CN107730044A - A kind of hybrid forecasting method of renewable energy power generation and load - Google Patents
A kind of hybrid forecasting method of renewable energy power generation and load Download PDFInfo
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Abstract
The invention discloses a kind of renewable energy power generation and the hybrid forecasting method of load, hybrid predicting includes the forecast model that data mining, variation mode decomposition and adaptive differential evolutionary learning machine are formed.Cluster feature is chosen according to the characteristics of power data and meteorological data first, carries out K mean cluster;The cluster of acquisition and the data of day proxima luce (prox. luc) to be predicted are carried out similarity differentiation, therefrom chooses and is used as training sample with the maximally related cluster of current predictive;Then variation mode decomposition is carried out to sample sequence, obtains multiple subsequences with different center frequency;Each subsequence is predicted respectively using adaptive differential evolutionary learning machine again;Finally the prediction result of each subsequence is superimposed to obtain final prediction result.The inventive method has the advantages that precision of prediction is high, speed is fast.
Description
Technical field
The invention belongs to generation of electricity by new energy and the technical field of intelligent grid, and in particular to one kind is based on data mining, change
The hybrid forecasting method of mode decomposition and adaptive differential evolutionary learning machine is divided to be predicted renewable energy power generation and load.
Background technology
More and more oozed with increasingly exhaustion, the regenerative resource (such as wind energy and solar energy) of traditional fossil energy
Thoroughly into power system, particularly in micro-capacitance sensor.Micro-capacitance sensor be it is a kind of in the form of micro- source integrate such as luminous energy, wind energy can
The renewable sources of energy, and to the small grids that load is powered.Yet with the randomness of renewable energy power generation, fluctuation and
The uncertainty of load, it is difficult to ensure the reliability and stability in micro-capacitance sensor operating process.Accurately may be used therefore, finding one kind
Renewable source of energy generation is micro-capacitance sensor reliability service with load forecasting method and further improves the pass of renewable energy utilization rate
Key.
The core accurately predicted is the analysis to historical sample data, but these data are often very huge,
How an important step that rationally effective sample be prediction is therefrom chosen.K mean algorithms are that one kind is concisely and efficiently data
Mining algorithm, its complexity is low, there is higher treatment effeciency to large data sets.Historical data is handled with it, to carry
Take effective sample data.
Consider the randomness of renewable energy power generation and load and non-stationary, only reach higher by primary signal
Precision of prediction.The decomposition method of non-stationary signal mainly has wavelet analysis and empirical mode decomposition (Empirical Mode at present
Decomposition,EMD).There is fundamental wave and choose the problem of difficult in wavelet analysis, empirical mode decomposition, which has mode and mixed, asks
Topic.Compared with both approaches, variation mode decomposition algorithm (Variational Mode Decomposition) has good
Mathematical theory basis, complexity is low, and has more preferable robustness in aspect of performance.
In the selection of forecasting tool, Artificial Neural Network generalization ability is not strong at present, is easily trapped into Local Minimum
Change;Selection of the SVMs to parameter is sensitive, and training speed is slow.In order to overcome disadvantages mentioned above, G.B.Huang et al.
Propose adaptive differential evolutionary learning machine (Self-Adaptive Evolutionary Extreme Learning
Machine, SaE-ELM) algorithm, the problem of algorithm overcomes traditional neural network generalization ability difference and training speed also has
Very big lifting.
The content of the invention
Present invention aims at provide a kind of accuracy it is higher, based on data mining, variation mode decomposition and adaptive poor
Evolutionary learning machine is divided to carry out the renewable energy power generation of hybrid predicting and the hybrid forecasting method of load.
To achieve the above object, following technical scheme is employed:Forecasting Methodology of the present invention is based on data mining, become
Divide the hybrid forecasting method of mode decomposition and adaptive differential evolutionary learning machine;First according to power data and the spy of meteorological data
Point chooses cluster feature, carries out K mean cluster;Using the data digging method of K mean cluster, data are drawn according to cluster feature
It is divided into multiple clusters;Then chosen using correlation coefficient process from cluster with the maximally related data of current predictive as training sample
This;For the time series signal of analysis of history data, signal decomposition is the son with different center frequency by variation Mode Decomposition
Sequence;Adaptive Evolutionary extreme learning machine be used to predict each subsequence as a kind of quick accurate predictive tools;Most
Afterwards, the prediction result by being superimposed the predicted value of all subsequences to generate final.
The specific construction step of Forecasting Methodology of the present invention is as follows:
Step 1, historical data, including power data and relevant weather data are collected, obtain training sample time series, and
Carry out data prediction;
Step 2, the cluster feature of sample to be clustered is determined according to meteorologic factor and generated output respectively;
Step 3, sample is clustered using K mean cluster algorithm;
Step 4, correlation coefficient process extraction and day relevant cluster to be predicted are as final training sample;
Step 5, input signal is decomposed using variation mode decomposition algorithm, acquisition is multiple to have different center frequency
Subsequence;
Step 6, adaptive differential evolutionary learning machine relevant parameter is adjusted, each subsequence is predicted;
Step 7, the predicted value of each subsequence is superimposed to obtain final prediction result.
