CN106127330A - Fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine - Google Patents

Abstract

The present invention proposes a kind of fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine.This method first passes through the fluctuating wind speed of ARMA method numerical simulation high-rise building 15 simulation point as sample data；By interpolation learning training, B-spline kernel function and radial direction base (RBF) kernel function linear combination is used to set up B RBF compound kernel function, and LSSVM model of based on B RBF compound kernel function, use population (PSO) optimized algorithm to make the forecast error minimum of model to find model optimized parameter further, thus use the parameter after optimizing to set up LSSVM model based on B RBF kernel function；Fluctuating wind speed sample predictions finally by levels goes out the fluctuating wind speed in intermediate layer, employing mean error, mean absolute error, root-mean-square error, correlation coefficient are as evaluation index, and compare with based on single B-spline (including 1 B-spline, 3 B-spline and 5 B-spline) LSSVM of kernel function and the predicting the outcome of LSSVM model of single RBF kernel function.

Description

Fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine

Technical field

The present invention relates to a kind of fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine, based on use B-spline- Radially the machine learning method of the least square method supporting vector machine (LSSVM) of base (B-RBF) compound kernel function predicts fluctuating wind Speed time-histories method.

Background technology

The method that Function Fitting is used by the support vector machine (SVM) of standard is mainly by empty from low-dimensional input for input sample Between be transformed into a high-dimensional feature space by nonlinear mapping, then make loss function minimum in this higher dimensional space thus Obtain linear fitting function.According to Mercer theorem, for support vector machine, function regression fitting problems can describe For solving a constrained quadratic programming problem, constraint number is equal to the capacity of sample, although used relevant kernel function Avoid " dimension disaster " that High Dimensional Mapping brings that solve of display, but every single-step iteration is required for carrying out the matrix of kernel function Computing, the internal memory occupied because of kernel matrix is along with the quantity of sample is in square increasing, and training also can consume long time, especially It can cause when the capacity of sample is bigger the training time long and be difficult to accept.Additionally, due to the accumulation of iteration error, also can The precision causing algorithm cannot meet requirement.Secondly, SVM is also required to carry out substantial amounts of matrix operations during secondary optimization, Under many circumstances, the time that optimizing algorithm takies often accounts for major part.The residual sum of square that least-squares estimation is estimated Minimum principle determine that sample regression function is a kind of effective regression estimates model method, it occupies act in data estimation The status of foot weight.Suykens notices that method of least square, for solving the advantage of support vector machine problem, first proposed A young waiter in a wineshop or an inn takes advantage of support vector machine (Least SquARMAes Support Vector Machine, LSSVM), at the SVM mesh of standard Scalar functions adds error sum of squares item, forms LSSVM model, the problem that SVM extensive computation can be efficiently solved.

LSSVM is used the kernel function in luv space to calculate and is transported by the inner product in nonlinear mapping to high-dimensional feature space Calculate, no matter use which kind of kernel function, all parameter g in this kind of kernel function can be brought in the foundation of regression function.The SVM of standard All having used punishment parameter C with LSSVM, be respectively intended to control insensitive loss function and error, punishment parameter C can be compromised mould The training error of type and complexity, i.e. realize empiric risk and the compromise of confidence risk, and C is excessive, although surface empiric risk Minimize, but the advantage not minimized due to confidence risk, therefore cannot realize the principle of structural risk minimization.Institute With, selected or construct suitable kernel function and corresponding nuclear parameter g thereof and the punishment parameter C prediction to being set up by kernel method The generalization ability of model has very important effect.

Kernel method is the general name of a series of advanced nonlinear transportation technology.Mercer demonstrates Mercer theorem； Aizermann, Bravermann, Rozoener are by inner product kernel function being used as in feature space about the research of potential function This thought introduces machine learning field.The common trait of kernel method is that the processing method of these nonlinear datas all applies Nuclear mapping.Kernel method initially with nonlinear mapping by initial data by data space map to feature space, and then in feature Space carries out the linear operation of correspondence, and owing to having used nonlinear mapping, and this nonlinear mapping is often extremely complex, Thus greatly strengthen nonlinear transportation ability.In essence, kernel method achieves data space, feature space and class Nonlinear transformation between other space.Kernel method has following feature: 1. kernel method has solid theoretical basis Kernel method is with Statistical Learning Theory for instructing；2. kernel method has preferable Generalization Ability utilizes kernel method to be trained Practise facility and have extraordinary Generalization Ability, because it has observed structural risk minimization；3. kernel method is more sane The capacity of resisting disturbance of kernel method is stronger；4. kernel method has powerful non-linear and higher-dimension disposal ability kernel method and utilizes core When function processes nonlinear problem in higher dimensional space, solve dimension disaster problem in higher dimensional space well.From the most several Individual aspect will be it can be seen that application kernel method will obtain significant effect in classification and identification.

