CN102183802A - Short-term climate forecast method based on Kalman filtering and evolution modeling - Google Patents

Abstract

The invention discloses a short-term climate forecast method based on Kalman filtering and evolution modeling. The method comprises the following steps of: establishing a linear model about a forecast factor by the Kalman filtering at first; and simulating an error sequence approaching the Kalman filtering by using a non-linear ordinary differential equation math model on the basis of the linear model a, and performing error forecast. An evolution algorithm is an evolution process for simulating the nature by using a computer, in particular a calculation method for solving complicated problems by simulating biological evolution processes, and has the intelligent characteristics of self-adaptation, self-organization, self-learning, internal parallelism and the like. The two algorithms are combined with each other, so the natural characteristic of the climate can be simulated better than being simulated by a pure linear model, so the climate forecast precision is enhanced. By the method, short-term sunshine duration, temperature and rainfall can be forecast, so future knowledge of the short-term climate can be provided.

Description

A kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling

Technical field

The invention belongs to a kind of method of Short-term Climate Forecast, relate in particular to a kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling.This method can be used for solving as fluctuate the in time prediction of bigger short-term climate such as sunshine time, temperature, is applicable to the prediction of long-term weather too.

Background technology

Along with developing rapidly of Chinese national economy, country more and more needs Short-term Climate Forecast more accurately, especially in state plan, agricultural, water conservancy and department such as prevent and reduce natural disasters.Short-term Climate Forecast is the advanced subject of international atmospheric science and field of earth sciences, also is an extremely difficult interdisciplinary difficult problem.Short-term Climate Forecast mainly faces three broad aspect difficult problems at present, at first is that the variation of weather exists a lot of uncertain factors, and short-term climate data time sequence undulatory property is too big, can't determine its accurate model.The secondth, extremely complicated to the predictive equation group of short term climatic change, and from mathematics with physically how correctly to characterize interaction between each factor, also solve fully.Thereby be faced with the difficulty of prediction theory, so Short-term Climate Forecast can not be continued to use the principle and the method for long-term climatic prediction, must be in the face of the weather system and the new theory and the method for variation development thereof of whole complexity, its technical merit also is subjected to the restriction and the restriction of other related discipline development.The deficiency of the 3rd data and data in order to disclose the both macro and micro rule of Short-term Climate Forecast, needs the historical data of a large amount of this respects.

It is accurately perfect weather numerical prediction pattern separating under condition for completeness that climatic elements observation data time series can be considered, and is the comprehensive evolution form of expression of each climatic factor and self mutual nonlinear interaction.Along with the diversification of meteorological observation method and the application of mainframe computer, particularly the meteorologist to the expansion of Climatic issues and deeply, the short-term climate numerical prediction has obtained certain progress, but most of prediction for short-term climate remains the observation data time series is carried out the linear modelling analysis, and the nonlinear model of some climatic predictions necessarily requires model nonlinear functions known, by artificial subjective estimation.Therefore the meteorological element time series that is necessary to find a kind of mathematical method to simulate objectively and has nonlinear characteristic.

Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling is in the linear model of Kalman filtering foundation and the nonlinear model results of interaction of evolutionary Modeling.Kalman filtering is adjusted regression coefficient according to data of bringing in constant renewal in and the error between the predicted value, reaches the purpose of real-time follow-up prediction.And the evolutionary Modeling method is based on genetic algorithm, and simulation organic evolution process is found the solution class computing method of challenge, and it has self-adaptation, self-organization, self study and inherent intelligent characteristics such as concurrency.Therefore the present invention is superimposed with linear model and nonlinear model, can not determine that at present the weather numerical model is under the situation of demonstration mathematic(al) representation of nonlinear partial differential equation group mesoclimate factor nonlinear interaction physical mechanism, approach the historical observation of meteorological element time series with nonlinear ordinary differential equation mathematical model district, and and then make Short-term Climate Forecast.They have the ability of continuous adjustment model parameter of the real time data utilized or expression formula simultaneously, make precision of prediction higher.At present, do not see have document openly to report based on the Short-term Climate Forecast of Kalman filtering and evolutionary Modeling.

