CN110909943A - Multi-scale multi-factor joint-driven monthly runoff probability forecasting method - Google Patents
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Abstract
The invention relates to the technical field of hydrological forecasting and discloses a multi-scale multi-factor joint-driven monthly runoff probability forecasting method which comprises the steps of S1, constructing an alternative forecasting variable set; s2 collecting historical observation data; s3 normalizing the preprocessed historical observation data; s4, carrying out importance scoring on the variables by using a random forest; s5, successively adding the input factors with higher variable importance evaluation values to the optimal input variable set; s6 training a Gaussian process regression model; s7, testing the calibrated model in S6 to obtain an optimal input variable set and a corresponding coupling forecasting model; s8 is used for evaluating the accuracy of the deterministic forecasting result of the coupling forecasting model in S7. Compared with the prior art, the method combines random forest and Gaussian process regression, improves the physical mechanism of the forecasting model, can fully exert the excellent reasoning capability of the Gaussian process regression, and realizes the depiction of the high-precision runoff forecasting result and the uncertain evolution rule thereof.
Description
Technical Field
The invention relates to the technical field of horizontal forecasting, in particular to a multi-scale multi-factor joint-driven monthly runoff probability forecasting method.
Background
The monthly runoff forecast has an abnormally important reference value for long-term scientific planning and management of the watershed water resources, and is an important precondition for scientific distribution of the watershed water and reasonable utilization of the water resources.
At present, the monthly runoff forecasting method mainly comprises a forecasting method based on a physical model and a data driving method. The data driving model does not need to deeply understand the physical mechanism of the hydrological cycle of the drainage basin, directly deeply excavates the correlation among hydrological variables such as runoff, rainfall, evaporation and the like from a data layer, and has the advantages of simple modeling, less basic data requirement, low calculation complexity and the like. When the observation data of the research area is insufficient, the potential physical mechanism of the hydrological phenomenon of the water circulation system of the area is unknown or only partially understood, the data-driven forecasting model is an excellent choice for flood forecasting. In addition, for medium-and-long-term runoff forecasting with a long forecasting period, reliable prediction data of key meteorological elements (precipitation, evaporation and air temperature) of a water circulation system in a long period of time in the future are difficult to obtain practically, so that a mode of forecasting medium-and-long-term runoff by utilizing a water balance principle and a physical hydrological model capable of reflecting each core link of water circulation has certain difficulty in practical operation. And the nonlinear mapping relation between the target variable (runoff) and the observation data of the influence variable (regional hydrometeorological elements) is directly mined, and the data-driven model for forecasting the runoff process in a future period can solve the embarrassment of the physical model in medium-long term forecasting.
The data-driven models can be further divided into prediction models based on mathematical statistics and intelligent prediction models based on machine learning according to the modeling basic theory of the data-driven models. The traditional mathematical statistics-based and representative hydrological model comprises: the ARMA model, the ARIMA model and improved versions thereof. The model generally assumes that the sequence to be predicted has stationarity and follows Gaussian distribution, however, the natural runoff process is subjected to the comprehensive action of various natural and unnatural factors, generally has the characteristics of nonlinearity and nonstationness, and the basic assumption of the mathematical statistics prediction model on the time sequence is difficult to satisfy. Therefore, such models have limited ability to predict runoff sequences with non-stationary characteristics. In recent years, with rapid development of theories and methods such as computer technology, data mining, artificial intelligence and the like, a machine learning model represented by an artificial neural network can well make up for the problem that a time sequence model is not enough to fit nonlinear and non-stable sequences, and is widely applied to the field of runoff forecasting. However, the data-driven model directly predicts from the data level, depends on the length and quality of observed data, and lacks a physical mechanism. Moreover, most of the current monthly runoff forecasting models are concentrated on deterministic single-value forecasting, and few forecasting models and methods capable of describing the uncertainty of forecasting results are available.
In order to solve the above technical problems, it is necessary to optimize a forecast model based on data driving.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the problems in the prior art, the invention provides a multi-scale multi-factor joint-driven monthly runoff probability forecasting method, which improves the physical basis of a data-driven model and solves the problem that the traditional deterministic single-value forecasting method is difficult to depict the uncertainty of a forecasting result.
