CN117151285A - Runoff forecasting method based on multi-element attention space-time diagram convolutional network - Google Patents

Runoff forecasting method based on multi-element attention space-time diagram convolutional network Download PDF

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CN117151285A
CN117151285A CN202311097283.1A CN202311097283A CN117151285A CN 117151285 A CN117151285 A CN 117151285A CN 202311097283 A CN202311097283 A CN 202311097283A CN 117151285 A CN117151285 A CN 117151285A
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陈佳雷
彭甜
葛宜达
王熠炜
张楚
孙娜
王政
李茜
钱诗婕
李燕妮
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Abstract

The invention discloses a runoff forecasting method based on a multi-element attention space-time diagram convolution network, which comprises the steps of firstly obtaining a drainage basin hydrologic historical data set; extracting topological relations of upstream and downstream stations of the drainage basin, and completing extraction of the topological relations of the drainage basin and construction of a graph structure model; establishing a geographic adjacency matrix based on a real space adjacency relationship, and analyzing multiple space-time dependencies of a basin runoff process; introducing a space-time diagram convolution network to extract the characteristics of the hydrological elements in space-time dimensions, constructing a neural network full-connection layer fused with multi-element forecasting results, and constructing a runoff forecasting model MASTGCN; initializing a bald eagle search optimization algorithm by using uniform initialization, introducing a multi-element learning strategy into the bald eagle search optimization algorithm to obtain a UMBES algorithm, optimizing super parameters in a MASTGCN model by using the UMBES algorithm, and predicting the runoff condition at the future moment by using the optimized MASTGCN model. The invention can effectively capture the dynamic space-time mode of the hydrological process and realize accurate runoff forecasting.

Description

Runoff forecasting method based on multi-element attention space-time diagram convolutional network
Technical Field
The invention belongs to the technical field of runoff forecasting, and particularly relates to a runoff forecasting method based on a multi-element attention space-time diagram convolution network.
Background
Under the comprehensive actions of a plurality of factors such as climate change, human activities, drainage basin undersides and the like, the runoff forming process is complex, has strong nonlinearity and non-stationary characteristics, and on the other hand, the runoff forming process has predictable characteristics under the influence of the periodicity and dynamic flow characteristics of the internal elements of the water circulation system. The traditional deterministic mathematical model mainly researches the influence of external appearance extremely random factors of a time sequence, and is difficult to characterize the inherent characteristics and evolution mechanism of a hydrologic process. The proposal and development of the chaos theory provide a path for researching the inherent dynamic characteristic of the runoff system and further analyzing and predicting the runoff, and the chaos dynamic characteristic of the runoff system is required to be further searched, the periodical change characteristics and dynamic fluidity of the complicated runoff of the river basin are revealed, the predictable characteristics of the runoff time sequence of the water circulation system of the river basin are clarified, and a pre-stage foundation is provided for analyzing and predicting the runoff process of the river basin. In addition, as multidisciplinary cross research methods such as mathematical statistics and time-frequency analysis are introduced into water science, the analysis of the multidisciplinary cross research methods in aspects such as the distribution rule, the change trend, the mutation property, the time-space variability and the like of the hydrological time sequence is greatly developed.
The strong influence of climate change and human activity causes the deep change of the water circulation process of the river basin and the time-space change rule of water resources, the consistency of elements in the water circulation of the river basin cannot be ensured, and more uncertainty is brought to the nonlinear comprehensive forecast of the runoff of the river basin and the development and utilization of the water resources. The existing research lays a good theoretical foundation for the dynamic characteristics and the space-time change rules of the runoffs, but still needs to combine specific river basin characteristics to innovate and develop various runoff characteristics and space-time change rule analysis methods, the various methods complement each other and are compared and verified with each other so as to accurately master the space-time change rules of the river basin weather hydrologic process and provide a foundation for further nonlinear runoff forecasting of the river basin.