Summary of the invention

The objective of the invention is to overcome above-mentioned prior art deficiency, a kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling is provided, the mode of utilizing Kalman filtering to combine with evolutionary Modeling, describe linear relationship between the predictor with the Kalman filtering recurrence system, constantly adjust regression coefficient according to its predicated error; The nonlinear model of being set up at the Kalman filtering error that stack is described by evolutionary Modeling on linear model based simultaneously, thus optimize forecast model, improve precision of prediction.

In order to reach above purpose, the present invention takes following technical scheme to be achieved:

Comprise the following steps:

A) historical data of predictor in the collection Climatic Forecast Models comprises in recent years sunshine time, temperature, relative humidity and rainfall amount;

B) determine predictor, put the historical data relevant with predictor in order, with the historical data staging treating, as a data project, the data after will handling simultaneously are divided into initial value and calculate sample and detect sample two parts with the combined action result of every segment data;

C) according to above-mentioned sample calculation Kalman filtering initial value:

Y _t＝X _tβ _t+e _t

Following formula is that Kalman filtering is measured equation, at first utilizes multiple linear regression to calculate regression coefficient β ₀,

Calculate dynamic noise variance battle array W again and measure noise variance matrix V;

D) set up Kalman's recurrence model according to above-mentioned sample: utilize step C) in the initial value and the Kalman's stepping type that calculate the data that detect sample are predicted, and compare with detecting sample, obtain the predicated error time series;

E) above-mentioned predicated error is carried out pre-service:

$x\left(t\right)=\stackrel{\‾}{x}\left(t\right)+\tilde{x}\left(t\right)$

$\tilde{x}\left(t\right)=x\left(t\right)-\stackrel{\‾}{x}\left(t\right)$

Predicated error is divided into smooth part and coarse part, and the hypothesis smooth part is by the macroclimate controlling factors, coarse part is by microcosmic climatic factor control, adopts following steps F respectively at decomposed data) and step G) mathematical model describe;

F) at step e) in smooth part time series item, come the feasible solution of problem of representation with chromosome, the form and the parameter that comprise feasible solution, utilize genetic manipulation in solution space, to search for then, select the superior and eliminate the inferior according to the sum of square of deviations between fitting expression and the actual value at last, try to achieve final separating, i.e. the non-linear expressions that match smooth part time series is best;

G) at step e) in coarse part time series item, with nature base small echo it is analyzed, from these time serieses, find out it and be subjected to the cyclic swing rule of climatic factor under influencing, realize coarse part seasonal effect in time series match and forecast function;

H) with step D) in the Kalman filtering and the step F that realize) and step G) in the evolutionary Modeling of carrying out at the Kalman filtering error respectively respectively climatic data time series models are separately done next step prediction with basic naturally small echo, and it is superimposed to predict the outcome, thereby realizes the Short-term Climate Forecast of Kalman filtering and evolutionary Modeling.

With step D) in, when the Kalman filtering recurrence model was predicted detecting sample, its Kalman filtering regression coefficient was made real-time adjustment according to predicated error.

Step e) in, can adjust the value of smooth parameter l as the case may be, l can be used for regulating time series

Smooth degree, l is big more,

Smooth more.

Step F) in, the Differential Equation Model that chromosome is represented is a tree expression formula, and its differential equation is separated by the Runge-Kutta method and obtained.

Step G) in, at the modeling of seasonal effect in time series coarse part, employing be multiple dimensioned natural fractal model.

Step H) in, Short-Range Climatic Prediction is the mode that linear prediction model combines with the nonlinear prediction model.

The Climatic Forecast Models that the present invention's proposition combines with nonlinear ordinary differential equation based on linear Kalman filtering: set up the linear relationship between each predictor in the climatic prediction with Kalman filtering, use the non-linear behavior of nonlinear differential equation match predictor simultaneously, wherein nonlinear differential equation adopts the evolutionary Modeling method to try to achieve, the Kalman filtering parameter and the differential equation all move in time and do instant adjustment, can better reflect premeasuring rule over time, improve precision of prediction.

