CN113837475A - Directed graph deep neural network runoff probability forecasting method, system, equipment and terminal - Google Patents

Directed graph deep neural network runoff probability forecasting method, system, equipment and terminal Download PDF

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CN113837475A
CN113837475A CN202111135983.6A CN202111135983A CN113837475A CN 113837475 A CN113837475 A CN 113837475A CN 202111135983 A CN202111135983 A CN 202111135983A CN 113837475 A CN113837475 A CN 113837475A
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CN113837475B (en
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刘永琦
侯贵兵
李媛媛
张剑
徐景锋
朱炬明
林若兰
李争和
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China Water Resources Pearl River Planning Surverying & Designing Co ltd
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Abstract

The invention belongs to the technical field of hydrology and water resources, and discloses a directed graph deep neural network runoff probability forecasting method, a system, equipment and a terminal, wherein the directed graph deep neural network runoff probability forecasting method comprises the following steps: constructing a hydrological site and meteorological site directed graph structure; establishing a directed graph deep neural network forecasting model by combining a spatial information capturing process and a characteristic aggregation process according to a multi-site directed graph; constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result; reconstructing a hidden Markov regression training data set by using a forecast result obtained by the digraph deep neural network and an actual measured runoff value; and training a hidden Markov regression model to obtain a runoff probability forecasting result. The invention combines the graph theory and the neural network model, captures the spatial information through convolution operation, and aggregates the rainfall runoff process through the multilayer network, thereby improving the runoff forecasting precision.

Description

Directed graph deep neural network runoff probability forecasting method, system, equipment and terminal
Technical Field
The invention belongs to the technical field of hydrology and water resources, and particularly relates to a method, a system, equipment and a terminal for forecasting the runoff probability of a directed graph deep neural network.
Background
At present, accurate and reliable runoff forecasting can provide beneficial data basis for reservoir group scheduling decision, and has great significance for increasing power generation benefit, reducing flood control risk and improving comprehensive utilization benefit of water resources. With the development of computer technology, machine learning and deep learning methods such as support vector machine regression, neural networks, long-short term memory networks and the like show excellent performance in runoff forecasting. However, the statistical-based black box model has two disadvantages: firstly, the black box model is only the transmission between data, and the model parameters of the black box model have no better physical explanation in the process of generating the hydrological runoff; secondly, the traditional forecasting model only forecasts a single point value and can not quantify uncertainty in forecasting. Therefore, how to establish a statistical learning model with certain physical significance and enable the statistical learning model to have the capability of interval prediction and probability prediction to quantify and forecast uncertainty is a theoretical and practical engineering problem which needs to be solved urgently.
Through the above analysis, the problems and defects of the prior art are as follows:
(1) the existing statistical-based black box model is only the transmission between data, and the model parameters of the statistical-based black box model have no good physical explanation in the process of generating the hydrological runoff.
(2) The traditional forecasting model only forecasts a single point value, and uncertainty in forecasting cannot be quantified.
The difficulty in solving the above problems and defects is: the general statistical model only considers the correlation of input and output data, and is difficult to establish a model considering the hydrological physical process; the runoff prediction error has the characteristics of 'abnormal' and 'variance difference', and the uncertainty of the prediction is difficult to quantify by using the general Gaussian distribution.
The significance of solving the problems and the defects is as follows: developing a deep learning model to a conceptual hydrological model, improving the hydrological prediction precision, and giving a reasonable parameter explanation; in addition, the uncertainty of the runoff forecast is quantified, richer and more reliable forecast information is provided for reservoir dispatching decision making, and a dispatching decision maker is facilitated to reasonably distribute water resources.
Disclosure of Invention
The invention provides a directed graph deep neural network runoff probability forecasting method, a directed graph deep neural network runoff probability forecasting system, directed graph deep neural network runoff probability forecasting equipment and a directed graph deep neural network runoff probability forecasting terminal, and particularly relates to a directed graph deep neural network runoff probability forecasting method, a directed graph deep neural network runoff probability forecasting system, directed graph deep neural network runoff probability forecasting equipment and a directed graph deep neural network runoff probability forecasting terminal, aiming at solving the technical problems that an existing statistical learning runoff forecasting method has no specific hydrological physical significance and uncertainty in forecasting cannot be quantified.
The invention is realized in such a way that a directed graph deep neural network runoff probability forecasting method comprises the following steps:
step one, constructing a hydrological site and meteorological site directed graph structure;
step two, establishing a directed graph deep neural network forecasting model by combining a space information capturing process and a feature aggregation process according to the multi-site directed graph;
constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result;
fourthly, reconstructing a hidden Markov regression training data set by the forecast result obtained by the directed graph deep neural network and the actual measuring runoff value;
and fifthly, training a hidden Markov regression model to obtain a runoff probability forecasting result.
