high caused influence of the information loss to precision of prediction of unstable wind series order is reduced in the method for the present invention use process, improves the precision of prediction of wind speed.
Description
Technical field
The present invention relates to forecasting wind speed technical fields, and in particular to a kind of short-term wind speed forecasting based on empirical mode decomposition
Method.
Background technique
The fast development of human civilization be unable to do without the exploitation of the energy, and existing fossil energy is not only limited but also can be to us
Ecological environment cause very big destruction, in order to society sustainable development, develop wind energy be even more important.Wind Power In China in 2016
Adding new capacity has accounted for the 42.7% of world market share, but the randomness of short-term wind-force, non-stationary restricts me
To wind energy using horizontal.Therefore, the precision of short-term wind speed forecasting develops for wind energy us and is very important.
Wind speed is the time series of a non-stationary, is directed to short-term wind speed forecasting, traditional Time series analysis method
That tranquilization processing is carried out to wind speed by the method for direct differential, the order that difference uses with the complexity of wind velocity signal and
Rise, although can finally reach flattening effect, each difference can all lose the information of wind series, to influence wind
The precision of speed prediction.
Summary of the invention
For the disadvantage that information utilization is lower and precision is insufficient in above-mentioned existing short-term wind speed forecasting, the present invention proposes one
Short-term wind speed forecasting method of the kind based on empirical mode decomposition.
In order to realize above-mentioned task, the invention adopts the following technical scheme:
A kind of short-term wind speed forecasting method based on empirical mode decomposition, comprising the following steps:
Step 1, original wind series are pre-processed
Missing values in original wind series, exceptional value are pre-processed, the strategy of use are as follows: for exceptional value and
Missing values are replaced with the wind speed average value before and after the numerical value；
Step 2, pretreated wind series are decomposed, wind speed subsequence is obtained
Step 2.1, for pretreated wind series e (t), all maximum points in the wind series are found out, are led to
Cross the envelope e that cubic spline functions form maximum pointmax(t), institute in the wind series is found out using same method
Some minimum points form minimum point envelope emin(t)；The mean value of minimum point envelope and maximum point envelope is denoted as
m1, m is subtracted with wind series e (t)1, obtain h1(t):
h1(t)=e (t)-m1Formula 2
Step 2.2, by h1(t) it regards a new signal sequence as, calculates its coefficient Dk；Wherein, kth time calculates h1(t)
Design factor DkFormula it is as follows:
Wherein, t is the serial number of air speed data, and T indicates signal sequence h1(t) data amount check in, h1 k-1(t)、h1 kIt (t) is the
K-1 times, kth time calculating DkH when coefficient1(t)；
Judgement factor DkValue whether between 0.1~0.2, if not if by h1(t) as e (t) and repetition step
2.1, add 1 then to execute step 2.2 value of k later；
Step 2.3, D is such as met after k iterationkBetween 0.1~0.2, then an empirical modal letter is obtained at this time
Number:
In above formula,H when iteration secondary for kth1(t), c1(t) the 1st intrinsic mode function is indicated；
Calculate the remainder of intrinsic mode function:
r1(t)=e (t)-c1(t) formula 5
Step 2.4, judge r1(t) whether function is monotonic function or is a constant, if so, explanation cannot divide again
Solution, decomposition terminate；Otherwise, e (t)=r is enabled1(t), step 2.1 is repeated to step 2.3, continues to obtain new empirical modal letter
Number；, then it is the sub- sequence of wind speed that all intrinsic mode functions and last time, which decompose the remainder of obtained intrinsic mode function,
Column；
Then wind series e (t) is indicated are as follows:
In above formula, ci(t) i-th of intrinsic mode function, r are indicatedn(t) it indicates to decompose obtained empirical modal for the last time
The remainder of function, n indicate decomposition number, then wind speed subsequence has n+1；
Step 3, determine that wind speed subsequence carries out the required order p of ARMA modeling0、q0；
Step 4, it determines optimal factor and carries out ARMA modeling
Taking iteration section is p ∈ [p0-5,p0+ 5], q ∈ [q0-5,q0+ 5], combine order p, q and substitute into MATLAB
Aic (p, q) information coefficient calculates function, calculates p, q and combines corresponding information coefficient aic；Take the smallest information coefficient aic corresponding
Order p, q as optimal factor, be denoted as pbest,qbest, ARMA modeling is carried out using the parameter；
Step 5, using step 3 and the identical method of step 4, the arma modeling of all wind speed subsequences is obtained；Each
The prediction result of arma modeling is denoted as a respectively1,a2,...,an+1, it is the final prediction result of wind series by result superposition,
It indicates are as follows:
Further, order needed for determination wind speed subsequence described in step 3 carries out ARMA modeling, comprising:
The sampling auto-correlation coefficient figure and sampling partial correlation coefficient figure for making wind speed subsequence, find sampling auto-correlation coefficient
Figure, sampling partial correlation coefficient figure when converging to confidence interval corresponding lag number as required order.