Description of drawings

Fig. 1 is a modeling process flow diagram of the present invention.

Fig. 2 is the ordinary differential equation tree structure diagram.

Fig. 3 is an evolutionary Modeling process flow diagram of the present invention.

Fig. 4 is of the present invention based on basic naturally wavelet algorithm process flow diagram.

Below in conjunction with accompanying drawing technical scheme of the present invention is described in further detail.

Embodiment

With reference to Fig. 1, Fig. 2, Fig. 3, shown in Figure 4, a kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling comprises the following steps:

A) historical data of predictor in the collection Climatic Forecast Models mainly comprises in recent years sunshine time, temperature, relative humidity and rainfall amount etc.;

B) determine predictor, put the historical data relevant in order with predictor.With the historical data staging treating, with the combined action result of every segment data as a data project.Data after will handling simultaneously are divided into initial value and calculate sample and detect sample two parts;

C) according to above-mentioned sample calculation Kalman filtering initial value:

Y _t＝X _tβ _t+e _t

Following formula is that Kalman filtering is measured equation, at first utilizes multiple linear regression to calculate regression coefficient β ₀,

Calculate dynamic noise variance battle array W again and measure noise variance matrix V.

D) set up Kalman's recurrence model according to above-mentioned sample: utilize step C) in the initial value and the Kalman's stepping type that calculate the data that detect sample are predicted, and compare with detecting sample, obtain the predicated error time series;

E) above-mentioned predicated error is carried out pre-service:

$x\left(t\right)=\stackrel{\‾}{x}\left(t\right)+\tilde{x}\left(t\right)$

$\tilde{x}\left(t\right)=x\left(t\right)-\stackrel{\‾}{x}\left(t\right)$

Predicated error is divided into smooth part and coarse part, and the hypothesis smooth part is by Macroscopic Factors control, coarse part is by microcosmic influence factors control, adopts following steps F respectively at decomposed data) and step G) mathematical model describe;

F) at step e) in smooth part time series item, come the feasible solution of problem of representation with chromosome, the form and the parameter that comprise feasible solution, utilize genetic manipulation in solution space, to search for then, select the superior and eliminate the inferior according to the sum of square of deviations between fitting expression and the actual value at last, try to achieve final separating, i.e. the non-linear expressions that match smooth part time series is best;

G) at step e) in coarse part time series item, with nature base small echo it is analyzed, from these time serieses, find out its microcosmic rule, realize coarse part seasonal effect in time series match and forecast function;

H) with step D) in the Kalman filtering and the step F that realize) and step G) in the evolutionary Modeling of carrying out at the Kalman filtering error respectively respectively climatic data time series models are separately done next step prediction with basic naturally small echo, and it is superimposed to predict the outcome, thereby realizes the Short-term Climate Forecast of Kalman filtering and evolutionary Modeling.

In the such scheme, step D) described Kalman filtering recurrence model at climatic prediction is:

${\hat{Y}}_t=X_t{\widehat{\mathrm{\β}}}_{t-1}---\left(1\right)$

R _t＝C _t-1+WY (2)

${\mathrm{\σ}}_t=X_t{R}_t{X}_t^T+V---\left(3\right)$

$A_t=R_t{X}_t^T{\mathrm{\σ}}_t^{-1}---\left(4\right)$

${\widehat{\mathrm{\β}}}_t={\widehat{\mathrm{\β}}}_{t-1}+A(Y_t-{\hat{Y}}_t)---\left(5\right)$

$C_t=R_t-A_t{\mathrm{\σ}}_t{A}_t^T---\left(6\right)$

In (1) formula be predictive equation,

Be predicted value, X _tBe predictor,

Being regression coefficient, is β _T-1Estimated value.C in the formula (2) _T-1For