Further, in the first step, the constructing a directed graph structure of the hydrological site and the meteorological site includes:
taking upstream hydrological stations and meteorological stations of the Yangtze river as research objects, and taking each hydrological station and meteorological station as points in a directed graph; determining the relationship between each hydrological site and other hydrological sites and meteorological sites according to the upstream and downstream relationship between the hydrological sites and the regions in which the meteorological sites are located and the hydrological sites, and connecting points with causal relationship by using vectors; and forming a directed graph by all the points and the vectors.
Further, in the second step, establishing a deep neural network prediction model of the directed graph according to the multi-site directed graph by combining a spatial information capturing process and a feature aggregation process, including:
the directed graph deep neural network model consists of a spatial information capturing process and a characteristic aggregation process; the spatial information capturing process is composed of a plurality of convolution layers and a full-connection layer, is used for capturing the influence of rainfall in an area range on the runoff of the hydrological site through convolution operation, is regarded as a rainfall runoff generating model in the hydrological model, and is expressed as follows:
Figure BDA0003282038800000031
where v is 1, …, NI is the index of the hydrologic site, L is the number of network layers in the process,
Figure BDA0003282038800000032
layer i in the process of capturing spatial information of representative v hydrological sites, SP (v) represents a meteorological site set of which rainfall influences the v hydrological site, PuRepresents rainfall information of the u-th meteorological site, Conv1D () represents convolution operation, fiFor the dimension of the i-th layer output space, kiIs the length of the convolution window, siFor the step size of the convolution, σ () represents the activation function of the fully-connected layer, which takes the form of a linear activation function, WvWeight of the full connection layer, bvIs the offset vector of the fully connected layer;
the characteristic aggregation process is composed of a plurality of layers of perception networks and is used for establishing the rainfall characteristics captured by the convolutional neural network and the nonlinear relation between the upstream runoff characteristics and the current hydrologic site runoff, the process is regarded as a confluence process in a hydrologic model, and the characteristic aggregation process is expressed as follows:
Figure BDA0003282038800000033
wherein L' is the number of network layers in the characteristic aggregation process,
Figure BDA0003282038800000034
layer I in the process of characteristic aggregation of representative v hydrological sites, SI (v) represents the upstream hydrological site set affecting the v hydrological site, IvRepresenting the early runoff information of the v-th hydrological site,
Figure BDA0003282038800000035
is the weight of the ith hidden layer,
Figure BDA0003282038800000036
for the bias vector of the ith hidden layer, delta () represents the activation function of the hidden layer, and the activation function adopts Sigmoid activation function, WtarWeight of the full connection layer, btarFor the offset vector of the fully-connected layer, the activation function of the σ () output layer, a linear activation function is used.
Further, in the third step, constructing a data set consisting of the forecast runoff and the forecast factors thereof, and training a deep neural network of the directed graph by adopting an Adam optimization algorithm to obtain a high-precision multistep long runoff forecast result, wherein the method comprises the following steps of:
the forecasting factors are real-time measured runoff data and rainfall data of all hydrology sites and meteorological sites, the forecasting values are future runoff values of target sites, and a training set consisting of the forecasting factors and the forecasting values is represented as follows:
D1＝[X,Y]
Figure BDA0003282038800000041
yt＝[Itar,t+1,...,Itar,t+C]；
wherein D is1Is a training set of the deep neural network model of the directed graph, and X is a forecasting factor X ═ X of the training sett,…,XT]Y is the predicted value of training set Y ═ Yt,…,yT]T is training integrated duration, J is the previous step length of the forecasting factor, C is the forecasting step length, Iv,tRepresents runoff of the v-th hydrological site in a time period t, Pu,tThe rainfall of the u-th meteorological station in the period t is shown, NI is the total number of the hydrological stations, NP is the total number of the meteorological stations, and tar is the forecast target station.
After the data set is constructed, carrying out normalization processing on the data, and setting parameters of a graph depth neural network, including the number of convolutional layers and the number of nodes of a full connection layer in each spatial information capturing process, the number of nodes of a sensing layer, the number of nodes of a hidden layer and the number of nodes of an output layer of a multi-layer sensing network, a network learning rate and a training algebra; training a directed graph deep neural network on a training set by combining an Adam optimization algorithm, and iteratively optimizing model parameters; obtaining a multistep long-path flow forecasting result Y according to the trained directed graph deep neural network modeltar。
Further, in the fourth step, the result Y of the runoff forecast obtained by the deep neural network of the training set directed graph in the third step is usedtarCombining the training set D ═ Y of hidden Markov regression with measured runoff Ytar,Y]。
Further, in the fifth step, the training of the hidden markov regression model to obtain a runoff probability forecasting result includes:
hidden Markov regression mainly comprises a hidden Markov model and probability forecasting, and parameters of the hidden Markov model are trained by adopting a Baum-Welch algorithm; wherein the joint probability distribution of hidden variables and observed variables of the hidden Markov model is represented as follows:
Figure BDA0003282038800000051
wherein D is2All observation sequences; z ═ Z1,...,zT]The hidden state variables at all the moments are taken as the hidden state variables; θ represents all the parameters to be trained of the hidden Markov model: pi ═ pi1,...,πK]Is a priori probability, pikRepresenting prior probability under a state K, wherein K is the number of model components; a is a state transition probability matrix of K, where AijRepresenting the transition probability of transitioning from the i-state to the j-state, phi ═ phi1,...,φK]For observing the parameters of the model, phikParameters representing a kth observation model;
the conditional probability distribution of the observed variables is defined as p (d)t|zt＝k,φk). When multivariate gaussian distribution is used as the observation model, the conditional probability distribution is:
p(dt|zt＝k,φk)＝N(dt|μk,∑k)；
wherein, mukIs the mean vector, Σ, of the observed values in the k-th statekThe covariance matrix of the observed values at the k-th state.
