CN106933778A - A kind of wind power combination forecasting method based on climbing affair character identification - Google Patents

A kind of wind power combination forecasting method based on climbing affair character identification Download PDF

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CN106933778A
CN106933778A CN201710052723.XA CN201710052723A CN106933778A CN 106933778 A CN106933778 A CN 106933778A CN 201710052723 A CN201710052723 A CN 201710052723A CN 106933778 A CN106933778 A CN 106933778A
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叶林
腾景竹
张慈杭
陈超宇
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China Agricultural University
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Abstract

The invention discloses a kind of wind power combination forecasting method based on climbing affair character identification, comprise the following steps:First, the historical wind speed and power data of wind power plant are processed using wavelet de-noising method, respectively obtains smooth curve;2nd, the curve that will be obtained carries out the feature recognition and extraction of climbing event using compression algorithm to it;3rd, the characteristic value of the climbing event of the wind power for being obtained step 2 using the method for fuzzy clustering is classified;4th, different climbing event types is trained respectively using statistical method and sets up forecast model;5th, the real-time wind speed test data and realtime power test data to wind power plant carry out step one to two, extract the characteristic value of the climbing event of real-time wind speed and power test data;6th, real-time wind speed and the characteristic value of the climbing event of power test data of the forecast model for being obtained using step 4 to extracting are classified, and are predicted using forecast model, finally obtain final combined prediction result.

Description

A kind of wind power combination forecasting method based on climbing affair character identification
Technical field
It is more particularly to a kind of based on wind power plant climbing affair character the present invention relates to operation and control of electric power system field The wind power combination forecasting method of identification.
Background technology
With the increasingly depleted and increasingly serious, wind energy, the sun of energy quagmire of the non-renewable resources such as coal, oil The regenerative resources such as energy, tide energy and biomass energy worldwide more receive much concern.Wind-power electricity generation is regenerative resource Technology is most ripe in generation technology, most Development volue regenerative resource.Development wind-powered electricity generation adjusts energy for ensureing energy security Source structure, mitigates environmental pollution, realizes that sustainable development etc. all has very important significance.
The intermittent nature of nature wind energy determines that wind power has very strong fluctuation, with wind-powered electricity generation number and dress The continuous increase of machine capacity, once wind-powered electricity generation is connected to the grid, this power swing will bring huge to the safety and economic operation of power network Big challenge.Wind speed and wind power are accurately predicted in advance, the pressure of power system peak regulation, frequency modulation can be alleviated, had Effect improves receiving ability of the power network to wind-powered electricity generation.
At present, with the raising of wind-powered electricity generation permeability in power network, scheduling and safety and stability of the wind-electricity integration to power system Bring very big challenge so that the Accurate Prediction of wind power becomes particularly important.Although the power forecasting method of routine is Wind power plant service requirement is reached, but when the i.e. wind power climbing event of instantaneous notable fluctuation for wind power occur, can be led Net instantaneity or permanent fault are sent a telegraph, great economic loss is caused.Therefore, study the characteristic of wind-powered electricity generation climbing and standard is carried out to it Really prediction, on the one hand can improve the accuracy that power network is estimated grid connected wind power power, contribute to power scheduling in advance to wind-powered electricity generation Climbing event is taken precautions against, and safeguards the stable operation of power network;On the other hand conventional power unit reply wind-powered electricity generation climbing event can be reduced Regulation and control burden, contribute to reduce power network spinning reserve capacity, reduce operating cost, the peace grid-connected to the extensive concentration of wind-powered electricity generation Full operation of stabilizing the economy is significant.
The content of the invention
In order to overcome the above-mentioned deficiencies of the prior art, the invention provides a kind of wind-powered electricity generation based on climbing affair character identification Power combination Forecasting Methodology.The method has taken into full account the popular research problem of current wind power prediction, the i.e. climbing of wind-powered electricity generation The power prediction of event.Using the compressed data means in a kind of brand-new data storage field, can be more rapidly and effectively Carry out the feature recognition and extraction of wind-powered electricity generation climbing event.Additionally, according to climbing event complex genesis, with non-linear, hysteresis quality, The characteristics of accurate Mathematical Modeling is difficult to set up to characterize, using the method for fuzzy clustering, concentrates from historical sample and searches out phase Like event classification and be trained and set up forecast model.The method strong adaptability, can effectively improve the prediction of wind-powered electricity generation Precision.The technical solution adopted in the present invention considers following factor:
1st, wind power plant historical wind speed data and historical power data;
2nd, the climbing direction of wind-powered electricity generation climbing event, climbing rate, climbing amplitude, time of climb and climbing time started;
3rd, the history year rule change of local wind farm data.