The error variance battle array, W is ε _tVariance matrix.σ in the formula (3) _tBe prediction error variance battle array, R _tBe the recursion value

The error variance battle array,

Be X _tTransposed matrix, V is e _tVariance matrix.A in the formula (4) _tBe gain matrix, Be σ _tInverse matrix.Y in the formula (5) _tIt is the actual measured value of predicted value.Formula (5) and formula (6) according to weather report the error recursion next step

And C _t

In the such scheme, it is step F) described that what adopt at smooth part seasonal effect in time series ordinary differential equation group serial evolutionary Modeling algorithm is two-stage evolutionary Modeling thought, promptly in GP (genetic programming) technical optimization model structure, nested process with GA (genetic algorithm) Optimization Model parameter, its basic step is as follows:

1) initialization model population

2) adopt GP technical optimization model structure

3) model is carried out simplicity and standardization processing

4) adopt the GA algorithm that the parameter of model is optimized

5) check whether satisfy end condition,, then jump to step 2 if do not have) continue to carry out, export the best model of matching degree in the population at last.

In the such scheme, step G) the basic naturally wavelet analysis of described coarse part seasonal effect in time series, the main thought of its expression is: at coarse part time series X=(x (t ₁), x (t ₂) ..., x (t _i) ..., x (t _n)) ^T, sort successively by every group of k data, constitute two-dimensional array x ₂(1:m _k, 1:k), wave function then

Value k the time interval is:

Naturally basic small echo is from wavelength

Beginning, search successively

Basic naturally small echo.

$F=\left(\frac{D^2}{l-1}\right)/\left(\frac{S^2}{n-1}\right)$

Wherein: ${\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000049696670000012.png"\; state="\{\{state\}\}">D</figure-callout>}}^2=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{m}_k{({{\tilde{x}}_i}^{\left(w\right)}-\stackrel{\&OverBar;}{x})}^2,$ ${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA0000049696670000012.png"\; state="\{\{state\}\}">S</figure-callout>}}^2=\underset{j=1}{\overset{m_k}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{(x_2(j,i)-{{\tilde{x}}_i}^{\left(w\right)})}^2$

Satisfy degree of freedom for (l-1, F n-l) distributes, if F 〉=F _a(α gets 0.05) just deducted this basic naturally small echo with the k-1 time residual sequence and launched in the cycle of time domain, obtains the k time residual error time series, and successively decreasing with wavelength then stops up to k=2.

In order to verify the superiority of the Short-term Climate Forecast method that the present invention is based on Kalman filtering and evolutionary Modeling, the present invention is described in further detail below in conjunction with embodiment.

The present invention is based on the Short-term Climate Forecast method of Kalman filtering and evolutionary Modeling, the modeling principle of modeling of the present invention is, at first multiple linear regression utilizes the climate history data to determine the Kalman filtering initial value, sets up Kalman filtering recurrence system model in conjunction with climate history data and initial value then.Utilize evolutionary Modeling and basic naturally small echo that the error between Kalman filtering predicted value and the actual measured value is optimized again; overcoming merely the defective of the linear model of setting up based on Kalman filtering, thereby realize Kalman filtering and evolutionary Modeling hybrid modeling method.To improve the Short-term Climate Forecast precision.

At above-mentioned particular problem, the Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling of the present invention's design specifically describes as follows:

1) data acquisition: at a large amount of historical climate data of climatic prediction, mainly obtain from the weather station, weather comprises the sunshine time, medial temperature, relative humidity of every day in former years etc.

2) determine the Kalman filtering initial value:, must at first determine the regression coefficient in the Kalman filtering recurrence system in order to make up the Kalman filtering forecast model

Error variance battle array C ₀, dynamic noise variance battle array W, measure the initial value of noise variance matrix V.At first determine predictor, set up multiple linear regression equations, separate by equation of linear regression according to known climatic data according to premeasuring:

Y＝Xβ+ε

β＝A ^-1B＝(X ^TX) ^-1(X ^TY)

Obtain the regression coefficient initial value.