Owing to the sample of sample space is mapped to high-dimensional feature space by the introducing of nuclear mapping, observation sample data are converted Visual angle.So many in the former insoluble problem of sample space current methods, high-dimensional feature space can be used line Property method completes easily, and need not know concrete mapping function.In the high-dimensional feature space introduced at present, right General problem concerning study is only sufficient to as linear process, because the dimension of General Multidimensional feature space is bigger than sample number.This When the linear process of kind high-dimensional feature space is mapped to the input space, be but equivalent to Nonlinear Processing.Realize nuclear mapping institute energy The kernel function used must is fulfilled for previously described Mercer theorem, and existing the most radially base (RBF) kernel function is exactly a kind of general All over the core used, it all shows good performance in pattern recognition and regression analysis.The performance of kernel method is at very great Cheng Kernel function is depended on, therefore the selection of kernel function and be constructed to the emphasis of Kernel-Based Methods research on degree.

But, research shows, if specific classification problem chooses at random kernel function, it will cause pushing away of this kernel function model Wide poor performance, even can not correctly classify, as a kind of data digging method, although Kernel-Based Methods need not process Priori, but the priori if, with field selects kernel function, i.e. selects suitably for concrete data characteristic Kernel function necessarily can improve the performance of Kernel-Based Methods, and this point has been demonstrate,proved in the data digging methods such as neutral net Bright.Research for kernel function at present is concentrated mainly in the system of selection of kernel function, but it is absolutely not kernel function research Final goal, even if because we have found a kind of extraordinary method, it is possible to ensure every time can be from some collections of functions In find certain optimal kernel function, its also simply relatively optimal in given collection of functions, be not necessarily problem to be solved Most effective kernel function, so the final goal of kernel function research is to determine optimal kernel function for concrete problem.

The theory of B-spline function is proposed in nineteen forty-six by Schoenberg, but paper until just being delivered for 1967. DeBoor Yu Cox in 1972 independently give the canonical algorithm calculated about batten.Owing to B-spline method remains many The simplicity of formula and the feasibility approached overcome again additive method and represent that brings does not possesses local property due to entirety Shortcoming, the most in theory or suffers from highly important meaning in application.The most many scholars are to according to core The main contributions of Functional Quality tectonic association kernel function research has: Shawe etc. point out, according to kernel function closure property, pass through core The simple operation of function can construct new practical kernel function.Smits etc. propose karyomerite and the concept of overall situation core the earliest, Advantage in combination with both constructs compound kernel function.Liu etc. construct kernel function product shape according to kernel function closure property again The combination core of formula, utilizes the compound kernel function of Polynomial kernel function and Radial basis kernel function product form to carry out benchmark data propping up Hold vector regression (SVR), and be used alone Polynomial kernel function or RBF kernel function compares, result display utilizes The SVR relatively monokaryon SVR of combination core has preferably stability and generalization.By overall situation kernel function B-spline core and local kernel function The B-RBF combination core that RBF core linear combination is constituted is applied to the prediction of fluctuating wind speed in above theoretical basis and has very well Estimated performance.

Summary of the invention

It is an object of the invention to provide a kind of fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine, solve The problems such as traditional support vector machine simulation precision on forecasting wind speed is the highest, time-consuming.And traditional numerical simulation with new The machine learning method LSSVM of type combines, and the data mining simulation being fluctuating wind speed by numerical simulation provides sample number According to, then by the fluctuating wind speed on machine learning method simulation and forecast requisite space, thus forming a whole set of can be wind force proofing design The simulating and predicting method of the Wind Velocity History curve needed for offer, not only reduces actual measurement cost, and has saved the substantial amounts of time Cost.

For reaching above-mentioned purpose, the present invention uses following technical proposals:

A kind of fluctuating wind speed Forecasting Methodology based on data mining, based on using B-RBF compound kernel function and using particle The machine learning method of the least square method supporting vector machine that group's method PSO optimizes, predicts fluctuating wind speed time series method, by known Height fluctuating wind speed sample data interpolation study and training, it was predicted that treat simulated altitude fluctuating wind speed time series；Concrete steps are such as Under:

1) select high-rise building, determine the parameter required for numerical simulation fluctuating wind speed: the building height of simulation and mould Intend each height of wind speed point, the mean wind speed of 10 meters of height, surface roughness values, ground roughness exponent, simulation phase at this Close function；

2) fluctuating wind speed time series that the setting quantity generated by ARMA method numerical simulation is distributed along high uniformity, as having The original systolic wind speed sample data of limit；And to the analogue value of power spectral density of the wind speed, auto-correlation function and cross-correlation function with The degree of agreement of respective objects value is tested, based on arma modeling simulation high-rise building Wind Velocity History feasible with checking Property；

