CN107704973A - Water level prediction method based on neutral net Yu local Kalman filtering mixed model - Google Patents
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Abstract
The present invention provides a kind of water level prediction method based on neutral net Yu local Kalman filtering mixed model, the original time series array of waterlevel data is gathered, using the stability of the true original time series array of the root mean square method of inspection；As stable condition is unsatisfactory for, then difference processing is carried out to initial data, until it passes through stability test；After stable data set is obtained, the water level time series lag period is determined using auto-correlation coefficient and partial correlation coefficient；Original time series array is split, original time series array is split as the training sample set that length is the water level time series lag period；Establish artificial neural network and train, generation artificial nerve network model obtains water level forecast result one day after；Water level forecast result one day after described in Kalman filtering amendment.The present invention can effectively realize waterlevel data reparation and short-term forecast, improve precision of prediction.
Description
Technical field
The invention belongs to Changjiang River Trunk Line navigation channel water level forecast field, and in particular to one kind is based on neutral net and local karr
The water level prediction method of graceful filtering mixed model.
Background technology
Short-term Interpretation Method of Area Rainfall is the important component of maritime administration, with inland river electronic channel chart (ECDIS) display, information
Issue closely related.Meanwhile water level prediction method research is hydrographic water resource, the important research content of Communication and Transportation Engineering.Make
For one of navigation channel element information, water level forecast precision is lifted, can be that inland waterway maritime affairs risk management and control carries with public service level
For technical support.
At present, water level prediction method, version are various, such as：Based on rolling average window (ARIMA) linear model
Water level prediction method, artificial nerve network model (ANN) nonlinear method etc..Linear method is the water level according to first some days
Data, the water level of some days after prediction.Linear method weakens water level and its dependent variable (such as to a certain extent：Tide, footpath
The features such as stream, river topography) between non-linear relation, usually with it is simple and convenient the characteristics of, but its precision is relatively low,
Especially in Complicated Time Series Prediction problem.In engineering, most of time sequence prediction problem can be classified as nonlinear problem,
Its potential changing rule is difficult to accurately be described by linear model.
The content of the invention
The technical problem to be solved in the present invention is：One kind is provided based on neutral net and local Kalman filtering mixed model
Water level prediction method, can effectively realize waterlevel data reparation and short-term forecast, improve precision of prediction.
The technical solution taken by the invention to solve the above technical problem is：One kind is based on neutral net and local karr
The water level prediction method of graceful filtering mixed model, it is characterised in that：It comprises the following steps：
S1, determine the water level time series data lag period：
The original time series array of waterlevel data is gathered, using the true original time series array of the root mean square method of inspection
Stability；As stable condition is unsatisfactory for, then difference processing is carried out to initial data, until it passes through stability test；Obtaining
After stable data set, water level time series lag period T is determined using auto-correlation coefficient and partial correlation coefficient；
S2, structure training sample set：
As the water level time series lag period T obtained by S1, original time series array is split, by original time sequence
Columns assembling and dismantling are divided into the training sample set that M length is T；
S3, the training sample set obtained based on S2, are established artificial neural network and trained, and generate artificial neural network mould
Type；And analog result is obtained, i.e., as input data using the final stage data based on training sample set obtained by S2 steps
For water level forecast result one day after；
Water level forecast result one day after described in S4, Kalman filtering amendment：
By original time series array, Kalman filtering equation of transfer is established；Ask for kalman gain COEFFICIENT KkAnd it is
System prediction error Pk, the result of water level forecast one day after of neural network prediction is modified.
As stated above, described S1 is specially：
Obtain the original time series array { x of waterlevel data1,x2,.....,xn, element number n；
Using the adf test function pair input datas { x of MATLAB R2015a softwares1,x2,.....,xnCarry out stabilization
Property examine；
If stability test result is unstable, to input data carry out difference processing, difference formula such as formula (1), and
By acquired results { y1,y2,.....,ynFormer input array is substituted, continue stability test；
yi=xi+1-xi(1),
If stability test result is steady, using MATLAB autocorr and parcorr functions, to stabilization time sequence
Row carry out ACF and PACF detections, detect in acquired results, the continuous maximum on confidence interval threshold, as data
The lag period T of sequence.