The technical scheme is as follows: the invention provides a multi-scale multi-factor joint-driven monthly runoff probability forecasting method, which comprises the following steps:
s1: constructing an alternative forecast variable set;
s2: collecting historical observation data of variable runoff to be predicted and alternative forecast variable input factors in S1;
s3: normalizing the historical observation data in the preprocessing S2 and dividing the processed data into training data and inspection data;
s4: performing variable importance evaluation on the data which is subjected to normalization processing in the S3 and is related to the runoff to be forecasted;
s5: setting the optimal input variable to be NULL, gradually adding the input factors with higher variable importance evaluation values in S4 to the optimal input variable set based on a sequence forward search strategy, and dividing the input factors into training data and inspection data;
s6: training a base forecast model by using the training data of the optimal input variable set in the S5 and storing;
s7: testing the calibrated model in the S6 by using the check data set in the S5 to obtain the prediction error of the input variable set at the moment and store the prediction error, traversing all input variables, wherein the variable set with the lowest prediction error is the optimal input variable set, and the corresponding model is the coupling model;
s8: and evaluating the accuracy of the certainty forecast result of the coupling model in the S7.
Further, the classification of the candidate predictor variables in S1 includes: regional hydrometeorological factors, large-scale circulation factors, and climate factors.
Further, in S4, the importance of the variable is evaluated by a random forest algorithm.
Further, the basis forecasting model in S6 adopts a gaussian process regression model.
Further, the accuracy assessment index in S8 includes a mean absolute percentage error, a certainty coefficient, and a correlation coefficient.
Has the advantages that:
(1) the invention adopts a random forest algorithm to analyze remote correlation variables such as solar activity, circulation factors, regional sea temperature and the like and high-dimensional and hysteresis nonlinear mapping relations between regional meteorological factors and regional runoff, discloses the influence degrees and action strengths of different atmospheric-ocean remote correlation factors and regional meteorological elements on runoff processes with different time scales, constructs a multi-scale runoff forecasting factor set containing the regional meteorological factors, climate and large-scale circulation factors, and can make up the defect that the physical mechanism of the traditional data-driven forecasting method is weaker.
(2) According to the method, historical contemporaneous runoff data is merged into a machine learning model, the data utilization rate is improved under the condition of limited data length, the multiple characteristics of uneven runoff annual trend and monthly change are fully mined, and the model forecasting performance is enhanced under the condition of limited sample learning. Random forests and Gaussian process regression are combined, a Gaussian process regression runoff forecasting model driven by atmosphere-ocean-land surface multi-scale factors in a combined mode is provided, historical contemporaneous hydrological, meteorological and climatic data are integrated into a machine learning model through a coupling model, on one hand, the physical mechanism of the forecasting model is improved, on the other hand, the excellent reasoning capability of the Gaussian process regression can be fully exerted, and the high-precision runoff forecasting result and the uncertain evolution rule thereof can be depicted.
(3) Compared with three comparison models, namely a PCC-GPR comparison model, a PCC-BP comparison model and a PCC-GRNN comparison model, which are formed by coupling the coupling model with a common Pearson Correlation Coefficient (PCC) selection input factor, a single GPR selection input factor and a BP and GRNN comparison model commonly used in the hydrological field, the model precision is greatly improved, particularly in the flood season with large runoff sequence fluctuation, the model is higher in robustness, reliability and precision, the uncertainty evolution rule of the forecast result can be drawn, and the monthly runoff forecasting method is wide in application prospect.
Drawings
FIG. 1 is a schematic flow chart of a monthly runoff probability forecasting method of the invention;
FIG. 2 is a schematic diagram of the estimation of the forecast result precision of the RF-GPR model (the coupling model of the invention) of the stone drum station in the next year;
FIG. 3 is a schematic diagram of the precision evaluation of the PCC-GPR model forecast result in the next year of the stone drum station;
FIG. 4 is a schematic diagram of the PCC-BP model forecasting result precision evaluation of the stone drum station in the next year;
FIG. 5 is a schematic diagram of the accuracy evaluation of the PCC-GRNN model forecast result in the future year of the stone drum station;
FIG. 6 is a schematic diagram of a runoff forecasting process and an uncertain interval of forecasting results of a coupling model of a drumstick station, wherein the forecasting period of the coupling model is 1 month;
fig. 7 is a schematic diagram of a runoff forecasting process and a forecasting result uncertain interval with a forecasting period of 7 months of a coupling model of a stone drum station.
Detailed Description
The present invention will be described in detail with reference to the accompanying drawings.
