CN104951834A - LSSVM (least squares support vector machine) wind speed forecasting method based on integration of GA (genetic algorithm) and PSO (particle swarm optimization) - Google Patents

Abstract

The invention provides an LSSVM (least squares support vector machine) wind speed forecasting method based on integration of GA (genetic algorithm) and PSO (particle swarm optimization). The method comprises the following steps: finite wind speed samples are divided into a training set and a testing set, and normalization processing is performed; GA and LSSVM related parameters are initialized; chromosome coding is performed, and initial population is generated randomly; the fitness corresponding to each chromosome is calculated, if requirements are met, the PSO in the fifth step is started directly, and if the requirements are not met, selection, crossover and mutation operation of the GA are performed; optimum parameter combination obtained with the GA is used for initializing the PSO related parameters; the optimum position fitness value of each particle is compared with the optimum position fitness value of the swarm; the final optimum parameter combination is output, and an optimized LSSVM model is obtained; a forecast wind speed time history spectrum is obtained. The LSSVM wind speed forecasting method based on integration of GA and PSO has the characteristics of high optimization precision, high convergence precision, fewer iterations, high success rate and the like.

Description

Based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population

Technical field

The present invention relates to a kind of based on the integrated LSSVM of intelligent optimization (least square method supporting vector machine) wind speed forecasting method, a kind of based on genetic algorithm (GA) and the integrated LSSVM fluctuating wind speed Forecasting Methodology of population (PSO) specifically.

Background technology

For tall and slender structure, large-span space structure and high voltage power transmission tower line system etc., the Stochastic Dynamic load that the class must considered when wind load is structural design is important.The design of wind load is improper not only can have influence on the level of comfort that people use building structure, but also building structure can be made to occur certain damage and fracture, brings huge life and property loss.Therefore, consider in engineering that the dynamic response of wind is extremely important, realize, to the Accurate Prediction of wind speed, there is very strong Practical meaning.

Support vector machine (SVM) is a kind of small-sample learning method that the Corpus--based Method theories of learning propose, and follows structural risk minimization principle.Utilize the good learning ability of support vector machine, the prognosis modelling of the Wind Velocity History to finite sample can be realized.The performance of support vector machine depends on the parameter of model, for the selection of parameter, does not also propose clear and definite theoretical foundation so far.Utilize intelligent optimization mode to carry out intelligent extraction to LSSVM model parameter and become a large focus.Common at present particle cluster algorithm, genetic algorithm, ant group algorithm and artificial bee colony algorithm etc. are mainly contained to the mode that LSSVM optimizes, to a certain extent, all kinds of optimized algorithm obtains certain effect in LSSVM parameter optimization, but the forecast model precision of prediction obtained and speed or not ideal enough.

Easily be absorbed in local optimum in conjunction with particle cluster algorithm, and other several optimized algorithms has the feature of stronger global optimizing ability.Therefore, the mode how using intelligent optimization method integrated carries out intelligent extraction to LSSVM model parameter, has a very big significance to obtain faster, that precision of prediction the is higher forecast model of LSSVM to wind speed of travelling speed.

Summary of the invention

The object of the present invention is to provide a kind of based on genetic algorithm and the integrated LSSVM fluctuating wind speed Forecasting Methodology of population, it utilizes the limited wind speed sample of certain wind field, sample is divided into training set and test set, initialization LSSVM model parameter, utilize that GA and PSO integration mode intelligent extraction LSSVM's have parameter combinations (C, σ) most, and then set up the LSSVM forecast model optimized, test set is predicted, obtains the Wind Velocity History spectrum predicted.