Further, in step 2, the cluster feature of sample to be clustered is determined according to meteorologic factor and generated output respectively:
For wind-powered electricity generation, influenceing its main weather conditions has temperature and wind speed;But similar weather condition can not protect
Data selected by card and the data of prediction day are also similar, and therefore, historical power data also serve as the feature of cluster;Final wind
The cluster feature of electricity is as follows:
d1=[tmin,tmax,tmean,smin,smax,smean,x1min,x1max,x1mean] (1)
Wherein, x1min,x1max,x1meanTo represent the maximum of wind power output, minimum value and average value in one day;tmin,
tmax,tmeanAnd smin,smax,smeanThe minimum value, maximum and average value of temperature and wind speed are represented respectively;
For photovoltaic, influenceing its main meteorologic factor has humidity and cloud amount, and performance number also serves as the feature of cluster;
The feature finally built is as follows:
d2=[hmin,hmax,hmean,cmin,cmax,cmean,x2min,x2max,x2mean] (2)
Wherein, x2min,x2max,x2meanRepresent minimum value, maximum and the average value that photovoltaic is contributed in one day;hmin,hmax,
hmeanAnd cmin,cmax,cmeanHumidity and the minimum value maximum and average value of cloud amount are represented respectively;
Influence load not only has a meteorologic factor, day type be also an important indicator of load prediction;According to it is meteorological because
Element and day type, the feature finally built are as follows:
d3=[tmin,tmax,tmean,dt,x3min,x3max,x3mean] (3)
Wherein, x3min,x3max,x3meanIt is the minimum value of load, maximum and average value in one day;tmin,tmax,t3meanGeneration
Minimum value, maximum and the average value of table temperature;dtIt is a day type.
Further, in step 3, K mean cluster is carried out according to the cluster feature of selection:
Given cluster sample X=[x1,...,xn], K mean algorithms are intended to determine k cluster centre C=[c1,...,ck]
And make it that following cost function is optimal:
Step 3.1:Initial classes k number is determined, and randomly chooses k initial cluster center;
Step 3.2:The distance (Euclidean distance) of sample and each cluster centre is calculated, and sample is referred to closest
In class;
Step 3.3:The center of each class is recalculated, such new center is used as using the average of every class each point;
Step 3.4:If reaching iterations or cluster centre is not changing stopping algorithm;Otherwise step is repeated
3.2 and 3.3.
Further, in step 4, correlation coefficient process extraction is with day relevant cluster to be predicted as final training sample:
The data similar to desired value are extracted in initial data after cluster corresponding to feature, it is specific as follows:It is given
Sample Xk=[xk1,xk2,...,xkN]TWith desired value Y=[y1,y2,...,yN]T;Correlation coefficient process calculates the formula of similarity such as
Under:
Wherein Cov (Xk, Y) and represent XkWith Y covariance;σXkIt is X with σ YkWith Y variance;r(Xk, Y) value represent sample
The similarity of sheet and target;Represent completely uncorrelated when this value is 0;It is higher that this value more levels off to 1 expression similarity,
Represent perfectly correlated when reaching 1;Expression negative correlation is variation tendency on the contrary, such case should when value is bears
To give up;After the completion of k values traversal, similarity highest is chosen from cluster as training sample.
Further, in step 5, input signal is decomposed using variation mode decomposition algorithm, acquisition is multiple to be had
The subsequence of different center frequency;Concretely comprise the following steps:
Step 5.1:Converted by Hilbert, obtain each mode ukUnilateral spectrum signal
Wherein j is imaginary unit, and " * " represents convolution algorithm, and δ (t) represents Dirac distribution;
Step 5.2:Spectrum signal is adjusted to corresponding Base BandWherein ωkFor mode k
Angular frequency;Corresponding constraint variation model is as follows:
In formula:{uk}={ u1,...,uKIt is to decompose K obtained modal components;{ωk}={ ω1,...,ωKIt is each
Centre frequency corresponding to mode;
Step 5.3:Former problem is turned into non-binding ask in order to solve above-mentioned optimization problem introducing Lagrange multiplier λ
Topic:
Step 5.4:U is alternately updated with multiplication operator alternating direction methodkAnd ωk, specific formula is as follows:
Step 5.5:Signal decomposition to be decomposed is K modal components.
Further, in step 6, adaptive differential evolutionary learning machine relevant parameter is adjusted, each subsequence is carried out pre-
Survey, concretely comprise the following steps:
Step 6.1:Given training set, hidden layer node L, activation primitive are g (x) single hidden layer feedforward neural network
Model can be expressed as:
A in formulaj∈RnAnd bj∈ R (j=1,2 ..., K) it is respectively j-th of input weights for implying node and biasing;gi
(aj,bj,xi) it is j-th of activation primitive for implying node;βjFor connection hidden layer and the output weights of output layer;yi∈RnFor net
Network output valve;
Step 6.2:This model is expressed in matrix as:
H β=T (10)
Wherein
Step 6.3:Linear system H β=T are solved by least square method, obtain unique solutionWhereinRepresent
Hidden layer output matrix H mole-Peng Luosi (Moore-Penrose) generalized inverse;
Step 6.4:Randomly generate NP initial population vector θk,gWeights are inputted comprising all hidden layers and hidden layer is inclined
Difference;
Step 6.5:By making a variation, intersecting and select in each training process, optimal θ is selectedk,g;
Step 6.6:Output weight matrix β now is obtained, obtains forecast model.