Aiming at the defects that the existing medium-long term hydrological prediction method is weak in physical foundation and cannot depict uncertainty of a prediction result, the invention provides a multi-scale multi-factor joint-driven monthly runoff probability prediction method. A physical mechanism formed by runoff of a water circulation system is used as an entry point, a random forest algorithm is adopted to identify a group of forecast factors closely related to forecast the monthly runoff from regional meteorological factors such as rainfall, air temperature and air pressure and various global scale climatic factors such as atmospheric circulation factor and sea level temperature, and then an atmosphere-ocean-land multi-scale multi-factor driven Gaussian process regression runoff forecasting model is established, so that a high-precision runoff forecasting result and uncertainty evolution characteristics of the high-precision runoff forecasting result are obtained, and theoretical basis and technical support are provided for scientific distribution of watershed water resources. The specific flow of the multi-scale multi-factor joint-driven monthly runoff probability forecasting method provided by the invention is detailed in figure 1.
The technical scheme of the invention is specifically explained according to the specific embodiment as follows:
the invention discloses a multi-scale multi-factor joint-driven monthly runoff probability forecasting method, which selects a rock drum hydrological station of a Jinshajiang river basin control station as a forecasting section, and comprises the following detailed steps:
step 1: and constructing an alternative forecast variable set. Taking a runoff process forming mechanism as an entry point, and primarily selecting forecast variables from regional hydrological meteorological factors (rainfall, air temperature, humidity and the like) related to runoff of the drainage basin, large-scale circulation factors and climatic factors (different sea level temperatures and the like) according to the correlation according to the characteristics of the hydrological meteorological climate of the drainage basin.
Step 2: and collecting historical observation data of variable runoff to be predicted and alternative input factors thereof. For example, the actual measurement monthly runoff flow data of the section 1961-.
And step 3: normalizing the observation data collected in the preprocessing step 2 and dividing the normalized data into training period data and inspection period data, such as: the normalized historical observation data from 1961 to 1997 are taken as training period data, and the normalized historical observation data from 1998 to 2010 are taken as inspection period data.
And 4, step 4: and selecting a forecasting factor set. And (3) fully utilizing the integrated learning advantage of the random forest algorithm to carry out variable importance assessment (VIM) on the alternative forecast variables related to the runoff to be forecasted.
And 5: and setting the optimal input variable to be NULL, gradually adding the input factors with higher variable importance evaluation values in the step 4 to the optimal input variable set based on a sequence forward search strategy, and dividing the optimal input variables into training data and inspection data.
Step 6: and (5) training and storing a base prediction model by using the training data of the optimal input variable set in the step (5), wherein the base prediction model used in the invention is a Gaussian process regression model.
The Gaussian process regression model is a novel machine learning method, the method not only has Bayes flexible inductive reasoning capability, but also has parallel processing, self-organizing, self-adapting and self-learning capabilities of machine learning methods such as a neural network and the like, and has obvious advantages in solving the high-dimensional complex regression problems of few samples and nonlinearity. The method overcomes the limitation that the traditional data driving model cannot depict the error of the forecast result. The invention adopts a Gaussian process regression model as a base prediction model to overcome the problem that the traditional data-driven model cannot depict the prediction uncertainty.
For n sets of training samples, D { (X, y) | X ∈ Rn×d,y∈RnY is the predicted variable runoff, and X is d input factors that affect the output variable y. The random process state set g (X) of the input variable X, { g (X)1),g(x2),…,g(xn) Obey n-dimensional joint Gaussian distribution, and according to the definition of Gaussian process, the random process state set g belongs to the Gaussian process, the probability function is marked as GP, and can be unique by a mean function E (X) and a covariance function matrix K (X, X)One of the determinations is:
g(X)~GP(E(X),K(X,X))
in gaussian process regression, the mapping relationship between an input factor X and a predicted variable y is generally regarded as a gaussian process g, and in consideration of noise pollution, the standard gaussian process regression model expression is as follows:
where ε is a white noise sequence that is independent of each other and obeys normal distribution,representing the variance of the noise, InIs an n-dimensional identity matrix.
The prior distribution of the target variable y is:
in the formula, K (X, X) is an n multiplied by n symmetric positive definite covariance matrix.
For test sample Dtest={(xtest,ytest)|xtest∈Rd,ytestE.g. R, according to the nature of Gaussian process, the following can be obtained: training target output y of input sample D and test sample DtestOutput y oftestObeying a joint gaussian distribution:
in the formula, K (x)test,X)=K(X,xtest)TFor testing input set x*An n × 1 order covariance function matrix with a training input variable X; k (x)test,xtest) For testing input variable xtestIts own covariance.