As stated above, described S2 is specially：
With any waterlevel data x in original time series arrayiStart, continuous T hydrographic data after selection, form M
Individual training sample set { xi,xi+1,.....,xi+T-1, and sample set is normalized operation, normalize process such as formula (2)
It is shown,
Wherein XnBe normalization after data set, XrIt is raw data set, Xmax、XminBe initial data concentrate maximum and
Minimum.
As stated above, described S3 is specially：
3.1st, artificial neural network is established using newff functions, it is reverse transmittance nerve network to determine neural network type；
The network number of plies is three layers, includes input layer, hidden layer and output layer；Wherein, input layer includes T node, and hidden layer includes 2*
T-1 node, output layer include 1 node；Training set is divided into network struction collection and validation data set two parts；
3.2nd, it is trained using train function pair artificial neural networks, to reach training round or meet to require error
Precision after training terminates, automatically generates artificial nerve network model as training termination condition；
3.3rd, waterlevel data is predicted using simulated function sim：Based on artificial nerve network model, 3.2 will be based on
Input data of the gained training sample set final stage data as sim functions, obtain analog result, as water level one day after
Prediction result.
As stated above, described S4 is specially：
Pass through the original time series array { x of waterlevel data1,x2,.....,xn, Kalman filtering equation of transfer is established,
Shown in its detailed process such as formula (3),
Xk=AXk-1+BUk-1+ w (k) (3),
XkIt is the water level of kth day；Xk-1It is the kth water level of -1 day；A and B is default system control parameters；Uk-1It is
The state-transition matrix of k-1 days, determined according to the autocorrelation parameter of water level；W (k) is error matrix；
Wherein, state-transition matrix Uk-1Determine shown in method such as formula (4),
Uk-1=2*Xk-2-Xk-3(4),
In formula, Xk-2It is the kth water level of -2 days；Xk-3It is the kth water level of -3 days；
Ask for kalman gain COEFFICIENT KkAnd system prediction error Pk, its detailed process such as formula (5), (6), (7) are shown,
Pk|k-1=BPK-1BT+ S (k-1) (5),
Kk=Pk|k-1[Pk|k-1+cov(w)]-1(6),
Pk=(1-Kk)Pk|k-1(7),
Wherein, B is control coefrficient, and cov (w) is error co-variance matrix；BTFor B transposed matrix；S (k-1) is k-1
When etching system control covariance；Pk|k-1It is Xk-1Corresponding covariance matrix；
After calculating kalman gain coefficient, the result of water level forecast one day after of neural network prediction is modified, had
Shown in body such as formula (8),
Xk=Xk-1+Kk(Yk-HXk-1) (8)
Wherein, YkIt is the water level forecast result one day after of neural network prediction, H is the parameter of measuring system, Xk-1For karr
Graceful filtering estimate, its value are estimated to obtain by state transition equation.
Beneficial effects of the present invention are：The present invention is modeled first with artificial neural network to water level historical data, profit
Water level is predicted with analog function；On this basis, neural network prediction result is carried out by Kalman filtering
Amendment, waterlevel data reparation and short-term forecast can be effectively realized, improve precision of prediction.
Embodiment
With reference to instantiation, the present invention will be further described.
The present invention provides a kind of water level prediction method based on neutral net Yu local Kalman filtering mixed model, and it is wrapped
Include following steps：
S1, determine the water level time series data lag period：
The original time series array of waterlevel data is gathered, using the root mean square method of inspection (ADF) true original time series
The stability of array；As stable condition is unsatisfactory for, then difference processing is carried out to initial data, until it passes through stability test；
After stable data set is obtained, determine that water level time series lags using auto-correlation coefficient (ACF) and partial correlation coefficient (PACF)
Phase T.
S1 is specially：
Obtain the original time series array { x of waterlevel data1,x2,.....,xn, element number n；
Using the adf test function pair input datas { x of MATLAB R2015a softwares1,x2,.....,xnCarry out stabilization
Property examine；
If stability test result is unstable, to input data carry out difference processing, difference formula such as formula (1), and
By acquired results { y1,y2,.....,ynFormer input array is substituted, continue stability test；
yi=xi+1-xi(1),
If stability test result is steady, using MATLAB autocorr and parcorr functions, to stabilization time sequence
Row carry out ACF and PACF detections, detect in acquired results, the continuous maximum on confidence interval threshold, as data
The lag period T of sequence.