Adopting an EM algorithm to iterate and optimize parameters theta of the model to be { pi, A, phi }, and obtaining a trained hidden Markov model; obtaining a conditional probability density function of a forecast value after a forecast factor is given according to the nature of Gaussian joint probability distribution, a probability multiplication formula and a Bayes formula by inference, wherein the conditional probability density function is shown as the following formula:
Figure BDA0003282038800000061
wherein the content of the first and second substances,
Figure BDA0003282038800000062
a conditional probability density function that is a prediction value;
Figure BDA0003282038800000063
a joint probability density function of the predictor and the predicted value; p (y)t) Edge probability density function, h, of the predictor yt(k) The probability is a forward probability and is obtained through a forward-backward algorithm;
Figure BDA0003282038800000064
and
Figure BDA0003282038800000065
respectively a mean vector and a covariance matrix of the prediction factor in the kth observation model;
Figure BDA0003282038800000066
and
Figure BDA0003282038800000067
the prediction value is the conditional mean vector and the covariance matrix of the k-th observation model respectively.
Another objective of the present invention is to provide a runoff probability forecasting system applying the directed graph deep neural network runoff probability forecasting method, where the runoff probability forecasting system includes:
the directed graph structure building module is used for building a directed graph structure of the hydrological site and the meteorological site;
the forecasting model building module is used for building a directed graph deep neural network forecasting model by combining a space information capturing process and a characteristic aggregation process according to the multi-site directed graph;
the forecasting model optimization module is used for constructing a data set consisting of the forecasting runoff and the forecasting factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecasting result;
the training data set construction module is used for reconstructing a hidden Markov regression training data set from the forecast result obtained by the directed graph deep neural network and the actual measurement runoff value;
and the runoff probability forecasting module is used for obtaining a runoff probability forecasting result by training the hidden Markov regression model.
It is a further object of the invention to provide a computer device comprising a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to perform the steps of:
constructing a hydrological site and meteorological site directed graph structure; establishing a directed graph deep neural network forecasting model by combining a spatial information capturing process and a characteristic aggregation process according to a multi-site directed graph; constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result; reconstructing a hidden Markov regression training data set by using a forecast result obtained by the digraph deep neural network and an actual measured runoff value; and training a hidden Markov regression model to obtain a runoff probability forecasting result.
It is another object of the present invention to provide a computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
constructing a hydrological site and meteorological site directed graph structure; establishing a directed graph deep neural network forecasting model by combining a spatial information capturing process and a characteristic aggregation process according to a multi-site directed graph; constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result; reconstructing a hidden Markov regression training data set by using a forecast result obtained by the digraph deep neural network and an actual measured runoff value; and training a hidden Markov regression model to obtain a runoff probability forecasting result.
Another objective of the present invention is to provide an information data processing terminal, which is used for implementing the runoff probability forecasting system.
By combining all the technical schemes, the invention has the advantages and positive effects that: the directed graph deep neural network runoff probability forecasting method provided by the invention combines a graph theory and a neural network model, captures spatial information through convolution operation, aggregates a rainfall runoff process through a multilayer network, improves the runoff forecasting precision, adopts a hidden Markov regression method to quantitatively describe the uncertainty of the runoff forecasting, and has important significance for water resource planning and management.
According to the invention, through constructing the directed graph structures of the hydrological site and the meteorological site, the spatial information capture is carried out on multi-site rainfall data by adopting the convolutional neural network, the rainfall runoff characteristics are aggregated by adopting the multilayer sensing network, the runoff producing and converging processes of the hydrological rainfall runoff are fully simulated, and the physical significance of different processes in the hydrological runoff forecasting is effectively explained.
According to the method, the single-point prediction value of the deep learning model is converted into the probability prediction result through a hidden Markov regression method, the uncertainty of the runoff prediction is quantitatively analyzed, and the prediction uncertainty information which cannot be obtained by the traditional prediction method under the determination is obtained.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments of the present invention will be briefly described below, and it is obvious that the drawings described below are only some embodiments of the present invention, and it is obvious for those skilled in the art that other drawings can be obtained according to the drawings without creative efforts.