C ₀Determine: C ₀Be

The error variance battle array, directly be taken as here: C ₀=[0] _{M * m}

W determines: W is dynamic noise ε _tVariance matrix, suppose that here it is a white noise, W can be expressed as:

$W=\left[\begin{array}{cccc}{\mathrm{\&omega;}}_1& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&omega;}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& {\mathrm{\&omega;}}_m\end{array}\right]$

Here

Way according to the multiple linear regression evaluation is tried to achieve, and we choose here is weather measurement data in 2004, like this

V determines: V is e _tThe variance battle array, suppose that equally it is a white noise, this V can be expressed as:

$V=\left[\begin{array}{cccc}{\mathrm{<figure-callout\; id="1"\; label="v"\; filenames="HDA0000049696670000012.png,HDA0000049696670000021.png"\; state="\{\{state\}\}">v</figure-callout>}}_1& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ 0& {\mathrm{<figure-callout\; id="2"\; label="v"\; filenames="HDA0000049696670000012.png"\; state="\{\{state\}\}">v</figure-callout>}}_2& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& v_m\end{array}\right]$

Utilize n the component of predictand Y to set up regression equation, obtain n residual error (q ₁, q ₂..., q _n), so:

$V=\left[\begin{array}{cccc}\frac{{\mathrm{<figure-callout\; id="1"\; label="q"\; filenames="HDA0000049696670000012.png,HDA0000049696670000021.png"\; state="\{\{state\}\}">q</figure-callout>}}_1^2}{k-m-1}& 0& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ 0& \frac{{\mathrm{<figure-callout\; id="2"\; label="q"\; filenames="HDA0000049696670000012.png"\; state="\{\{state\}\}">q</figure-callout>}}_2^2}{k-m-1}& \&CenterDot;\&CenterDot;\&CenterDot;& 0\\ \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;& \&CenterDot;\&CenterDot;\&CenterDot;\\ 0& 0& \&CenterDot;\&CenterDot;\&CenterDot;& \frac{q_n^2}{k-m-1}\end{array}\right]$

Wherein k is a sample size, k＞m+1.

3) set up the Kalman filtering forecast model: the Kalman filtering forecast model is based upon on the basis of following recurrence system:

${\hat{Y}}_t=X_t{\widehat{\mathrm{\&beta;}}}_{t-1}---\left(1\right)$

R _t＝C _t-1+WY (2)

${\mathrm{\&sigma;}}_t=X_t{R}_t{X}_t^T+V---\left(3\right)$

$A_t=R_t{X}_t^T{\mathrm{\&sigma;}}_t^{-1}---\left(4\right)$

${\widehat{\mathrm{\&beta;}}}_t={\widehat{\mathrm{\&beta;}}}_{t-1}+A(Y_t-{\hat{Y}}_t)---\left(5\right)$

$C_t=R_t-A_t{\mathrm{\&sigma;}}_t{A}_t^T---\left(6\right)$

In (1) formula be predictive equation,

Be predicted value, X _tBe predictor,

Being regression coefficient, is β _T-1Estimated value.C in the formula (2) _T-1For

The error variance battle array, W is ε _tVariance matrix.σ in the formula (3) _tBe prediction error variance battle array, R _tBe the recursion value The error variance battle array,

Be X _tTransposed matrix, V is e _tVariance matrix.A in the formula (4) _tBe gain matrix,

Be σ _tInverse matrix.Y in the formula (5) _tIt is the actual measured value of predicted value.Formula (5) and formula (6) according to weather report the error recursion next step

And C _t

Carry out Short-term Climate Forecast by the Kalman filtering recurrence system, and deduct predicted value, thereby obtain time series about prediction difference with measured value.

4) evolutionary Modeling: for further improving the precision of prediction of Kalman filtering, the present invention adopts the nonlinear model that stack is set up by evolutionary Modeling on the basis of Kalman filtering linear model.Evolutionary Modeling is with the evolutionary process of computer simulation the Nature, with the feasible solution that chromosome comes problem of representation, carries out genetic manipulation then and searches in solution space, selects excellent individual, and a generation generation develops like this, finally tries to achieve the best feasible solution of problem.

