CN102323970A - Hydrological time series prediction method based on multiple-factor wavelet neural network model - Google Patents

Abstract

The invention discloses a hydrological time series prediction method based on a multiple-factor wavelet neural network model. The invention provides a multiple-factor wavelet neural network model used for predicting the hydrological time sequence. The model takes a multiple-time sequence message as input, and the multiple time sequence message not only comprises the current wavelet coefficient of a prediction target time sequence but also comprises the current wavelet coefficient of other time sequences relevant to the time sequence; mutual information between the multiple-time sequence message and the prediction target time sequence serves as a measurement for judging the relevance of the multiple-time sequence message and the prediction target time sequence; other time sequences of strong relevance are selected; and a wavelet function selection criteria based on the a coefficient of weighted correlation is further utilized to select the optimal wavelet function for the model. Compared with the prior art, the method disclosed by the invention has the advantages of higher prediction accuracy and better expandability and practical value.

Description

Hydrological Time Series Forecasting Methodology based on the multiple-factor wavelet-neural network model

Technical field

The present invention relates to a kind of complicated time series forecasting method, relate in particular to a kind of Hydrological Time Series Forecasting Methodology, belong to the Hydrological Forecasting Technique field based on the multiple-factor wavelet-neural network model.

Background technology

Research on Time Series Data Mining mainly comprises: prediction, classification, similarity searching and sequential mode mining, and complicated time series forecasting is one of challenging problem in data mining field.Solve one of complicated time series forecasting problem preferably method be based on the time series forecasting method of wavelet-neural network model.

Wavelet analysis is a landmark progress on the Fourier analysis development history, and therefore the advantage that localizes simultaneously when having, frequently is described as mathematics " microscope ".Only can provide frequency domain representation to compare with Fourier analysis, wavelet transformation can provide the time-frequency local characteristic simultaneously, and has overcome the limited shortcoming of resolution of short time discrete Fourier transform.Discrete wavelet decomposes can carry out multiple dimensioned decomposition to time series, can extract the interval components series of different frequency, realizes the seasonal effect in time series frequency division is studied.Many resolution decomposition function by means of small echo; Can obtain the multi-scale characteristic of resolution " from coarse to fine " from original series; Study through to these wavelet characters can have the description of dominance more to the potential multifactor change procedure of seasonal effect in time series, so network is more prone to the contact and the rule of the inherence between " catching " input and output data.On the contrary, be difficult to describe complex time sequences usually based on the network of traditional single resolution study, chaos sequence for example, its speed of convergence is slow, and generalization ability is poor.Wavelet transformation resolves into complex time sequences the detail signal and the background signal of some different frequencies; Detail signal is a HFS; Background signal is a low frequency part; They are original time series performances on the different frequency interval, and relatively the proportion of original series is different, thereby the effect that the prediction of original time series is played is different.Wavelet-network model has combined many distinguishings and the strong non-linear of neural network of the time domain-frequency field on signal Processing of wavelet analysis to approach characteristic, has the advantage of the two concurrently.The model of setting up in the above described manner is called Wavelet-network model (Wavelet Network Model), notes by abridging to be WNN.

A lot of scholars study the time series forecasting of different field Wavelet-network model, for example: [Chen Yue-hui, Yang Bo; Dong Ji-wen.Time-series prediction using a local linear wavelet neural network.Neurocomputing, 2006,69 (6): 449-465], [Dash P.K.; Nayak Maya, Senapati M.R., et al; Mining for similarities in time series data using wavelet-based feature vectors and neural networks; Engineering Applications of Artificial Intelligence, 2007,20 (2): 185-201], [Gan Xiaobing; Liu Ying; And Austin Francis R.:A prediction method for time series based on wavelet neural networks.Proceedings of CIS2005, pp:902-908], [Benaouda D., Murtagh Fionn; And Starck Jean-Luc; Et al.Wavelet-based nonlinear multiscale decomposition model for electricity load forecasting.Neurocomputing, 2006,70 (1-3): 139-154], [Chen Di; Feng Hai-Hang; Lin Qing-jia; Et al, Multi-scale Internet traffic prediction using wavelet neural network combined model, Proceedings of First International Conference on Communications and Networking in China; 2006, pp:1-5], [Li Aiguo, Qin Zheng; Moving window secondary autoregressive model prediction Nonlinear Time Series; Chinese journal of computers, 2004,27 (07): 1004-1008] etc.But these documents only are to utilize wavelet decomposition that the single track time series is decomposed.The information that only relies on the predicted time sequence self to provide, the effect that improves for precision of prediction has certain limitation.And in the physical sense, the intrasystem sequence of many time often has correlativity.