Further, in step 6, the differential evolution learning machine algorithm is as follows:
Initialization:NP initial population vector of initialization is used as first generation population, wherein each population vector includes institute
There are input weights to be biased with hidden layer
The a wherein generated at randomjAnd bj(j=1,2 ..., L) is respectively hidden layer input weights and biasing, and G is generation of evolving
Number, k=1,2 ..., NP;
Calculate output weight matrix and root-mean-square error (RMSE):
WhereinIt is Hk,GMoore-Penrose generalized inverses, Hk,GForm it is as follows:
By the RMSE obtained, the vectorial θ in G+1 generations can be determined by formulak,G+1:
In the first generation, the individual cognition that the root-mean-square error of gained is minimum is stored in θbest,1In, its root-mean-square error is
Variation and intersection:For each object vector of current generation, the acquisition of trial vector can pass through four kinds of basic plans
Slightly;If probability parameter is Pl,G(l=1,2,3,4), it is represented in the mutation operation in G generations, uses strategy " l " probability;Four
The expression formula of kind strategy is as follows:
St1:DE/rand/1
St2:DE/rand-to-best/2
St3:DE/rand/2
St4:DE/current-to-rand/1
Wherein, k is the random number between 0~1;Mutagenic factor F is step-size in search, its value Normal Distribution N (0.5,
0.3);R1, r2, r3, r4, r5 are mutually different random integers between 1~NP.
It is LP, probability parameter P to make learning cyclel,GValue be updated according to following rule:
(1) as G≤LP, each selected probability of strategy is equal, i.e.,
(2) as G >=LP,
Wherein, Sl,GValue obtained by formula:
Wherein ε is the normal number of a very little, in order to avoid the generation of zero success rate;nsl,gAnd nfl,gRespectively in g
The number for the trial vector for being successfully entered the next generation and being dropped is drawn in generation by l-th of Mutation Strategy, while will each be tried
The number for testing vector is recorded;When iterations is more than LP, recorded data will be replaced by data of new generation before;
After the completion of mutation operation, trial vectorCan be by by θk,GWith its variation vectorCrossover operation acquisition is carried out, the formula of crossover operation is as follows:
Wherein, crossover probability CR Normal Distributions N (0.5,1), jrandIt is the positive integer of the random value in [1, L],
randjIt is the random number between 0~1;
Evaluation:The trial vector u in G+1 generationsk,G+1Equally evaluated with formula (14), and repeat variation and intersect
Step and evaluation procedure, stop until reaching maximum iteration.
Compared with prior art, the invention has the advantages that:
1st, wind-powered electricity generation, photovoltaic and load are predicted respectively using a set of forecast model, reduce learning cost.
2nd, the use of data mining algorithm can preferably excavate effective information, and K averages from a large amount of historical datas
Algorithm is used so that whole process very time-saving and efficiency.
3rd, introducing variation mode decomposition makes the data after decomposition show stronger regularity and stationarity, and this method is decomposed
Effect is good, as a result accurately, improves precision of prediction.
4th, using adaptive differential evolutionary learning machine as forecasting tool, this method overcomes traditional neural network training speed
The shortcomings that slow and generalization ability difference, further increase precision of prediction.
Brief description of the drawings
Fig. 1 is the FB(flow block) of the inventive method;
Fig. 2 is Clustering and selection effect diagram of the present invention;
Fig. 3 is variation mode decomposition effect diagram of the present invention;
Fig. 4 is 48-h wind-powered electricity generations prediction result figure of the present invention;
Fig. 5 is 48-h photovoltaics prediction result figure of the present invention;
Fig. 6 is 48-h load prediction results figure of the present invention.
Embodiment
Due to the complexity of renewable energy power generation and load, directly prediction certainly will cause prediction effect to be deteriorated, the present invention
Primary signal is clustered first and therefrom chooses optimal cluster, and is carried out VMD decomposition, obtains some modal components, so
Each component is predicted with adaptive differential evolutionary learning machine respectively afterwards, finally the prediction result of each component, which adds up, obtains most
Whole predicted value.Renewable energy power generation and load prediction flow chart based on hybrid predicting are as shown in figure 1, comprise the following steps that:
Step 1, data prediction:First, usually contained in historical data many irrational beyond normal range (NR)
Data, these data can have undesirable effect to prediction, therefore substitute these data using averaging method.
Wherein, i ∈ { 1,2,3 } represent wind-powered electricity generation, photovoltaic and load respectively;Δ t represents the sampling time.
In the step, in order to eliminate the influence of varying number level size and different dimensions to precision of prediction, to inputting number
It is according to being normalized, data are regular in the range of [0-1].
Wherein, pi(t)=[pi(t),pi(t-Δt),...,pi(t-(N-1)Δt)]TRepresent N number of continuous historical time section
Δ t power output, its corresponding regular result is xi(t)=[xi(t),xi(t-Δt),...,xi(t-(D-1)Δt)]T;E
=[1,1 ..., 1]T∈RN×1;pmax,iAnd pmin,iIt is minimum and maximum performance number.
Step 2, cluster feature is chosen:In order to facilitate cluster, data characteristics is first extracted:
For wind-powered electricity generation, influenceing its main weather conditions has temperature and wind speed.But similar weather condition can not protect
Data selected by card are similar with the data for predicting day, and therefore, historical power data also serve as the sample of cluster.Final wind-powered electricity generation
Cluster sample it is as follows:
d1=[tmin,tmax,tmean,smin,smax,smean,x1min,x1max,x1mean]
For photovoltaic, influenceing its main meteorologic factor has humidity and cloud amount, and performance number also serves as the feature of cluster.