Fig. 3 is an evolutionary Modeling process flow diagram of the present invention.

The present invention adopts the evolution algorithmic of genetic program design, is expressed as follows the differential equation with tree:

$\frac{{\mathrm{dy}}^{\left(n\right)}\left(t\right)}{\mathrm{dt}}=f(t,y^{\left(1\right)},y^{\left(2\right)},...,y^{\left(n\right)})$

For example will

y ⁽⁴⁾(t)＝y ⁽³⁾+4y ⁽¹⁾*y ⁽²⁾-t*e ^y

Be expressed as Fig. 2 form, corresponding to the content regions nature manifold D={R of the leaf node of setting, y ₁, y ₂, y ₃..., y _n, the content of the nonleaf node of tree is taken from computing collection O={+ ,-, * ,/, exp, sin, cos, ln} is so the model space is determined by the height H of manifold D, computing collection O and number.When tree type expression formula determines that promptly available Runge-Kutta method calculates separates y ^*(t) at t constantly in succession ₂..., t _mValue matrix Y ^*Thereby, computation model error of fitting: ‖ Y-Y ^*‖ after best model is determined, just can use t to assess the quality of this model _mValue do starting condition and predict.

Therefore the evolutionary Modeling key step is:

(1) determines the parameter (comprising population number P, each population scale n, maximum evolution algebraically Maxgeno, maximal tree depth D etc.) of evolutionary Modeling and some controlled variable of parallel algorithm (comprising the mobility ρ between population, migration generation frequency g etc.);

(2) each population carries out the process of evolutionary Modeling independently, comprises initialization, structure of models optimization and parameter optimization (carrying out selection-hybridization-variation) of population and individual fitness value assessment.Each population carries out message exchange with other populations in the process of evolutionary Modeling simultaneously:

1. every g generation the m in the current population best individuality sent to other δ population (its copy of reservation in former population).Wherein m is by mobility ρ and sub-population size n _cDecision.

M of 2. being subjected to be sended over by other populations every the g pickup is individual, and replaces m individuality the poorest in the current population.

(3) when population runs to maximum algebraically Maxgeno, program stops, and selects optimum individual as final forecast model.

5) natural somatotype model: Fig. 4 is of the present invention based on basic naturally wavelet algorithm process flow diagram, at coarse part time series X=(x (t ₁), x (t ₂) ..., x (t _i) ..., x (t _n)) ^T, sort successively by every group of k data, constitute two-dimensional array x ₂(1:m _k, 1:k), wave function then

Value k the time interval is:

Naturally basic small echo is from wavelength

Beginning, search successively

Basic naturally small echo,

$F=\left(\frac{D^2}{l-1}\right)/\left(\frac{S^2}{n-1}\right)$

Wherein: ${\mathrm{<figure-callout\; id="2"\; label="D"\; filenames="HDA0000049696670000012.png"\; state="\{\{state\}\}">D</figure-callout>}}^2=\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{m}_k{({{\tilde{x}}_i}^{\left(w\right)}-\stackrel{\&OverBar;}{x})}^2,$ ${\mathrm{<figure-callout\; id="2"\; label="S"\; filenames="HDA0000049696670000012.png"\; state="\{\{state\}\}">S</figure-callout>}}^2=\underset{j=1}{\overset{m_k}{\mathrm{\&Sigma;}}}\underset{i=1}{\overset{l}{\mathrm{\&Sigma;}}}{(x_2(j,i)-{{\tilde{x}}_i}^{\left(w\right)})}^2$

Satisfy degree of freedom for (l-1, F n-l) distributes, if F 〉=F _a(α gets 0.05) just deducted this basic naturally small echo with the k-1 time residual sequence and launched in the cycle of time domain, obtains the k time residual error time series, and successively decreasing with wavelength then stops up to k=2.