Hydrologic forecast (for example Runoff Forecast) has great significance to the adjustmenting management of water resource and the decision-making of flood control and disaster reduction.Yet because the combined influence of factors such as weather and underlying surface, runoff shows complicated non-linear and non-stationary characteristic, generally comprises determinacy composition and random element.Neural network has the ability of very strong processing large-scale complex nonlinear kinetics system; Be widely used in the river course river forcasting; Can discern the complex nonlinear relation between water movement change procedure and its factor of influence, for the river course river forcasting provides a new approach.The composition more complicated of runoff sequence self contains multiple radio-frequency component in a runoff, thus be necessary it is carried out the research of branch frequency, and method of wavelet provides a kind of technology of time frequency analysis easily.The method that small echo and neural network are used in combination obtains extensive concern in recent years, and utilizing this built-up pattern to carry out hydrologic(al) prognosis becomes the research focus.Having proposed a kind of Wavelet-network model in the document [fourth is brilliant for Wang Wensheng, bear Hua Kang, the Wavelet-network model pre-test of daily flow prediction, hydroscience progress, 2004,15 (3): 382-386] is used for daily flow is predicted.This Wavelet-network model is on the basis of three-layer neural network; With t constantly the wavelet coefficient

that decomposes of original signal be the model (T is a leading time) that output makes up as input with the original signal f (t+T) in the t+T moment.Yet the wavelet coefficient that this Wavelet-network model also only utilizes single time series to decompose out, to predicting future, the predictive ability of model is limited.Because the wavelet coefficient that decomposes out from original time series, comprised time series changed in earlier stage in long-time memory and short time memory, adding more in earlier stage, wavelet coefficient often can not play better booster action to target of prediction.And the adding of wavelet coefficient in earlier stage, the pattern that makes is imported number to be increased, and the complexity of corresponding training pattern set also increases, to confirming and training time proposition requirements at the higher level of neural network structure.For more complicated time series,, can not better portray following differentiation of time series only according to this seasonal effect in time series wavelet coefficient in early stage.In fact runoff has correlationship with intrasystem other hydrographic features, has tangible influence relation like upstream and downstream relation station or relevant hydrographic features (comprising flow, water level, temperature and precipitation etc.) diameter stream of standing.

The time series data of different field has different qualities, only utilizes that to decompose with a kind of wavelet function be inappropriate.Document [Sang Yanfang, Wang Dong, wavelet function system of selection in the hydrology sequence wavelet analysis; The water conservancy journal, 2008,39 (3): 295-300] from sequence reconstruct angle; Use DSMC; Through the actual measurement hydrology sequence in simulated data and station, Lijin, the Yellow River and Zhejiang territory, white streams, inquiring into wavelet analysis influences the factor that wavelet function is selected, and then sets up the foundation of choose reasonable wavelet function.Result of study shows that the variation characteristic of sequence self is the important factor in order that wavelet function is selected.Document [Liu Suyi, Quan Xianzhang, Zhang Yongchuan; Different wavelet function diameter flow analysis results' influence, HYDROELECTRIC ENERGY science, 2003; 21 (1): 29-31.], several kinds of influences that wavelet function is predicted runoff under the multiple dimensioned framework have been contrasted through the experimental technique of the multiple dimensioned forecast model of training.For different pieces of information, particularly under the mass data situation, use the Wrapper method in this similar characteristics selection to confirm that optimum wavelet function is more consuming time.

Summary of the invention

Technical matters to be solved by this invention is to overcome the deficiency that prior art is carried out the Hydrological Time Series prediction with single time series as the input of wavelet-neural network model, and a kind of Hydrological Time Series Forecasting Methodology based on the multiple-factor wavelet-neural network model is provided.

Hydrological Time Series Forecasting Methodology based on the multiple-factor wavelet-neural network model of the present invention; At first set up wavelet neural network Hydrological Time Series forecast model according to Hydrological Time Series to be predicted; Carry out the Hydrological Time Series prediction according to the forecast model of setting up then; It is characterized in that said wavelet neural network Hydrological Time Series forecast model is a multiple-factor wavelet neural network Hydrological Time Series forecast model, with sequence information of many time as input; Not only comprise the current wavelet coefficient of target of prediction seasonal effect in time series, also comprise the current wavelet coefficient of the sequence At All Other Times that time series is relevant therewith.

