CN111539564A - Daily runoff time sequence prediction method based on ESMD and NNBR - Google Patents
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Abstract
The invention discloses a daily runoff time series prediction method based on ESMD and NNBR, which comprises the following steps: s1, collecting historical actual measurement daily runoff time sequence data, and decomposing the historical actual measurement daily runoff sequence to obtain a subsequence and a daily runoff sequence decomposition residual error; s2, establishing NNBRs for the decomposed subsequences, and predicting the daily flux through the NNBRs; s3, reconstructing the daily runoff flow prediction result and the daily runoff sequence decomposition residual error of each subsequence through an ESMD algorithm to obtain a daily runoff prediction sequence. The method combines NNBR and ESMD, and decomposes, predicts and reconstructs different components forming the hydrological process, so that the prediction precision of the daily runoff time sequence is effectively improved compared with a single NNBR model, the reservoir scheduling operation mode and the hydropower station power generation plan can be optimized according to the daily runoff time sequence, and the working energy efficiency of the reservoir hydropower station is improved.
Description
Technical Field
The invention relates to the technical field of runoff prediction, in particular to a daily runoff time series prediction method based on ESMD and NNBR.
Background
The runoff prediction has important significance for the operation management of a reservoir hydropower station, is an important basis for correctly making an optimal scheduling operation mode of the reservoir and a power generation plan of the hydropower station, and directly influences the operation mode and the working energy efficiency of the reservoir. For the short-term runoff forecasting, due to the influences of comprehensive factors such as climate, basin underlying surface conditions, human activities and the like, the daily runoff shows stronger characteristics such as nonlinearity, variability and multi-scale, so that the forecasting difficulty of the daily runoff is increased. At present, methods adopted for runoff forecasting at home and abroad mainly comprise a cause analysis method, a statistical analysis method, a gray system method, a fuzzy algorithm, an artificial neural network, wavelet analysis, a combination of the methods and the like. Due to the factors of all aspects such as basin conditions, various models have advantages, disadvantages and applicable conditions.
Therefore, a method for accurately predicting the radial flow under various watershed conditions is needed.
Disclosure of Invention
The invention aims to provide a daily runoff time sequence prediction method based on ESMD and NNBR, which aims to solve the problems in the prior art and effectively improve the prediction precision of the daily runoff time sequence.
In order to achieve the purpose, the invention provides the following scheme: the invention provides a daily runoff time series prediction method based on ESMD and NNBR, which comprises the following steps:
s1, collecting historical actual measurement daily runoff time sequence data, decomposing the historical actual measurement daily runoff sequence by using an extreme point symmetric model decomposition (ESMD) to obtain a subsequence and a daily runoff sequence decomposition residual error;
s2, establishing a nearest neighbor sampling regression model NNBR for the subsequences obtained by decomposition in the step S1, and predicting each subsequence through the NNBR;
and S3, reconstructing the prediction result of each subsequence in the step S2 and the daily runoff sequence decomposition residual error obtained in the step S1 through an ESMD algorithm to obtain a prediction sequence of daily runoff.
Preferably, the daily runoff time series prediction method based on the ESMD and the NNBR further comprises the precision calculation of the daily runoff prediction result.
Preferably, the accuracy calculation index of the daily runoff prediction result comprises: relative error, average relative error level, deterministic coefficient, process yield.
Preferably, the specific method for decomposing the historical measured daily runoff sequence by using the ESMD in step S1 includes:
s1.1, calculating all extreme points in daily runoff time sequence data, wherein the extreme points comprise a maximum point and a minimum point;
s1.2, sequentially connecting all adjacent extreme points, and marking the middle point of a connecting line between the adjacent extreme points;
s1.3, respectively adding middle points of left and right boundaries of the extreme points by a linear difference method;
s1.4, constructing a plurality of interpolation curves by using the midpoints of connecting lines between adjacent extreme points and the midpoints of left and right boundaries;
s1.5, repeating the steps S1.1-S1.4 to carry out iterative computation on the average value of the interpolation curve to obtain a first subsequence of daily runoff time sequence data Y;
s1.6, repeating the steps S1.1-S1.5 to carry out iterative computation on the subsequence of the daily runoff time sequence data until the residual error does not exceed any extreme point in the daily runoff time sequence data, and obtaining the decomposition residual error of the daily runoff time sequence data;
s1.7, setting an integer interval, changing the iteration times on the integer interval, repeating the steps S1.1-S1.6, and calculating the variance sigma of the residual error2And making sigma/sigma0Graph against number of iterations, where σ0Is dayStandard deviation of runoff time series data;
s1.8, passage σ/σ0Obtaining a relation graph with the iteration times to obtain sigma/sigma0And (4) taking the value of the corresponding iteration times when the value is the minimum value, and repeating the steps from S1.1 to S1.6 to obtain the daily runoff sequence decomposition residual error.