S2, structure training sample set：
As the water level time series lag period T obtained by S1, original time series array is split, by original time sequence
Columns assembling and dismantling are divided into the training sample set that M length is T.
S2 is specially：
With any waterlevel data x in original time series arrayiStart, continuous T hydrographic data after selection, form M
Individual training sample set { xi,xi+1,.....,xi+T-1, and sample set is normalized operation, normalize process such as formula (2)
It is shown,
Wherein XnBe normalization after data set, XrIt is raw data set, Xmax、XminBe initial data concentrate maximum and
Minimum.
S3, the training sample set obtained based on S2, are established artificial neural network and trained, and generate artificial neural network mould
Type；And analog result is obtained, is as input data using the final stage data based on the obtained training sample sets of S2
Water level forecast result one day after.
S3 is specially：
3.1st, artificial neural network is established using newff functions, it is reverse transmittance nerve network to determine neural network type；
The network number of plies is three layers, includes input layer, hidden layer and output layer；Wherein, input layer includes T node, and hidden layer includes 2*
T-1 node, output layer include 1 node；Training set is divided into network struction collection and validation data set two parts.
In the present embodiment, network parameter is specifically configured to：Transmission function uses tansig functions, train epochs 1000 times,
Target error precision is 0.001；Training set is divided into two parts, and network struction collection accounts for the 80% of former state notebook data, validation data set
20% is accounted for, data set is all upset.
3.2nd, it is trained using train function pair artificial neural networks, to reach training round or meet to require error
Precision after training terminates, automatically generates artificial nerve network model as training termination condition；
3.3rd, waterlevel data is predicted using simulated function sim：Based on artificial nerve network model, 3.2 will be based on
Input data of the final stage data of obtained sample set as sim functions, obtain analog result, as water level one day after
Prediction result.
Water level forecast result one day after described in S4, Kalman filtering amendment：
By original time series array, Kalman filtering equation of transfer is established；Ask for kalman gain COEFFICIENT KkAnd it is
System prediction error Pk, the result of water level forecast one day after of neural network prediction is modified.
S4 is specially：
Pass through the original time series array { x of waterlevel data1,x2,.....,xn, Kalman filtering equation of transfer is established,
Shown in its detailed process such as formula (3),
Xk=AXk-1+BUk-1+ w (k) (3),
XkIt is the water level of kth day；Xk-1It is the kth water level of -1 day；A and B is default system control parameters, the present embodiment
In be arranged to 1；Uk-1It is the kth state-transition matrix of -1 day, is determined according to the autocorrelation parameter of water level；Assuming that water level when
Between change be linear, w (k) is error matrix, and 0 is set in the present embodiment；
Wherein, state-transition matrix Uk-1Determine shown in method such as formula (4),
Uk-1=2*Xk-2-Xk-3(4),
In formula, Xk-2It is the kth water level of -2 days；Xk-3It is the kth water level of -3 days；
Ask for kalman gain COEFFICIENT KkAnd system prediction error Pk, its detailed process such as formula (5), (6), (7) are shown,
Pk|k-1=BPK-1BT+ S (k-1) (5),
Kk=Pk|k-1[Pk|k-1+cov(w)]-1(6),
Pk=(1-Kk)Pk|k-1(7),
Wherein, B is control coefrficient, and cov (w) is error co-variance matrix；BT(k) transposed matrix for being B (k)；S(k-1)
For k-1 when etching system control covariance；Pk|k-1It is Xk-1Corresponding covariance matrix；
After calculating kalman gain coefficient, the result of water level forecast one day after of neural network prediction is modified, had
Shown in body such as formula (8),
Xk=Xk-1+Kk(Yk-HXk-1) (8)
Wherein, YkIt is the water level forecast result one day after of neural network prediction, H is the parameter of measuring system, is taken in this example
It is worth for 1, Xk-1For Kalman Filter Estimation value, its value is estimated to obtain by state transition equation,
For the enough time series forecasting problems of training sample, artificial nerve network model has unique advantage.
Influenceed by factors such as mankind's activity, cooperative reservoir water dispatch, rainfalls, freshwater line usually presents non-thread
Property, the feature of local big ups and downs, carry out the localization of time (space) frequency, multiscale analysis is that lifting navigation channel water level is pre-
Survey the important directions of precision.Therefore, the present invention, which proposes one kind, is based on artificial neural network (ANN) and local Kalman filtering
(KF) water level prediction method of mixed model, the more single artificial neural network of method precision or Kalman filtering have a distinct increment.