Fig. 1 is a flowchart of a method for predicting runoff probability of a deep neural network of a directed graph according to an embodiment of the present invention.
Fig. 2 is a block diagram of a runoff probability forecasting system according to an embodiment of the present invention;
in the figure: 1. a directed graph structure building module; 2. a forecasting model building module; 3. a forecasting model optimization module; 4. a training data set construction module; 5. and a runoff probability forecasting module.
Fig. 3 is a schematic structural diagram of a directed graph constructed by a hydrological site and a meteorological site upstream of the Yangtze river according to an embodiment of the present invention.
FIG. 4 is a chart of probability forecast uncertainty analysis from 10/1998 to 28/10/Yichang station in an embodiment of the present invention.
Fig. 5(a) and 5(b) are graphs of probability forecast uncertainty analysis for the yichang station over the test period provided by an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail with reference to the following embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
Aiming at the problems in the prior art, the invention provides a method, a system, equipment and a terminal for forecasting the runoff probability of a directed graph deep neural network, and the invention is described in detail below by combining with the attached drawings.
As shown in fig. 1, the method for predicting the runoff probability of the directed graph deep neural network according to the embodiment of the present invention includes the following steps:
step 1, constructing a hydrological site and meteorological site directed graph structure;
step 2, establishing a directed graph deep neural network forecasting model according to the multi-site directed graph by combining a space information capturing process and a feature aggregation process;
step 3, constructing a data set consisting of the forecast runoff and the forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result;
step 4, reconstructing a hidden Markov regression training data set by using a forecast result obtained by the directed graph deep neural network and an actual measuring runoff value;
and 5, training a hidden Markov regression model to obtain a runoff probability forecasting result.
As shown in fig. 2, the runoff probability forecasting system provided by the embodiment of the present invention includes:
the directed graph structure building module 1 is used for building a directed graph structure of a hydrological site and a meteorological site;
the forecasting model building module 2 is used for building a directed graph deep neural network forecasting model by combining a space information capturing process and a feature aggregation process according to the multi-site directed graph;
the forecasting model optimizing module 3 is used for constructing a data set consisting of the forecasting runoff and the forecasting factors thereof, and training a directed graph deep neural network by adopting an Adam optimizing algorithm to obtain a high-precision multi-step long runoff forecasting result;
the training data set construction module 4 is used for reconstructing a hidden Markov regression training data set by using a forecast result obtained by the directed graph deep neural network and an actual measurement runoff value;
and the runoff probability forecasting module 5 is used for obtaining a runoff probability forecasting result by training the hidden Markov regression model.
The technical solution of the present invention is further described below with reference to specific examples.
Examples
The method for forecasting the runoff probability of the digraph deep neural network based on the digraph deep neural network provided by the embodiment of the invention comprises the following steps:
step 1, constructing a hydrological site and meteorological site directed graph structure;
step 2, establishing a directed graph deep neural network forecasting model by combining a space information capturing process and a characteristic aggregation process according to the multi-site directed graph;
step 3, constructing a data set consisting of the forecast runoff and the forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result;
step 4, reconstructing a hidden Markov regression training data set by using a forecast result obtained by the directed graph deep neural network and an actual measured runoff value;
and 5, training a hidden Markov regression model to obtain a runoff probability forecasting result.
Step 1, constructing a hydrological site and meteorological site directed graph structure.
The embodiment of the invention takes upstream hydrological stations and meteorological stations of the Yangtze river as research objects, and takes each hydrological station and meteorological station as points in a directed graph; determining the relationship between each hydrological site and other hydrological sites and meteorological sites according to the upstream and downstream relationship between the hydrological sites and the regions in which the meteorological sites are located and the hydrological sites, and connecting points with causal relationship by using vectors; all points and vectors are formed into a directed graph, as shown in fig. 3.
And 2, establishing a directed graph deep neural network forecasting model by combining a space information capturing process and a characteristic aggregation process according to the multi-site directed graph.
The directed graph deep neural network model mainly comprises a spatial information capturing process and a characteristic aggregation process. The spatial information capturing process is composed of a plurality of convolution layers and a full-connection layer, and mainly aims to capture the influence of rainfall in an area range on the runoff of the hydrological site through convolution operation, and the process can be regarded as a rainfall runoff generating model in a hydrological model. The spatial information capture process can be expressed as follows:
Figure BDA0003282038800000101
Figure BDA0003282038800000102
Figure BDA0003282038800000103
where v is 1, …, NI is the index of the hydrologic site, L is the number of network layers in the process,
Figure BDA0003282038800000104
layer i in the process of capturing spatial information of representative v hydrological sites, SP (v) represents a meteorological site set of which rainfall influences the v hydrological site, PuRepresents rainfall information of the u-th meteorological site, Conv1D () represents convolution operation, fiFor the dimension of the i-th layer output space, kiIs the length of the convolution window, siFor the convolution step size, σ () represents the activation function of the fully-connected layer, the invention uses a linear activation function, WvWeight of the full connection layer, bvIs the bias vector for the fully connected layer.