Further, in step 4, if p0- 5 or q0- 5 value is then set to 0 less than 0.
Compared with prior art, the present invention having following technical characterstic:
In order to overcome influence of the information loss caused by difference to prediction result, present invention employs empirical mode decompositions
Complicated wind speed is decomposed into multiple relatively steady by method by the advanced row empirical mode decomposition of original wind speed of non-stationary complexity
Sub- wind series, select stable wind velocity signal to carry out time series modeling, can either so reduce due to difference rank
The excessive bring information loss of number, and the demand of prediction can be reached, to reach a higher prediction level, efficiently solve
The problem of the precision of prediction deficiency as caused by higher difference tranquilization processing.
Detailed description of the invention
Fig. 1 is the flow diagram of the method for the present invention；
(a) of Fig. 2 is that there are the schematic diagrames of exceptional value in wind series, is (b) showing there are missing values in wind series
It is intended to, unit: m/s；
Fig. 3 is the coefficient figure of pretreated wind series；
(a) of Fig. 4 is sampling auto-correlation coefficient figure, is (b) sampling partial correlation coefficient figure；
Fig. 5 is the forecasting wind speed effect picture of the method for the present invention.
Specific embodiment
Present invention will now be described in further detail with reference to the embodiments and the accompanying drawings, but embodiments of the present invention are unlimited
In this.
Present embodiment discloses a kind of short-term wind speed forecasting methods based on empirical mode decomposition, as shown in Figure 1, specific packet
Include following steps:
Step 1, original wind series are pre-processed
Missing values in original wind series, exceptional value are pre-processed, the strategy of use are as follows: for exceptional value and
Missing values are replaced with the wind speed average value before and after the numerical value, to guarantee the integrality of data.Wherein, exceptional value refer to and other
Numerical value compared to obvious data bigger than normal or less than normal, such as using and N times of average data deviation or more data as exceptional value.
In the present embodiment, data source is the U.S. Lincoln Capital Airport on December 17,1 day to 2017 December in 2017
By hour totally 400 hours air speed datas as object, prediction utilizes preceding 300 hours measured values, predicts the wind speed by hour
Data.
As shown in Fig. 2, it is exceptional value that air speed value, which is 999.99, and air speed value is the data of NAN in original wind series
It indicates missing values, its former and later two hour data is averaged instead i.e.: (3.1+5.1)/2=4.5 substitution 999.99,
NAN is substituted with (5.7+5.7)/2=5.7, and processing result is as shown in Figure 3.Final process the result is that complete, believable.
Step 2, pretreated wind series are decomposed, wind speed subsequence is obtained
Step 2.1, for pretreated wind series e (t), all maximum points in the wind series are found out, are led to
Cross the envelope e that cubic spline functions form maximum pointmax(t), institute in the wind series is found out using same method
Some minimum points form minimum point envelope emin(t)；The mean value of minimum point envelope and maximum point envelope is denoted as
m1, m is subtracted with wind series e (t)1, obtain h1(t):
h1(t)=e (t)-m1Formula 2
Step 2.2, by h1(t) it regards a new signal sequence as, calculates its coefficient Dk；Wherein, kth time calculates h1(t)
Design factor DkFormula it is as follows:
Wherein, t is the serial number of air speed data, and T indicates signal sequence h1(t) data amount check in, h1 k-1(t)、h1 kIt (t) is the
K-1 times, kth time calculating DkH when coefficient1(t)。
Judgement factor DkValue whether between 0.1~0.2, if not if by h1(t) as e (t) and repetition step
2.1, add 1 then to execute step 2.2 value of k later.