This method is based on non-linear artificial neural network and linear Kalman filter, carries out the Yangtze River waterway average daily water level time
Series Modeling.Prediction result, the error of nonlinear method are modified using the linear structural feature of Kalman filtering, carried
Precision of prediction has been risen, has made up the deficiency of existing method.Water level prediction method provided by the invention can effectively realize that Changjiang River Trunk Line is navigated
Road waterlevel data reparation and short-term forecast.
The present invention carries out Artificial Neural Network Modeling using Yangtze River waterway history waterlevel data, and is filtered by local Kalman
Wave method realizes neural network prediction modified result.Artificial nerve network model possesses complex system modeling advantage, comprehensive
Consider the environmental impact factors such as tide, runoff, wind direction；Meanwhile prediction knot is linearly corrected by local kalman filter method
Fruit, it compensate for reduction of the nonlinear organization to features such as navigation channel water level localised waving, seasonalities.
Carry out water level forecast application for Engineering Projects (Ma'an Mountain's gaging station), specific implementation step is as follows：
Step 1：Determine the lag period.The stability of water level time series, such as phase are confirmed with the method for inspection (ADF) using side
Stability condition is unsatisfactory for, then carries out difference processing to initial data, until it passes through stability test.For stablizing data
Collection, water level time series lag period N is determined using auto-correlation coefficient (ACF) and partial correlation coefficient (PACF).Its detailed process
For：
1. obtain the one-dimensional continuous array of the average daily water levels of Ma'an Mountain gaging station 2013-2016, { x1,x2,.....,x1460}。
2. use adf test function pairs input array { x in MATLAB R2015a1,x2,.....,x1460Carry out stabilization
Property examine.It is specific as follows：
adftest(x)；
3. it was found that stationary test is not by carrying out difference processing, difference formula such as formula (1) to input data, and incite somebody to action
Acquired results { y1,y2,.....,y1459Former list entries is substituted, it is transferred to step 2..
yi=xi+1-xi (1)
4. using MATLAB adftest function pairs input array { y1,y2,.....,y1459Carry out stability test.Inspection
It is 1 to test result, i.e. current sequence data are stationary time series data.
5. using MATLAB autocorr and parcorr function pairs { y1,y2,.....,y1459Carry out ACF and PACF inspections
Survey.Detect in acquired results, the continuous maximum on confidence interval threshold, be gained lag period result T.Hysteresis
Phase result is 5.It is specific as follows：
Aic=autocorr (y, 360)；
Paic=parcorr (y, 360)；
Step 2：Training sample set is built.By the gained lag period 5 in step 1, original series collection is decomposed, will be original
Sequence sets are decomposed into the training sample set that 1455 length are 5.Specific decomposition method：Any water level number is concentrated with original series
According to xiStart, continuous 5 hydrographic datas after selection, form 1455 training sample set { x1,x2,.....,x5, and to sample
Operation is normalized in collection, shown in normalization process such as formula (2).
Wherein XnBe normalization after data set, XrIt is raw data set, Xmax, XminBe initial data concentrate maximum and
Minimum.It is specific as follows：
[inputn, inputps]=mapminmax (input_train)；
Step 3：Artificial neural network training is carried out using MATLAB train functions, and utilizes sim function pairs god of net warp
Network is tested.Its detailed process is：
1. establish artificial neural network using newff functions.It is backpropagation neural network to determine artificial neural network type
Network (BP), the network number of plies are three layers, include input layer, hidden layer and output layer.Wherein, input layer includes 5 nodes, implies
Layer includes 9 nodes, and output layer includes 1 node.Network parameter is specifically configured to：Transmission function uses tansig functions, instruction
Practice step number 1000 times, target error precision is 0.001.Wherein, training set includes two parts：Network struction collection accounts for original sample
The 80% of data, validation data set account for 20%, and data set is all upset.It is specific as follows：
Net=newff (inputn, outputn, 9, ' tansig'})；
Net.trainParam.epochs=1000；
Net.trainParam.goal=0.001；
2. being trained using train function pair artificial neural networks, training process will to reach training round or satisfaction
Seek error precision and stop.Training terminates rear system and automatically generates an artificial nerve network model, each weights and implicit series of strata
Number can be inquired about in MATLAB softwares.It is specific as follows：
Net=train (net, inputn, outputn)；
3. generation network is predicted using simulated function sim.Using current sample set final stage data as sim letters
Several input parameters, obtain analog result；The result is water level forecast result one day after.It is specific as follows：
Ann=sim (net, inputn_test)；
BPoutput=mapminmax (' reverse', ann, outputps)；
Step 4:Local Kalman filtering amendment prediction result.Its detailed process is as follows：
1. pass through original array { x1,x2,.....,x1460, establish Kalman filtering equation of transfer coefficient.Its detailed process
As shown in formula (3).XkIt is the water level of kth day, A and B are system control parameters, and A, B are arranged to 1 in the present invention.UkIt is state
Transfer matrix, determined according to the auto-correlation of water level, it is assumed that the time change of water level is linear.wkIt is error matrix,
The random number within 1 is put in the present invention.