The nonlinear comprehensive forecasting of complex runoff in a river basin is a space-time sequence forecasting problem influenced by various uncertain factors such as rainfall, climate change and human activities, and the current solving method for the problem can be mainly divided into a physical model and a data driving type. The physical model is mainly based on hydrologic concepts, aims at simulating a natural hydrologic cycle process of a river basin, generalizes various elements in the hydrologic cycle by analyzing key factors of the hydrologic cycle process of the river basin, and establishes a mathematical model capable of truly reflecting the relation among the elements and the hydrologic cycle process by using various algebra, partial differential or integral equations. In actual forecasting, because the accuracy of the physical model is seriously dependent on the accuracy of weather information such as rainfall, when effective and accurate weather information cannot be obtained, the model cannot work, and most hydrologic model parameters are difficult to determine, so that the model is complicated to realize, and the development of the physical model is greatly limited. The modeling processing capacity of the data driven model for multidimensional space-time data input is insufficient, and the problems of model transparency, physical interpretability and the like are lacking.
The machine learning model can mine rule information existing in data through methods such as linear regression, curve fitting and parameter estimation, and a function mapping relation between historical hydrological meteorological elements and forecasting vectors is established, so that the runoff in a longer time in the future is accurately forecasted. However, the traditional machine learning method cannot perform deep feature extraction on data, has insufficient modeling processing capacity on multidimensional space-time data input, and is difficult to adapt to a large data background with massive data as input, so that the effect of a model is limited. Deep learning models lack model transparency and physical interpretability, and existing methods are not capable of modeling spatial dependencies between sites and are not suitable for processing graph structure data.
In order to solve the problems, researchers try to generalize the convolutional neural network to a graph convolution network of any structural graph, and the problem that the conventional convolutional neural network model cannot process graph network information is solved by directly utilizing the graph structural information to extract the space-time characteristics of data. However, how to utilize a space-time diagram convolution network to generalize a water resource system with the climate change-human activity-drainage basin sublevel surface multi-element coupling effect into a graph structure model, model the space-time dependence among massive hydro-meteorological data, further extract the space-time characteristics of multiple hydro-meteorological elements, improve the accuracy and reliability of runoff forecasting, and is a research direction with great prospect in the drainage basin hydro-meteorological forecasting field.
Disclosure of Invention
The invention aims to: the invention provides a runoff forecasting method based on a multi-element attention space-time diagram convolution network, which effectively captures a dynamic space-time mode of a hydrological meteorological process and realizes accurate runoff forecasting.
The technical scheme is as follows: the invention discloses a runoff forecasting method based on a multi-element attention space-time diagram convolution network, which comprises the following steps:
(1) Acquiring hydrologic related historical data of the inner diameter of the river basin in advance, and preprocessing the historical data;
(2) Extracting topological relations of upstream and downstream stations of the river basin, and generalizing a water resource system with the effects of climate change, human activity and multi-element coupling of the underlying surface of the river basin into a graph structure;
(3) Establishing a geographic adjacency matrix based on a real space adjacency relationship, constructing a potential dependency matrix based on a non-adjacent sub-basin runoff time sequence correlation relationship, and analyzing multiple time-space dependencies of basin runoff processes on time elements, period elements, meteorological elements and space elements;
(4) Carrying out feature extraction on geographic information by adopting four-dimensional space-time convolution blocks, wherein each one-dimensional space-time convolution block comprises a layer of space-time attention mechanism and a layer of space-time diagram convolution network; wherein the spatiotemporal attention mechanism captures the dynamic correlation of the runoff sequence; the space-time diagram convolution network comprises two time gating convolution layers and a space diagram convolution layer; constructing an output layer based on time gating convolution and a fully connected neural network, and constructing a runoff forecasting model MASTGCN based on a multi-element attention space-time diagram convolution network;
(5) Initializing the initial bald eagle population position by using a uniform initialization method; introducing the improved multi-element learning into a bald eagle search optimization algorithm BES to obtain a UMBES algorithm;
(6) Optimizing super parameters including the number of hidden layer nodes and learning rate of the MASTGCN model in the step (4) by utilizing UMBES, obtaining corresponding optimal parameters, and predicting the runoff condition at the future moment by utilizing the optimized MASTGCN runoff forecasting model to obtain a runoff condition forecasting result at the future moment.