The invention discloses the following technical effects:
the method combines NNBR and ESMD, and decomposes, predicts and reconstructs different components forming the hydrological process, so that the prediction precision of the daily runoff time sequence is effectively improved compared with a single NNBR model, the reservoir scheduling operation mode and the hydropower station power generation plan can be optimized according to the daily runoff time sequence, and the working energy efficiency of the reservoir hydropower station is improved.
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings needed to be used in the embodiments will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings without inventive exercise.
FIG. 1 is a flow chart of a daily runoff time series prediction method based on ESMD and NNBR of the present invention;
FIG. 2 shows an ESMD-based decomposition result according to an embodiment of the present invention;
FIG. 3 shows the result of the daily runoff prediction of a Model1-Model12 according to an embodiment of the present invention;
fig. 4 is a comparison result of the measured value and the predicted value of the daily runoff in the embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
Referring to fig. 1, the invention provides a daily runoff time series prediction method based on ESMD and NNBR, which includes the following steps:
s1, collecting historical actual measurement daily runoff time sequence data Y ═ x1,x2,…,xnAnd decomposing the historical actual measurement daily runoff sequence by using an ESMD (Extreme-point Symmetric Mode Decomposition) to obtain a subsequence and a daily runoff sequence Decomposition residual error.
The extreme point symmetric mode decomposition ESMD can decompose nonlinear time series signals to obtain amplitudes and frequencies of different modes, and can identify hydrological process composition of time series.
The specific method for decomposing the historical actual measurement daily runoff sequence by using the ESMD comprises the following steps:
s1.1, calculating all extreme points S in daily runoff time sequence data YiI is more than or equal to 1 and less than or equal to n, wherein the extreme points comprise maximum points and minimum points;
s1.2, connecting all adjacent extreme points S in sequenceiAnd use of F in combinationiMarking the middle point of a connecting line between adjacent extreme points, wherein i is more than or equal to 1 and less than or equal to n;
s1.3, respectively adding middle points F of left and right boundaries of extreme points by a linear interpolation method0And Fn；
S1.4, constructing p interpolation curves L by using the obtained n +1 middle points1,…,Lp(p is not less than 1), and the average value L of the interpolation curve is (L)1+…+Lp)/p。
S1.5, repeating the steps S1.1-S1.4 to carry out iterative calculation on the average value of the interpolation curve, and when the absolute value L is equal to*If the absolute value is less than or equal to the allowable error, or the iteration time reaches a preset maximum iteration time K, obtaining a first subsequence Model1 of the daily runoff time sequence data Y;
s1.6, repeating the steps S1.1-S1.5 to carry out iterative computation on the subsequence of the daily runoff time sequence data Y until the residual error R does not exceed any extreme point in the daily runoff time sequence data Y, so as to obtain a decomposition residual error R of the daily runoff time sequence data Y;
s1.7, setting an integer interval [ Kmin,Kmax]In the integer interval [ Kmin,Kmax]Changing the maximum iteration number K, repeating the steps S1.1-S1.6 to obtain a residual R, and calculating the variance sigma of the residual R2And making sigma/sigma0Graph of relation to K, where σ0Is the standard deviation of daily runoff time series data Y;
S1.8、σ/σ0taking the corresponding K value when the minimum value is taken as K0，K0∈[Kmin,Kmax]Is a reaction of K0Substituting the step S1.5, and repeating the steps S1.1-S1.6 to obtain a daily runoff sequence decomposition residual error which is marked as R0Sequential decomposition residual R of daily runoff0An optimal AGM (adaptive global mean) curve is obtained.
S2, for the subsequences obtained by decomposition in the step S1, NNBRs (nearest neighbor sampling regression models) are established, and prediction of each subsequence is carried out through the NNBRs.