3) B-RBF compound kernel function is substituted Radial basis kernel function RBF and add in LSSVM data digging method, by right Fluctuating wind speed sample data in known altitude region carries out learning and training, and sets up LSSVM based on B-RBF compound kernel function Fluctuating wind speed forecast model；

4) by, in the sample data of input interval two-layer to forecast model, exporting the fluctuating wind of intermediate layer corresponding time Speed, and use mean absolute error, root-mean-square error, correlation coefficient as evaluation index, is analyzed result, assess based on The accuracy of the LSSVM of B-RBF compound kernel function.

Above-mentioned steps 2) in arma modeling following formula represent:

$v\left(t\right)=-\underset{k=1}{\overset{p}{\Σ}}{\mathrm{\ψ}}_k\·v(t-k\mathrm{\Δ}t)+N\left(t\right)---\left(1\right)$

In formula: v (t), v (t-k Δ t) be respectively M, space point t and t-k Δ t fluctuating wind speed time series to Amount；P is the exponent number of arma modeling；Δ t is the time step of simulation wind speed；ψ_kArma modeling autoregressive coefficient matrix, for M × M rank square formation；N (t)=L n (t), L are lower triangular matrix, n (t) be M dimension average be 0 variance be 1 separate white noise to Amount.

Suykens et al. proposes LSSVM algorithm.It is a deformation of standard SVM.SVM is solved quadratic programming by it Problem is converted into and solves system of linear equations.Avoid insensitive loss function, greatly reduce complexity of the calculation.LSSVM's Training has only to solve a system of linear equations, is not only easy to realize, and drastically increases training effectiveness, in pattern recognition It is widely used with in the problems such as regression modeling.

The Function Estimation problem of LSSVM can be described as solving following problem.

If given sample data set T={ (x_i,y_i) ..., (x_l,y_l), wherein: x_i∈Rⁿ, y_i∈ R, i=1,2, 3,…,l.It is also contemplated that with function f (x)=ω ψ (x)+b, sample data is fitted, and make match value and actual value Error is minimum, and wherein input sample is mapped in high-dimensional feature space by nonlinear mapping ψ (x).The regression problem of LSSVM is permissible It is expressed as following form:

$min\[\frac{1}{2}\left|\right|\mathrm{\ω}|{|}^2+\frac{1}{2}C\underset{i=1}{\overset{l}{\Σ}}{e}_i^2\]---\left(2\right)$

s.t.[y_i-(ω·ψ(x_i)+b)=e_i], i=1,2,3 ..., l

In formula: e_i∈ R is error, e ∈ R^l×lFor error vector；As SVM, C for punishment parameter, but herein in order to Control the punishment degree to error, if training data has bigger noise, then should suitably select less C；ψ (x) is non- Linear Mapping, is mapped to high-dimensional feature space by input sample:Weight vectorBiasing b ∈ R.

For solving the optimization problem of formula (2), can introduce Lagrange multiplier, defining its Lagrange function is following shape Formula:

$L(\mathrm{\ω},b,e,\mathrm{\α})=\frac{1}{2}\left|\right|\mathrm{\ω}|{|}^2+\frac{1}{2}C\underset{i=1}{\overset{l}{\Σ}}{e}_i^2-\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\α}}_i(\mathrm{\ω}\·\mathrm{\ψ}(x_i)+b+e_i-y_i)---\left(3\right)$

By KKT condition, above formula derivation is obtained:

$\left\{\begin{array}{c}\frac{\∂L}{\∂\mathrm{\ω}}=0\→\mathrm{\ω}=\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\α}}_i\mathrm{\ψ}\left(x_i\right)\\ \frac{\∂L}{\∂b}=0\→\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\α}}_i=0\\ \frac{\∂L}{\∂e_i}=0\→{\mathrm{\α}}_i={\mathrm{Ce}}_i\\ \frac{\∂L}{\∂{\mathrm{\α}}_i}=0\→\mathrm{\ω}\·\mathrm{\ψ}\left(x_i\right)+b+e_i-y_i=0\end{array}\right.,i=1,2,...,l---\left(4\right)$

These conditions of formula (4) are similar with the optimal conditions of the SVM of standard, simply α_i=Ce_iSo that each sample number Strong point is all made that contribution to regression estimates function, and is more than supporting vector.Simultaneous Equations, eliminates ω and e_i, order: α= [α₁,α₂,…α_l]^T, Q=[1,1 ... 1]^T, Y=[y₁,y₂,…y_l]^T, I is unit matrix, then the solution of formula (4) gained is:

$\left[\begin{array}{c}0\\ Y\end{array}\right]=\left[\begin{array}{cc}0& Q^T\\ Q& K+C^{-1}I\end{array}\right]\left[\begin{array}{c}b\\ \mathrm{\α}\end{array}\right]---\left(5\right)$

In formula: K represents kernel function: K (x, x')=ψ (x) ψ (x'),

Can be in the hope of α by solving system of linear equations formula (5)_iAnd b, therefore obtain the regressive prediction model of LSSVM:

$f\left(x\right)=\underset{i=1}{\overset{l}{\Σ}}{\mathrm{\α}}_{i}K(x,x_i)+b---\left(6\right)$

In different applications, given different computational methods and polytype data, kernel function is defined on In these data, it is clear that as long as mapping and its refineization, kernel method in view of embedding according to existing issue custom-made This characteristic determine varied property of kernel function kind.As LSSVM with SVM, mainly there is 1. Polynomial kernel function: K (x, x')=tanh [b (x x')+c], 2. Radial basis kernel function (RBF): K (x, x')=(x x'+1)^d, 3.Sigmoid core Function: K (x, x')=exp [-(x-x')²/(σ²)] etc..

B-Spline Kernel mainly has two kinds, the B-Spline Kernel of the most limited node and the B-Spline Kernel of infinite node.

(1) the B-Spline Kernel of limited node

N dimension p rank (p is nonnegative integer) the B-Spline Kernel of limited node is defined in Rⁿ×RⁿOn such a function, It is to be expanded by the one-dimensional p rank Spline Kernel on R × R.It is true that the node set set in the given one-dimensional spaceThe most corresponding one-dimensional p rank (p is nonnegative integer) Spline Kernel is:

$K(x,x^{\′};t_1,...,t_m)=\underset{i=1}{\overset{m}{\Σ}}{(x-t_i)}_{+}^p{(x^{\′}-t_i)}_{+}^p,\∀x,x^{\′}\∈R---\left(7\right)$

Wherein,

Now by one-dimensional Spline Kernel K₁Definition n ties up Spline Kernel.If the node set on given n-dimensional spaceAnd remember t₁={ t₁₁,…,t_1n}^T,…,t_m={ t_m1,…,t_mn}^T, x=([x]₁,…[x]_n)^T, x'= ([x']₁,…[x']_n)^T, then n dimension p rank Spline Kernel is defined as:

$K(x,x^{\′})=K(x,x^{\′};t_1,...,t_m)=\underset{i=1}{\overset{n}{\Π}}{K}_1\{{\[x\]}_i,{\[x^{\′}\]}_i;t_{1i},...,t_{mi}\}---\left(9\right)$

(2) the B-Spline Kernel of infinite node

Similar with limited node situation, we the most first define the one-dimensional p rank Spline Kernel of infinite node.This Spline Kernel is Based on 0 standard Spline Kernel function B₀(x)

$B_0\left(x\right)=\left\{\begin{array}{cc}0,& \left|x\right|>\frac{1}{2}\\ \frac{1}{2},& \left|x\right|=\frac{1}{2}\\ 1,& \left|x\right|<\frac{1}{2}\end{array}\right.---\left(10\right)$

Be given.It is true that define one-dimensional p rank Spline Kernel it is

$K(x,x^{\&prime;})=B_{2p+1}(x-x^{\&prime;}),\&ForAll;x,x^{\&prime;}\&Element;R---\left(11\right)$

Wherein B_2p+1X () is 2p+1 rank B-spline functions,HereMake convolution algorithm, i.e.AndIt is to 2p+2 B₀Carry out what 2p+1 convolution algorithm obtained.I.e.

Thus definable n ties up Spline Kernel.Note x=([x]₁,…[x]_n)^T, x'=([x']₁,…[x']_n)^T, then n dimension p rank sample Bar core is

$K(x,x^{\&prime;})=\underset{i=1}{\overset{n}{\&Pi;}}{K}_1({\&lsqb;x\&rsqb;}_i,{\&lsqb;x^{\&prime;}\&rsqb;}_i)=\underset{i=1}{\overset{n}{\&Pi;}}{B}_{2p+1}({\&lsqb;x\&rsqb;}_i,{\&lsqb;x^{\&prime;}\&rsqb;}_i)---\left(12\right)$

Kernel-Based Methods is a kind of modular method, and it can be divided into kernel function design and algorithm to design two parts, core Specifically comprising the following steps that of method

(1) collect and arrange sample, and be standardized；

(2) select or construct kernel function；

(3) by kernel function, input sample is for conversion into kernel matrix, namely input data is passed through non-linear letter Number is mapped to higher-dimension Hilbert feature space；

(4) at higher-dimension Hilbert feature space, kernel matrix is implemented various linear algorithms；

(5) nonlinear model in the input space is obtained.