Further, the historical data in the step (1) comprises a data set of flow of day, ten days, month and year, a data set of potential geographic dependence, a data set of proximity sequence, a data set of historical meteorological elements and a data set of human activity trend of the control hydrologic station.
Further, the implementation process of the step (2) is as follows:
dividing a river basin into different sub-river basins, determining outlet control sites of the sub-river basins, abstracting a spatial relationship between the sub-river basins into an undirected and weight-free graph G= (V, E, A), displaying a physical relationship between a river basin water system and hydrologic sites, wherein V represents a set of all sub-river basin control sites, and each sub-river basin control site is a node in the graph G; e represents the graph GRepresents a main or tributary of a river basin; a= { A for adjacency matrix between sub-basin control sites geo ,A rel Represented by (A), where A geo ∈R n×n Is a geographic adjacency matrix, A rel ∈R n×n An adjacency matrix for potential spatial dependencies;
the whole watershed shares |v|=n sub-watershed, then the sub-watershed control site set is defined as:
V＝{v 1 ,...,v n ,...,v N } (1)
wherein n refers to an nth sub-basin site;
order theRepresenting the runoff value of the sub-basin n at the time T (1.ltoreq.t), the set of runoff values of all the sub-basins at the time T is represented as:
order theA historical meteorological element sequence P representing the value of a meteorological element of a sub-basin n at the time t t The method comprises the following steps:
based on the historical time sequence of all node runoffs and meteorological elements on the graph G, the time length of the sub-basin control site in the future is T p The prediction of the radial flow value in the time period of (2) is as follows:
Y＝(y 1 ,y 2 ,...,y N ) (4)
in the method, in the process of the invention,representing the sub-basin n from time l+1 to time l+T p And h is the forecast period of the runoff forecast.
Further, the implementation process of the step (3) is as follows:
establishing a geographic adjacency matrix based on a real space adjacency relation by considering that larger runoff mobility exists between spatially adjacent sub-watershed, and describing the local spatial dependence of peripheral sub-watershed runoffs on a target vector; specifically, for any two different sub-watershed i and j, its geographic adjacency matrix is represented as follows:
in the method, in the process of the invention,representing sub-watershed i and j as adjacent sub-watershed +.>Representing non-adjacency;
constructing a potential dependency matrix based on non-adjacent sub-drainage basin runoff time sequence correlation, and describing potential dependency relations between upstream and downstream non-adjacent sub-drainage basins; specifically, for any two different sub-watershed i and j, its potential dependency matrix is represented as follows:
adopting a chaos phase space reconstruction theory and Copula entropy correlation analysis to quantify the time correlation and dependence of the basin runoff process on time elements, period elements and meteorological elements;
quantitative analysis of time dependence of drainage basin runoff process on periodicity and adjacent moment by using chaos phase space reconstruction theory and Copula entropy correlation analysis respectively, and cutting off subscripts T along a time axis respectively h And T p Is the input of two components of the model at the moment of approach and the moment of periodical repetition, t 0 Time of day two sequencesThe sets are denoted as:
the Copula entropy correlation analysis is further utilized to intercept the subscript as T m Historical meteorological elements of (a).