6) carry out climatic prediction with institute's established model: the Kalman filtering forecast model among the present invention and the evolutionary Modeling of carrying out at the Kalman filtering error and basic naturally small echo are done next step prediction to climatic data time series models separately respectively, and it is superimposed to predict the outcome, thereby realizes the Short-term Climate Forecast of Kalman filtering and evolutionary Modeling.

Claims (6)

1. the Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling is characterized in that, comprises the following steps:

A) historical data of predictor in the collection Climatic Forecast Models comprises in recent years sunshine time, temperature, relative humidity and rainfall amount;

B) determine predictor, put the historical data relevant with predictor in order, with the historical data staging treating, as a data project, the data after will handling simultaneously are divided into initial value and calculate sample and detect sample two parts with the combined action result of every segment data;

C) according to above-mentioned sample calculation Kalman filtering initial value:

Y _t＝X _tβ _t+e _t

Following formula is that Kalman filtering is measured equation, at first utilizes multiple linear regression to calculate regression coefficient β ₀,

Calculate dynamic noise variance battle array W again and measure noise variance matrix V;

D) set up Kalman's recurrence model according to above-mentioned sample: utilize step C) in the initial value and the Kalman's stepping type that calculate the data that detect sample are predicted, and compare with detecting sample, obtain the predicated error time series;

E) above-mentioned predicated error is carried out pre-service:

$x\left(t\right)=\stackrel{\&OverBar;}{x}\left(t\right)+\tilde{x}\left(t\right)$

$\tilde{x}\left(t\right)=x\left(t\right)-\stackrel{\&OverBar;}{x}\left(t\right)$

Predicated error is divided into smooth part and coarse part, and the hypothesis smooth part is by the macroclimate controlling factors, coarse part is by microcosmic climatic factor control, adopts following steps F respectively at decomposed data) and step G) mathematical model describe;

F) at step e) in smooth part time series item, come the feasible solution of problem of representation with chromosome, the form and the parameter that comprise feasible solution, utilize genetic manipulation in solution space, to search for then, select the superior and eliminate the inferior according to the sum of square of deviations between fitting expression and the actual value at last, try to achieve final separating, i.e. the non-linear expressions that match smooth part time series is best;

G) at step e) in coarse part time series item, with nature base small echo it is analyzed, from these time serieses, find out it and be subjected to the cyclic swing rule of climatic factor under influencing, realize coarse part seasonal effect in time series match and forecast function;

H) with step D) in the Kalman filtering and the step F that realize) and step G) in the evolutionary Modeling of carrying out at the Kalman filtering error respectively respectively climatic data time series models are separately done next step prediction with basic naturally small echo, and it is superimposed to predict the outcome, thereby realizes the Short-term Climate Forecast of Kalman filtering and evolutionary Modeling.

2. a kind of Short-term Climate Forecast method according to claim 1 based on Kalman filtering and evolutionary Modeling, it is characterized in that, with step D) in, when the Kalman filtering recurrence model was predicted detecting sample, its Kalman filtering regression coefficient was made real-time adjustment according to predicated error.

3. a kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling according to claim 1 is characterized in that step e) in, can adjust the value of smooth parameter l as the case may be, l can be used for regulating time series

Smooth degree, l is big more, Smooth more.

4. a kind of Short-term Climate Forecast method according to claim 1 based on Kalman filtering and evolutionary Modeling, it is characterized in that, step F) in, the Differential Equation Model that chromosome is represented is a tree expression formula, and its differential equation is separated by the Runge-Kutta method and obtained.

5. a kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling according to claim 1 is characterized in that step G) in, at the modeling of seasonal effect in time series coarse part, employing be multiple dimensioned natural fractal model.

6. a kind of Short-term Climate Forecast method based on Kalman filtering and evolutionary Modeling according to claim 1 is characterized in that step H) in, Short-Range Climatic Prediction is the mode that linear prediction model combines with the nonlinear prediction model.

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