CN101852871A - Short-term climate forecasting method based on empirical mode decomposition and numerical value set forecasting - Google Patents

Abstract

The invention discloses a short-term climate forecasting method based on empirical mode decomposition and numerical value set forecasting. The invention adopts a way of integrating a numerical value set forecasting technology and a mean generating function stepwise regression model and combines a new empirical mode decomposition (EMD) method for processing a data sequence. The short-term climate forecasting method comprises the following steps of: firstly, decomposing a non-stationary climate data sequence into a stationary intrinsic mode function (IMF) component with multi-scale feature; then constructing different forecasting models for each IMF by a way of set forecasting and stepwise regression analysis; and finally linearly fitting to form a forecasting result. When the system is used for short-term forecasting, a user can cut out the appointed sequence length and forecasting length according to the actual data demand and vnlrpfalgp select a forecasting model parameter in a set forecasting process. Compared with a direct or single forecasting method, the invention has better forecasting capacity for the variation trend of climate and sudden climate.

Description

Short-term Climate Forecast method based on empirical modal decomposition and numerical value DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM

Technical field

The present invention relates to a kind of based on empirical modal decompose and ensemble forecast technique to the short-term forecasting (5-10) of climosequence data (20-50), be applicable to that sudden variation needs responsive situation about holding to weather, as diastrous weathers such as frost (cooling), heavy rains.

Background technology

Climatic prediction is an important branch of atmospheric science, and climate change prediction then is meteorological stations at different levels one of the main content of Short-term Climate Forecast of commencing business.

Weather system is a kind of dissipation, has the high-order nonlinear system in a plurality of unstable sources that its complicated inside interacts and freely changes and caused climatic variability and complicacy, has also caused the multiple dimensioned characteristic of climate change ^[1-3]Because we are very few to the understanding in lithosphere, hydrosphere, cryosphere, biosphere (comprising mankind's activity) at present, data accuracy that is accumulated and completeness are very not enough, therefore with regard to the present mankind to regard to the understanding of weather system, it is impossible setting up the nonlinear kinetics system of equations that accurate reflection weather system changes ^[4], this has just brought great difficulty to the kinetic theory research of climate change prediction.

Just present, we have two aspects at the basis of carrying out Short-term Climate Forecast work of relying: the one, tight supervision has been carried out in climate change, utilize various instruments to carry out time sight in the world, thereby accumulated mass data about its past and present situation; The 2nd, weather system is a physical system, by the research of physics and mathematics, has known the physics law that some climate changes should be followed, and can represent with mathematical linguistics ^[5,6]In fact second method is exactly a kind of time series forecasting method.

Time series is meant with the successive observed value of a kind of phenomenon on different time arranges the set of number sequence that forms.The basic thought of time series forecasting method is: when change the future of a phenomenon of prediction, predict future with the past behavior of this phenomenon.Promptly disclose the time dependent rule of phenomenon, this rule is extended to future by the seasonal effect in time series historical data, thereby to making prediction the future of this phenomenon.Along with development of computer, particularly developed the classical modeling of Model Identification, parameter estimation and the diagnostic check of a whole set of random time sequence in nineteen sixty-eight since famous statistician Box and Jenkins ^[7]Since the method, the development of time series forecasting is very fast, in the existing application widely of every field such as meteorology, astronomy, electric power, medical science, biology, economy, finance and computing machine, and demonstrate great vitality and importance day by day, become an independently important branch of mathematics.Existing so far many experts, scholar are engaged in the research of this respect, and have set up more complete theory and the application system of a cover ^[8,9]

The present invention is a kind of Forecasting Methodology at weather, belong to a kind of of time series forecasting, and consider the singularity of weather system, two kinds of processing in forecasting process, have been added to the data sequence, be empirical modal decompose (Empirical ModeDecomposition, EMD) and ensemble forecast technique.The EMD method is to a signal (or its derivative in essence, decide on required decomposition precision) carry out tranquilization and handle, consequently the fluctuation of different scale in the signal or trend are decomposed step by step and come, produce a series of data sequences with different characteristic yardstick, each sequence is called an intrinsic mode functions (Intrinsic Mod Function, IMF) component, different components become stationary signal, make that the processing such as data prediction of back are reasonable more, effective.DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM is incorporated in the numerical forecasting at single-mode forecast uncertainty, it has filtered the random element in the forecast, thereby can obtain a metastable forecast conclusion, among the present invention sequential value is handled according to preassigned number of members, reconfigure and ask ensemble average again, reduce in the hope of the probability that obtains unstable solution.