Further, the dynamic correlation implementation process of capturing the runoff sequence by adopting the space-time attention mechanism in the step (4) is as follows:
the space-time attention mechanism is used for adaptively capturing dynamic correlations between different space-time dimension nodes, and comprises a space attention mechanism and a time attention mechanism which are respectively used for capturing the dynamic correlations of the mutual influence of runoff sequences of different sites and the correlations between runoff processes of different times of the same site; the spatial attention matrix H for the example of the adjacent sequence is expressed as:
H＝U m ·δ((X h W 1 )W 2 (W 3 X h ) T +b m ) (9)
in the process, data is inputWherein N, C in T represents the number of top points, the number of input channels and the length of the input data time dimension respectively; u (U) m ,b m ∈R N×N ，W 1 ∈R T ，/>Representing the learned parameters; delta (·) represents the activation function; h i,j Representing the attention coefficient of node i to node j; h'. i,j Representing the normalized attention coefficient, and further obtaining a normalized spatial attention matrix H';
proximity sequence X h The time attention matrix T of (1) is expressed as:
T＝U n ·δ(((X h ) T V 1 )V 2 (V 3 X h )+b n ) (11)
in U n ,b n ∈R T×T ，V 1 ∈R N ,Representing the learned parameters; delta (·) represents the activation function; t (T) i,j Representing the attention coefficient of node i to node j; t'. i,j Representing the normalized attention coefficient, and further obtaining a normalized time attention matrix T'; the normalized time and space attention moment array is applied to the current input data to obtain the adjusted input data:
and then carrying out space-time feature mining based on the adjusted input data.
Further, the time-gated convolutional layer in the step (4) is composed of a one-dimensional convolutional neural network and a gated linear unit, and is used for extracting the characteristics of the hydrological meteorological elements in the time dimension; the calculation formula is as follows:
where tconv (·) represents a one-dimensional convolution function;denoted by length L w For inputting data +.>Mapping to a single output; />Wherein Y is 1 ,Y 2 Is of the same dimension and has a reduced length T-L w +1；
Dividing into sections by using gating linear unitsProcessing is performed to improve the nonlinear learning ability of the MASTGCN model to obtain the output S of the time-gated convolutional layer.
Further, the space characteristics of the flow domain runoff process are mined by the space map convolution layer in the step (4), and the state of the space convolution layer is rapidly propagated when the space map convolution layer is realized by applying a layer of time-gating convolution layer; the space diagram convolution layer adopts a K-order chebyshev polynomial to carry out approximate calculation on the Laplacian matrix L of the diagram so as to capture the space dependence among the diagram structure data, and the calculation formula of the output F of the space diagram convolution layer is as follows:
wherein gconv (·) represents a space diagram convolution function; k is a super parameter;is a k-order chebyshev polynomial, θ k As coefficients thereof; θ max Is the maximum eigenvalue of matrix L;
after obtaining the output F of the space diagram convolution layer, a layer of time gating convolution layer is applied again to realize the rapid propagation of the state of the space convolution layer, so as to obtain the output of the space-time convolution blockFor adjacent sequence X h The result of the space-time convolution block processing is as follows:
X' h ＝tconv(gonv(tconv(H'X h T'))) (19)。
further, the implementation process of constructing the output layer based on the time-gated convolution and the fully-connected neural network in the step (4) is as follows:
for data X 'after space-time convolution block processing' h Obtaining potential space-time expression of adjacent sequences by adopting output layer processing based on time gating convolution and fully connected neural networkSimilarly, obtaining potential space-time expression of the rest space-time sequences after being processed by the space-time convolution block and the output layer; fusing the forecast values of different sequences, wherein the final forecast result is expressed as:
wherein, the ". As used herein, the Hadamard product is the multiplication of the corresponding elements in the matrix; w (W) g ，W h ，W p ，W m Respectively represent the parameters learned by four different time space convolution block components, reflecting the geographic potential dependency sequence X g Adjacent sequence X h Periodically repeating sequence X p Historical meteorological element sequence X m The degree of influence on the target sequence;respectively representing the forecast values of the four groups of sequences.