Further, the said At All Other Times sequence relevant with the target of prediction time series, be according to mutual information (mutual information) between itself and the target of prediction time series as the tolerance of passing judgment on both correlativitys, the mutual information value is bigger, then correlativity is strong; Specifically confirm according to following method:

Step 1, provide and some original list entries I1 that sequence O to be predicted maybe be relevant, I2 ..., In, n are the list entries numbers;

Step 2, treat forecasting sequence O and original list entries I1, I2 ..., In carries out discretize, obtains discrete series Do, D1, and D2 ..., Dn;

Step 3, calculate Do and D1 respectively, D2 ..., the mutual information between the Dn, the result is designated as M1, M2 ..., Mn;

Step 4, according to M1, M2 ..., Mn, the original list entries Ii that the selects Mi＞Th correlated series during as sequence wavelet neural network modeling to be predicted, i is the integer between 1 to N; Th is a pre-set threshold.

Further, employed wavelet function is confirmed according to following method in the said multiple-factor wavelet neural network Hydrological Time Series forecast model:

Step 1, use wavelet function to be selected to make up wavelet neural network Hydrological Time Series forecast model respectively and predict;

Step 2, for each wavelet function to be selected, obtain the related coefficient vector according to following method respectively:

To the wavelet decomposition sequence on the varying level, the related coefficient of the wavelet coefficient sequence of respectively small echo sequence coefficient of autocorrelation of statistical forecast object time sequence, and target of prediction time series and the At All Other Times sequence relevant with the target of prediction time series; Adopt the related coefficient on each level of method synthesis of weighting at last, obtain the related coefficient vector;

Step 3, according to adopting each wavelet function to predict resulting related coefficient vector, confirm the final wavelet function that uses.

Wherein, two seasonal effect in time series related coefficients obtain according to following method:

Suppose two time serieses be respectively X (1), X (2) ..., X (n) >, Y (1), Y (2) ..., Y (n) >, seasonal effect in time series length is N; Then the related coefficient between these two time serieses is according to computes,

${\widehat{\mathrm{\ρ}}}_T=\frac{N}{N-T}\frac{\underset{t=1}{\overset{N-T}{\mathrm{\Σ}}}(X_t-\stackrel{\‾}{X})(Y_{t+T}-\stackrel{\‾}{Y})}{\sqrt{\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(X_t-\stackrel{\‾}{X})}^2\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(Y_t-\stackrel{\‾}{Y})}^2}},$

In the formula;

is two related coefficients that the sequence time lag is T;

is the average of first sequence, and

is the average of second sequence;

Single seasonal effect in time series time lag is the coefficient of autocorrelation of T, obtains according to following method:

Move right T position of this time series generated a new time series, calculate this time series and newly-generated seasonal effect in time series related coefficient, the coefficient of autocorrelation that it is T that the related coefficient that obtains is this time series time lag according to following formula then.

The present invention proposes a kind of multiple-factor prediction model based on wavelet neural network and be used for the Hydrological Time Series prediction; This model with sequence information of many time as input; Not only comprise the current wavelet coefficient of target of prediction seasonal effect in time series; The current wavelet coefficient that also comprises the sequence At All Other Times that time series therewith is relevant, and according to its with the target of prediction time series between mutual information as the tolerance of passing judgment on both correlativitys, the strong sequence At All Other Times of selection correlativity; Further utilize wavelet function choice criteria, be the optimum wavelet function of this Model Selection based on weighted correlation coefficient.Compare prior art, the inventive method has higher forecasting accuracy, and better extensibility and practical value.

Description of drawings

Fig. 1 is the structural representation of multiple-factor prediction model based on wavelet neural network of the present invention;

Fig. 2 confirms the schematic flow sheet of relevant sequence At All Other Times for the present invention;

Fig. 3 selects the schematic flow sheet of optimal wavelet function for the present invention.

Embodiment

Below in conjunction with accompanying drawing technical scheme of the present invention is elaborated:

Multiple-factor prediction model based on wavelet neural network of the present invention with sequence information of many time as input; Not only comprise the current wavelet coefficient of target of prediction seasonal effect in time series; The current wavelet coefficient that also comprises the sequence At All Other Times that time series is relevant therewith; Its structure is as shown in Figure 1, and the website that wherein will predict is A, and the website relevant with A is B to I.Also can this multiple-factor prediction model based on wavelet neural network be called the river course Wavelet-network model, note by abridging and be RWNN.