List of references

[1] Lin Zhenshan, Yang Xiuqun. theoretical climatology [M]. Nanjing: publishing house of Nanjing University, 1996.

[2] Lin Zhenshan. weather modeling, diagnosis and Study on Forecast [M]. Beijing: Meteorology Publishing House, 1996.

[3] You Weihong. the multiple technologies method research [M] of the multiple dimensioned diagnostic analysis of climate change and prediction. Beijing: Meteorology Publishing House, 1998.

[4] Lin Zhenshan, Deng Ziwang, You Weihong. the several basic problems [J] in the theoretical climatology. tropical meteorology newspaper, 1995,11 (2): 187-192.

[5] Hu Zengzhen, Huang Ronghui. the latest developments [J] of long-range weather forecasting business and method research. meteorological science and technology, 1993, (1): 1-10.

[6] You Weihong. to the check [J] of Yunnan Province observatory long-range weather forecasting in recent years. Yunnan meteorology, 1992, (2): 30-31.

[7]Pawlak?Z.Rough?Sets[J].International?Journal?of?Computer?and?information?Science，1982，11(5)：341-356.

[8]Hu?Xiao?Hua，Cercone?N.Learning?in?relational?databases：a?rough?set?approaeh[J].Computational?Intelligence，1995，11(2)：323-337.

[9] offspring of kingdom, in flood, Yang Dachun. based on the Decision Table Reduction [J] of conditional information entropy. Chinese journal of computers, 2002,25 (7): 759

Summary of the invention

The present invention seeks to the climatic prediction method that instability and nonlinear characteristic at the climatic data sequence provide a kind of complex method.With empirical mode decomposition method with all give birth to function progressively regression model and ensemble forecast technique combine, carry out climatic prediction.This invention has better prediction ability for the variation tendency and the sudden weather of weather.

The present invention adopts following technical scheme for achieving the above object:

The present invention is based on the Short-term Climate Forecast method of empirical modal decomposition and numerical value DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM, comprise following step:

(1) data is carried out the z-score standardization: use z-score to be normalized into scale value v ' the original value v of original list entries A, promptly

$v^{\′}=\frac{v-\stackrel{\‾}{A}}{{\mathrm{\σ}}_A},$

Wherein

And σ _ABe respectively the average and the standard deviation of original list entries;

(2) the described scale value v ' of step (1) usefulness EMD algorithm is decomposed, draw n IMF component and a trend component, wherein n is the natural number greater than 1;

(3) the described n that decomposites of step (a 2) IMF component is handled with numerical value set forecasting procedure respectively, wherein line number is number of members s; The element of specifying each row to remove at random, the forecast element reduces line by line, finally constitutes one and has the capable elongated sequence set of s;

(4) at last to the described all living function model of sequence set structure of handling gained by the IMF component of step (3), prediction and calculation also writes down the result, then every group result is fitted to the forecast result of an IMF component, again n the forecast final forecast of linear fit one-tenth as a result that comprises different characteristic separated at last.

Preferably, the described empirical modal decomposition algorithm of step (2) EMD, in the screening process of decomposing, employing is provided with the size of two standard deviation SD between the continuous iteration result between 0.2 to 0.3, and maximum iteration time is the stop condition that 200 conducts are appended, and adopts the extreme value continuation method to come the end points extreme value of match sequence.

Preferably, in described n IMF component of step (2) and the trend component, the corresponding random element of first IMF component, first to n corresponding periodic component of IMF component, trend component are residual error Rn correspondence trend composition.

Preferably, the element described in the step (3) in each row, null value does not participate in forecast.