On the basis of factors above, a kind of wind power combination forecasting method based on climbing affair character identification, bag Include following steps:
S1, the historical wind speed and historical power data of wind power plant are processed using wavelet de-noising method, respectively obtain light Sliding historical wind speed curve and historical power curve, to eliminate the interference of grass;
S2, using compression algorithm, the smooth historical wind speed curve and historical power curve obtained to step S1 are climbed The feature recognition of slope event, then will identify that the climbing event come carries out characteristics extraction;
S3, the characteristic value of the climbing event for being extracted step S2 using the method for fuzzy clustering are classified, and are made Optimum cluster model, obtains different climbing event types;
S4, the different climbing event type obtained to step S3 using statistical method are trained and set up prediction respectively Model;
S5, real-time wind speed test data and realtime power test data to wind power plant carry out the process of step S1 to S2, Extract the characteristic value of the climbing event of real-time wind speed test data and realtime power test data;
S6, the forecast model obtained using step S4 are tested the real-time wind speed test data and realtime power that extract The characteristic value of the climbing event of data is classified, and is predicted using forecast model, finally obtains final combined prediction As a result.
On the basis of such scheme, the process of wavelet de-noising is described in step S1:
S11, the time series to historical wind speed data and historical power data carry out Fourier's treatment, by discrete signal Switch to continuous signal;
S12, power spectrumanalysis is carried out to continuous signal, draw its spectrum waveform;
The spectrum waveform feature of S13, analysis continuous signal, and then waveform is fitted, parametric equation is obtained after fitting, Solution draws Power Spectrum Distribution result;
Inverse transformation is carried out after S14, the parameter of change equation, filtered result is drawn.
On the basis of such scheme, compression algorithm described in step S2 is revolving door (SDT) algorithm, and the revolving door is calculated Method is a kind of trends of straight line compression algorithm.
Event of climbing on the basis of such scheme, described in step S2 is based on based on Fast Field (FFP) algorithm The climbing event definition of FFP algorithms is:If P is wind-powered electricity generation historical power time series,It is smooth by the wind-powered electricity generation after denoising Historical power curve,It is the wind-powered electricity generation historical power smooth sequence after being changed through SDT algorithms, the historical power smooth sequence For recognizing climbing event, it is calculated by formula (1):
Wherein SDT is the SQL with compression algorithm principle;Δ E is responsive parameter, and value is smaller, be can recognize that The climbing event procedure duration it is shorter, climbing height it is lower;Value is bigger, the recognizable climbing event procedure duration More long, climbing height is higher.
When the conversion signal of wind-powered electricity generation historical power time seriesAbsolute value greater-than match climb event criterion During threshold parameter λ, i.e.,
WhenDuring for negative value, what is identified is lower climbing event, whenBe on the occasion of when, what is identified is upper climbing thing Part.
On the basis of such scheme, the threshold value of the upper climbing event is 20.0%cap, and the threshold value of lower climbing event is 15.0%cap.
On the basis of such scheme, the characteristic value includes:Climbing rate Rr, climbing amplitude RA, time started RTsWith hold Continuous time RTl
On the basis of such scheme, the specific steps that step S3 is classified characteristic value using the method for fuzzy clustering It is as follows:
S31, assume that each climbing event has a m characteristic value, and n sample composition eigenmatrix:
S32, the eigenmatrix in S31 is normalized:
S33, the fuzzy membership that each characteristic value is calculated using the method for fuzzy clustering:
Wherein,It is i-th data to the j degree of membership of cluster centre;I=1,2 .., m, j=1,2 .., c, c are number According to hard plot clusters number;vijAnd σijCenter and the width of Gaussian function are represented respectively;
S34, optimum cluster model is made by the nearest principle of fuzzy membership, obtain different climbing event types.