The nearest neighbor sampling regression model NNBR avoids making certain assumption on the dependent form and the probability distribution form of a research object, is a nonparametric model based on data driving and without identifying parameters, and has the basic idea that: there is a certain relation between the occurrence and development of the objective world, and the future motion trail has similarity with the history, i.e. the future development pattern can be searched from the known numerous patterns.
The specific method for predicting the daily runoff through the NNBR comprises the following steps:
known subsequence { Xt}nWherein X istDependent on the previous P neighbouring history values Xt-1，Xt-2，…，Xt-pDefining a feature vector Dt＝(Xt-1,Xt-2,…Xt-p)，XtIs DtIs based on the current feature vector D, based on the subsequent values of (t ═ P +1, P +2, … n)i＝(Xi-1,Xi-2,…Xi-p)，i∈[1，P]To predict DiSubsequent value X ofi。
In the feature vector Dt＝(Xt-1,Xt-2,…Xt-p) In the method, K nearest neighbor feature vectors are selected and recorded as D1(i)，D2(i)，…，DK(i)，K∈[1，t]The corresponding subsequent values are X respectively1(i)，X2(i)，…，XK(i)(ii) a Wherein the nearest neighbor passes through DiAnd DtThe Euclidean distance between the two is judged, the smaller the distance is, DiAnd DtThe closer to the nearest neighbor, the Euclidean distance is calculated as shown in formula (1), and K nearest neighbor feature vectors D1(i)，D2(i)，…，DK(i)And DiThe Euclidean distance between them is marked as R1(i)，R2(i)，…，RK(i)；
Wherein R ist(i)Represents DiAnd DtThe Euclidean distance between; dij,dtjAre respectively Di，DtThe jth element of (1).
Rj(i)The smaller, thej(i)And DiThe more adjacent, then Xi＝Xj(i)Possibility of (2) Wj(i)The larger (j ═ 1,2, …, K); that is, Xj(i)To XiThe greater the contribution of (c); wherein, the handle Wj(i)Represents Xj(i)Sampling weight of, see Wj(i)Distance from Euclidean Rj(i)In inverse proportion.
The single subsequence NNBR is represented by formula (2):
wherein K is the nearest neighbor number,
s3, by ESMDThe algorithm predicts the result of each subsequence in step S2 and the residual R obtained in step S10And reconstructing to obtain a prediction sequence of daily runoff.
S4, calculating the precision of the daily runoff prediction result; calculating the accuracy of the daily runoff prediction result through the following indexes:
1) relative error;
the specific calculation method of the relative error is shown as the formula (3):
2) average relative error levels;
the average relative error level of multiple predictions is represented by averaging the absolute values of the relative errors.
3) A certainty coefficient;
according to the hydrological information specification, the certainty coefficient DC is the degree of coincidence between the prediction process and the actual measurement process, as shown in equation (4):
wherein, y0(i) Is an actual measurement value; y isc(i) Is a predicted value;
is the mean value of measured values; n is the sequence length.
4) The process qualification rate;
when the predicted error is smaller than the allowable error, the prediction is qualified; the percentage of the ratio of the number of qualified predictions to the total number of predictions is the process yield, which represents the overall accuracy level of the multiple predictions, as shown in equation (5):
wherein QR is the process qualification rate; n is the qualified prediction times; and m is the total prediction times.
The first embodiment is as follows:
obtaining a measured daily runoff time sequence { x (i) in 41 years in 1960-2001 of the Hua county station in Wei river basin; and i is 1,2, … n, 28 days are taken in 2 months every year, 365 days are counted every year, and the data of the 2001-year daily runoff is predicted by adopting 1960-2000 actual measurement daily runoff time sequence data for model calibration.
First, the time series data of the actual daily runoff in 1960-.
Secondly, NNBRs are respectively established for Model1, models 2, … and Model12 subsequences, the feature vector dimension p is taken as 3, and the nearest neighbor number K is taken as
Annual daily runoff in 2001 was predicted by NNBR.