From above-mentioned steps, it is the committed step in Kernel-Based Methods that sample data consideration convey turns to nuclear matrix.Due to The input space is stealthy mapping to nonlinear mapping φ (x) of feature space, it is impossible to determine embodying of this mapping phi (x) Formula, that uniquely can investigate is nuclear matrix K (x, x').By this way, nuclear matrix is for providing between input sample and learning algorithm One platform.Only by nuclear matrix, learning algorithm just can receive the information about feature space core input data, therefore Nuclear matrix has core status in kernel function learns.

About the effectiveness of combination core, have theorem as follows:

Given training set X=(x₁,…,x_p) and kernel function K (x, x'), define core interior element K (x_u,x_v), wherein u, v= 1 ..., the matrix of p is nuclear matrix or Gram matrix, if being symmetrical and positive semidefinite for its nuclear matrix of all of training set X , then function K is effective core.

The expression formula of RBF kernel function is:

$K(x,x^{\&prime;})=\exp (-\frac{{(x-x^{\&prime;})}^2}{{\mathrm{\&sigma;}}^2})---\left(13\right)$

Therefore its nuclear matrix can be configured to according to expression formula:

$K(x_u,x_v)=\exp (-\frac{\left|\right|x_u-x_v|{|}^2}{{\mathrm{\&sigma;}}^2})\&RightArrow;\left\{\begin{array}{c}0,x_u=x_v\\ \exp (-\frac{\left|\right|x_u-x_v|{|}^2}{{\mathrm{\&sigma;}}^2}),x_u\&NotEqual;x_v\end{array}\right.---\left(14\right)$

And knowable to above formula, nuclear matrix K (x_u,x_v) have the property that

$K(x_u,x_v)=\left\{\begin{array}{c}0,x_u=x_v\\ k(x_u,x_v)=k(x_v,x_u),x_u\&NotEqual;x_v\end{array}\right.---\left(15\right)$

The expression formula of B-spline kernel function is:

$K(x,x^{\&prime;};t_1,...,t_m)=\underset{i=1}{\overset{m}{\&Sigma;}}{(x-t_i)}_{+}^p{(x^{\&prime;}-t_i)}_{+}^p---\left(16\right)$

Therefore its nuclear matrix can be configured to according to expression formula:

$K(x_u,x_v;t_1,...,t_m)=\underset{i=1}{\overset{m}{\&Sigma;}}{(x_u-t_i)}_{+}^{2p}---\left(17\right)$

Then its nuclear matrix K (x_u,x_v) have the property that

$K(x_u,x_v;t_i,...,t_m)=\left\{\begin{array}{c}\underset{i=1}{\overset{m}{\&Sigma;}}{(x_u-t_i)}_{+}^{2p},x_u=x_v\\ k(x_u,x_v)=k(x_v,x_u),x_u\&NotEqual;x_v\end{array}\right.---\left(18\right)$

Being understood compound kernel function nuclear matrix by two above nuclear matrix is:

$K(x_u,x_v;t_1,...,t_m)=\mathrm{\&alpha;}\&CenterDot;\exp \left(\frac{-(x_u-x_v)}{{\mathrm{\&sigma;}}^2}\right)+(1-\mathrm{\&alpha;})\&CenterDot;\underset{i=1}{\overset{m}{\&Sigma;}}{(x_u-t_i)}_{+}^p{(x_v-t_i)}_{+}^p---\left(19\right)$

Wherein, α is the weight coefficient that compound kernel function is affected by two kinds of kernel functions of regulation.For ensureing that B-RBF combines core letter Number does not change the weight of the reasonable of former mapping space, B-spline core and RBF core and is 1, now K (x_u,x_v；t₁,…,t_m) it is B-spline core and the convex combination of RBF core.When α=1, compound kernel function deteriorates to RBF kernel function；During α=0, compound kernel function moves back Turn to B-spline kernel function.By regulating the value of α, compound kernel function can be made to adapt to different data distributions.

Compound kernel function nuclear matrix K (x_u,x_v) have the property that

$K(x_u,x_v)=\left\{\begin{array}{c}(1-\mathrm{\&alpha;})\underset{i=1}{\overset{m}{\&Sigma;}}{(x_u-t_i)}_{+}^{2p},x_u=x_v\\ k(x_u,x_v)=k(x_v,x_u),x_u\&NotEqual;x_v\end{array}\right.---\left(20\right)$

B-RBF compound kernel function is the character both with analytical function, has again the character of numerical function, and merges The Local Property of RBF is the most a little.In combination core, sequence node, exponent number and the number of B-Spline Kernel function；RBF kernel function Core width cs；And combining weights factor alpha choose most important.B-RBF combination core meets the positive definite bar of Mercer theorem Part.B-RBF compound kernel function is applied in fluctuating wind speed prediction by the present invention.