The present invention adopts following technical proposals: the present invention is based on genetic algorithm and the integrated LSSVM fluctuating wind speed Forecasting Methodology of population comprises the steps:

The first step: the limited wind speed sample getting a wind energy turbine set, is divided into training set, test set two parts by limited wind speed sample, and is normalized respectively;

Second step: initialization genetic algorithm correlation parameter, arranges LSSVM model kernel functional parameter C and regularization parameter σ scope C ∈ [C _min, C _max] and σ ∈ [σ _min, σ _max], binary coding is carried out to chromosome, produces initial population at random;

3rd step: carry out training study to LSSVM by training set, carries out the prediction of test set, and calculate each the chromosomal fitness in colony, whether evaluation algorithm convergence criterion meets, if meet best parameter group, enters the 5th step, otherwise enters the 4th step;

4th step: design genetic operator and the operational factor determining genetic algorithm, carries out the selection of genetic algorithm, intersection, mutation operation; Check whether and meet stopping criterion for iteration, if do not meet, return second step; Otherwise algorithm terminates to export best parameter group and enters the 5th step;

5th step: utilize the best parameter group that genetic algorithm obtains, initialization population correlation parameter; By training set, training study is carried out to LSSVM, calculate the fitness value that each particle is current, again the current fitness value of each particle and the optimal-adaptive angle value of this particle self are compared, if more excellent, then using the optimal location of position current for particle as this particle;

6th step: self optimal location fitness value of each particle is compared, if more excellent, then using the optimal location of the optimal location of this particle as colony with the fitness value of colony optimal location; Check whether and meet iteration optimizing termination condition, if meet, terminate optimizing, obtain optimum solution; Otherwise return second step;

7th step: utilize the best parameter group that the 6th step obtains, sets up the LSSVM forecast model optimized; Test set is predicted, obtains the fluctuating wind speed time series spectrum predicted; Computational prediction result also compares analysis with the mean absolute percentage error of GA-LSSVM, PSO-LSSVM forecast sample data, mean absolute error and root-mean-square error respectively.

Preferably, in the above-mentioned first step, normalized formula is formula:

$f:x\→y=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$

In formula, x _minthe minimum value of x, x _maxbe the maximal value of x, utilize this formula whole for the scope of x to [0,1].

Preferably, in second step, chromosome coding mode adopts binary coding, as shown in the formula:

$C=C_{min}+\frac{b}{2^m-1}(C_{\max }-C_{\min })$

$\mathrm{\σ}={\mathrm{\σ}}_{min}+\frac{b}{2^m-1}({\mathrm{\σ}}_{\max }-{\mathrm{\σ}}_{\min })$

Wherein b is binary number, and m is word length, C _max, C _minthe maximal value allowed for regularization parameter C and minimum value, σ _max, σ _minthe maximal value allowed for kernel functional parameter σ and minimum value.

Preferably, in the 3rd step, each chromosome fitness get computing formula as shown in the formula:

$f=\frac{1}{MSE}=\frac{l}{\underset{i=1}{\overset{l}{\Σ}}{(y_i-{\hat{y}}_i)}^2}$

Wherein f is fitness function, and MSE is the square error of test set data, y _iwith be respectively actual value and the predicted value of test set.

Preferably, in described 4th step, the selection opertor of genetic algorithm adopts fitness rule of three, by this individuality of ratio-dependent shared in whole colony fitness of ideal adaptation degree by select probability; The probability P that individual i is selected _iwith the accumulated probability Q of this individuality _icomputing formula as shown in the formula:

$P_i=\frac{f_i}{\underset{i=1}{\overset{N}{\Σ}}{f}_i}$

$Q_i=\underset{j=1}{\overset{i}{\Σ}}{P}_j,j=1,2,...i$

Wherein N is population scale, f _ibe i-th chromosomal fitness.

Preferably, in described 4th step, the crossover operator computing formula of genetic algorithm as shown in the formula:

c ₁＝p ₁a+p ₂(1-a)

c ₂＝p ₁(1-a)+p ₂a

In formula, p ₁, p ₂be right two individualities of an assembly; c ₁, c ₂for the new individuality obtained after interlace operation; A is random random number being positioned at (0,1) interval produced.