The characteristic aggregation process is composed of a multilayer perception network, aims to establish the rainfall characteristics captured by the convolutional neural network and the nonlinear relation between the upstream runoff characteristics and the current hydrological site runoff, and can be regarded as a confluence process in a hydrological model. The characteristic polymerization process can be expressed as follows:
Figure BDA0003282038800000111
Figure BDA0003282038800000112
Figure BDA0003282038800000113
wherein L' is the number of network layers in the characteristic aggregation process,
Figure BDA0003282038800000114
layer I in the process of characteristic aggregation of representative v hydrological sites, SI (v) represents the upstream hydrological site set affecting the v hydrological site, IvRepresenting the v-th hydrological siteThe information of the runoff in the early stage,
Figure BDA0003282038800000115
is the weight of the ith hidden layer,
Figure BDA0003282038800000116
for the bias vector of the ith hidden layer, delta () represents the activation function of the hidden layer, the invention adopts Sigmoid activation function, WtarWeight of the full connection layer, btarThe invention uses a linear activation function for the bias vector of the fully-connected layer, the activation function of the σ () output layer.
And 3, constructing a data set consisting of the forecast runoff and the forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result.
The forecasting factors are real-time measured runoff data and rainfall data of all hydrology sites and meteorological sites, the forecasting values are future runoff values of the target sites, and a training set consisting of the forecasting factors and the forecasting values can be expressed as follows:
D1＝[X,Y]
Figure BDA0003282038800000117
yt＝[Itar,t+1,...,Itar,t+C]
wherein D is1Is a training set of the deep neural network model of the directed graph, and X is a forecasting factor X ═ X of the training sett,…,XT]Y is the predicted value of training set Y ═ Yt,…,yT]T is training integrated duration, J is the previous step length of the forecasting factor, C is the forecasting step length, Iv,tRepresents runoff of the v-th hydrological site in a time period t, Pu,tThe rainfall of the u-th meteorological station in the period t is shown, NI is the total number of the hydrological stations, NP is the total number of the meteorological stations, and tar is the forecast target station.
After the data set is constructed, the data is normalized, and parameters of a graph depth neural network are set, including every timeThe number of convolution layers and the number of nodes of a full connection layer in the process of capturing the spatial information, the number of sensing layers, the number of nodes of a hidden layer and the number of nodes of an output layer of a multi-layer sensing network, the network learning rate and the training algebra. And training a directed graph deep neural network on a training set by combining an Adam optimization algorithm, and iteratively optimizing model parameters. Obtaining a multistep long-path flow forecasting result Y according to the trained directed graph deep neural network modeltar。
Step 4, obtaining the result Y of the forecast runoff by the training set directed graph deep neural network in the step 3tarCombining the training set D ═ Y of hidden Markov regression with measured runoff Ytar,Y]。
And 5, training a hidden Markov regression model to obtain a runoff probability forecasting result.
Hidden Markov regression is mainly composed of a hidden Markov model and probability forecasting, and firstly, parameters of the hidden Markov model are trained by adopting a Baum-Welch algorithm. The joint probability distribution of hidden variables and observed variables of the hidden Markov model is represented as follows:
Figure BDA0003282038800000121
wherein D is2All observation sequences; z ═ Z1,...,zT]The hidden state variables at all the moments are taken as the hidden state variables; θ represents all the parameters to be trained of the hidden Markov model: pi ═ pi1,...,πK]Is a priori probability, pikRepresenting prior probability under a state K, wherein K is the number of model components; a is a state transition probability matrix of K, where AijRepresenting the transition probability of transitioning from the i-state to the j-state, phi ═ phi1,...,φK]For observing the parameters of the model, phikRepresenting the parameters of the k-th observation model. The conditional probability distribution of the observed variables is defined as p (d)t|zt＝k,φk). When multivariate gaussian distribution is used as the observation model, the conditional probability distribution is:
p(dt|zt＝k,φk)＝N(dt|μk,∑k)
wherein, mukIs the mean vector, Σ, of the observed values in the k-th statekThe covariance matrix of the observed values at the k-th state.
And (3) iteratively optimizing the parameters theta of the model by adopting an EM algorithm, wherein the parameters theta is { pi, A, phi }, and obtaining the trained hidden Markov model. Then, a conditional probability density function of a forecast value after a forecast factor is given is obtained through inference according to the properties of Gaussian joint probability distribution, a probability multiplication formula and a Bayes formula, and the conditional probability density function is as follows:
Figure BDA0003282038800000131
wherein the content of the first and second substances,
Figure BDA0003282038800000132
a conditional probability density function that is a prediction value;
Figure BDA0003282038800000133
a joint probability density function of the predictor and the predicted value; p (y)t) Edge probability density function, h, of the predictor yt(k) The probability is a forward probability and can be obtained through a forward-backward algorithm;
Figure BDA0003282038800000134
and
Figure BDA0003282038800000135
respectively a mean vector and a covariance matrix of the prediction factor in the kth observation model;
Figure BDA0003282038800000136
and
Figure BDA0003282038800000137
the prediction value is the conditional mean vector and the covariance matrix of the k-th observation model respectively.