Described step 3) in LSSVM fluctuating wind speed forecast model based on B-RBF compound kernel function specifically set up step Rapid as follows:

A) suitable kernel function is selected: use B-spline kernel function and RBF kernel function to carry out the B-RBF of linear combination structure Compound kernel function carries out model training as the kernel function of LSSVM；

B) according to the character of B-spline function, determine that nuclear parameter p i.e. B-spline kernel function number of times is 3, and punish parameter C, RBF The core width cs of core and the optimum value of combining weights factor alpha are all obtained by PSO algorithm；

C) determination of PSO algorithm parameter: determine scale and the evolution number of times of population, sets c₁And c₂、w_maxAnd w_minValue, Randomly generate r₁And r₂；According to step 2) in the initial ranges of model parameter that obtains of cross validation, determine that search volume is limited to [-X_max,X_max], including [-X_max,X_max] and [-g_max,g_max]；

D) PSO initialization of population: the PSO algorithm parameter set according to step c), produces the initial position X of particle with initial Speed V；

E) set up LSSVM predict regression model: the input value of incoming inspection sample, calculate fitness value；At regression problem In, the fitness value of LSSVM is sample standard deviation square error；

F) according to position and the speed of fitness value more new particle；

G) judge to evolve whether meet end condition, typically whether reach requirement as end condition with error: if being unsatisfactory for, Then return step e) and re-establish forecast model calculating particle fitness value progressive updating；If meeting end condition, then stop Iteration, exports overall situation optimum position as the optimal parameter of model；

H) LSSVM forecast model, i.e. based on B-RBF compound kernel function LSSVM model are set up by model optimal parameter.

Compared with prior art, the present invention has following prominent substantive distinguishing features and a significant advantage:

On the one hand, the advantage of LSSVM can approach arbitrarily complicated non-linear relation fully, can learn and adapt to not Determine that the behavioral characteristics of system, great convenient black box modeling function are conciliate the ability in terms of linear prediction by no means, be one Plant one of machine learning method of excellent performance, its distinctive feature can be played in a lot of fields.But how preference pattern The most there is not a generally acknowledged universal method in parameter, and model parameter plays vital work to the performance of model With.On the other hand, B-RBF combination core has coordinated B-spline core and the generalization ability of RBF core and learning capacity, at fluctuating wind Speed Forecasting Methodology has expanded a kind of new thinking.

In sum, B-RBF compound kernel function is applied to LSSVM fluctuating wind speed forecast model, as a kind of machine A kind of innovation of device learning method, great feasibility.

Accompanying drawing explanation

Fig. 1 is that fluctuating wind speed based on B-RBF compound kernel function LSSVM predicts flow chart.

Fig. 2 is the fluctuating wind speed prediction with PSO-RBF-LSSVM, B-LSSVM method of PSO-B-RBF-LSSVM method prediction The wind speed amplitude contrast of wind speed and desired value.

Fig. 3 is the fluctuating wind speed prediction with PSO-RBF-LSSVM, B-LSSVM method of PSO-B-RBF-LSSVM method prediction The auto-correlation contrast of wind speed and desired value.

Fig. 4, Fig. 5 are fluctuating wind speed and PSO-RBF-LSSVM, B-LSSVM method of PSO-B-RBF-LSSVM method prediction The cross-correlation contrast of prediction of wind speed and desired value.Wherein, Fig. 4 is interpolation lower height (30m) and desired value height (40m) Contrast, Fig. 5 is the contrast of interpolation high height (50m) and desired value height (40m).

Detailed description of the invention

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

Embodiment one:

See Fig. 1, a kind of fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine, specifically comprise the following steps that

1) select high-rise building, determine the parameter required for numerical simulation fluctuating wind speed: the building height of simulation and mould Intend each height of wind speed point, the mean wind speed of 10 meters of height, surface roughness values, ground roughness exponent, simulation phase at this Closing function, the fluctuating wind speed time series that the setting quantity generated by ARMA method numerical simulation is distributed along high uniformity, as limited Original systolic wind speed sample data；

2) PSO algorithm is used to carry out the determination of parameter.Determine scale and the evolution number of times of population, set c₁And c₂、w_maxWith w_minValue, randomly generate r₁And r₂；According to step 2) in the initial ranges of model parameter that obtains of cross validation, determine search sky Between be limited to [-X_max,X_max], including [-X_max,X_max] and [-g_max,g_max].The PSO algorithm parameter set, it is possible to produce grain The initial position X and initial velocity V of son；

3) nuclear matrix of B-RBF compound kernel function is set up, by the fluctuating wind speed sample data in known altitude region Carry out learning and training, set up LSSVM fluctuating wind speed forecast model based on B-RBF compound kernel function with this；

4) by, in the sample data of input interval two-layer to forecast model, exporting the fluctuating wind of intermediate layer corresponding time Speed, and use mean absolute error, root-mean-square error, correlation coefficient as evaluation index, is analyzed result, assess based on The accuracy of the LSSVM of B-RBF compound kernel function.