On the basis of such scheme, using ExtremeLearningMachine (ELM) algorithm to different climbing event classes in step S4 Type is trained respectively, and regulation ELM algorithm parameters make various climbing events set up an optimal Clustering Model.
Need adjustment input weights and hidden layer biasing different from conventional function approximation theory, in ExtremeLearningMachine algorithm only Wanting activation primitive can infinitely lead, and input weights and hidden layer biasing can be randomly assigned, once the value being randomly assigned is being calculated Calligraphy learning starts to be updated in algorithm parameter, and hidden layer output matrix H is just uniquely determined and keeps constant, instruction Practice a neutral net to be equivalent to find a least square solution for linear system, if the number of hidden layer node and input Sample number is equal, then this Single hidden layer feedforward neural networks (SLFN) just can approach these training examples with zero error.
The ExtremeLearningMachine algorithm is concretely comprised the following steps:
1) input weights and hidden layer biasing are randomly assigned;
For N number of different training sample { xj,yj, xjIt is n × 1 dimensional input vector, yjIt is m × 1 dimension output vector, tool There is D hidden node and can infinitely lead activation primitivegX the SLFN structures of () can approach this N number of sample with zero error, that is, exist βiiAnd bi, make ∑ | | yj-rj| |=0, can also be written as form:
In formula:ωiIt is n × 1 dimensional vector, represents the connection weight of input layer and the neuron of hidden layer;βiFor m × 1 tie up to Amount, represents the connection weight of hidden layer and output layer neuron;biIt is the biasing of hidden layer neuron;rjIt is the output of network;g X () is activation primitive, can be " sig ", " rbf ", the diversified forms such as " sin ".
2) hidden layer output matrix H is calculated;
This N number of equation can be write as matrix form:
H β=R (7)
Wherein, β is output layer weight matrix, and R is desired output;
3) global optimum's output weights of ELM algorithms are calculated;
H+It is the generalized inverse matrix of H.
Beneficial effect:
Wind power combined prediction the method based on climbing affair character identification of the present invention, has taken into full account mesh The power prediction of the climbing event of the popular research problem of preceding wind power prediction, i.e. wind-powered electricity generation.Stored up using a kind of brand-new data The compressed data means in field are deposited, the feature recognition and extraction of wind-powered electricity generation climbing event can be more rapidly and effectively carried out.This Outward, according to climbing event complex genesis, with non-linear, hysteresis quality, it is difficult to the characteristics of setting up accurate Mathematical Modeling to characterize, Concentrated from historical sample using fuzzy clustering and search out the classification of similar case and be trained and set up forecast model.The method Strong adaptability, can effectively improve the precision of prediction of wind-powered electricity generation.
Brief description of the drawings
The present invention has drawings described below:
A kind of schematic flow sheets of the wind power combination forecasting method based on climbing affair character identification of Fig. 1.
Specific embodiment
Above-mentioned is only the general introduction of technical solution of the present invention, in order to better understand technological means of the invention, below With reference to accompanying drawing, the present invention is described in further detail with specific embodiment.
As shown in figure 1, a kind of wind power combination forecasting method based on climbing affair character identification of the present invention, Comprise the following steps:
Step S1. is obtained for the historical wind speed data and historical power data of wind power plant after being processed using wavelet de-noising method To smooth historical wind speed curve and historical power curve, to eliminate the interference of grass.
Useful signal is usually expressed as low frequency signal or relatively steady, and noise signal is usually expressed as high frequency letter Number.After being decomposed to noisy primary signal using wavelet de-noising method, noisy part is concentrated mainly in high-frequency signal.First to going through The time series of history air speed data and historical power data carries out Fourier's treatment, and discrete signal is switched into continuous signal.And Power spectrumanalysis is carried out to continuous signal, its spectrum waveform is drawn, the spectrum waveform feature of continuous signal is analyzed, and then to waveform It is fitted, parametric equation is obtained after fitting, solution draws Power Spectrum Distribution result.Contravariant is carried out after the parameter for changing equation Change, draw filtered result.
Step S2. uses compression algorithm, to being processed by step S1 after resulting smooth historical wind speed curve and Historical power curve carries out the feature recognition of climbing event, then will identify that the climbing event come carries out characteristics extraction.