Hydrological Time Series Forecasting Methodology based on the multiple-factor wavelet-neural network model of the present invention, carry out according to following steps:

Step 10, definite sequence input time of being correlated with;

In information theory, the uncertainty that entropy H (X) is used to measure stochastic variable X.Suppose that X is a discrete random variable, entropy H (X) is defined as:

$H\left(X\right)=-\underset{i}{\mathrm{\Σ}}p\left(x_i\right)\log p\left(x_i\right)$

Can only weigh the uncertain different of unitary variant with entropy, mutual information can be used to weigh quantity of information total between two above stochastic variables.Suppose that Y is another discrete random variable, then the mutual information I (X between X and the Y; Y) be defined as:

$I(X;Y)=\underset{i}{\mathrm{\Σ}}\underset{j}{\mathrm{\Σ}}p(x_i,x_j)\log \frac{p(x_i,y_j)}{p\left(x_i\right)p\left(y_j\right)},$

Can prove that mutual information and entropy have following relation:

I(X；Y)＝H(X)-H(X|Y)＝H(Y)-H(Y|X)，

I(X；Y)＝H(X)+H(Y)-H(X，Y)

Obviously, mutual information is big more between two stochastic variables, and correlativity is strong more between them.Detailed content about mutual information can be referring to document [Cover and Thomas, 1991T.M.Cover and J.A.Thomas, Elements of In formation Theory, Wiley, New York (1991) .].See that from the time series forecasting angle mutual information is big more between two sequences, then accurate more through another sequence of one of them sequence prediction.And, owing to possibly have nonlinear dependence between the sequence before the wavelet transformation, and mutual information can reflect the non-linear dependencies between the different variablees just.Therefore, as the tolerance of passing judgment on both correlativitys, proposition is confirmed method based on the list entries of mutual information, and is as shown in Figure 2 with mutual information between the time series in the present invention, specifically confirms relevant sequence input time according to following method:

Step 11, provide and some original list entries I1 that sequence O to be predicted maybe be relevant, I2 ..., In, n are the list entries numbers;

Step 12, treat forecasting sequence O and original list entries I1, I2 ..., In carries out discretize, obtains discrete series Do, D1, and D2 ..., Dn; Continuous variable discretization method commonly used mainly contains two kinds: equidistant partitioning and equiprobability partitioning; General latter's effect is relatively good; The preferred document of the present invention [Fraser and Swinney, 1986 A.M.Fraser an d H.L.Swinney, Independent coordinates for strange attractors from mutual informatio n; Phys.Rev.A 33 (2) (1986), pp.1134-1140] in the equiprobability partitioning that proposes time series is carried out discretize;

Step 13, calculate Do and D1 respectively, D2 ..., the mutual information between the Dn, the result is designated as M1, M2 ..., Mn;

Step 14, according to M1, M2 ..., Mn, the original list entries Ii that the selects Mi＞Th correlated series during as sequence wavelet neural network modeling to be predicted, i is the integer between 1 to N; Th is a pre-set threshold, this threshold value preferred 0.15.

Step 20, relevant list entries and the target sequence of confirming carried out wavelet decomposition, carry out small echo according to weighted correlation coefficient and select;

Wavelet decomposition is a kind of effective PROBLEM DECOMPOSITION and feature extraction instrument, and following table 1 has been enumerated present common several kinds of wavelet functions and characteristic thereof.

Table 1 is used wavelet function always

Small echo	Orthogonality	Filter factor length	Support width	Symmetry
					Haar	Yes	2	1	No
Db2	Yes	4	3	Far?from
					Db3	Yes	6	5	Far?from
bior4.4	No	9	8	Yes
					B3?spline	No	5	4	Yes

But in specific field, have time series data of different nature, with the different wavelet function these data are decomposed, the components series that is produced has influence in various degree to the forecast model performance of setting up.Because wavelet filter has various supports length and the filtering property of self,, make the wavelet coefficient sequence after decomposing to improve the performance of forecast model so should select a suitable small echo that concrete time series is decomposed.The present invention uses the input of the wavelet coefficient of t different time sequence constantly as model, and is output as the t+T raw data of predicted time sequence.For the multiple-factor forecast model, establish the wavelet coefficient that t model input constantly comprises the predicted time sequence

Input with expansion Be output as the future value x of original time series _a(t+T).Target of prediction x _a(t+T) also contain tie element on each frequency separation, i.e. wavelet coefficient on the varying level

According to (specifically can be in the time series analysis referring to document [PBrockwell about the stationary time series prediction theory; A.Davis, Time series:theory and methods, 2nd.edition; New York; Springer, (Springer series in statistics), 2002]); Be provided with target of prediction time series { X (t); T=1 ..., the coefficient of autocorrelation in the T time interval of n}

exists again and { X (t); T=1; ..., time series { Y (t), t=1 that n} is relevant; ...; The related coefficient in the n} and the T time interval between the two

is if

and

is big more, so target of prediction time series { X (t), t=1; ..., the prediction variance of n} is just more little.