The method takes the hydrological station position forecasting object of the Yichang station at the upstream of the Yangtze river, the hydrological station and the meteorological station of the Yichang station as forecasting factors, adopts the daily average data from 1970 to 1997 as a training set and the daily average data from 1998 to 2004 as a testing set, forecasts the runoff of the Yichang station in three days in the future, and forecasts according to the probability forecasting method of the runoff of the directed graph deep neural network shown in the figure 2. The performance of the forecasting method is evaluated by two evaluation indexes, namely Root Mean Square Error (RMSE) and Nash coefficient (NSE), and the uncertainty of probability forecasting is analyzed.
Table 1 and table 2 show the RMSE and NSE evaluation index values of the Directed Graph Deep Neural Network (DGDNN) model, the long-short term memory neural network model (LSTM), the gated cyclic unit model (GRU), and the neural network model (ANN), respectively. The smaller the RMSE index value, the better, the NSE is a relative value ranging from minus infinity to 1, the closer the predicted value is to the real-scale runoff value. As can be seen from tables 1 and 2, the prediction accuracy of the method for predicting the depth neural network of the directed graph is higher than that of other comparison models, and the prediction performance is superior.
TABLE 1 RMSE values of future three-day runoff forecast of four models
Figure BDA0003282038800000141
TABLE 2 NSE values for runoff forecasting of three days in the future for the four models
Figure BDA0003282038800000142
And further analyzing the uncertainty of the forecast on the basis of the forecast precision evaluation. Fig. 4 shows 95% and 70% confidence intervals of probability prediction with the time axis as abscissa and the forecast runoff interval and the observed runoff value as ordinate. It can be obviously seen from the figure that the width of the forecast interval in the flood season is generally larger than that of the forecast interval in the dry season, which represents that the uncertainty of the runoff forecast in the flood season is larger than that of the dry season. Fig. 5 shows 95% and 70% confidence intervals of the probability forecast with the forecast mean as the abscissa, and it is obvious from the graph that the confidence intervals become wider with the increase of the forecast mean, which proves that the probability forecast of the present invention better describes the characteristic of forecast uncertainty "variance". In summary, fig. 4 and fig. 5 prove that the present invention can effectively estimate the runoff forecast uncertainty in different scheduling periods, and therefore can provide a reliable runoff probability forecast value for scheduling decisions.
Table 3 shows the experimental data of the forecast runoff and the actual runoff of DGDNN, LSTM, GRU and ANN on part of the date.
TABLE 3 Experimental data for forecasting runoff and actual runoff for DGDNN, LSTM, GRU, ANN
Figure BDA0003282038800000143
Figure BDA0003282038800000151
In the description of the present invention, "a plurality" means two or more unless otherwise specified; the terms "upper", "lower", "left", "right", "inner", "outer", "front", "rear", "head", "tail", and the like, indicate orientations or positional relationships based on the orientations or positional relationships shown in the drawings, are only for convenience in describing and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed in a particular orientation, and be operated, and thus, should not be construed as limiting the invention. Furthermore, the terms "first," "second," "third," and the like are used for descriptive purposes only and are not to be construed as indicating or implying relative importance.
In the above embodiments, the implementation may be wholly or partially realized by software, hardware, firmware, or any combination thereof. When used in whole or in part, can be implemented in a computer program product that includes one or more computer instructions. When loaded or executed on a computer, cause the flow or functions according to embodiments of the invention to occur, in whole or in part. The computer may be a general purpose computer, a special purpose computer, a network of computers, or other programmable device. The computer instructions may be stored in a computer readable storage medium or transmitted from one computer readable storage medium to another, for example, the computer instructions may be transmitted from one website site, computer, server, or data center to another website site, computer, server, or data center via wire (e.g., coaxial cable, fiber optic, Digital Subscriber Line (DSL), or wireless (e.g., infrared, wireless, microwave, etc.)). The computer-readable storage medium can be any available medium that can be accessed by a computer or a data storage device, such as a server, a data center, etc., that includes one or more of the available media. The usable medium may be a magnetic medium (e.g., floppy Disk, hard Disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., Solid State Disk (SSD)), among others.
The above description is only for the purpose of illustrating the present invention and the appended claims are not to be construed as limiting the scope of the invention, which is intended to cover all modifications, equivalents and improvements that are within the spirit and scope of the invention as defined by the appended claims.

Claims (10)

1. A method for forecasting the runoff probability of a directed graph deep neural network is characterized by comprising the following steps:
step one, constructing a hydrological site and meteorological site directed graph structure;
step two, establishing a directed graph deep neural network forecasting model by combining a space information capturing process and a feature aggregation process according to the multi-site directed graph;
constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result;
fourthly, reconstructing a hidden Markov regression training data set by the forecast result obtained by the directed graph deep neural network and the actual measuring runoff value;
and fifthly, training a hidden Markov regression model to obtain a runoff probability forecasting result.