Further, the implementation process of the step (5) is as follows:
(51) Setting an objective function of a BES algorithm as a runoff prediction accuracy rate, and determining the population size, the iteration number, the dimension size and the upper and lower limits of a search space;
(52) And initializing the initial bald eagle position by adopting a uniform initializing method, wherein the formula of the improved initializing mode is as follows:
P i ＝P i L +r(P i U -P i L ) (21)
wherein P is i Representing the initial position of the ith hydrological site, L is the lower boundary of a search interval, U is the upper boundary of the search interval, and r is [0,1]A uniform random number therebetween;
(53) Calculating a fitness value by taking the runoff prediction accuracy as an objective function, and obtaining an optimal solution according to the calculated fitness;
(54) A selection phase, in which the hydrologic site identifies and selects the best region in the selected search space:
P new,i ＝P best +α*r(P mean -P i ) (22)
where α is a parameter controlling the change of position, P best Is the current optimal position, P mean Information indicating the utilization of all the previous points;
in the searching stage, each hydrologic site searches for new relevant position information in the selected searching space and moves in different directions in the spiral space so as to speed up the searching speed:
wherein θ (i) and r (i) are the polar angle and the polar diameter of the spiral equation when a search relation is established between the ith hydrological site and the neighbor site; a and R are parameters for controlling the spiral track, and the variation ranges are (5, 10) and (0.5, 2) respectively; rand is a random number in (0, 1), and x (i) and y (i) represent the position of the ith hydrological site in polar coordinates;
(55) Introducing a multi-element learning strategy to update the position information of the hydrologic site; the position is randomly divided into two parts, one part is learned from the historical site position of the current hydrological site position, the other parts are learned from the optimal position in the current hydrological site position, and the specific implementation process is as follows:
wherein j is a positive integer less than i; p is p j,new Representing j hydrologic sites in the current population; a and b are random numbers from 0 to 1; p is p best,new The position of the hydrological site which is the optimal solution of the current population;
(56) In the dive phase, the current hydrologic sites sway from the best position of the search space to their target positions, all points also moving toward the best point, the mathematical expression of which is shown in equation (25):
wherein c1, c2 e [1,2] increases the moving strength of the historical hydrologic site to the optimal point and the central point.
Further, the implementation process of the step (6) is as follows:
(61) Initializing relevant parameters of the BES algorithm, including population, dimension, maximum iteration number, upper and lower limits of a search space and current iteration number;
(62) Calculating predicted values trained by fusion modelsAnd the actual value Y of the sample i The root mean square error is taken as the fitness value Fit of each individual in the BES algorithm:
(63) According to a position updating strategy, updating the position of each bald eagle in the population, calculating the fitness value of each individual, and sequencing the fitness values;
(64) Calculating the individual position again by utilizing a multivariate learning strategy, calculating the individual position and the individual fitness value, comparing the individual position and the individual fitness value obtained in the step (63), and selecting an optimal position corresponding to the optimal fitness value;
(65) Judging whether the maximum iteration times are reached, if so, outputting an optimal solution, extracting the super parameters of the MASTGCN model, and otherwise, returning to the step (63).
The beneficial effects are that: compared with the prior art, the invention has the beneficial effects that:
1. according to the invention, the time correlation and the dependence of the quantitative basin runoff process on time elements (adjacent time periods), periodic elements (periodic repetition) and meteorological elements (rainfall, evaporation, temperature, humidity, wind speed and the like) are analyzed by adopting a chaos phase space reconstruction theory and Copula entropy correlation analysis, so that the data complexity can be effectively reduced, the purpose of reducing the running time of a model is achieved, and the overall efficiency is improved;
2. the method creatively combines the graph convolution network with a multi-element attention mechanism, extracts the topological relation of the upstream and downstream hydrological stations of the watershed, effectively captures the dynamic space-time mode of the hydrological process, builds a multidimensional space-time scale and multisource data-driven attention space-time graph convolution network runoff forecasting model, can fully mine the time dependence and space correlation characteristics between input vectors and target vectors, further provides a brand new method for modeling the space-time big data of the watershed and accurately forecasting the runoff, can provide important data support for reasonable development, optimal configuration and efficient utilization of water resources, and has important theoretical significance and engineering practical value for reducing flood disaster loss and realizing sustainable utilization of the water resources;
3. aiming at the problems that the bald hawk searching optimization algorithm has low convergence rate, is easy to fall into local optimization and the like in the optimizing process, the uniform initializing method is adopted to initialize the population, so that centralized distribution of initialized individuals is avoided, a multi-element learning updating mode is added in an updating stage, the utilization capacity of the individuals to indirect layer information is improved, and the searching efficiency is improved; the super parameters of the runoff forecasting model are optimized by using an improved bald eagle searching optimization algorithm, so that the future runoff condition can be effectively forecasted, and the forecasting precision of the model is improved.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a schematic diagram of a multi-element attention space-time diagram convolution network runoff forecasting model structure;
FIG. 3 is a diagram showing a hydrological site distribution of Jinshajiang river basin provided by the invention;
fig. 4 is a diagram showing a space-time feature extraction structure according to the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings.