Using revolving door (Swinging door trending, the SDT) algorithm in data compression algorithm, SDT algorithms are A kind of trends of straight line compression algorithm, it is that it is possible to find out straight line as most long as possible and becomes compared with the advantage of other compression algorithms Gesture carries out data compression, eliminates influence of the noise to data so that the identification of climbing event is more complete, so that as far as possible Avoid the missing of feature recognition and cross identification situation and occur.
Climbing event definition based on FFP algorithms is:If P is wind-powered electricity generation historical power time series,It is by after denoising The smooth historical power curve of wind-powered electricity generation,It is the wind-powered electricity generation historical power smooth sequence after being changed through SDT algorithms, the history Power smooth sequence can be used to recognize climbing event, is calculated by formula (1):
Wherein SDT is the SQL with compression algorithm principle;Δ E is responsive parameter, and value is smaller, be can recognize that The climbing event procedure duration it is shorter, climbing height it is lower;Value is bigger, the recognizable climbing event procedure duration More long, climbing height is higher.
When the conversion signal of wind-powered electricity generation historical power time seriesAbsolute value greater-than match climb event criterion During threshold parameter λ, i.e.,
WhenDuring for negative value, what is identified is lower climbing event, whenBe on the occasion of when, what is identified is upper climbing thing Part.This definition needs given two parameter lambdas and Δ E.λ is the threshold value for determining whether to occur climbing event, the threshold of upper climbing event It is 20.0%cap to be worth, and the threshold value of lower climbing event is 15.0%cap.Additionally, will identify that the climbing event come carries out characteristic value Extract, characteristic value includes:Climbing rate Rr, climbing amplitude RA, time started RTsWith duration RTl
The characteristic value of the climbing event that step S3. is extracted step S2 using the method for fuzzy clustering is classified, Optimum cluster model is made, different climbing event types are obtained.
Because the factor that influence climbing event occurs is intricate, the physical mechanism for being formed to it so far is not done also completely It is clear.Therefore, it is a basic thought for the system with typical blur based on wind-powered electricity generation climbing event, by genetic analysis, system Meter analysis method is combined with Fuzzy Analysis, it is established that the fuzzy relation between climbing event and corresponding climbing characteristic value, Carry out cluster analysis.
Assuming that each climbing event has m characteristic value, and n sample constitutes eigenmatrix:
Because dimension is inconsistent, first the eigenmatrix in S31 is normalized:
The fuzzy membership of each characteristic value is calculated using fuzzy clustering algorithm:
Wherein,It is i-th data to the j degree of membership of cluster centre;I=1,2 .., m, j=1,2 .., c, c are number According to hard plot clusters number, 4 are taken herein;vijAnd σijCenter and the width of Gaussian function are represented respectively.It is nearest by fuzzy membership Principle can make optimum cluster model, obtain different climbing event types.
Step S4. is trained and sets up forecast model respectively using statistical method to different climbing event types.
Different climbing event types is trained using ExtremeLearningMachine (ELM) algorithm, regulation ELM algorithm parameters make Various climbing events set up an optimal Clustering Model,
Need adjustment input weights and hidden layer biasing different from conventional function approximation theory, in ExtremeLearningMachine algorithm only Wanting activation primitive can infinitely lead, and input weights and hidden layer biasing can be randomly assigned, once the value being randomly assigned is being calculated Calligraphy learning starts to be updated in algorithm parameter, and hidden layer output matrix H is just uniquely determined and keeps constant, instruction Practice a neutral net to be equivalent to find a least square solution for linear system, if the number of hidden layer node and input Sample number is equal, then this Single hidden layer feedforward neural networks (SLFN) just can approach these training examples with zero error.
The ExtremeLearningMachine algorithm is concretely comprised the following steps:
1) input weights and hidden layer biasing are randomly assigned;
For N number of different training sample { xj,yj, xjIt is n × 1 dimensional input vector, yjIt is m × 1 dimension output vector, tool There is D hidden node and can infinitely lead activation primitivegX the SLFN structures of () can approach this N number of sample with zero error, that is, exist βiiAnd bi, make ∑ | | yj-rj| |=0, can also be written as form:
In formula:ωiIt is n × 1 dimensional vector, represents the connection weight of input layer and the neuron of hidden layer;βiFor m × 1 tie up to Amount, represents the connection weight of hidden layer and output layer neuron;biIt is the biasing of hidden layer neuron;rjIt is the output of network;g X () is activation primitive, can be " sig ", " rbf ", the diversified forms such as " sin ".