Preferably, in described 4th step, the mutation operator of genetic algorithm, selects i-th individual jth gene to carry out mutation operation, as shown in the formula:

$C_{\mathrm{ij}}=\left\{\begin{array}{c}{C}_{\mathrm{ij}}+(C_{\mathrm{ij}}-C_{\max })f\left(g\right),r\≥0.5\\ C_{\mathrm{ij}}+(C_{\min }-C_{\mathrm{ij}})f\left(g\right),r\≤0.5\end{array}\right.$

f(g)＝r′(1-g/T)

Wherein, C _min, C _maxfor the bound of gene, r, r ' the be random number between [0,1], g is for when evolution number of times, and T is maximum evolutionary generation.

Preferably, in described 5th step and the 6th step, the formula that particle upgrades oneself speed and position as shown in the formula:

x＝x+v

Wherein: v is the speed of particle; X is the position of current particle; r ₁and r ₂it is the random number between (0,1); C ₁and C ₂it is Studying factors.

The beneficial effect that the present invention brings: compared with adaptive genetic algorithm, particle cluster algorithm, have based on genetic algorithm and the integrated hybrid optimization algorithm of particle cluster algorithm that to optimize precision high, convergence precision is high, iterations is few, success ratio high, embodies good robustness and speed of convergence faster.

Accompanying drawing explanation

Fig. 1 is the forecasting wind speed of numerical simulation and the comparison schematic diagram of actual wind speed spectrum.

Fig. 2 is the comparison schematic diagram of the air speed value relative error of numerical simulation.

Fig. 3 is the process flow diagram schematic diagram of GA+PSO-LSSVM numerical prediction simulation wind speed.

Embodiment

Below in conjunction with accompanying drawing, enforcement of the present invention is further described.

The present invention adopts kernel function to be the LSSVM of radial basis function, and next the kernel functional parameter σ of method fast selecting the best that application GA and PSO is integrated and regularization parameter C combines.Genetic algorithm is searched for from trail, wide coverage, and global optimizing ability is strong, but easy Premature Convergence, be absorbed in local optimum; Particle cluster algorithm utilizes adaptive value to carry out evaluation system, and carry out certain random search according to adaptive value, insensitive to the initialization of population, and search speed is fast, and local search ability is strong.Therefore, genetic algorithm and particle cluster algorithm are combined, genetic algorithm is adopted to carry out global search, determine the field that optimum solution exists, the optimum solution initialization particle cluster algorithm so utilizing genetic algorithm to obtain, and then by the Local Search of particle cluster algorithm, realize the effective search of non-convex space, obtain precision higher in actual computation and speed faster.

The present invention is based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population comprises the steps:

The first step, gets the limited wind speed sample of a wind energy turbine set, wind speed sample is divided into training set, test set two parts, and is normalized respectively; Such as, get the air speed data of a wind energy turbine set from 23:25 on the 12nd April 18:55 to 2011 year on the 8th April in 2011, in 10min, obtain a wind speed, totally 600 wind speed points.Get front 500 wind speed as training set, rear 100 wind speed, as test set, are normalized.

In the above-mentioned first step, normalized formula is formula (1):

$f:x\→y=\frac{x-x_{\min }}{x_{\max }-x_{\min }}---\left(1\right)$

In formula, x _minthe minimum value of x, x _maxbe the maximal value of x, utilize this formula whole for the scope of x to [0,1].

Second step: initialization genetic algorithm correlation parameter (population size N, maximum evolutionary generation T, crossover probability P _c, mutation probability P _m), LSSVM model kernel functional parameter C and regularization parameter σ scope are set with σ ∈ [σ _min, σ _max], binary coding is carried out to chromosome, produces initial population at random; Such as initialization genetic algorithm, arranges Population in Genetic Algorithms scale N ₁=50, maximum evolutionary generation T=100, crossover probability P _c=0.7, mutation probability P _m=0.05; Kernel functional parameter and regularization parameter scope C ∈ [10 are set ^-1, 10 ³] and σ ∈ [10 ^-2, 10 ²], binary coding is carried out to kernel functional parameter and regularization parameter, produces initial population at random.