The feature finally built is as follows:
d2=[hmin,hmax,hmean,cmin,cmax,cmean,x2min,x2max,x2mean]
Influence load not only has a meteorologic factor, day type be also an important indicator of load prediction.According to it is meteorological because
Element and day type, the feature of final framework are as follows:
d3=[tmin,tmax,tmean,dt,x3min,x3max,x3mean]
Final d1,d2,d3It is identified as the cluster feature of wind-powered electricity generation, photovoltaic and load.
Step 3, k mean clusters are carried out according to the cluster feature of selection, comprised the following steps that:
(1) initial classes k number is determined, and randomly chooses k initial cluster center;
(2) distance (present invention take be Euclidean distance) of sample and each cluster centre is calculated, and sample is referred to
In closest class;
(3) center of each class is recalculated, such new center is used as using the average of every class each point;
(4) if reaching iterations or cluster centre is not changing stopping algorithm;Otherwise repeat step (2) and
Step (3).
Step 4, optimal cluster is chosen by correlation coefficient process, its formula is as follows:
The value of coefficient correlation is higher closer to both 1 representative similarities, is chosen after the completion of k values traversal with target similarity most
Data corresponding to high cluster are as sample.
Step 5, variation mode decomposition, input signal x are carried out to pretreated power sequence signali(t) its specific point
It is as follows to solve step:
(1) converted by Hilbert, obtain each mode ukUnilateral spectrum signalWherein j
For imaginary unit, " * " represents convolution algorithm, and δ (t) represents Dirac distribution
(2) spectrum signal is adjusted to corresponding Base BandWherein ωkFor mode k angular frequency
Rate.Corresponding constraint variation model is as follows:
In formula:{uk}={ u1,...,uKIt is to decompose K obtained modal components;{ωk}={ ω1,...,ωKIt is each
Centre frequency corresponding to mode.
(3) former problem is turned into non-binding problem in order to solve above-mentioned optimization problem introducing Lagrange multiplier λ:
(4) u is alternately updated using multiplication operator alternating direction methodkAnd ωk, specific formula is as follows:
(5) by signal x to be decomposedi(t) K modal components are decomposed into.
Step 6, build data set and be predicted:With adaptive differential evolutionary learning machine to regenerative resource and load
It is predicted.Learning model needs multigroup training set, trains set representations as follows:
Wherein xim(t) r row training datas are included;C represents lag time window, and each row all correspond to export as follows:
tim(t)=[xim(t),xim(t-Δt),...,xim(t-(r-1)Δt)]T
(1) giveAs training set, hidden layer node L, before activation primitive is g (x) single hidden layer
Feedback neural network model can be expressed as:
A in formulaj∈RnAnd bj∈ R (j=1,2 ..., K) it is respectively j-th of input weights for implying node and biasing;gi
(aj,bj,xi) it is j-th of activation primitive for implying node;βjFor connection hidden layer and the output weights of output layer;yi∈RnFor net
Network output valve;
(2) this model is expressed in matrix as:H β=T
Wherein
(3) linear system H β=T are solved by least square method, obtains unique solutionWhereinRepresent hidden layer
Output matrix H mole-Peng Luosi (Moore-Penrose) generalized inverse;
(4) NP initial population vector θ is randomly generatedk,gInclude all hidden layer weights and hidden layer deviation.
(5) optimal θ is selected by making a variation, intersecting and select in each training processk,g;
(6) output weight matrix β now is obtained, obtains forecast model;
Illustrated below by example, renewable energy power generation and load data are tested from U.S.'s new energy here
Room.The result of Clustering and selection is as shown in Figure 2.Wherein wind-powered electricity generation data are divided into 7 clusters, and photovoltaic data are divided into 5 clusters, bear
Lotus data are divided into 8 clusters.According to formula of correlation coefficient, the phase of data and test data corresponding to each cluster is calculated respectively
Like degree.Finally, the 6th group cluster of wind-powered electricity generation, the 1st group cluster of photovoltaic, and the 5th group cluster of load are chosen as training data, he
Coefficient correlation be respectively:0.9195,0.8001 and 0.8588.Before variation mode decomposition is carried out, the mould of mode decomposition
State number K it needs to be determined that, the present invention final decomposition number is determined by observing centre frequency.By taking wind-powered electricity generation as an example, when K values are equal to
When 4, the frequency of mode 4 and mode 3 occurs overlapping, it means that occurred crossing and decomposes, therefore mode number is defined as 3.In addition,
Level of noise α=2000 of mode decomposition, time step τ=0.2.The discomposing effect of wind-powered electricity generation is as shown in Figure 3.Mode 1 includes low
Frequency component, it can reflect the variation tendency of wind-powered electricity generation.Mode 2 and mode 3 include the signal of higher frequency, trickleer change
It can be embodied in both.
Regenerative resource and load are predicted with adaptive differential evolutionary learning machine.Learning model is it needs to be determined that defeated
Enter parameter, its form is as shown in table 1:
Table 1
Training set is predicted according to above-mentioned form input adaptive differential evolution learning machine, and the prediction knot that will be obtained
Fruit is contrasted with other method.Method 1 is institute's extracting method of the present invention, and method 2 is conventional limit learning machine method, and method 3 is
Traditional learning machine adds clustering algorithm.The 48-h prediction curves of wind-powered electricity generation, photovoltaic and load are respectively such as Fig. 4, shown in 5,6.It can be seen that this is pre-
Survey method can improve precision of prediction.