2) hidden layer output matrix H is calculated;
This N number of equation can be write as matrix form:
H β=R (7)
Wherein β is output layer weight matrix, and R is desired output;
3) global optimum's output weights of ELM algorithms are calculated;
H+It is the generalized inverse matrix of H.
Step S5. carries out the mistake of step S1 to S2 to the real-time wind speed test data and realtime power test data of wind power plant Journey, extracts the characteristic value of the climbing event of real-time wind speed test data and realtime power test data.
According to step S1 to S2 real-time wind speed test data and realtime power test data are carried out same treatment and point Analysis, extracts the characteristic value of climbing event:Climbing rate Rr, climbing amplitude RA, time started RTsWith duration RTl
Real-time wind speed test data and real-time work(that step S6. is extracted using the forecast model that step S4 is obtained to step S5 The characteristic value of the climbing event of rate test data is classified, and is predicted using forecast model, finally obtains final group Conjunction predicts the outcome.
Using same criteria for classification, the real-time wind speed test that the forecast model obtained according to step S4 is extracted to step S5 The characteristic value of the climbing event of data and realtime power test data is classified, respectively with the ExtremeLearningMachine for having trained Algorithm is tested with four kinds of corresponding forecast models.
The above, is only preferred embodiments of the invention, and any formal limitation, ability are not made to the present invention Field technique personnel make a little simple modification, equivalent variations or decoration using the technology contents of the disclosure above, all fall within the present invention Protection domain in.
The content not being described in detail in this specification belongs to prior art known to professional and technical personnel in the field.

Claims (9)

1. it is a kind of based on climbing affair character identification wind power combination forecasting method, it is characterised in that:Comprise the following steps:
S1, the historical wind speed and historical power data of wind power plant are processed using wavelet de-noising method, respectively obtained smooth Historical wind speed curve and historical power curve, to eliminate the interference of grass;
S2, using compression algorithm, the smooth historical wind speed curve and historical power curve obtained to step S1 carry out climbing thing The feature recognition of part, then will identify that the climbing event come carries out characteristics extraction;
S3, the characteristic value of the climbing event for being extracted step S2 using the method for fuzzy clustering are classified, and are made optimal Clustering Model, obtains different climbing event types;
S4, the different climbing event type obtained to step S3 using statistical method are trained and set up prediction mould respectively Type;
S5, real-time wind speed test data and realtime power test data to wind power plant carry out the process of step S1 to S2, extract The characteristic value of the climbing event of real-time wind speed test data and realtime power test data;
S6, the forecast model obtained using step S4 are to the real-time wind speed test data and realtime power test data that extract The characteristic value of climbing event classified, and be predicted using forecast model, finally obtain final combined prediction result.
It is 2. as claimed in claim 1 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: The process of wavelet de-noising is described in step S1:
S11, the time series to historical wind speed data and historical power data carry out Fourier's treatment, and discrete signal is switched to Continuous signal;
S12, power spectrumanalysis is carried out to continuous signal, draw its spectrum waveform;
The spectrum waveform feature of S13, analysis continuous signal, and then waveform is fitted, parametric equation is obtained after fitting, solve Draw Power Spectrum Distribution result;
Inverse transformation is carried out after S14, the parameter of change equation, filtered result is drawn.
It is 3. as claimed in claim 1 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: Compression algorithm described in step S2 is revolving door algorithm, and the revolving door algorithm is a kind of trends of straight line compression algorithm.