In second step, chromosome coding mode adopts binary coding, specifically such as formula (2) and (3):

$C=C_{min}+\frac{b}{2^m-1}(C_{\max }-C_{\min })---\left(2\right)$

$\mathrm{\σ}={\mathrm{\σ}}_{min}+\frac{b}{2^m-1}({\mathrm{\σ}}_{max}-{\mathrm{\σ}}_{\min })---\left(3\right)$

Wherein b is binary number, and m is word length, C _max, C _minthe maximal value allowed for regularization parameter C and minimum value, σ _max, σ _minthe maximal value allowed for kernel functional parameter σ and minimum value.

3rd step: carry out training study to LSSVM by training set, carries out the prediction of test set, calculates each the chromosomal fitness in colony, whether evaluation algorithm convergence criterion meets, if meet output parameter combination (C, σ) to enter the 5th step, otherwise enter the 4th step;

In 3rd step, each chromosome fitness gets computing formula as shown in the formula (4):

$f=\frac{1}{MSE}=\frac{l}{\underset{i=1}{\overset{l}{\Σ}}{(y_i-{\hat{y}}_i)}^2}---\left(4\right)$

Wherein f is fitness function, and MSE is the square error of test set data, y _iwith be respectively actual value and the predicted value of test set.

4th step: design genetic operator (genetic operator comprises selection opertor, crossover operator and mutation operator) and determine the operational factor of genetic algorithm, carries out the selection of genetic algorithm, intersection, mutation operation; Check whether and meet stopping criterion for iteration, if do not meet, return second step; Otherwise algorithm terminates to export best parameter group (C, σ) and enters the 5th step;

In 4th step:

The selection opertor of genetic algorithm adopts fitness rule of three, by this individuality of ratio-dependent shared in whole colony fitness of ideal adaptation degree by select probability.The probability P that individual i is selected _iwith the accumulated probability Q of this individuality _icomputing formula is as shown in the formula (5) and formula (6):

$P_i=\frac{f_i}{\underset{i=1}{\overset{N}{\Σ}}{f}_i}---\left(5\right)$

$Q_i=\underset{j=1}{\overset{i}{\Σ}}{P}_j,j=1,2,...i---\left(6\right)$

Wherein N is population scale, f _ibe i-th chromosomal fitness.

The crossover operator computing formula of genetic algorithm is as shown in the formula (7) and formula (8):

c ₁＝p ₁a+p ₂(1-a) (7)

c ₂＝p ₁(1-a)+p ₂a (8)

In formula, p ₁, p ₂be right two individualities of an assembly; c ₁, c ₂for the new individuality obtained after interlace operation; A is random random number being positioned at (0,1) interval produced.

The mutation operator of genetic algorithm, select i-th individual jth gene to carry out mutation operation, namely as shown in the formula (9) and formula (10):

$C_{\mathrm{ij}}=\left\{\begin{array}{c}{C}_{\mathrm{ij}}+(C_{\mathrm{ij}}-C_{\max })f\left(g\right),r\≥0.5\\ C_{\mathrm{ij}}+(C_{\min }-C_{\mathrm{ij}})f\left(g\right),r\≤0.5\end{array}\right.---\left(9\right)$

f(g)＝r′(1-g/T) (10)

Wherein, C _min, C _maxfor the bound of gene, r, r ' the be random number between [0,1], g is for when evolution number of times, and T is maximum evolutionary generation.

5th step: the best parameter group (C, σ) utilizing genetic algorithm to obtain, initialization population correlation parameter; By training set, training study is carried out to LSSVM, calculate the fitness value that each particle is current, again the current fitness value of each particle and the optimal-adaptive angle value of this particle self are compared, if more excellent, then using the optimal location of position current for particle as this particle; Population population scale N is such as set ₂=35, maximum iteration time M ₂=120, Studying factors C ₁=2, C ₂=2.With the LSSVM model corresponding to each particle vector, learning sample is predicted respectively, obtain the fitness value of each particle current location, then by fitness value current for all particles and the individual extreme value p of this particle _bestcompare, if more excellent, then using the optimal location of position current for particle as this particle, current fitness value is as individual extreme value p _best;