According to above-mentioned thought; The present invention is directed to the multiple-factor wavelet-neural network model that is proposed; A kind of wavelet function choice criteria based on weighted correlation coefficient has been proposed; To the wavelet decomposition sequence on the varying level, the small echo sequence coefficient of autocorrelation of statistical forecast object time sequence and target of prediction time series and multiple-factor seasonal effect in time series wavelet coefficient serial correlation coefficient adopt the related coefficient on each level of method synthesis of weighting at last; As shown in Figure 3, specifically select optimum wavelet function according to following method:

Step 21, use wavelet function to be selected to make up wavelet neural network Hydrological Time Series forecast model respectively and predict;

Step 22, for each wavelet function to be selected, obtain the related coefficient vector according to following method respectively:

To the wavelet decomposition sequence on the varying level, the related coefficient of the wavelet coefficient sequence of respectively small echo sequence coefficient of autocorrelation of statistical forecast object time sequence, and target of prediction time series and the At All Other Times sequence relevant with the target of prediction time series; Adopt the related coefficient on each level of method synthesis of weighting at last, obtain the related coefficient vector;

Step 23, according to adopting each wavelet function to predict resulting related coefficient vector, confirm the final wavelet function that uses.

Wherein, two seasonal effect in time series related coefficients obtain according to following method:

Suppose two time serieses be respectively X (1), X (2) ..., X (n) >, Y (1), Y (2) ..., Y (n) >, seasonal effect in time series length is N; Then the related coefficient between these two time serieses is according to computes,

${\widehat{\mathrm{\ρ}}}_T=\frac{N}{N-T}\frac{\underset{t=1}{\overset{N-T}{\mathrm{\Σ}}}(X_t-\stackrel{\‾}{X})(Y_{t+T}-\stackrel{\‾}{Y})}{\sqrt{\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(X_t-\stackrel{\‾}{X})}^2\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(Y_t-\stackrel{\‾}{Y})}^2}},$

In the formula;

is two related coefficients that the sequence time lag is T;

is the average of first sequence, and

is the average of second sequence;

Single seasonal effect in time series time lag is the coefficient of autocorrelation of T, obtains according to following method:

Move right T position of this time series generated a new time series, calculate this time series and newly-generated seasonal effect in time series related coefficient, the coefficient of autocorrelation that it is T that the related coefficient that obtains is this time series time lag according to following formula then.

For example, for being input as

With Be output as x _a(t+1) forecast model, computing method such as table 2 utilize the weighing vector of last column to come the decomposition result of the different wavelet functions of comparison.

The wavelet function of table 2 two-factor wavelet network input is selected index calculating method

Suppose a time series for X (1), X (2) ..., X (n) >, another time related sequence be Y (1), Y (2) ..., Y (n) >, seasonal effect in time series length is N.The related coefficient definition is then arranged like formula (1), concrete computing method such as formula (2).

${\mathrm{\ρ}}_T={\mathrm{\ρ}}_{t,t+T}=\frac{\mathrm{Cov}(X\left(t\right),Y(t+T))}{\sqrt{\mathrm{var}\left(X\left(t\right)\right)\mathrm{var}\left(Y(t+T)\right)}}---\left(1\right)$

${\widehat{\mathrm{\ρ}}}_T=\frac{\frac{1}{N-T}\underset{t=1}{\overset{N-T}{\mathrm{\Σ}}}(X_t-\stackrel{\‾}{X})(Y_{t+T}-\stackrel{\‾}{Y})}{\sqrt{\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(X_t-\stackrel{\‾}{X})}^2\frac{1}{N}\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(Y_t-\stackrel{\‾}{Y})}^2}}=\frac{N}{N-T}\frac{\underset{t=1}{\overset{N-T}{\mathrm{\Σ}}}(X_t-\stackrel{\‾}{X})(Y_{t+T}-\stackrel{\‾}{Y})}{\sqrt{\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(X_t-\stackrel{\‾}{X})}^2\underset{t=1}{\overset{N}{\mathrm{\Σ}}}{(Y_t-\stackrel{\‾}{Y})}^2}}---\left(2\right)$

The time lag of calculating the single track sequence is the T coefficient of autocorrelation, only need make X (1), X (2) ..., X (n)>T the position that move right generate new sequence, then with new sequence replacement Y (1), Y (2) ..., Y (n)>get final product according to formula (2) calculating.