It is 4. as claimed in claim 1 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: Based on Fast Field algorithm, the climbing event definition based on Fast Field algorithm is event of climbing described in step S2:If P is wind Electric historical power time series,Be by the smooth historical power curve of the wind-powered electricity generation after denoising,It is to turn through SDT algorithms Wind-powered electricity generation historical power smooth sequence after changing, the historical power smooth sequence is used for recognizing climbing event, is calculated by formula (1) Obtain:
P ‾ S D T = S D T ( P ‾ , Δ E ) - - - ( 1 )
Wherein SDT is the SQL with compression algorithm principle;Δ E is responsive parameter, and value is smaller, and recognizable climbs The slope event procedure duration is shorter, and climbing height is lower;Value is bigger, and the recognizable climbing event procedure duration gets over Long, climbing height is higher;
When the conversion signal of wind-powered electricity generation historical power time seriesAbsolute value greater-than match climb the threshold value of event criterion During parameter lambda, whenDuring for negative value, what is identified is lower climbing event, whenBe on the occasion of when, what is identified is upper climbing thing Part.
It is 5. as claimed in claim 4 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: The threshold value of the upper climbing event is 20.0%cap, and the threshold value of lower climbing event is 15.0%cap.
It is 6. as claimed in claim 1 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: Characteristic value includes described in step S2:Climbing rate Rr, climbing amplitude RA, time started RTsWith duration RTl
It is 7. as claimed in claim 6 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: Using the method for fuzzy clustering by comprising the following steps that characteristic value is classified in step S3:
S31, assume that each climbing event has a m characteristic value, and n sample composition eigenmatrix:
X = x 11 x 12 ... x 1 n x 21 x 22 ... x 2 n ... ... ... ... x m 1 x m 2 ... x m n = ( x i j ) - - - ( 3 )
S32, the eigenmatrix in S31 is normalized:
X ^ = x ^ 11 x ^ 12 ... x ^ 1 n x ^ 21 x ^ 22 ... x ^ 2 n ... ... ... ... x ^ m 1 x ^ m 2 ... x ^ m n = ( x ^ i j ) - - - ( 4 )
S33, the fuzzy membership that each characteristic value is calculated using the method for fuzzy clustering:
μ j i ( x ) = exp [ - 1 2 ( x i - v i j ) 2 σ i j 2 ] - - - ( 5 )
Wherein,It is i-th data to the j degree of membership of cluster centre;I=1,2 .., m, j=1,2 .., c, c are that data are hard Partition clustering number;vijAnd σijCenter and the width of Gaussian function are represented respectively;
S34, optimum cluster model is made by the nearest principle of fuzzy membership, obtain different climbing event types.
It is 8. as claimed in claim 1 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: Different climbing event types is trained respectively using ExtremeLearningMachine algorithm in step S4, ExtremeLearningMachine algorithm is adjusted Parameter makes various climbing events set up an optimal Clustering Model.
It is 9. as claimed in claim 8 to be based on the wind power combination forecasting method that climbing affair character is recognized, it is characterised in that: The ExtremeLearningMachine algorithm is concretely comprised the following steps:
1) input weights and hidden layer biasing are randomly assigned;
For N number of different training sample { xj,yj, xjIt is n × 1 dimensional input vector, yjIt is m × 1 dimension output vector, with D Hidden node and can infinitely lead the Single hidden layer feedforward neural networks structure of activation primitive g (x) and this N number of sample can be approached with zero error , that is, there is β in thisiiAnd bi, make ∑ | | yj-rj| |=0, can also be written as form:
Σ i = 1 D β i g ( ω i T x j + b i ) = y j , j = 1 , ... , N - - - ( 6 )
In formula:ωiIt is n × 1 dimensional vector, represents the connection weight of input layer and the neuron of hidden layer;βiIt is m × 1 dimensional vector, Represent the connection weight of hidden layer and output layer neuron;biIt is the biasing of hidden layer neuron;rjIt is the output of network;g(x) It is activation primitive;
2) hidden layer output matrix H is calculated;
Write N number of equation as matrix form:
H β=R (7)
H = g ( ω 1 T x 1 + b 1 ) ... g ( ω D T x 1 + b D ) . . . ... . . . g ( ω 1 T x N + b 1 ) ... g ( ω D T x N + b D ) N × D - - - ( 8 )
β = β 1 T . . . β D T D × m a n d R = r 1 T . . . r D T N × m - - - ( 9 )
β is output layer weight matrix, and R is desired output;
3) global optimum's output weights of ELM algorithms are calculated;
β ^ = H + R - - - ( 10 )
H+It is the generalized inverse matrix of H.
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