Claims (8)
- A kind of 1. hybrid forecasting method of renewable energy power generation and load, it is characterised in that:The Forecasting Methodology is based on number According to the hybrid forecasting method of excavation, variation mode decomposition and adaptive differential evolutionary learning machine;It is gentle according to power data first The characteristics of image data, chooses cluster feature, carries out K mean cluster;It is special according to cluster using the data digging method of K mean cluster Data are divided into multiple clusters by sign;Then chosen from cluster using correlation coefficient process and made with the maximally related data of current predictive For training sample;For the time series signal of analysis of history data, signal decomposition is with different centers by variation Mode Decomposition The subsequence of frequency;Adaptive Evolutionary extreme learning machine be used to predict each height as a kind of quick accurate predictive tools Sequence;Finally, the prediction result by being superimposed the predicted value of all subsequences to generate final.
- 2. the hybrid forecasting method of a kind of renewable energy power generation according to claim 1 and load, it is characterised in that tool Body comprises the following steps:Step 1, historical data, including power data and relevant weather data are collected, obtain training sample time series, and carry out Data prediction;Step 2, the cluster feature of sample to be clustered is determined according to meteorologic factor and generated output respectively;Step 3, sample is clustered according to cluster feature using K mean cluster algorithm;Step 4, using correlation coefficient process extraction and day relevant cluster to be predicted as final training sample;Step 5, input signal is decomposed using variation mode decomposition algorithm, obtains multiple sons with different center frequency Sequence;Step 6, adaptive differential evolutionary learning machine relevant parameter is adjusted, each subsequence is predicted;Step 7, the predicted value of each subsequence is superimposed to obtain final prediction result.
- 3. the hybrid forecasting method of a kind of renewable energy power generation according to claim 2 and load, it is characterised in that:Step In rapid 2, the cluster feature of sample to be clustered is determined according to meteorologic factor and generated output respectively:For wind-powered electricity generation, influenceing its main weather conditions has temperature and wind speed;But similar weather condition cannot be guaranteed institute It is also similar that data, which are chosen, with the data for predicting day, and therefore, historical power data also serve as the feature of cluster;Final wind-powered electricity generation Cluster feature is as follows:d1=[tmin,tmax,tmean,smin,smax,smean,x1min,x1max,x1mean] (1)Wherein, x1min,x1max,x1meanTo represent the maximum of wind power output, minimum value and average value in one day;tmin,tmax, tmeanAnd smin,smax,smeanThe minimum value, maximum and average value of temperature and wind speed are represented respectively;For photovoltaic, influenceing its main meteorologic factor has humidity and cloud amount, and performance number also serves as the feature of cluster;Finally The feature of structure is as follows:d2=[hmin,hmax,hmean,cmin,cmax,cmean,x2min,x2max,x2mean] (2)Wherein, x2min,x2max,x2meanRepresent minimum value, maximum and the average value that photovoltaic is contributed in one day;hmin,hmax,hmean And cmin,cmax,cmeanHumidity and the minimum value maximum and average value of cloud amount are represented respectively;Influence load not only has a meteorologic factor, day type be also an important indicator of load prediction;According to meteorologic factor and Day type, the feature finally built are as follows:d3=[tmin,tmax,tmean,dt,x3min,x3max,x3mean] (3)Wherein x3min,x3max,x3meanIt is the minimum value of load, maximum and average value in one day;tmin,tmax,t3meanRepresent temperature Minimum value, maximum and the average value of degree;dtIt is a day type.
- 4. the hybrid forecasting method of a kind of renewable energy power generation according to claim 2 and load, it is characterised in that:Step In rapid 3, K mean cluster is carried out according to the cluster feature of selection:Given cluster sample X=[x1,...,xn], K mean algorithms are intended to determine k cluster centre C=[c1,...,ck] and cause Following cost function is optimal:<mrow> <mtable> <mtr> <mtd> <mrow> <mi>J</mi> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>r</mi> <mrow> <mi>n</mi> <mi>k</mi> </mrow> </msub> <mo>|</mo> <mo>|</mo> <msubsup> <mi>x</mi> <mi>i</mi> <mrow> <mo>(</mo> <mi>j</mi> <mo>)</mo> </mrow> </msubsup> <mo>-</mo> <msub> <mi>c</mi> <mi>j</mi> </msub> <mo>|</mo> <msup> <mo>|</mo> <mn>2</mn> </msup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> <mrow> <mo>(</mo> <mn>1</mn> <mo>)</mo> </mrow> <msub> <mi>r</mi> <mrow> <mi>n</mi> <mi>k</mi> </mrow> </msub> <mo>&Element;</mo> <mo>{</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>}</mo> <mo>&ForAll;</mo> <mi>n</mi> <mo>,</mo> <mi>k</mi> <mo>,</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>k</mi> </munderover> <msub> <mi>u</mi> <mrow> <mi>n</mi> <mi>k</mi> </mrow> </msub> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mo>&ForAll;</mo> <mi>k</mi> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>Step 3.1:Initial classes k number is determined, and randomly chooses k initial cluster center;Step 3.2:The distance (Euclidean distance) of sample and each cluster centre is calculated, and sample is referred in closest class Go;Step 3.3:The center of each class is recalculated, such new center is used as using the average of every class each point;Step 3.4:If reaching iterations or cluster centre is not changing stopping algorithm;Otherwise step 3.2 is repeated With 3.3.