Step 2.3, D is such as met after k iterationkBetween 0.1~0.2, then an empirical modal letter is obtained at this time
Number:
In above formula,H when iteration secondary for kth1(t), c1(t) the 1st intrinsic mode function is indicated.
Calculate the remainder of intrinsic mode function:
r1(t)=e (t)-c1(t) formula 5
Step 2.4, judge r1(t) whether function is monotonic function or is a constant, if so, explanation cannot divide again
Solution, decomposition terminate, and otherwise, enable e (t)=r1(t), step 2.1 is repeated to step 2.3, continues to obtain new intrinsic mode function；
It is wind speed component that then all intrinsic mode functions and last time, which decompose the remainder of obtained intrinsic mode function, namely
Wind speed subsequence；
Then wind series e (t) may be expressed as:
In above formula, ci(t) i-th of intrinsic mode function, r are indicatedn(t) it indicates to decompose obtained empirical modal for the last time
The remainder of function, n indicate decomposition number, then wind speed subsequence has n+1.
In the present embodiment, wind series, which are finally decomposed, obtains 8 wind speed subsequences.
Step 3, determine that wind speed subsequence carries out the required order of ARMA modeling
Here by taking the 2nd wind speed subsequence that the present embodiment obtains as an example, the sampling auto-correlation system of wind speed subsequence is made
Number figure (Sample Autocorrection) and sampling partial correlation coefficient figure (Sample Partial
Autocorrelation), as shown in figure 4, sampling auto-correlation coefficient figure and sampling partial correlation coefficient figure be it is convergent, sampling from
Related coefficient figure converges to confidence interval when lagging number Lag=10, and samples partial correlation coefficient figure when lagging number Lag=2
Confidence interval is converged to, therefore the preliminary value of order p, q needed for wind speed subsequence progress experience ARMA modeling are respectively
10,2, it is denoted as p0=10, q0=2.
The step is estimated using empirical method, and the value of optimal factor p, q for finally estimating will be as steps 4
Important references.
Step 4, it determines optimal factor and carries out ARMA modeling
Generally, order p, q needed for step 3 carries out experience ARMA modeling based on the wind speed subsequence that empirical method obtains
It is not necessarily optimal, needs to be further processed.
Taking iteration section is p ∈ [p0-5,p0+ 5], q ∈ [q0-5,q0+ 5], if p0- 5 or q0- 5 value is less than 0, then by it
It is set to 0；Thus most 10*10=100 order p, q combinations are generated, aic (p, the q) information coefficient substituted into MATLAB calculates
Function calculates p, q and combines corresponding information coefficient aic；Take the smallest information coefficient aic corresponding order p, q as best rank
Number, is denoted as pbest,qbest, then optimal factor needed for the wind speed subsequence carries out ARMA modeling is pbest,qbest, i.e. ARMA
(pbest,qbest), ARMA modeling is carried out using the parameter.
In the present embodiment, the iteration section of the 2nd wind speed subsequence is taken p ∈ [5,15], q ∈ [0,7], the raw 10*7=of common property
The aic (p, q) that 70 order combinations substitute into MATLAB calculates information coefficient, corresponding p, the q 8,2 of the smallest information coefficient,
Then pbest=8, qbest=2, therefore this wind speed subsequence model can take ARMA (8,2).
Step 5, using step 3 and the identical method of step 4, the arma modeling of all wind speed subsequences is obtained；Each
The prediction result of arma modeling is denoted as a respectively1,a2,...,an+1, it is the final prediction result of wind series by result superposition,
It indicates are as follows:
The final prediction result of the present embodiment is as shown in Figure 5.
Parameter comparison result using the method for the present invention and traditional ARMA modeling is as shown in table 1, it can be seen that the present invention
Method effectively improves precision of prediction.
1 the method for the present invention of table and traditional ARMA modeling parameters compare
| Model index | MSE | MAPE |
| Traditional ARMA modeling | 0.7001 | 14.8204 |
| The method of the present invention | 0.4939 | 9.8496 |
The above embodiment is a preferred embodiment of the present invention, but embodiments of the present invention are not by above-described embodiment
Limitation, other any changes, modifications, substitutions, combinations, simplifications made without departing from the spirit and principles of the present invention,
It should be equivalent substitute mode, be included within the scope of the present invention.