2. The method for forecasting runoff probability of a directed graph deep neural network of claim 1, wherein in the first step, the constructing the directed graph structure of the hydrological site and the meteorological site comprises:
taking hydrological sites and meteorological sites of a drainage basin as research objects, and taking each hydrological site and each meteorological site as points in a directed graph; determining the relationship between each hydrological site and other hydrological sites and meteorological sites according to the upstream and downstream relationship between the hydrological sites and the regions in which the meteorological sites are located and the hydrological sites, and connecting points with causal relationship by using vectors; and forming a directed graph by all the points and the vectors.
3. The method for forecasting runoff probability of a directed graph deep neural network according to claim 1, wherein in the second step, the building of the directed graph deep neural network forecasting model according to the multi-site directed graph by combining a spatial information capturing process and a feature aggregation process comprises:
the directed graph deep neural network model consists of a spatial information capturing process and a characteristic aggregation process; the spatial information capturing process is composed of a plurality of convolution layers and a full-connection layer, is used for capturing the influence of rainfall in an area range on the runoff of the hydrological site through convolution operation, is regarded as a rainfall runoff generating model in the hydrological model, and is expressed as follows:
Figure FDA0003282038790000011
Figure FDA0003282038790000012
Figure FDA0003282038790000013
where v is 1, …, NI is the index of the hydrologic site, L is the number of network layers in the process,
Figure FDA0003282038790000021
layer i in the process of capturing spatial information of representative v hydrological sites, SP (v) represents a meteorological site set of which rainfall influences the v hydrological site, PuRepresents rainfall information of the u-th meteorological site, Conv1D () represents convolution operation, fiFor the dimension of the i-th layer output space, kiIs the length of the convolution window, siFor the step size of the convolution, σ () represents the activation function of the fully-connected layer, which takes the form of a linear activation function, WvWeight of the full connection layer, bvIs the offset vector of the fully connected layer;
the characteristic aggregation process is composed of a plurality of layers of perception networks and is used for establishing the rainfall characteristics captured by the convolutional neural network and the nonlinear relation between the upstream runoff characteristics and the current hydrologic site runoff, the process is regarded as a confluence process in a hydrologic model, and the characteristic aggregation process is expressed as follows:
Figure FDA0003282038790000022
Figure FDA0003282038790000023
Figure FDA0003282038790000024
wherein L' is the number of network layers in the characteristic aggregation process,
Figure FDA0003282038790000025
layer I in the process of characteristic aggregation of representative v hydrological sites, SI (v) represents the upstream hydrological site set affecting the v hydrological site, IvRepresenting the early runoff information of the v-th hydrological site,
Figure FDA0003282038790000026
is the weight of the ith hidden layer,
Figure FDA0003282038790000027
for the bias vector of the ith hidden layer, delta () represents the activation function of the hidden layer, and the activation function adopts Sigmoid activation function, WtarWeight of the full connection layer, btarFor the offset vector of the fully-connected layer, the activation function of the σ () output layer, a linear activation function is used.
4. The method for forecasting the runoff probability of the directed graph deep neural network according to claim 1, wherein in the third step, the step of constructing a data set consisting of the forecasted runoff and the forecasting factors thereof, and training the directed graph deep neural network by using an Adam optimization algorithm to obtain the multi-step long-runoff forecasting result with high precision comprises the following steps:
the forecasting factors are real-time measured runoff data and rainfall data of all hydrology sites and meteorological sites, the forecasting values are future runoff values of target sites, and a training set consisting of the forecasting factors and the forecasting values is represented as follows:
D1＝[X,Y]
Figure FDA0003282038790000031
yt＝[Itar,t+1,...,Itar,t+C]；
wherein D is1Is a training set of the deep neural network model of the directed graph, and X is a forecasting factor X ═ X of the training sett,…,XT]Y is the predicted value of training set Y ═ Yt,…,yT]T is training integrated duration, J is the previous step length of the forecasting factor, C is the forecasting step length, Iv,tRepresents runoff of the v-th hydrological site in a time period t, Pu,tThe rainfall of the u-th meteorological site in the period t is shown, NI is the total number of the hydrological sites, NP is the total number of the meteorological sites, and tar is a forecast target site;
after the data set is constructed, carrying out normalization processing on the data, and setting parameters of a graph depth neural network, including the number of convolutional layers and the number of nodes of a full connection layer in each spatial information capturing process, the number of nodes of a sensing layer, the number of nodes of a hidden layer and the number of nodes of an output layer of a multi-layer sensing network, a network learning rate and a training algebra; training a directed graph deep neural network on a training set by combining an Adam optimization algorithm, and iteratively optimizing model parameters; obtaining a multistep long-path flow forecasting result Y according to the trained directed graph deep neural network modeltar。
5. The method for forecasting the runoff probability of the directed graph deep neural network of claim 1, wherein in the fourth step, the runoff forecasting result Y obtained by the directed graph deep neural network in the training set in the third step is usedtarCombining the training set D ═ Y of hidden Markov regression with measured runoff Ytar,Y]。