- 5. the hybrid forecasting method of a kind of renewable energy power generation according to claim 2 and load, it is characterised in that:Step In rapid 4, correlation coefficient process extraction is with day relevant cluster to be predicted as final training sample:The data similar to desired value are extracted in initial data after cluster corresponding to feature, it is specific as follows:Given sample Xk =[xk1,xk2,...,xkN]TWith desired value Y=[y1,y2,...,yN]T;The formula that correlation coefficient process calculates similarity is as follows:<mrow> <mi>r</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mi>C</mi> <mi>o</mi> <mi>v</mi> <mrow> <mo>(</mo> <msub> <mi>X</mi> <mi>k</mi> </msub> <mo>,</mo> <mi>Y</mi> <mo>)</mo> </mrow> </mrow> <mrow> <msub> <mi>&sigma;X</mi> <mi>k</mi> </msub> <mi>&sigma;</mi> <mi>Y</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>Wherein Cov (Xk, Y) and represent XkWith Y covariance;σXkIt is X with σ YkWith Y variance;r(Xk, Y) value represent sample and The similarity of target;Represent completely uncorrelated when this value is 0;It is higher that this value more levels off to 1 expression similarity, when up to Represent perfectly correlated when to 1;Expression negative correlation is variation tendency on the contrary, such case should give house when value is bears Abandon;After the completion of k values traversal, similarity highest is chosen from cluster as training sample.
- 6. the hybrid forecasting method of a kind of renewable energy power generation according to claim 2 and load, it is characterised in that:Step In rapid 5, input signal is decomposed using variation mode decomposition algorithm, obtains multiple sub- sequences with different center frequency Row;Concretely comprise the following steps:Step 5.1:Converted by Hilbert, obtain each mode ukUnilateral spectrum signalWherein j For imaginary unit, " * " represents convolution algorithm, and δ (t) represents Dirac distribution;Step 5.2:Spectrum signal is adjusted to corresponding Base BandWherein ωkFor mode k angle Frequency;Corresponding constraint variation model is as follows:<mrow> <mtable> <mtr> <mtd> <mrow> <munder> <mi>min</mi> <mrow> <mo>{</mo> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>}</mo> <mo>,</mo> <mo>{</mo> <msub> <mi>&omega;</mi> <mi>k</mi> </msub> <mo>}</mo> </mrow> </munder> <mo>{</mo> <munder> <mo>&Sigma;</mo> <mi>k</mi> </munder> <mo>|</mo> <mo>|</mo> <msub> <mo>&part;</mo> <mi>t</mi> </msub> <mo>&lsqb;</mo> <mrow> <mo>(</mo> <mi>&delta;</mi> <mo>(</mo> <mi>t</mi> <mo>)</mo> <mo>+</mo> <mfrac> <mi>j</mi> <mrow> <mi>&pi;</mi> <mi>t</mi> </mrow> </mfrac> <mo>)</mo> </mrow> <mo>*</mo> <msub> <mi>u</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>j&omega;</mi> <mi>k</mi> </msub> <mi>t</mi> </mrow> </msup> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>}</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mo>.</mo> <mi>t</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow> <munder> <mo>&Sigma;</mo> <mi>k</mi> </munder> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>=</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>In formula:{uk}={ u1,...,uKIt is to decompose K obtained modal components;{ωk}={ ω1,...,ωKIt is each mode Corresponding centre frequency;Step 5.3:Former problem is turned into non-binding problem in order to solve above-mentioned optimization problem introducing Lagrange multiplier λ:<mrow> <mtable> <mtr> <mtd> <mrow> <mi>L</mi> <mrow> <mo>(</mo> <mo>{</mo> <msub> <mi>u</mi> <mi>k</mi> </msub> <mo>}</mo> <mo>,</mo> <mo>{</mo> <msub> <mi>&omega;</mi> <mi>k</mi> </msub> <mo>}</mo> <mo>,</mo> <mi>&lambda;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mi>&alpha;</mi> <munder> <mo>&Sigma;</mo> <mi>k</mi> </munder> <mo>|</mo> <mo>|</mo> <msub> <mo>&part;</mo> <mi>t</mi> </msub> <mo>&lsqb;</mo> <mo>(</mo> <mrow> <mi>&delta;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mi>j</mi> <mrow> <mi>&pi;</mi> <mi>t</mi> </mrow> </mfrac> </mrow> <mo>)</mo> <mo>*</mo> <msub> <mi>u</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>&rsqb;</mo> <msup> <mi>e</mi> <mrow> <mo>-</mo> <msub> <mi>j&omega;</mi> <mi>k</mi> </msub> <mi>t</mi> </mrow> </msup> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mo>+</mo> <mo>|</mo> <mo>|</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munder> <mo>&Sigma;</mo> <mi>k</mi> </munder> <msub> <mi>u</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>|</mo> <msubsup> <mo>|</mo> <mn>2</mn> <mn>2</mn> </msubsup> <mo>+</mo> <mo><</mo> <mi>&lambda;</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>,</mo> <mi>f</mi> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>-</mo> <munder> <mo>&Sigma;</mo> <mi>k</mi> </munder> <msub> <mi>u</mi> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>t</mi> <mo>)</mo> </mrow> <mo>></mo> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>Step 5.4:U is alternately updated with multiplication operator alternating direction methodkAnd ωk, specific formula is as follows:<mrow> <msubsup> <mover> <mi>u</mi> <mo>^</mo> </mover> <mi>k</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfrac> <mrow> <mover> <mi>f</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>&Sigma;</mi> <mrow> <mi>i</mi> <mo>&NotEqual;</mo> <mi>k</mi> </mrow> </msub> <msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mi>i</mi> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <mo>+</mo> <mfrac> <mrow> <mover> <mi>&lambda;</mi> <mo>^</mo> </mover> <mrow> <mo>(</mo> <mi>w</mi> <mo>)</mo> </mrow> </mrow> <mn>2</mn> </mfrac> </mrow> <mrow> <mn>1</mn> <mo>+</mo> <mn>2</mn> <mi>&alpha;</mi> <msup> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>-</mo> <msub> <mi>&omega;</mi> <mi>k</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow><mrow> <msubsup> <mi>&omega;</mi> <mi>k</mi> <mrow> <mi>n</mi> <mo>+</mo> <mn>1</mn> </mrow> </msubsup> <mo>=</mo> <mfrac> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <mi>&omega;</mi> <mo>|</mo> <msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>d</mi> <mi>&omega;</mi> </mrow> <mrow> <msubsup> <mo>&Integral;</mo> <mn>0</mn> <mi>&infin;</mi> </msubsup> <mo>|</mo> <msub> <mover> <mi>u</mi> <mo>^</mo> </mover> <mi>k</mi> </msub> <mrow> <mo>(</mo> <mi>&omega;</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mi>d</mi> <mi>&omega;</mi> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>Step 5.5:Signal decomposition to be decomposed is K modal components.