Step 30, the wavelet function of adopt selecting, to input time sequence carry out wavelet decomposition, set up the multiple-factor wavelet-neural network model;

Step 40, training multiple-factor wavelet-neural network model;

Step 50, according to given input multisequencing wavelet conversion coefficient constantly, as the input of multiple-factor wavelet-neural network model, obtain final predicted value.

Be predicted as example with the daily flow in flood season at station, Wangjiaba Dam below and further specify technical scheme of the present invention and beneficial effect.

At first with the selection of carrying out wavelet function based on the wavelet function choice criteria of weighted correlation coefficient of the present invention.The selection of wavelet function should be relevant with concrete research object; The daily flow process in flood season at contrast station, different year Wangjiaba Dam; The daily flow sequence in 2003 of finding to stand is comparatively typical; Select the data information that flood season in 2003, the daily flow sequence was selected as wavelet function adaptability, experimental data also comprises the daily flow data in flood season of the same period in 2003 at the station, three main upper reaches (Ban Tai, Xi County and Huangchuan) at station, Wangjiaba Dam.This experiment selects for use following small echo that daily flow sequence datas in 2003 of above-mentioned four websites are carried out three horizontal wavelet decomposition, participates in its corresponding low-pass filter of small echo such as table 3 relatively.

Table 3 wavelet function and low-pass filter thereof

Because the daily flow sequence of Wangjiaba Dam website is bigger with the composition correlativity of self, so make its weight coefficient α _Wjb=0.6, again because Ban Tai and station, Huangchuan all on sprout, the Xi County stands on the big tributary, so make α _Xix=0.2, α _Bt=0.1, α _Hc=0.1.Be that weight allocation is { α _Bt, α _Xix, α _Hc, α _Wjb}={ 0.1,0.2,0.1,0.6}.When making T=1, each different wavelet function is seen table 4 (because length limits, omitted weighting concrete data before, only provided the related coefficient after the weighting in the literary composition) to the correlativity statistics of time series decomposition result.

Each wavelet decomposition rear weight related coefficient of table 4

	d 1	d 2	d 3	c 3
					B3?spline	0.4933	0.7681	0.8538	0.9627
Haar	0.3813	0.7075	0.8290	0.9572
					db2	0.2286	0.6299	0.8009	0.9492
db3	0.1652	0.6217	0.8030	0.9427
					coifl	0.1835	0.6172	0.7982	0.9470
bior1.3	0.2875	0.6843	0.8210	0.9518
					bior2.2	0.3268	0.4997	0.7627	0.9245
bior4.4	0.1669	0.5611	0.7873	0.9419
					rbio4.4	0.1730	0.6472	0.8080	0.9440

Can know that from table 4 each corresponding subsequence related coefficient of sequence and target sequence is maximum after the B3spline wavelet decomposition, the Haar small echo is slightly poorer than the result of B3spline.We can also find that db2 is poorer than the statistics of Haar small echo, and the wavelet coefficient that this wavelet decomposition of explaining that support width is big in the same family is come out can't make prediction be more prone to.If select a unaccommodated small echo that the daily flow data at four stations such as Wangjiaba Dam are decomposed; To cause very poor statistics; Bior2.2 small echo for example; Statistics on each level is all relatively poor, explains that it decomposes these three stations daily flow data to fail effectively to extract to predicting favourable characteristic.

With station, Wangjiaba Dam daily flow as forecasting object; Choose main with it relevant three research station: Ban Tai, Xi County, Huangchuan, this three station is respectively the website on the three big tributaries, the upper reaches, and the data time span is 2000-2007; The daily flow data that only comprise annual flood season; Be specially 2000-2005 annual data interval and be 6-1 to 10-1 day, interval 5-1 to 10-1 day of 2006 annual datas, the interval 5-15 to 10-1 of 2007 annual datas.As training set, data in 2006 and 2007 were as test set with the data in 2000 to 2005 for this paper.

(1) foundation of river course Wavelet-network model

According to top wavelet function selection result; The data of Haar small echo and B3spline wavelet decomposition are preferably to the fitness of the river course Wavelet-network model at station, Wangjiaba Dam on the meaning of related coefficient, so at first adopt these two kinds of small echos that the daily flow sequence at Wangjiaba Dam, Ban Tai, Xi County and four stations, Huangchuan done 3 horizontal decomposition respectively.Then with this four station the same day wavelet coefficient as the input of neural network,, as output predicting the outcome of two kinds of wavelet decomposition compared with the target of prediction (daily flow of 1d, 2d, 3d time span of forecast) at station, Wangjiaba Dam.