The present invention is based on the Short-term Climate Forecast method of empirical modal decomposition and ensemble forecast technique, non-linear, non-stationary property according to climatic time series, at first utilizing the empirical modal decomposition technique that time series is carried out tranquilization handles, at the interference or the coupling information that reduce on the basis of the feature of retention time sequence own between sequence, utilize again ensemble forecast technique and equal living functions progressively the mode that combines of regression model carry out time series forecasting.All give birth to the method that function progressively returns with respect to single use, can effectively improve prediction accuracy, be particularly suitable for handling the non-stationary climatic time series of precipitation year by year or temperature variation.

Description of drawings

Fig. 1 is based on the method flow diagram of the climate time sequence forecasting method of empirical modal decomposition and numerical value ensemble forecast technique;

Fig. 2 carries out the concrete processing flow chart that empirical modal decomposes to climatic time series;

Fig. 3 is to use DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM and all gives birth to the progressively Forecasting Methodology process flow diagram that combines of regression model of function.

Embodiment

Be elaborated below in conjunction with the technical scheme of accompanying drawing to invention:

The present invention is based on the method that empirical modal decomposes this brand-new processing sequence data, at first the nonlinear data sequence of non-stationary is resolved into the new data sequence that several represent a stack features yardstick, earlier original data sequence is decomposed into the stack of various different characteristic waveforms.Wherein one of most critical step was the extreme point match signal envelope by signal, and what the present invention adopted is most widely used cubic spline functions method.Cubic spline function needs the single order of signal two end datas or second derivative as its border known conditions, and as can be known by the principle of EMD algorithm, can't directly obtain the extreme value of two-end-point correspondence, in the application aspect the Short-term Climate Forecast, adopt the extreme value continuation method at the present invention as end points extreme value approximating method.The present invention specifically may further comprise the steps:

(1) data are carried out the z-score standardization, this method is carried out standardization of data based on the average (mean) and the standard deviation of raw data.Use z-score to be normalized into v ' the original value v of A, promptly

$v^{\′}=\frac{v-\stackrel{\‾}{A}}{{\mathrm{\σ}}_A}$

Wherein v is an initial value,

And σ _ABe respectively the average and the standard deviation of sequence.

(2) pretreated data are decomposed with the EMD algorithm, draw n IMF component.Time series generally comprises random element, periodic component and trend composition.In general more corresponding accidents of random element or noise in the time series, corresponding temperature Change cycle of periodic component, the then corresponding long-term big Changing Pattern of trend composition.Decompose through EMD, former sequence is broken down into several IMF components and a trend component, the corresponding random element of IMF1 (first component), IMF2, IMF3 ... corresponding each periodic component such as IMFn, the corresponding trend composition of residual error Rn.And the amplitude maximum of IMF1, wavelength is the shortest, and stationarity is the poorest, along with the increase of decomposing number of times, the non-stationary behavior of component reduces gradually, and different component represents sequence at the fluctuation pattern of different time on the cycle, more can accurately reflect the variation of former sequence, and keep the feature of former sequence own;

(3) the described some IMF components that decomposite of step (2) are handled with numerical value set forecasting procedure respectively, wherein line number is number of members s.The element (null value does not participate in forecast) of specifying each row to remove at random, the forecast element reduces line by line, finally constitutes one and has the capable elongated sequence set of s.

(4) at last to the described all living function model of sequence set structure of handling gained by the IMF component of step (3), prediction and calculation also writes down the result, then every group result is fitted to the forecast result of an IMF component, again n the forecast final forecast of linear fit one-tenth as a result that comprises different characteristic separated at last.

The described empirical modal decomposition algorithm of step 2, in the screening process of decomposing, employing is provided with the size of two standard deviation SD between the continuous iteration result between 0.2 to 0.3, and maximum iteration time is the stop condition that 200 conducts are appended, and adopts the extreme value continuation method to come the end points extreme value of match sequence.

DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM described in the step (3) belongs to a kind of of numerical model DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM, and single relatively deterministic prediction has been considered the error that the various combination scheme causes forecast in the numerical model DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM.