Embodiment two:

This fluctuating wind speed Forecasting Methodology based on the LSSVM model using B-RBF compound kernel function, specifically comprises the following steps that

The first step, the high-rise building selecting certain city's centre-height to be 150 meters, the point taken every 10 meters along short transverse is made For each simulation wind speed point.Other relevant parameters are shown in Table 1:

Table 1 associated analog parameter

Represent the mean wind speed that 10m highly locates.

Second step, the fluctuating wind speed time series that the some generated by ARMA method numerical simulation is distributed along high uniformity, As limited original systolic wind speed sample data.

In order to verify effectiveness based on machine learning method prediction, need a part of sample data group is used for engineering Practising, another part sample data group is for predicting the fluctuating wind speed that verifier learning method is simulated.The present invention is by arma modeling The sample data generated is divided into two parts: take front 500s fluctuating wind speed value as learning sample, 500s air speed value conduct below Checking sample.

3rd step, adds B-RBF compound kernel function in LSSVM data digging method, by some height region Fluctuating wind speed sample data carry out learning and training, set up LSSVM fluctuating wind speed based on B-RBF compound kernel function prediction mould Type.Interpolation machine learning is: take several groups of fluctuating wind speed learning samples being separated by two layer height districts as input, intermediate layer height Wind speed learning sample, as output, is trained, thus sets up forecast model, such as: 10m and 30m, 30m and 50m, 50m and Fluctuating wind speed time series sample at 70m, 70 and 90m, 90m and 110m, 110m and 130m and 130m and 150m as input, Fluctuating wind speed time series at 20m, 40m, 60m, 80m, 100m, 120m and 140m, as output, carries out learning training and predicts Inspection.Specifically comprising the following steps that of this step

1) suitable kernel function is selected.Employing B-spline kernel function and RBF kernel function are carried out linear combination structure by the present invention B-RBF compound kernel function carry out model training as the kernel function of LSSVM.

2) according to the character of B-spline function, determine that the B-spline kernel function number of times of the i.e. present invention of nuclear parameter p is 3, and punish The optimum value of parameter C, the core width cs of RBF core and combining weights factor alpha is all obtained by PSO algorithm.

3) determination of PSO algorithm parameter.Determine scale and the evolution number of times of population, set c₁And c₂、w_maxAnd w_minValue, Randomly generate r₁And r₂；According to step 2) in the initial ranges of model parameter that obtains of cross validation, determine that search volume is limited to [-X_max,X_max], including [-X_max,X_max] and [-g_max,g_max]。

4) PSO initialization of population: according to step 3) the PSO algorithm parameter that sets, it is possible to produce the initial position X of particle With initial velocity V；

5) set up LSSVM predict regression model: the input value of incoming inspection sample, calculate fitness value；At regression problem In, the fitness value of LSSVM is sample standard deviation square error；

6) according to position and the speed of fitness value more new particle；

7) judge to evolve whether meet end condition, typically whether reach requirement as end condition with error: if being unsatisfactory for, Then return step 5) re-establish forecast model calculating particle fitness value progressive updating；If meeting end condition, then stop Iteration, exports overall situation optimum position as the optimal parameter of model；

8) LSSVM forecast model, i.e. based on B-RBF compound kernel function LSSVM model are set up by model optimal parameter.

4th step, by the checking sample of input interval two-layer to LSSVM forecast model based on B-RBF compound kernel function In, the fluctuating wind speed of output intermediate layer corresponding time, and use mean absolute error MAE, root-mean-square error RMSE, correlation coefficient Result, as evaluation index, is analyzed by R, assesses the accuracy of LSSVM based on B-RBF compound kernel function.For body directly perceived Reveal the superiority of the present invention, have employed B-spline (including 1 B-spline, 3 B-spline and 5 B-spline) kernel function and Radially the LSSVM machine learning method of base (RBF) kernel function has done identical prediction work, as a comparison.