To before the neural network model training, the Mid-Range standardization is done in input, after being done the natural logarithm conversion, delivery rate also it is standardized to [1,1], and utilize the Neural Network Toolbox of Matlab to realize the training of neural network model then.On the basis of standard BP algorithm, use the L-M numerical optimization to accelerate neural metwork training speed, and use the Bayesian regularization method to guarantee the generalization ability of training network.Adopt trial and error to confirm optimum neural network hidden node number.For the neural network model of using the Haar small echo, the optimum hidden node of 1d, 2d and 3d time span of forecast is respectively 4,5 and 5; And for the neural network model of Application of B 3spline small echo, the optimum hidden node of 1d, 2d and 3d time span of forecast is respectively 5,4 and 6.To different initial weights, adopt the method for repeatedly training to choose the generation optimization model then.The network that obtains with training is at last simulated on test set, produces prediction output.The original output of network need be carried out anti-Mid-Range standardization, obtains data Y, because original flow has been done the natural logarithm conversion as output, so need carry out anti-natural logarithm conversion to Y, finally obtains predicting the outcome of raw data.

(2) evaluation of result index

For time series forecasting, evaluation criterion commonly used has mean absolute error (MAE) and average relative error (MRE), its computing formula such as formula (3) and (4).

$\mathrm{MAE}=\frac{1}{T}\underset{i=1}{\overset{T}{\mathrm{\Σ}}}|p_i-a_i|---\left(3\right)$

$\mathrm{MRE}=\frac{1}{T}\underset{i=1}{\overset{T}{\mathrm{\Σ}}}\frac{|p_i-a_i|}{a_i}---\left(4\right)$

P wherein _i, a _iBe respectively the predicted value and the actual value of i observation in T the observation.

In addition,, calculate the qualified predicted number of relative error within 20%, obtain qualification rate, be designated as ER_ZP20 according to the definition of " Hydrological Information and Forecasting standard " qualification rate.Again owing to be flood forecasting, the high flow capacity rate in the right direction when we have also considered the prediction direction accuracy and flood takes place.Rate in the right direction is direction variation symmetry value (DVS) again, and suc as formula (5), wherein P is a time span of forecast.For the accuracy of judging than high flow direction, flow is added up its rate in the right direction greater than 500 prediction, be designated as DVS_HF.

$\mathrm{DVS}=\frac{1}{T-P}\underset{i=P}{\overset{T}{\mathrm{\Σ}}}\mathrm{\Φ}\left((a_i-a_{i-P})(p_i-p_{i-P})\right);\mathrm{\Φ}\left(x\right)=\left\{\begin{array}{c}1,x>0\\ 0,x\≤0\end{array}\right.---\left(5\right)$

(3) Haar small echo and B3spline wavelet decomposition modeling result are relatively

Table 5 has provided Wavelet-network model the predicting the outcome on test set based on Haar wavelet decomposition and B3spline wavelet decomposition.

Table 5Haar and B3spline Wavelet-network model different time span of forecast results' on test set comparison

Can know that from table 5 on the 1d time span of forecast, the ER_ZP20 index of B3spline is better than the index of Haar; Wavelet-network model based on the B3spline wavelet decomposition on MAE and MRE index is poorer slightly than the model based on the Haar wavelet decomposition; DVS and the DVS_HF of B3spline are better; On the 2d time span of forecast, the MRE of B3 spline and qualification rate index all are better than the index of Haar, but under qualification rate only is about 60% situation, see that from DVS and DVS_HF index predicting the outcome of Haar small echo is better than the result of B3spline small echo slightly; On the 3d time span of forecast, under the very low situation of qualification rate, DVS_HF shows that B3 spline small echo result is superior to the result of Haar small echo slightly.

B3 spline small echo predicts the outcome and is better than the Haar small echo generally, and this has also verified the correctness of wavelet function system of selection of the present invention.

(4) the Wavelet-network model result with simple sequence compares

Table 6 has shown that river course of the present invention Wavelet-network model (RWNN) and Wavelet-network model (WNN) are in the test set statistics on the different evaluation index of closing.

