CN102651095A - Wind speed time series forecasting method based on unstable period - Google Patents

Abstract

The invention belongs to the field of time series forecast analysis, and particularly discloses a wind speed time series forecasting method based on an unstable period. The method comprises the following steps of: performing phase space reconstruction on a wind speed time series with a chaotic characteristic, determining the delay time of the phase space reconstruction by a mutual information method, determining the optimal unstable period and embedding dimension by solving a target function, and forecasting and analyzing a wind speed at a future time with a value nearby the unstable period. The wind speed time series forecasting method based on the unstable period mainly aims to be applied to the field of the forecast analysis for the wind speed time series with chaotic characteristic.

Description

A kind of wind speed time series forecasting method based on the unstable cycle

Technical field

The invention belongs to the time series forecasting analysis field, relate to a kind of method that is used for the wind speed time series forecasting, particularly a kind of to having the wind speed time series of chaotic characteristic, through finding the solution the method for best unstable cycle realization forecast analysis.

Background technology

Serious day by day along with global energy anxiety and environmental pollution; The development and use of wind energy obtain the generally attention of various countries; Wind energy is a kind of regenerative resource of cleaning, and the development wind-power electricity generation becomes a kind of effective measures of improving energy structure, reducing environmental pollution and preserve the ecological environment.But wind speed has intermittence, randomness and probabilistic characteristics, and this has proposed challenge to the wind-electricity integration technology.At present, one of key technical problem that solves wind-electricity integration is exactly a forecasting wind speed, and effectively forecasting wind speed can make power scheduling department in time adjust operation plan, thereby guarantees the quality of power supply, reduces the margin capacity of system, reduces the Operation of Electric Systems cost

At present, existing forecasting wind speed method has: persistence forecasting method, Kalman filtering method, time series method and neural net method etc.The persistence forecasting method will be recently any wind speed observed reading as the predicted value of any down.This method is simple, is traditional prediction methods, the benchmark of other Forecasting Methodologies of Chang Zuowei.There is the advantage that on-the-fly modifies the prediction weights in Kalman filtering method, relies on the prediction recurrence equation can obtain higher precision, but sets up Kalman's state equation and measure comparatively difficulty of equation.The quantity of information that time series method utilizes is less, model to decide rank method directiveness not strong.Artificial neural network is found the solution very effectively the complex nonlinear problem, but also exists speed of convergence slow, and data are huge, are absorbed in defectives such as local minimum easily.In addition, some researchers are often being contained chaotic characteristic through wind speed seasonal effect in time series dynamical property analysis is found in the wind series.Can combine the phase space reconfiguration theory to carry out forecast analysis research for wind speed time series, but there is the problem that is difficult for choosing in the parameter of phase space reconfiguration with chaotic characteristic.

Therefore, to the character of wind series self, the prediction analysis method that designs a kind of simple and feasible has important use and is worth.

Summary of the invention

Technical matters to be solved by this invention is, designs a kind of wind speed time series forecasting analytical approach, can realize forecast analysis to the wind speed time series with chaotic characteristic.

The technical scheme that the present invention adopted is: a kind of wind speed time series forecasting method based on the unstable cycle; Wind speed time series to having chaotic characteristic conducts a research; Utilize known wind speed time series to carry out phase space reconfiguration; Utilize mutual information method to confirm the time delay of phase space reconfiguration, confirm the unstable cycle of the best and embed dimension, utilize near last value of unstable cycle to realize the forecast analysis of wind speed constantly in future through finding the solution target function.

The objective of the invention is to propose a kind of wind speed time series forecasting analytical approach based on the unstable cycle; Realize forecast analysis through finding the solution the unstable cycle information that contains in the wind speed time series with chaotic characteristic, thereby improve the estimated performance of wind series following wind speed.

Embodiment

Below in conjunction with embodiment the present invention is done further explain.

According to chaology, chaotic motion has infinite a plurality of unsettled periodic orbit, therefore can carry out phase space reconfiguration to the wind speed time series with chaotic characteristic, and think that the wind speed phase space after the reconstruct also has the dynamic behavior similar with original system.After wind series continued a period of time, wind series can arrive near certain unstable periodic orbits, and promptly the air speed value of this moment and near the value the last unstable cycle are very approaching.Therefore can near the air speed value the last cycle be predicted as the air speed value of this moment.

Phase space reconfiguration is the basis of Chaotic Time Series Analysis, for the wind speed time series with chaotic characteristic { x (i) }, and i=1,2 ..., n is m if embed dimension, and be τ time delay, and then phase space reconstruction does

Y(i)＝{x(i)，x(i+τ)，...，x(i+(m-1)τ)} (1)

Wherein, i=1,2 ..., N; N=n-(m-1) τ; N is the seasonal effect in time series sampling number.Time delay with embed the quality that choosing of dimension directly have influence on phase space reconfiguration and the precision of prediction of sequence.The present invention selects mutual information method to choose time delay.