In the modeling process, a prediction strategy of gradually sliding backwards is used, such as predicting the flow 1 month and 1 day in 2001, constructing a feature vector by using the flow from 29 days 12 months in 2000 to 31 days 12 months in 2000, and constructing the feature vector by using the data 12 months and 31 days in 2000 and before; predicting the flow rate at 1/2/2001 by constructing a feature vector by using the flow rate from 30/12/2000 to 1/2001, and predicting by constructing a feature vector by using data at 1/2001 and before; and so on.
The daily runoff prediction results of Model1-Model12 in 2001 are shown in FIG. 3;
and thirdly, reconstructing the prediction results of the models 1-Model12 and R by an ESMD algorithm to obtain a prediction sequence of the daily runoff in 2001 in Hua county station. The comparison result between the measured value and the predicted value of the daily runoff in 2001 in the Hua county station is shown in fig. 4.
The daily runoff prediction accuracy based on ESMD and NNBR is shown in Table 1, and both meet the requirement of 20% of the design error of the specification.
TABLE 1
In the description of the present invention, it is to be understood that the terms "longitudinal", "lateral", "upper", "lower", "front", "rear", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", and the like, indicate orientations or positional relationships based on those shown in the drawings, are merely for convenience of description of the present invention, and do not indicate or imply that the referenced devices or elements must have a particular orientation, be constructed and operated in a particular orientation, and thus, are not to be construed as limiting the present invention.
The above-described embodiments are merely illustrative of the preferred embodiments of the present invention, and do not limit the scope of the present invention, and various modifications and improvements of the technical solutions of the present invention can be made by those skilled in the art without departing from the spirit of the present invention, and the technical solutions of the present invention are within the scope of the present invention defined by the claims.
Claims (4)
1. A daily runoff time series prediction method based on ESMD and NNBR is characterized by comprising the following steps:
s1, collecting historical actual measurement daily runoff time sequence data, decomposing the historical actual measurement daily runoff sequence by using an extreme point symmetric model decomposition (ESMD) to obtain a subsequence and a daily runoff sequence decomposition residual error;
s2, establishing a nearest neighbor sampling regression model NNBR for the subsequences obtained by decomposition in the step S1, and predicting each subsequence through the NNBR;
and S3, reconstructing the prediction result of each subsequence in the step S2 and the daily runoff sequence decomposition residual error obtained in the step S1 through an ESMD algorithm to obtain a prediction sequence of daily runoff.
2. The ESMD and NNBR based daily runoff time series predicting method according to claim 1, wherein said ESMD and NNBR based daily runoff time series predicting method further comprises an accuracy calculation of a daily runoff prediction result.
3. The ESMD and NNBR-based daily runoff time series prediction method according to claim 2, wherein the accuracy calculation indexes of the daily runoff prediction result comprise: relative error, average relative error level, deterministic coefficient, process yield.
4. The method for predicting the daily runoff time series based on the ESMD and the NNBR as claimed in claim 1, wherein the step S1 is a specific method for decomposing the historical measured daily runoff time series by using the ESMD, and comprises the following steps:
s1.1, calculating all extreme points in daily runoff time sequence data, wherein the extreme points comprise a maximum point and a minimum point;
s1.2, sequentially connecting all adjacent extreme points, and marking the middle point of a connecting line between the adjacent extreme points;
s1.3, respectively adding middle points of left and right boundaries of the extreme points by a linear difference method;
s1.4, constructing a plurality of interpolation curves by using the midpoints of connecting lines between adjacent extreme points and the midpoints of left and right boundaries;
s1.5, repeating the steps S1.1-S1.4 to carry out iterative computation on the average value of the interpolation curve to obtain a first subsequence of daily runoff time sequence data Y;
s1.6, repeating the steps S1.1-S1.5 to carry out iterative computation on the subsequence of the daily runoff time sequence data until the residual error does not exceed any extreme point in the daily runoff time sequence data, and obtaining the decomposition residual error of the daily runoff time sequence data;
s1.7, setting an integer interval, changing the iteration times on the integer interval, repeating the steps S1.1-S1.6, and calculating the variance sigma of the residual error2And making sigma/sigma0Graph against number of iterations, where σ0Is the standard deviation of daily runoff time series data;
s1.8, passage σ/σ0Obtaining a relation graph with the iteration times to obtain sigma/sigma0And (4) taking the value of the corresponding iteration times when the value is the minimum value, and repeating the steps from S1.1 to S1.6 to obtain the daily runoff sequence decomposition residual error.
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