WNN compares with the result of RWNN on different time span of forecasts on table 6 test set

Can know that from table 6 RWNN model all indexs on different time span of forecasts all are superior to the WNN model, this has demonstrated fully the raising of extended model estimated performance.According to " Hydrological Information and Forecasting standard " evaluation criterion, for the 1d time span of forecast, the river course Wavelet-network model satisfies the standard of first class forecast, and Wavelet-network model only satisfies the standard of second class forecast; For the time span of forecast of 2d, the river course Wavelet-network model satisfies the third class Forecast Standard, can be used for reference to the property forecast, and the Wavelet-network model precision is lower than third class; For 3d time span of forecast situation; Two model accuracies all are lower than third class; But can find out that from DVS and DVS_HF the river course Wavelet-network model shows better on the direction prediction performance, particularly on the direction forecast accuracy (DVS_HF) of high flow capacity; The river course Wavelet-network model is higher than 15 percentage points of Wavelet-network model, and the reference property that is suitable for doing the 3d time span of forecast is estimated newspaper.Simultaneously, on the DVS_HF index, the RWNN of 1d time span of forecast exceeds 12 percentage points than WNN, reaches 86%, can answer the problem of " inferior daily flow is to raise or reduction " in the flood peak process, paid close attention to more reliably.

Claims (6)

1. Hydrological Time Series Forecasting Methodology based on the multiple-factor wavelet-neural network model; This method is at first set up wavelet neural network Hydrological Time Series forecast model according to Hydrological Time Series to be predicted; Carry out the Hydrological Time Series prediction according to the forecast model of setting up then; It is characterized in that said wavelet neural network Hydrological Time Series forecast model is a multiple-factor wavelet neural network Hydrological Time Series forecast model, with sequence information of many time as input; Not only comprise the current wavelet coefficient of target of prediction seasonal effect in time series, also comprise the current wavelet coefficient of the sequence At All Other Times that time series is relevant therewith.

2. according to claim 1 based on the Hydrological Time Series Forecasting Methodology of multiple-factor wavelet-neural network model; It is characterized in that; The said At All Other Times sequence relevant with the target of prediction time series; Be according to mutual information between itself and the target of prediction time series as the tolerance of passing judgment on both correlativitys, the mutual information value is bigger, then correlativity is strong; Specifically confirm according to following method:

Step 1, provide and some original list entries I1 that sequence O to be predicted maybe be relevant, I2 ..., In, n are the list entries numbers;

Step 2, treat forecasting sequence O and original list entries I1, I2 ..., In carries out discretize, obtains discrete series Do, D1, and D2 ..., Dn;

Step 3, calculate Do and D1 respectively, D2 ..., the mutual information between the Dn, the result is designated as M1, M2 ..., Mn;

Step 4, according to M1, M2 ..., Mn selects Mi>and the original list entries Ii of the Th correlated series during as sequence wavelet neural network modeling to be predicted, i is the integer between 1 to N; Th is a pre-set threshold.

3. like the said Hydrological Time Series Forecasting Methodology of claim 2, it is characterized in that, adopt the equiprobability partitioning to treat forecasting sequence O and original list entries I1 based on the multiple-factor wavelet-neural network model, I2 ..., In carries out discretize.

4. like the said Hydrological Time Series Forecasting Methodology of claim 2, it is characterized in that the value of said threshold value Th is 0.15 based on the multiple-factor wavelet-neural network model.

5. like each said Hydrological Time Series Forecasting Methodology of claim 1-4 based on the multiple-factor wavelet-neural network model; It is characterized in that employed wavelet function is confirmed according to following method in the said multiple-factor wavelet neural network Hydrological Time Series forecast model:

Step 1, use wavelet function to be selected to make up wavelet neural network Hydrological Time Series forecast model respectively and predict;

Step 2, for each wavelet function to be selected, obtain the related coefficient vector according to following method respectively:

To the wavelet decomposition sequence on the varying level, the related coefficient of the wavelet coefficient sequence of respectively small echo sequence coefficient of autocorrelation of statistical forecast object time sequence, and target of prediction time series and the At All Other Times sequence relevant with the target of prediction time series; Adopt the related coefficient on each level of method synthesis of weighting at last, obtain the related coefficient vector;

Step 3, according to adopting each wavelet function to predict resulting related coefficient vector, confirm the final wavelet function that uses.

6. like the said Hydrological Time Series Forecasting Methodology of claim 5, it is characterized in that two seasonal effect in time series related coefficients obtain according to following method based on the multiple-factor wavelet-neural network model:

Suppose that two time serieses are respectively

,

, seasonal effect in time series length does NThen the related coefficient between these two time serieses is according to computes,

，

In the formula;

is two related coefficients that the sequence time lag is T;

is the average of first sequence, and

is the average of second sequence;

Single seasonal effect in time series time lag is the coefficient of autocorrelation of T, obtains according to following method:

Move right T position of this time series generated a new time series, calculate this time series and newly-generated seasonal effect in time series related coefficient, the coefficient of autocorrelation that it is T that the related coefficient that obtains is this time series time lag according to following formula then.

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