And 7: and 5, testing the calibrated Gaussian process regression model by using the test data set of the optimal input variable set in the step 5 to obtain the prediction error of the input variable set at the moment and store the prediction error, traversing all the input variables, wherein the variable set with the lowest prediction error is the optimal input variable set, and the corresponding model is the coupling model.
Training input data X and output y given conditions, new input XtestThe predicted value y can be deduced from the Bayesian posterior probability mathematical formulatestThe posterior distribution of (A) is:
p(ytest|X,y,xtest)~N(E(ytest),cov(ytest))
in the formula, E (y)test) For a new input variable xtestCorresponding output ytestThe mean value of (a); cov (y)test) Is a predicted value ytestTo measure the uncertainty of the prediction result.
And 8: and (3) taking three common precision evaluation indexes of average absolute percentage error (MAPE), certainty coefficient (NSE) and correlation coefficient R, and carrying out precision evaluation on the certainty result of the coupling model in the step 7, wherein the precision evaluation indexes are not limited to the 3 indexes, and the 3 indexes are taken in the embodiment.
Referring to FIGS. 2-5, the forecast accuracy assessment of the three comparative models, PCC-GPR, PCC-BP and PCC-GRNN, is formed by coupling the commonly used Pearson Correlation Coefficient (PCC) selection input factors with a single GPR and the commonly used BP and GRNN models in the hydrological field in the future year of the RF-GPR model (the coupled model of the present invention, RF refers to the random forest algorithm, and GPR refers to the Gaussian process regression model). The comparison result shows that the RF-GPR model can effectively improve the monthly runoff forecasting precision compared with a PCC-GPR model, a PCC-BP model and a PCC-GRNN model.
Fig. 6 and 7 show the runoff forecasting process and the forecasting result uncertain interval when the coupled model RF-GPR model has forecast periods of 1 and 7 months, wherein 1961-1997 are training data, and 1998-2010 are testing data, and the figures prove that the method provided by the invention not only has a high and reliable forecasting result, but also can depict the uncertainty of the forecasting result, can provide richer forecasting information for the drainage basin management department, and is a monthly runoff forecasting method with a wider application prospect.
The above embodiments are merely illustrative of the technical concepts and features of the present invention, and the purpose of the embodiments is to enable those skilled in the art to understand the contents of the present invention and implement the present invention, and not to limit the protection scope of the present invention. All equivalent changes and modifications made according to the spirit of the present invention should be covered within the protection scope of the present invention.
Claims (5)
1. A multi-scale and multi-factor combined driven monthly runoff probability forecasting method is characterized by comprising the following steps:
s1: constructing an alternative forecast variable set;
s2: collecting historical observation data of variable runoff to be predicted and alternative forecast variable input factors in S1;
s3: normalizing the historical observation data in the preprocessing S2 and dividing the processed data into training data and inspection data;
s4: performing variable importance evaluation on the data which is subjected to normalization processing in the S3 and is related to the runoff to be forecasted;
s5: setting the optimal input variable to be NULL, gradually adding the input factors with higher variable importance evaluation values in S4 to the optimal input variable set based on a sequence forward search strategy, and dividing the input factors into training data and inspection data;
s6: training a base forecast model by using the training data of the optimal input variable set in the S5 and storing;
s7: testing the calibrated model in the S6 by using the check data set in the S5 to obtain the prediction error of the input variable set at the moment and store the prediction error, traversing all input variables, wherein the variable set with the lowest prediction error is the optimal input variable set, and the corresponding model is the coupling model;
s8: and evaluating the accuracy of the certainty forecast result of the coupling model in the S7.
2. The multi-scale multi-factor joint driven monthly runoff probability forecasting method according to claim 1, wherein the alternative forecasting variable classification in the S1 comprises: regional hydrometeorological factors, large-scale circulation factors, and climate factors.
3. The multi-scale and multi-factor joint driven monthly runoff probability forecasting method according to claim 1, wherein the variable importance evaluation is performed in the S4 through a random forest algorithm.
4. The multi-scale multi-factor joint driven monthly runoff probability forecasting method according to claim 1, wherein the basic forecasting model in the S6 adopts a Gaussian process regression model.
5. The multi-scale multi-factor joint driven monthly runoff probability forecasting method according to claim 1, wherein the accuracy assessment indexes in the step S8 comprise average absolute percentage error, certainty coefficient and correlation coefficient.
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