A seasonal effect in time series mutual information can be expressed as:

$I(Q,S)=H\left(Q\right)-H\left(Q\right|S)$

(2)

$=-\underset{i}{\mathrm{\Σ}}P\left(q_i\right)\log P\left(q_i\right)-\underset{j}{\mathrm{\Σ}}P\left(s_j\right)+\underset{i}{\mathrm{\Σ}}\underset{j}{\mathrm{\Σ}}P(s_j,q_i)\log P(s_j,q_i)$

Wherein, P (q _i) and P (s _j) be respectively incident q among Q and the S _i, and s _jProbability.P (s _j, q _i) be incident s _jWith incident q _iThe joint distribution probability.Confirmed as optimum delay time pairing time delay when seasonal effect in time series mutual information function reached minimum value first.

If the wind speed time series of being studied has chaotic characteristic, through the dynamics of the reducible system of phase space reconstruction.Be that phase space after the reconstruct will have chaotic attractor and the dynamics similar with original system.Because chaos system has infinite a plurality of unsettled periodic orbit.After chaos system persistent movement a period of time, system can move near certain unstable periodic orbits.The present invention's research has the wind speed seasonal effect in time series forecasting problem of chaotic characteristic, and therefore near the value the unstable periodic orbits capable of using is predicted the value of following sequence.Employing formula (3) is asked for the cycle of the best unstable periodic orbits of phase space after the reconstruct.

$J(m,T)=\frac{\underset{i=0}{\overset{n-(m-1)\mathrm{\τ}-T}{\mathrm{\Σ}}}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}|\frac{\underset{k=-L}{\overset{L}{\mathrm{\Σ}}}x(T+i+\mathrm{j\τ}+k)}{2L+1}-x(i+\mathrm{j\τ})|}{m(n-(m-1)\mathrm{\τ}-T)}---\left(3\right)$

In the formula, n is the length of sequence, and T is the unstable cycle of chaos time sequence, and m is for embedding dimension.M and T between the given area in, corresponding different J.The T of correspondence and m elected the best unstable cycle and embedding dimension of chaos time sequence phase space reconstruction as when J got minimum value.

The best unstable cycle of system is in case confirm that the i of system predicted value x (i) constantly can realize prediction by formula (4) by near the numerical value the last unstable cycle in a short time.

$x\left(i\right)=\frac{\underset{k=-L}{\overset{L}{\mathrm{\Σ}}}x(i-T+k)}{2L+1}+e---\left(4\right)$

Wherein, e is a predicated error, in the actual computation process, can adopt the error of a moment predicted value and actual value to estimate.

Embodiment

Utilize said method that the wind series in somewhere is carried out forecast analysis, air speed data was whenever gathered once at a distance from 10 minutes, utilized mutual information method to ask for delay time T=4.Utilize formula (3) to try to achieve best dimension m=5, best unstable cycle T=108 of embedding.The Lyapunov index that utilizes the Wolf method to try to achieve this sequence is 0.271, has chaotic characteristic.Utilize the inventive method, persistence forecasting method and ARMA (2,1) modelling that following 500 minutes wind speed is carried out forecast analysis.The average error that the inventive method gained predicts the outcome is 2.3161, and square error is 0.41841, and error sum of squares is 492.67; The average error that persistence forecasting method gained predicts the outcome is 3.27, and square error is 0.51836, and error sum of squares is 671.75, and the average error that ARMA (2,1) method gained predicts the outcome is 2.6978, and square error is 0.45364, and error sum of squares is 514.48.Through error performance relatively, it is thus clear that the inventive method has good estimated performance.

Claims (3)

1. wind speed time series forecasting method based on the unstable cycle; It is characterized in that utilizing known wind speed time series to carry out phase space reconfiguration with chaotic characteristic; Utilize mutual information method to confirm the time delay of phase space reconfiguration; Confirm the unstable cycle of the best and embed dimension through finding the solution target function, utilize near last value of unstable cycle to realize the forecast analysis of wind speed constantly in future.

2. a kind of wind speed time series forecasting method based on the unstable cycle according to claim 1 is characterized in that, described definite best unstable cycle with the target function that embeds dimension is:

$J(m,T)=\frac{\underset{i=0}{\overset{n-(m-1)\mathrm{\τ}-T}{\mathrm{\Σ}}}\underset{j=0}{\overset{m}{\mathrm{\Σ}}}|\frac{\underset{k=-L}{\overset{L}{\mathrm{\Σ}}}x(T+i+\mathrm{j\τ}+k)}{2L+1}-x(i+\mathrm{j\τ})|}{m(n-(m-1)\mathrm{\τ}-T)}---\left(1\right)$

Wherein, n is the length of sequence, and T is the unstable cycle of chaos time sequence; M is for embedding dimension; M and T between the given area in, corresponding different J, corresponding T and m elected the best unstable cycle and embedding dimension of chaos time sequence phase space reconstruction as when J got minimum value.

3. a kind of wind speed time series forecasting method based on the unstable cycle according to claim 1 is characterized in that, the described following prediction of wind speed is constantly asked for by following formula:

$x\left(i\right)=\frac{\underset{k=-L}{\overset{L}{\mathrm{\Σ}}}x(i-T+k)}{2L+1}+e---\left(2\right)$

Wherein, e is a predicated error, in the actual computation process, can adopt the error of a moment predicted value and actual value to estimate.