As shown in fig. 1, the invention provides a runoff forecasting method based on a multi-element attention space-time diagram convolution network, which specifically comprises the following steps:
step 1: acquiring a daily, ten-day, month and year flow data set, a geographic potential dependent data set, a nearby sequence data set, a historical meteorological element data set and a human activity trend data set of a watershed main control hydrologic station; the obtained historical data set is preprocessed.
Step 2: the topological relation of upstream and downstream stations of the river basin is extracted, and a water resource system with the climate change-human activity-bedding surface multi-element coupling effect is generalized into a graph structure model.
As shown in fig. 3, the Jinsha river basin is taken as a research area, the trend of the river basin water system is taken as a basis, the Arcgis software is adopted to divide the Jinsha river basin into different sub-basins, the outlet control sites of the sub-basins are determined, and the spatial relationship among the sub-basins is abstracted into an undirected and weight-free graph g= (V, E, a). The graph model shown in FIG. 4 shows the physical relationship between the watershed water system and the hydrologic stations, V represents the set of all sub-watershed control stations in the investigation region, and V represents the set of all sub-watershed control stations in the investigation regionEach sub-basin control site is a node in graph G; e represents the edge set in FIG. G, representing the main or tributary flow of the investigation region; a= { A for adjacency matrix between sub-basin control sites geo ,A rel Represented by (A), where A geo ∈R n×n Is a geographic adjacency matrix, A rel ∈R n×n Is a potential spatial dependency adjacency matrix. Assuming that the entire basin has |v|=n sub-basins, the set of sub-basin control sites can be defined as:
V＝{v 1 ,...,v n ,...,v N } (1)
where n refers to the nth sub-basin site.
Order theRepresenting the runoff value of the sub-basin n at the time T (1.ltoreq.t), the set of runoff values of all the sub-basins at the time T is represented as:
order theA historical meteorological element sequence P representing the value of a meteorological element of a sub-basin n at the time t t The method comprises the following steps:
based on the historical time sequence of all node runoffs and meteorological elements on the graph G, the duration of a sub-basin control site in a research area in the future is T p The prediction of the radial flow value in the time period of (2) is as follows:
Y＝(y 1 ,y 2 ,...,y N ) (4)
in the method, in the process of the invention,representing the sub-basin n from time l+1 to time l+T p And h is the forecast period of the runoff forecast.
Step 3: establishing a geographic adjacency matrix based on a real space adjacency relationship, constructing a potential dependency matrix based on non-adjacent sub-basin runoff time sequence correlation relationship, and analyzing multiple time-space dependencies of basin runoff processes on time elements (adjacent time periods), periodic elements (periodic repetition), meteorological elements and space elements (different sites).
(3.1) considering that larger runoff mobility exists between the adjacent sub-watershed in space, establishing a geographic adjacency matrix based on a real space adjacency relation, and describing the local spatial dependence of peripheral sub-watershed runoffs on a target vector, specifically, for any two different sub-watershed i and j, the geographic adjacency matrix is expressed as follows:
in the method, in the process of the invention,representing sub-watershed i and j as adjacent sub-watershed +.>Indicating non-adjacency.
(3.2) constructing a potential dependency matrix based on the non-adjacent sub-basin runoff time sequence correlation, and describing the potential dependency relationship between the upstream non-adjacent sub-basins and the downstream non-adjacent sub-basins, specifically, for any two different sub-basins i and j, the potential dependency matrix is expressed as follows:
and (3.3) quantifying the time dependence and dependence of the basin runoff process on time elements (adjacent time periods), periodic elements (periodic repetition) and meteorological elements (rainfall, evaporation, temperature, humidity, wind speed and the like) by adopting a chaotic phase space reconstruction theory and Copula entropy correlation analysis.