W=randn (1,10) * 0.1；
2. ask for kalman gain COEFFICIENT KkAnd system prediction error Pk, its detailed process such as formula (5), (6), (7) institute
Show.Wherein, B is control coefrficient, and cov (w) is error co-variance matrix.Wherein, systematic error initialization value is 1, and Kalman increases
It is as follows that benefit and system prediction error ask for process：
P (1)=1；
P_1 (k)=P (k-1)+cov (v)；
K (k)=P_1 (k)/(P_1 (k)+cov (w))；
X_est_1 (k)=X_est (k-1)；
X_est (k)=X_est_1 (k)+K (k) * (Y (k)-X_est_1 (k))；
P (k)=(1-K (k)) * P_1 (k)；
3. after asking for kalman gain, neural network prediction result is modified.Specific such as formula (8) is shown.
Xk=Xk-1+Kk(Yk-HXk-1) (8)
Wherein, YkIt is true measurement, is replaced in the present invention by neural network prediction end value.Xk-1For local card
Kalman Filtering estimate, its value is estimated by state transition equation, specific as follows：
Kalman (k)=(X_est (k)-X (k))/X (k)；
Acquired results Kalman (k) is the waterlevel data after the reparation of local Kalman filtering.Use institute of the present invention
Method is stated, Ma'an Mountain, Wuhu, Nanjing, big logical, 5, Anqing gaging station 2013-2016 data are predicted, experimental result table
Bright, water level forecast precision can reach 0.2m, average forecasting error 0.185m, and relative error can be controlled in less than 5%.
Above example is merely to illustrate the design philosophy and feature of the present invention, and its object is to make technology in the art
Personnel can understand present disclosure and implement according to this, and protection scope of the present invention is not limited to above-described embodiment.It is so all
The equivalent variations made according to disclosed principle, mentality of designing or modification, protection scope of the present invention it
It is interior.
Claims (5)
- A kind of 1. water level prediction method based on neutral net Yu local Kalman filtering mixed model, it is characterised in that：It is wrapped Include following steps：S1, determine the water level time series data lag period：The original time series array of waterlevel data is gathered, using the stabilization of the true original time series array of the root mean square method of inspection Property；As stable condition is unsatisfactory for, then difference processing is carried out to initial data, until it passes through stability test；It is stable obtaining After data set, water level time series lag period T is determined using auto-correlation coefficient and partial correlation coefficient；S2, structure training sample set：As the water level time series lag period T obtained by S1, original time series array is split, by original time series number Assembling and dismantling are divided into the training sample set that M length is T；S3, the training sample set obtained based on S2, are established artificial neural network and trained, and generate artificial nerve network model；And It is as latter as input data, acquisition analog result using the final stage data based on training sample set obtained by S2 steps Its water level forecast result；Water level forecast result one day after described in S4, Kalman filtering amendment：By original time series array, Kalman filtering equation of transfer is established；Ask for kalman gain COEFFICIENT KkAnd system prediction Error Pk, the result of water level forecast one day after of neural network prediction is modified.