Embodiment:

As shown in Figure 1, example of the present invention comprises the steps:

Step 10 is carried out the climatic time series of input yardstick of many time by the empirical modal decomposition algorithm and is decomposed, and (Intrinsic Mode Function is IMF) with a trend component to obtain several eigenmode state function components.Different components have represented sequence at the fluctuation pattern of different time on the cycle, more can accurately reflect the variation of former sequence, and the feature of retention time sequence own.

As shown in Figure 2, the treatment scheme that empirical modal decomposes specifically may further comprise the steps:

Step 101 is represented climatic time series with sequence X (t), and t is the time, and it is carried out the Z-SCORE standardization, obtains sequence S (t).

Step 101a judges that whether the extreme value number of S (t) is greater than 2.If sequence then is described necessity of tranquilization is arranged, execution in step 102, otherwise the explanation sequence is stably, need not decompose or decompose and finish, execution in step 108.

Step 102 makes H (t)=S (t), and the iterative operation of IMF component is extracted in beginning in H (t).

Step 103 is found out local maximum point and minimum point all among the sequence H (t).

Step 104 pair all maximum value and minimum point form coenvelope line H by cubic spline interpolation _Max(t) and lower envelope line H _Min(t), make H (t) satisfy H _Min(t)≤H (t)≤H _Max(t).Wherein the fitting problems for the frontier point extreme value adopts the extreme value continuation method of end points to solve.

Step 105 is calculated the arithmetic mean of envelope up and down

And from H (t), deduct i.e. H (t)=H (t)-m (t).

Step 105a judges that whether H (t) has satisfied the decision condition that becomes the IMF component, comprises following 3 points:

1. extreme value is counted and is counted consistent with zero passage or differ one at the most;

2. the arithmetic mean of envelope approaches 0 up and down;

3. the value that limits twice standard deviation SD between the continuous result is between 0.2～0.3, wherein

$\mathrm{SD}=\underset{t=0}{\overset{T}{\mathrm{\Σ}}}\left[\frac{{|H_{(k-1)}\left(t\right)-H_k\left(t\right)|}^2}{{H^2}_{(k-1)}\left(t\right)}\right]$

Wherein, H _(k-1)(t) and H _k(t) be that k represents the number of processes of this process in step 103 double result to the step 105.The span of SD is limited between 0.2～0.3 usually.

If satisfy above-mentioned three conditions simultaneously, execution in step 106 continues execution in step 103 otherwise return.

Step 106 is successfully extracted IMF component, i.e. an IMF _i(t)=H _k(t).

Step 107 deducts the IMF component of extraction from S (t), i.e. S (t)=S (t)-IMF ₁(t), and execution in step 101a judge the extreme value number of S (t).

Step 108 all IMF components this moment all are extracted out, and remaining S (t) then shows as a dullness or approximate dull trend term, is called trend component R _n(t).

Step 109 time series X (t) realizes that empirical modal decomposes, promptly

$X\left(t\right)=\underset{i=1}{\overset{n}{\mathrm{\Σ}}}{\mathrm{IMF}}_i\left(t\right)+R_n\left(t\right)$

Step 20 and step 30 specify as follows as shown in Figure 3:

Step 20 is handled with numerical value set forecasting procedure described each component of step 10, and establishing former sequence length is N, and the requirement forecast step-length is M, and member variable is S, and concrete steps are as follows:

(1) at first construct some forecast members of DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM by certain rule, number of members is combined into a forecast matrix then smaller or equal to N.The present invention's employing is forecast X (t) and is measured different elongated sequences S time, constitutes the DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM member of one group of capable N row of S, is specified the member variable S size that will revise by the user.

(2) each group treats that prediction sequence carries out dynamic modeling according to above-mentioned mathematical model, then by step 30 all give birth to function progressively regression model draw the forecasting sequence of certain-length, comprise former sequence match numerical value and forecast numerical value.

(3) each group prediction sequence is formed the forecast matrix, the prediction or the match numerical value in corresponding time are adjusted to same column by certain algorithm, carry out linear fit, drawing a length is predicting the outcome of (N+M), is used for the IMF component match of back.