The evaluation index of 2 two kinds of kernel method simulations of table

The change of LSSVM based on B-RBF compound kernel function prediction fluctuating wind speed amplitude and desired value base as can be seen from Figure 2 This is consistent, can be seen that again that from Fig. 3 and Fig. 4 the auto-correlation function of its predictive value can coincide well with desired value.Also may be used by table 2 To find out, compared with the LSSVM prediction using single B-spline core and PSO-RBF kernel function, utilize PSO to optimize and use B-RBF Mean absolute error and the root-mean-square error of the LSSVM model of compound kernel function are the least, and correlation coefficient is the biggest.Therefore, Can be concluded that (PSO-B-RBF-LSSVM model) uses the arteries and veins of the LSSVM based on B-RBF compound kernel function of PSO optimization Dynamic forecasting wind speed more advantage.

Claims (3)

1. a fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine, it is characterised in that based on using B-RBF group Synkaryon function also uses the machine learning method of least square method supporting vector machine that particle swarm optimization PSO optimizes, predicts fluctuating wind Speed time-histories method, is learnt by the interpolation of known height fluctuating wind speed sample data and training, it was predicted that treat that simulated altitude is pulsed Wind Velocity History；Specifically comprise the following steps that

1) select high-rise building, determine the parameter required for numerical simulation fluctuating wind speed: the building height of simulation and simulation wind Each height of speed point, the mean wind speed of 10 meters of height at this, surface roughness values, ground roughness exponent, simulation are correlated with letter Number；

2) fluctuating wind speed time series that the setting quantity generated by ARMA method numerical simulation is distributed along high uniformity, as limited Original systolic wind speed sample data；And to the analogue value of power spectral density of the wind speed, auto-correlation function and cross-correlation function with corresponding The degree of agreement of desired value is tested, with checking feasibility based on arma modeling simulation high-rise building Wind Velocity History；

3) B-RBF compound kernel function is substituted Radial basis kernel function RBF and add in LSSVM data digging method, by known Fluctuating wind speed sample data in height region carries out learning and training, and sets up LSSVM based on B-RBF compound kernel function pulsation Forecasting wind speed model；

4) by, in the sample data of input interval two-layer to forecast model, exporting the fluctuating wind speed of intermediate layer corresponding time, and Using mean absolute error, root-mean-square error, correlation coefficient as evaluation index, be analyzed result, assessment is based on B-RBF The accuracy of the LSSVM of compound kernel function.

Fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine the most according to claim 1, it is characterised in that: Described step 2) in arma modeling following formula represent:

$v\left(t\right)=-\underset{k=1}{\overset{p}{\&Sigma;}}{\mathrm{\&psi;}}_k\&CenterDot;v(t-k\mathrm{\&Delta;}t)+N\left(t\right)---\left(1\right)$

In formula: (t-k Δ t) is respectively M, the space point fluctuating wind speed time series vector in t and t-k Δ t for v (t), v；p Exponent number for arma modeling；Δ t is the time step of simulation wind speed；ψ_kIt is arma modeling autoregressive coefficient matrix, for M × M rank Square formation；N (t)=L n (t), L are lower triangular matrix, n (t) be M dimension average be 0 variance be 1 separate white noise vector.

Fluctuating wind speed Forecasting Methodology based on least square method supporting vector machine the most according to claim 1, it is characterised in that: Described step 3) in the concrete establishment step of LSSVM fluctuating wind speed forecast model based on B-RBF compound kernel function as follows:

A) suitable kernel function is selected: use B-spline kernel function and RBF kernel function to carry out the B-RBF combination of linear combination structure Kernel function carries out model training as the kernel function of LSSVM；

B) according to the character of B-spline function, determine that nuclear parameter p i.e. B-spline kernel function number of times is 3, and punish parameter C, RBF core The optimum value of core width cs and combining weights factor alpha is all obtained by PSO algorithm；

C) determination of PSO algorithm parameter: determine scale and the evolution number of times of population, sets c₁And c₂、w_maxAnd w_minValue, at random Produce r₁And r₂；According to step 2) in the initial ranges of model parameter that obtains of cross validation, determine search volume be limited to [- X_max,X_max], including [-X_max,X_max] and [-g_max,g_max]；

D) PSO initialization of population: the PSO algorithm parameter set according to step c), produces initial position X and the initial velocity of particle V；

E) set up LSSVM predict regression model: the input value of incoming inspection sample, calculate fitness value；In regression problem, The fitness value of LSSVM is sample standard deviation square error；

F) according to position and the speed of fitness value more new particle；

G) judge to evolve whether meet end condition, typically whether reach requirement as end condition with error: if being unsatisfactory for, then return Return step e) and re-establish forecast model calculating particle fitness value progressive updating；If meeting end condition, then stop iteration, Overall situation optimum position is exported as the optimal parameter of model；

H) LSSVM forecast model, i.e. based on B-RBF compound kernel function LSSVM model are set up by model optimal parameter.