Quantitative analysis of time dependence of drainage basin runoff process on periodicity and adjacent moment by using chaos phase space reconstruction theory and Copula entropy correlation analysis respectively, and cutting off subscripts T along a time axis respectively h And T p Is the input of two components of the model at the moment of approach and the moment of periodical repetition, t 0 The two sets of sequences at time are denoted as:
the Copula entropy correlation analysis is further utilized to intercept the subscript as T m Historical meteorological elements of (a).
Step 4: carrying out feature extraction on geographic information by adopting four-dimensional space-time convolution blocks, wherein each one-dimensional space-time convolution block comprises a layer of space-time attention mechanism and a layer of space-time diagram convolution network; wherein the spatiotemporal attention mechanism captures the dynamic correlation of the runoff sequence; the space-time diagram convolution network comprises two time gating convolution layers and a space diagram convolution layer; and (3) building an output layer based on time gating convolution and a fully-connected neural network, and building a runoff forecasting Model (MASTGCN) based on a Multi-element Attention space diagram convolution network.
(4.1) aiming at the mutual influence weight among different time-space scene learning nodes, introducing a time-space attention mechanism to adjust the input data. As shown in fig. 2, the core of the multi-element attention space-time diagram convolution network is the design of a space-time convolution block structure, the invention adopts 4-dimensional convolution blocks to extract the characteristics of geographic information, and each one-dimensional space-time convolution block comprises a layer of space-time attention mechanism and a layer of space-time diagram convolution network. The space-time attention mechanism can adaptively capture the dynamic correlation between different space-time dimension nodes, and comprises a space attention mechanism and a time attention mechanism which are respectively used for capturing the dynamic correlation of the mutual influence of different site runoff sequences and the correlation between the runoff processes of different times of the same site. Taking the example of a neighbor sequence, its spatial attention matrix H can be expressed as:
H＝U m ·δ((X h W 1 )W 2 (W 3 X h ) T +b m ) (9)
in the process, data is input(N,C in T represents the number of top points, the number of input channels, and the length of the input data time dimension, respectively; u (U) m ,b m ∈R N×N ，W 1 ∈R T ,/>Representing the learned parameters; delta (·) represents the activation function; h i,j Representing the attention coefficient of node i to node j; h'. i,j The normalized attention coefficient is represented, and a normalized spatial attention matrix H' is obtained.
Proximity sequence X h The time attention matrix T of (2) can be expressed as:
T＝U n ·δ(((X h ) T V 1 )V 2 (V 3 X h )+b n ) (11)
in U n ,b n ∈R T×T ，V 1 ∈R N ,Representing the learned parameters; delta (·) represents the activation function; t (T) i,j Representing the attention coefficient of node i to node j; t'. i,j The normalized attention coefficient is represented, and a normalized time attention matrix T' is obtained.
The normalized time and space attention moment array is applied to the current input data to obtain the adjusted input data:
and then carrying out space-time feature mining based on the adjusted input data.
(4.2) extracting the characteristics of the hydrological elements in the time dimension by adopting a time-gating convolution layer. The space-time diagram convolution network comprises two time-gated convolution layers and one space-diagram convolution layer. The time gating convolution layer consists of a one-dimensional convolution neural network and a gating linear unit.
The adjacent sequences after adjustment of the space-time attention mechanism are obtained according to the step (4.1)The calculation formula of the time gating convolution layer is as follows:
where tconv (·) represents a one-dimensional convolution function;denoted by length L w For inputting data +.>Mapping to a single output; />Wherein Y is 1 ,Y 2 Is of the same dimension and has a reduced length T-L w +1。
Dividing into sections by using gating linear unitsAnd processing to improve the nonlinear learning capacity of the model, and finally obtaining the output S of the time-gating convolution layer.