6. The method for forecasting runoff probability of a directed graph deep neural network according to claim 1, wherein in the fifth step, the training of the hidden markov regression model to obtain the runoff probability forecasting result comprises:
hidden Markov regression mainly comprises a hidden Markov model and probability forecasting, and parameters of the hidden Markov model are trained by adopting a Baum-Welch algorithm; wherein the joint probability distribution of hidden variables and observed variables of the hidden Markov model is represented as follows:
Figure FDA0003282038790000041
wherein D is2All observation sequences; z ═ Z1,...,zT]The hidden state variables at all the moments are taken as the hidden state variables; θ represents all the parameters to be trained of the hidden Markov model: pi ═ pi1,...,πK]Is a priori probability, pikRepresenting prior probability under a state K, wherein K is the number of model components; a is a state transition probability matrix of K, where AijRepresenting the transition probability of transitioning from the i-state to the j-state, phi ═ phi1,...,φK]For observing the parameters of the model, phikParameters representing a kth observation model;
the conditional probability distribution of the observed variables is defined as p (d)t|zt＝k,φk) (ii) a When multivariate gaussian distribution is used as the observation model, the conditional probability distribution is:
p(dt|zt＝k,φk)＝N(dt|μk,∑k)；
wherein, mukIs the mean vector, Σ, of the observed values in the k-th statekA covariance matrix of observed values at the kth state;
adopting an EM algorithm to iterate and optimize parameters theta of the model to be { pi, A, phi }, and obtaining a trained hidden Markov model; obtaining a conditional probability density function of a forecast value after a forecast factor is given according to the nature of Gaussian joint probability distribution, a probability multiplication formula and a Bayes formula by inference, wherein the conditional probability density function is shown as the following formula:
Figure FDA0003282038790000042
wherein the content of the first and second substances,
Figure FDA0003282038790000043
a conditional probability density function that is a prediction value;
Figure FDA0003282038790000044
a joint probability density function of the predictor and the predicted value; p (y)t) Edge probability density function, h, of the predictor yt(k) The probability is a forward probability and is obtained through a forward-backward algorithm;
Figure FDA0003282038790000045
and
Figure FDA0003282038790000046
respectively a mean vector and a covariance matrix of the prediction factor in the kth observation model;
Figure FDA0003282038790000051
and
Figure FDA0003282038790000052
the prediction value is the conditional mean vector and the covariance matrix of the k-th observation model respectively.
7. A runoff probability forecasting system applying the directed graph deep neural network runoff probability forecasting method according to any one of claims 1 to 6, wherein the runoff probability forecasting system comprises:
the directed graph structure building module is used for building a directed graph structure of the hydrological site and the meteorological site;
the forecasting model building module is used for building a directed graph deep neural network forecasting model by combining a space information capturing process and a characteristic aggregation process according to the multi-site directed graph;
the forecasting model optimization module is used for constructing a data set consisting of the forecasting runoff and the forecasting factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecasting result;
the training data set construction module is used for reconstructing a hidden Markov regression training data set from the forecast result obtained by the directed graph deep neural network and the actual measurement runoff value;
and the runoff probability forecasting module is used for obtaining a runoff probability forecasting result by training the hidden Markov regression model.
8. A computer device, characterized in that the computer device comprises a memory and a processor, the memory storing a computer program which, when executed by the processor, causes the processor to carry out the steps of:
constructing a hydrological site and meteorological site directed graph structure; establishing a directed graph deep neural network forecasting model by combining a spatial information capturing process and a characteristic aggregation process according to a multi-site directed graph; constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result; reconstructing a hidden Markov regression training data set by using a forecast result obtained by the digraph deep neural network and an actual measured runoff value; and training a hidden Markov regression model to obtain a runoff probability forecasting result.
9. A computer-readable storage medium storing a computer program which, when executed by a processor, causes the processor to perform the steps of:
constructing a hydrological site and meteorological site directed graph structure; establishing a directed graph deep neural network forecasting model by combining a spatial information capturing process and a characteristic aggregation process according to a multi-site directed graph; constructing a data set consisting of the forecast runoff and forecast factors thereof, and training a directed graph deep neural network by adopting an Adam optimization algorithm to obtain a high-precision multi-step long runoff forecast result; reconstructing a hidden Markov regression training data set by using a forecast result obtained by the digraph deep neural network and an actual measured runoff value; and training a hidden Markov regression model to obtain a runoff probability forecasting result.
10. An information data processing terminal, characterized in that the information data processing terminal is configured to implement the runoff probability forecasting system according to claim 7.
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