6th step: by self optimal location fitness value p of each particle _bestwith the fitness value g of colony's optimal location _bestrelatively, if more excellent, then using the optimal location of the optimal location of this particle as colony, i.e. self optimal location fitness value p of this particle _bestas the fitness value g of colony's optimal location _best.Check whether and meet iteration optimizing termination condition (reaching the maximum iteration time or default precision that preset), if meet, terminate optimizing, obtain optimum solution (C, σ); Otherwise return second step;

In the 5th step and the 6th step, particle upgrades the formula of oneself speed and position as shown in the formula (11), formula (12):

x＝x+v (12)

Wherein: v is the speed of particle; X is the position of current particle; r ₁and r ₂it is the random number between (0,1); C ₁and C ₂it is Studying factors.

7th step: utilize the best parameter group (C, σ) that the 6th step obtains, sets up the LSSVM forecast model optimized; Test set is predicted, obtains the fluctuating wind speed time series spectrum predicted; Computational prediction result also compares analysis, in table 1 with the mean absolute percentage error (MAPE) of GA-LSSVM, PSO-LSSVM forecast sample data, root-mean-square error (RMSE) and mean absolute error (MAE) respectively:

The evaluation index table of table 1 three kinds of method simulations

Above step can reference diagram 3, gives implementing procedure of the present invention intuitively.Can intuitively find out from Fig. 1, the predicted data image obtained in conjunction with the LSSVM model that GA, PSO are integrated and reality more identical.Can intuitively find out from Fig. 2, the predicted data relative error image obtained in conjunction with the LSSVM model that GA, PSO are integrated is more close to zero axle.Can find out intuitively table 1 data, the mean absolute percentage error (MAPE) in conjunction with the integrated LSSVM model prediction data of GA, PSO is compared GA optimized algorithm and be have dropped 56.1%, compares PSO optimized algorithm and have dropped 40.2%; Root-mean-square error (RMSE) is compared GA optimized algorithm and be have dropped 49.0%, compares PSO optimized algorithm and have dropped 46.9%; Mean absolute error (MAE) is compared GA optimized algorithm and be have dropped 50%, compares PSO optimized algorithm and have dropped 43.5%.

The present invention carries out intelligent selection by GA and PSO Integrated Algorithm to the model parameter of LSSVM, obtain the LSSVM model optimized, utilize the wind speed of known time section to carry out training study to LSSVM model, achieve more accurately, predict more quickly the wind speed of unknown time period.

Claims (8)

1., based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, it is characterized in that, it comprises the steps:

The first step: the limited wind speed sample getting a wind energy turbine set, is divided into training set, test set two parts by limited wind speed sample, and is normalized respectively;

Second step: initialization genetic algorithm correlation parameter, arranges LSSVM model kernel functional parameter C and regularization parameter σ scope C ∈ [C _min, C _max] and σ ∈ [σ _min, σ _max], binary coding is carried out to chromosome, produces initial population at random;

3rd step: carry out training study to LSSVM by training set, carries out the prediction of test set, and calculate each the chromosomal fitness in colony, whether evaluation algorithm convergence criterion meets, if meet best parameter group, enters the 5th step, otherwise enters the 4th step;

4th step: design genetic operator and the operational factor determining genetic algorithm, carries out the selection of genetic algorithm, intersection, mutation operation; Check whether and meet stopping criterion for iteration, if do not meet, return second step; Otherwise algorithm terminates to export best parameter group and enters the 5th step;

5th step: utilize the best parameter group that genetic algorithm obtains, initialization population correlation parameter; By training set, training study is carried out to LSSVM, calculate the fitness value that each particle is current, again the current fitness value of each particle and the optimal-adaptive angle value of this particle self are compared, if more excellent, then using the optimal location of position current for particle as this particle;

6th step: self optimal location fitness value of each particle is compared, if more excellent, then using the optimal location of the optimal location of this particle as colony with the fitness value of colony optimal location; Check whether and meet iteration optimizing termination condition, if meet, terminate optimizing, obtain optimum solution; Otherwise return second step;

7th step: utilize the best parameter group that the 6th step obtains, sets up the LSSVM forecast model optimized; Test set is predicted, obtains the fluctuating wind speed time series spectrum predicted; Computational prediction result also compares analysis with the mean absolute percentage error of GA-LSSVM, PSO-LSSVM forecast sample data, mean absolute error and root-mean-square error respectively.