Step 30 adopts step 20 to handle some groups of forecast matrixes of gained, sets up and all gives birth to progressively regression model of function, and establishing time series is that its mathematical model of X (t) is as follows:

X(t)＝{X(1)，X(2)，......X(N)}(301)

N is a sample size in the formula.For period T, define it and all give birth to function and be

$X_T\left(i\right)=T/N\underset{j=1}{\overset{T}{\mathrm{\Σ}}}X(i+\mathrm{jT})---\left(302\right)$

I=1 in the formula, 2 ..., T; 1≤T≤M;

To X _T(t) do periodically continuation, then can obtain the extension sequence, promptly obtain M-1 predictor sequence

Formula (302) and (303) regression problem: the f that comes from different backgrounds and possess different abilities _T(t) be predictor, X (t) is a predictand.Obtain following forecast model by separate regression steps progressively

$X\left(t\right)=a_0+\underset{T=2}{\overset{M}{\mathrm{\Σ}}}{a}_i{f}_T\left(t\right)+e\left(t\right),(t=\mathrm{1,2},...,N)---\left(304\right)$

A wherein ₀, a _iBe undetermined coefficient, e (t) is a white noise.Try to achieve a with the stepwise regression analysis method ₀And a _iBehind the coefficient, obtain following match prognostic equation.Have for match:

$X^{\′}\left(t\right)=a_0+\underset{i=2}{\overset{M}{\mathrm{\Σ}}}{a}_i{f}_i\left(t\right)---\left(305\right)$

Have for forecast:

$X^{\′}(N+p)=a_0+\underset{i=2}{\overset{M}{\mathrm{\Σ}}}{a}_i{f}_i(N+p)---\left(306\right)$

P=1,2 ... for forecast is counted.

Step 40 obtains former weather seasonal effect in time series with step 20 and the described component of step 30 the mode by linear combination of predicting the outcome and finally predicts the outcome.Predict the outcome with direct usefulness all give birth to function progressively the result of forecast of regression model compare, stationarity strengthens, can not the property forecast reduction, according to checking to actual weather numerical value, its reflection to climatic change trend is more accurate than direct single prediction, holds better to the unexpected variation of weather.

Claims (4)

1. one kind is decomposed based on empirical modal and the Short-term Climate Forecast method of numerical value DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM, it is characterized in that comprising following step:

(1) data is carried out the z-score standardization: use z-score to be normalized into scale value v ' the original value v of original list entries A, promptly

$v^{\′}=\frac{v-\stackrel{\‾}{A}}{{\mathrm{\σ}}_A},$

Wherein

And σ _ABe respectively the average and the standard deviation of original list entries;

(2) the described scale value v ' of step (1) usefulness EMD algorithm is decomposed, draw n IMF component and a trend component, wherein n is the natural number greater than 1;

(3) the described n that decomposites of step (a 2) IMF component is handled with numerical value set forecasting procedure respectively, wherein line number is number of members s; The element of specifying each row to remove at random, the forecast element reduces line by line, finally constitutes one and has the capable elongated sequence set of s;

(4) at last to the described all living function model of sequence set structure of handling gained by the IMF component of step (3), prediction and calculation also writes down the result, then every group result is fitted to the forecast result of an IMF component, again n the forecast final forecast of linear fit one-tenth as a result that comprises different characteristic separated at last.

2. the Short-term Climate Forecast method based on empirical modal decomposition and numerical value DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM according to claim 1, it is characterized in that, the described empirical modal decomposition algorithm of step (2) EMD, in the screening process of decomposing, employing is provided with the size of two standard deviation SD between the continuous iteration result between 0.2 to 0.3, and maximum iteration time is the stop condition that 200 conducts are appended, and adopts the extreme value continuation method to come the end points extreme value of match sequence.

3. the Short-term Climate Forecast method based on empirical modal decomposition and numerical value DATA PROCESSING IN ENSEMBLE PREDICTION SYSTEM according to claim 1, it is characterized in that, in described n IMF component of step (2) and the trend component, the corresponding random element of first IMF component, first to n corresponding periodic component of IMF component, trend component are the corresponding trend composition of residual error Rn.

4. the Short-term Climate Forecast method based on empirical modal decomposition and ensemble forecast technique according to claim 1 is characterized in that, the element described in the step (3) in each row, and null value does not participate in forecast.

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