Claims (3)
1. a kind of short-term wind speed forecasting method based on empirical mode decomposition, which comprises the following steps:
Step 1, original wind series are pre-processed
Missing values in original wind series, exceptional value are pre-processed, the strategy of use are as follows: for exceptional value and missing
Value, is replaced with the wind speed average value before and after the numerical value；
Step 2, pretreated wind series are decomposed, wind speed subsequence is obtained
Step 2.1, for pretreated wind series e (t), all maximum points in the wind series is found out, pass through three
Secondary spline interpolation function forms the envelope e of maximum pointmax(t), it is found out using same method all in the wind series
Minimum point forms minimum point envelope emin(t)；The mean value of minimum point envelope and maximum point envelope is denoted as m1,
M is subtracted with wind series e (t)1, obtain h1(t):
h1(t)=e (t)-m1Formula 2
Step 2.2, by h1(t) it regards a new signal sequence as, calculates its coefficient Dk；Wherein, kth time calculates h1(t) it calculates
Coefficient DkFormula it is as follows:
Wherein, t is the serial number of air speed data, and T indicates signal sequence h1(t) data amount check in, h1 k-1(t)、h1 kIt (t) is kth -1
Secondary, kth time calculates DkH when coefficient1(t)；
Judgement factor DkValue whether between 0.1~0.2, if not if by h1(t) it is used as e (t) and repeats step 2.1, it
1 is added then to execute step 2.2 value of k afterwards；
Step 2.3, D is such as met after k iterationkBetween 0.1~0.2, then an intrinsic mode function is obtained at this time:
In above formula,H when iteration secondary for kth1(t), c1(t) the 1st intrinsic mode function is indicated；
Calculate the remainder of intrinsic mode function:
r1(t)=e (t)-c1(t) formula 5
Step 2.4, judge r1(t) whether function is monotonic function or is a constant, if so, explanation cannot decompose again, point
Solution terminates；Otherwise, e (t)=r is enabled1(t), step 2.1 is repeated to step 2.3, continues to obtain new intrinsic mode function, then institute
Having experience mode function and last time to decompose the remainder of obtained intrinsic mode function is wind speed subsequence；
Then wind series e (t) is indicated are as follows:
In above formula, ci(t) i-th of intrinsic mode function, r are indicatedn(t) it indicates to decompose obtained intrinsic mode function for the last time
Remainder, n indicates to decompose number, then wind speed subsequence has n+1；
Step 3, determine that wind speed subsequence carries out the required order p of ARMA modeling0、q0；
Step 4, it determines optimal factor and carries out ARMA modeling
Taking iteration section is p ∈ [p0-5,p0+ 5], q ∈ [q0-5,q0+ 5], by order p, q combine substitute into MATLAB in aic (p,
Q) information coefficient calculates function, calculates p, q and combines corresponding information coefficient aic；Take the corresponding order of the smallest information coefficient aic
P, q is denoted as p as optimal factorbest,qbest, ARMA modeling is carried out using the parameter；
Step 5, using step 3 and the identical method of step 4, the arma modeling of all wind speed subsequences is obtained；Each ARMA
The prediction result of model is denoted as a respectively1,a2,...,an+1, it is the final prediction result of wind series by result superposition, indicates
Are as follows:
2. as described in claim 1 based on the short-term wind speed forecasting method of empirical mode decomposition, which is characterized in that step 3 institute
Order needed for the determination wind speed subsequence stated carries out ARMA modeling, comprising:
Make wind speed subsequence sampling auto-correlation coefficient figure and sampling partial correlation coefficient figure, find sampling auto-correlation coefficient figure,
Sample partial correlation coefficient figure when converging to confidence interval corresponding lag number as required order.
3. as described in claim 1 based on the short-term wind speed forecasting method of empirical mode decomposition, which is characterized in that in step 4,
If p0- 5 or q0- 5 value is then set to 0 less than 0.
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| CN111563236A (en) * | 2020-04-20 | 2020-08-21 | 中国科学院数学与系统科学研究院 | Short-term wind speed prediction method and device |
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| CN111563236A (en) * | 2020-04-20 | 2020-08-21 | 中国科学院数学与系统科学研究院 | Short-term wind speed prediction method and device |
| CN111563236B (en) * | 2020-04-20 | 2021-07-02 | 中国科学院数学与系统科学研究院 | Short-term wind speed prediction method and device |
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