2. according to claim 1 based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, it is characterized in that, in the described first step, the formula of normalized is following formula:

$f:x\→y=\frac{x-x_{\min }}{x_{\max }-x_{\min }}$

In formula, x _minthe minimum value of x, x _maxbe the maximal value of x, utilize this formula whole for the scope of x to [0,1].

It is 3. according to claim 1 that based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, it is characterized in that, in described second step, chromosome coding mode adopts binary coding, as shown in the formula:

$C=C_{\min }+\frac{b}{2^m-1}(C_{\max }-C_{\min })$

$\mathrm{\σ}={\mathrm{\σ}}_{\min }+\frac{b}{2^m-1}({\mathrm{\σ}}_{\max }-{\mathrm{\σ}}_{\min })$

Wherein b is binary number, and m is word length, C _max, C _minthe maximal value allowed for regularization parameter C and minimum value, σ _max, σ _mi _nthe maximal value allowed for kernel functional parameter σ and minimum value.

4. according to claim 1ly to it is characterized in that based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, in described 3rd step, each chromosome fitness get computing formula as shown in the formula:

$f=\frac{1}{MSE}=\frac{l}{\underset{i=1}{\overset{l}{\Σ}}{(y_{\stackrel{\·}{i}}-{\hat{y}}_i)}^2}$

Wherein f is fitness function, and MSE is the square error of test set data, y _iwith be respectively actual value and the predicted value of test set.

5. according to claim 1 based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, it is characterized in that, in described 4th step:

The selection opertor of genetic algorithm adopts fitness rule of three, by this individuality of ratio-dependent shared in whole colony fitness of ideal adaptation degree by select probability; The probability P that individual i is selected _iwith the accumulated probability Q of this individuality _icomputing formula as shown in the formula:

$P_i=\frac{f_i}{\underset{i=1}{\overset{N}{\Σ}}{f}_i}$

$Q_i=\underset{j=1}{\overset{i}{\Σ}}{P}_j,j=1,2,...i$

Wherein N is population scale, f _ibe i-th chromosomal fitness.

6. according to claim 1ly to it is characterized in that, in described 4th step: in described 4th step based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, the crossover operator computing formula of genetic algorithm as shown in the formula:

c ₁＝p ₁a+p ₂(1-a)

c ₂＝p ₁(1-a)+p ₂a

In formula, p ₁, p ₂be right two individualities of an assembly; c ₁, c ₂for the new individuality obtained after interlace operation; A is random random number being positioned at (0,1) interval produced.

7. according to claim 1ly it is characterized in that based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, in described 4th step, the mutation operator of genetic algorithm, selects i-th individual jth gene to carry out mutation operation, as shown in the formula:

$C_{\mathrm{ij}}=\left\{\begin{array}{c}{C}_{\mathrm{ij}}+(C_{\mathrm{ij}}-C_{\max })f\left(g\right),r\≥0.5\\ C_{\mathrm{ij}}+(C_{\min }-C_{\mathrm{ij}})f\left(g\right),r\≤0.5\end{array}\right.$

f(g)＝r′(1-g/T)

Wherein, C _min, C _maxfor the bound of gene, r, r ' the be random number between [0,1], g is for when evolution number of times, and T is maximum evolutionary generation.

8. according to claim 1ly to it is characterized in that based on genetic algorithm and the integrated LSSVM wind speed forecasting method of population, in described 5th step and the 6th step, the formula that particle upgrades oneself speed and position as shown in the formula:

$v=\mathrm{\ω}\×v+C_1\×r_1\×(p_{best}-x)+C_2\×r_2\×(g_{best}-x)$

x＝x+v

Wherein: v is the speed of particle; X is the position of current particle; r ₁and r ₂it is the random number between (0,1); C1 and C2 is Studying factors.