- 7. the hybrid forecasting method of a kind of renewable energy power generation according to claim 2 and load, it is characterised in that:Step In rapid 6, adaptive differential evolutionary learning machine relevant parameter is adjusted, each subsequence is predicted, concretely comprised the following steps:Step 6.1:Given training set, hidden layer node L, activation primitive are g (x) single hidden layer BP network model It can be expressed as:<mrow> <msub> <mi>y</mi> <mi>i</mi> </msub> <mo>=</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>K</mi> </munderover> <msub> <mi>&beta;</mi> <mi>j</mi> </msub> <msub> <mi>g</mi> <mi>i</mi> </msub> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>b</mi> <mi>j</mi> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>,</mo> <mi>i</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mo>...</mo> <mo>,</mo> <mi>N</mi> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>A in formulaj∈RnAnd bj∈ R (j=1,2 ..., K) it is respectively j-th of input weights for implying node and biasing;gi(aj, bj,xi) it is j-th of activation primitive for implying node;βjFor connection hidden layer and the output weights of output layer;yi∈RnIt is defeated for network Go out value;Step 6.2:This model is expressed in matrix as:H β=T (10)WhereinStep 6.3:Linear system H β=T are solved by least square method, obtain unique solutionWhereinRepresent implicit Layer output matrix H mole-Peng Luosi (Moore-Penrose) generalized inverse;Step 6.4:Randomly generate NP initial population vector θk,gWeights and hidden layer deviation are inputted comprising all hidden layers;Step 6.5:By making a variation, intersecting and select in each training process, optimal θ is selectedk,g;Step 6.6:Output weight matrix β now is obtained, obtains forecast model.
- 8. the hybrid forecasting method of a kind of renewable energy power generation according to claim 2 and load, it is characterised in that:Step In rapid 6, the differential evolution learning machine algorithm is as follows:Initialization:NP initial population vector of initialization is used as first generation population, wherein each population vector is comprising all defeated Enter weights to bias with hidden layer<mrow> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>g</mi> </mrow> </msub> <mo>=</mo> <mo>&lsqb;</mo> <msubsup> <mi>a</mi> <mrow> <mn>1</mn> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msubsup> <mi>a</mi> <mrow> <mi>L</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> <mi>T</mi> </msubsup> <mo>,</mo> <msub> <mi>b</mi> <mrow> <mn>1</mn> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>,</mo> <mo>...</mo> <mo>,</mo> <msub> <mi>b</mi> <mrow> <mi>L</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>&rsqb;</mo> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>11</mn> <mo>)</mo> </mrow> </mrow>The a wherein generated at randomjAnd bj(j=1,2 ..., L) is respectively hidden layer input weights and biasing, and G is evolutionary generation, k =1,2 ..., NP;Calculate output weight matrix and root-mean-square error (RMSE):<mrow> <msub> <mi>RMSE</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> <mo>=</mo> <msqrt> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>N</mi> </munderover> <mo>|</mo> <mo>|</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>j</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>L</mi> </munderover> <msub> <mi>&beta;</mi> <mi>j</mi> </msub> <mi>g</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mrow> <mi>j</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>b</mi> <mrow> <mi>j</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>)</mo> </mrow> </mrow> </msub> <mo>,</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>-</mo> <msub> <mi>t</mi> <mi>i</mi> </msub> <mo>|</mo> <mo>|</mo> </mrow> <mrow> <mi>m</mi> <mo>&times;</mo> <mi>N</mi> </mrow> </mfrac> </msqrt> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>13</mn> <mo>)</mo> </mrow> </mrow>WhereinIt is Hk,GMoore-Penrose generalized inverses, Hk,GForm it is as follows:By the RMSE obtained, the vectorial θ in G+1 generations can be determined by formulak,G+1:<mrow> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <msub> <mi>RMSE</mi> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </msub> <mo>-</mo> <msub> <mi>RMSE</mi> <msub> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>></mo> <mi>&lambda;</mi> <mo>&CenterDot;</mo> <msub> <mi>RMSE</mi> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </msub> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <msub> <mi>RMSE</mi> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </msub> <mo>-</mo> <msub> <mi>RMSE</mi> <msub> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo><</mo> <mi>&lambda;</mi> <mo>&CenterDot;</mo> <msub> <mi>RMSE</mi> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow></mrow> </mtd> <mtd> <mrow> <mi>a</mi> <mi>n</mi> <mi>d</mi> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <mo>|</mo> <msub> <mi>&beta;</mi> <msub> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> <mo>+</mo> <mn>1</mn> </mrow> </msub> </msub> <mo>|</mo> <mo>|</mo> <mo><</mo> <mo>|</mo> <mo>|</mo> <msub> <mi>&beta;</mi> <msub> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> </msub> <mo>|</mo> <mo>|</mo> <mo>,</mo> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>e</mi> <mi>l</mi> <mi>s</mi> <mi>e</mi> <mo>.