- 2. the water level prediction method according to claim 1 based on neutral net Yu local Kalman filtering mixed model, It is characterized in that：Described S1 is specially：Obtain the original time series array { x of waterlevel data1,x2,.....,xn, element number n；Using the adf test function pair input datas { x of MATLAB R2015a softwares1,x2,.....,xnCarry out stability inspection Test；If stability test result is unstable, difference processing is carried out to input data, difference formula such as formula (1), and by institute Obtain result { y1,y2,.....,ynFormer input array is substituted, continue stability test；yi=xi+1-xi(1),If stability test result is steady, using MATLAB autocorr and parcorr functions, stabilization time sequence is entered Row ACF and PACF are detected, and are detected in acquired results, the continuous maximum on confidence interval threshold, as data sequence Lag period T.
- 3. the water level prediction method according to claim 1 based on neutral net Yu local Kalman filtering mixed model, It is characterized in that：Described S2 is specially：With any waterlevel data x in original time series arrayiStart, -1 hydrographic data of continuous T after selection, form M instruction Practice sample set { xi,xi+1,.....,xi+T-1, and sample set is normalized operation, shown in normalization process such as formula (2),<mrow> <msub> <mi>X</mi> <mi>n</mi> </msub> <mo>=</mo> <mn>0.05</mn> <mo>+</mo> <mn>0.9</mn> <mfrac> <mrow> <msub> <mi>X</mi> <mi>r</mi> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> <mrow> <msub> <mi>X</mi> <mi>max</mi> </msub> <mo>-</mo> <msub> <mi>X</mi> <mrow> <mi>m</mi> <mi>i</mi> <mi>n</mi> </mrow> </msub> </mrow> </mfrac> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> <mo>,</mo> </mrow>Wherein XnBe normalization after data set, XrIt is raw data set, Xmax、XminIt is the maximum and minimum that initial data is concentrated Value.
- 4. the water level prediction method according to claim 1 based on neutral net Yu local Kalman filtering mixed model, It is characterized in that：Described S3 is specially：3.1st, artificial neural network is established using newff functions, it is reverse transmittance nerve network to determine neural network type；Network The number of plies is three layers, includes input layer, hidden layer and output layer；Wherein, input layer includes T node, and hidden layer includes 2*T-1 Node, output layer include 1 node；Training set is divided into network struction collection and validation data set two parts；3.2nd, it is trained using train function pair artificial neural networks, to reach training round or meet to require error precision As training termination condition, after training terminates, artificial nerve network model is automatically generated；3.3rd, waterlevel data is predicted using simulated function sim：Based on artificial nerve network model, 3.2 gained will be based on Input data of the final stage data of training sample set as sim functions, obtain analog result, as water level forecast one day after As a result.
- 5. the water level prediction method according to claim 1 based on neutral net Yu local Kalman filtering mixed model, It is characterized in that：Described S4 is specially：Pass through the original time series array { x of waterlevel data1,x2,.....,xn, Kalman filtering equation of transfer is established, it has Shown in body process such as formula (3),Xk=AXk-1+BUk-1+ w (k) (3),XkIt is the water level of kth day；Xk-1It is the kth water level of -1 day；A and B is default system control parameters；Uk-1It is kth -1 day State-transition matrix, determined according to the autocorrelation parameter of water level；W (k) is error matrix；Wherein, state-transition matrix Uk-1Determine shown in method such as formula (4),Uk-1=2*Xk-2-Xk-3(4),In formula, Xk-2It is the kth water level of -2 days；Xk-3It is the kth water level of -3 days；Ask for kalman gain COEFFICIENT KkAnd system prediction error Pk, its detailed process such as formula (5), (6), (7) are shown,Pk|k-1=BPK-1BT+ S (k-1) (5),Kk=Pk|k-1[Pk|k-1+cov(w)]-1(6),Pk=(1-Kk)Pk|k-1(7),Wherein, B is control coefrficient, and cov (w) is error co-variance matrix；BTFor B transposed matrix；S (k-1) is that kth -1 day is System control covariance；Pk|k-1It is Xk-1Corresponding covariance matrix；After calculating kalman gain coefficient, the result of water level forecast one day after of neural network prediction is modified, specifically such as Shown in formula (8),Xk=Xk-1+Kk(Yk-HXk-1) (8)Wherein, YkIt is the water level forecast result one day after of neural network prediction, H is the parameter of measuring system, Xk-1Filtered for Kalman Ripple estimate, its value are estimated to obtain by state transition equation.
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