</mo> </mrow> </mtd> <mtd> <mrow></mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>15</mn> <mo>)</mo> </mrow> </mrow>In the first generation, the individual cognition that the root-mean-square error of gained is minimum is stored in θbest,1In, its root-mean-square error isVariation and intersection:For each object vector of current generation, the acquisition of trial vector can pass through four kinds of elementary tactics;If Probability parameter is Pl,G(l=1,2,3,4), it is represented in the mutation operation in G generations, uses strategy " l " probability;Four kinds of plans Expression formula slightly is as follows:Wherein, k is the random number between 0~1;Mutagenic factor F is step-size in search, its value Normal Distribution N (0.5, 0.3);R1, r2, r3, r4, r5 are mutually different random integers between 1~NP;It is LP, probability parameter P to make learning cyclel,GValue be updated according to following rule:(1) as G≤LP, each selected probability of strategy is equal, i.e.,(2) as G >=LP,Wherein, Sl,GValue obtained by formula:<mrow> <msub> <mi>S</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>G</mi> </mrow> </msub> <mo>=</mo> <mfrac> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>g</mi> <mo>=</mo> <mi>G</mi> <mo>-</mo> <mi>L</mi> <mi>P</mi> </mrow> <mrow> <mi>G</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>ns</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>g</mi> </mrow> </msub> </mrow> <mrow> <munderover> <mo>&Sigma;</mo> <mrow> <mi>g</mi> <mo>=</mo> <mi>G</mi> <mo>-</mo> <mi>L</mi> <mi>P</mi> </mrow> <mrow> <mi>G</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <msub> <mi>ns</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>g</mi> </mrow> </msub> <mo>+</mo> <munderover> <mo>&Sigma;</mo> <mrow> <mi>g</mi> <mo>=</mo> <mi>G</mi> <mo>-</mo> <mi>L</mi> <mi>P</mi> </mrow> <mrow> <mi>G</mi> <mo>-</mo> <mn>1</mn> </mrow> </munderover> <mrow> <msub> <mi>nf</mi> <mrow> <mi>l</mi> <mo>,</mo> <mi>g</mi> </mrow> </msub> </mrow> </mrow> </mfrac> <mo>+</mo> <mi>&epsiv;</mi> <mo>,</mo> <mrow> <mo>(</mo> <mi>l</mi> <mo>=</mo> <mn>1</mn> <mo>,</mo> <mn>2</mn> <mo>,</mo> <mn>3</mn> <mo>,</mo> <mn>4</mn> <mo>)</mo> </mrow> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>16</mn> <mo>)</mo> </mrow> </mrow>Wherein ε is the normal number of a very little, in order to avoid the generation of zero success rate;nsl,gAnd nfl,gRespectively in g generations The number of trial vector for being successfully entered the next generation and being dropped is drawn by l-th of Mutation Strategy, at the same will each test to The number of amount is recorded;When iterations is more than LP, recorded data will be replaced by data of new generation before;After the completion of mutation operation, trial vectorCan be by by θk,GWith its variation vectorCrossover operation acquisition is carried out, the formula of crossover operation is as follows:<mrow> <msubsup> <mi>u</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> <mi>j</mi> </msubsup> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msubsup> <mi>v</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> <mi>j</mi> </msubsup> <mo>,</mo> </mrow> </mtd> <mtd> <mtable> <mtr> <mtd> <mrow> <mi>i</mi> <mi>f</mi> </mrow> </mtd> <mtd> <mrow> <mo>(</mo> <msub> <mi>rand</mi> <mi>j</mi> </msub> <mo>&le;</mo> <mi>C</mi> <mi>R</mi> <mo>)</mo> <mi>o</mi> <mi>r</mi> <mo>(</mo> <mi>j</mi> <mo>=</mo> <msub> <mi>j</mi> <mrow> <mi>r</mi> <mi>a</mi> <mi>n</mi> <mi>d</mi> </mrow> </msub> <mo>)</mo> </mrow> </mtd> </mtr> </mtable> </mtd> </mtr> <mtr> <mtd> <mrow> <msubsup> <mi>&theta;</mi> <mrow> <mi>k</mi> <mo>,</mo> <mi>G</mi> </mrow> <mi>j</mi> </msubsup> <mo>,</mo> </mrow> </mtd> <mtd> <mrow> <mi>O</mi> <mi>t</mi> <mi>h</mi> <mi>e</mi> <mi>r</mi> <mi>w</mi> <mi>i</mi> <mi>s</mi> <mi>e</mi> <mi>o</mi> <mi>r</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>17</mn> <mo>)</mo> </mrow> </mrow>Wherein, crossover probability CR Normal Distributions N (0.5,1), jrandIt is the positive integer of the random value in [1, L], randj It is the random number between 0~1;Evaluation:The trial vector u in G+1 generationsk,G+1Equally evaluated with formula (14), and repeat variation and intersect step And evaluation procedure, stop until reaching maximum iteration.
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