And (4.3) constructing a space diagram convolution layer to excavate the space characteristics of the flow field runoff process, and applying a layer of time-gating convolution layer to realize the rapid propagation of the state of the space convolution layer.
The space diagram convolution layer adopts a K-order chebyshev polynomial to carry out approximate calculation on the Laplacian matrix L of the diagram so as to capture the space dependence among the diagram structure data, and the calculation formula of the output F of the space diagram convolution layer is as follows:
wherein gconv (·) represents a space diagram convolution function; k is a super parameter;is a k-order chebyshev polynomial, θ k As coefficients thereof; θ max Is the maximum eigenvalue of matrix L.
After obtaining the output F of the space diagram convolution layer, a layer of time gating convolution layer is applied again to realize the rapid propagation of the state of the space convolution layer, so as to obtain the output of the space-time convolution blockFor adjacent sequence X h The result of the space-time convolution block processing is as follows:
X' h ＝tconv(gonv(tconv(H'X h T'))) (19)
and (4.4) constructing an output layer based on the time-gated convolution and the fully-connected neural network on the basis of the step (4.3) to obtain potential space-time expression of a single component, and finally fusing the forecasting results of different components to obtain runoff forecasting values of all sub-watershed future moments.
For data X 'after space-time convolution block processing' h Obtaining potential space-time expression of adjacent sequences by adopting output layer processing based on time gating convolution and fully connected neural networkSimilarly, the potential space-time expression of the rest space-time sequences after being processed by the space-time convolution block and the output layer can be obtained, and finally, the forecast values of different sequences are fused, and the final forecast result can be expressed as:
wherein, the ". As used herein, the Hadamard product is the multiplication of the corresponding elements in the matrix; w (W) g ，W h ，W p ，W m Respectively represent the parameters learned by four different time space convolution block components, reflecting the geographic potential dependency sequence X g Adjacent sequence X h Periodically repeating sequence X p Historical meteorological element sequence X m The degree of influence on the target sequence;the forecast values for the 4 sets of sequences are shown separately.
Step 5: improvements are made to the bald eagle search optimization algorithm (Bald Eagle Search, BES): initializing the initial bald eagle population position by using a uniform initialization method; and introducing the improved multi-element learning into a balying searching optimization algorithm to obtain a UMBES algorithm, and improving the global searching capability of the balying searching algorithm.
And (5.1) setting an objective function of the BES algorithm as the accuracy of the radial flow prediction, and determining the population size, the iteration number, the dimension size and the upper and lower limits of the search space.
And (5.2) initializing the initial bald eagle position by adopting a uniform initialization method, wherein the improved initialization mode formula is as follows:
P i ＝P i L +r(P i U -P i L ) (21)
wherein P is i Representing the initial position of the ith hydrological site, L is the lower boundary of a search interval, U is the upper boundary of the search interval, and r is [0,1]A uniform random number therebetween.
And (5.3) calculating an fitness value according to the objective function, and obtaining an optimal solution according to the calculated fitness.
(5.4) a selection stage, in which the hydrologic sites identify and select the best areas (based on the number of foods) in the selected search space where they can predate. The mathematical representation is specifically modified as shown in equation (22):
P new,i ＝P best +α*r(P mean -P i ) (22)
wherein alpha is a parameter for controlling position change, and the value is 1.5,2]。P best Is the current optimal position, P mean Indicating information using all the points before.
In the searching stage, each hydrologic site searches for new relevant position information in the selected searching space and moves in different directions in the spiral space so as to speed up the searching. The optimum position of the dive is expressed by a mathematical formula (23):
wherein θ (i) and r (i) are the polar angle and the polar diameter of the spiral equation when a search relation is established between the ith hydrological site and the neighbor site; a and R are parameters for controlling the spiral track, and the variation ranges are (5, 10) and (0.5, 2) respectively; rand is a random number in (0, 1), and x (i) and y (i) represent the positions of the ith hydrological site in polar coordinates, and the values are (-1, 1).
(5.5) introducing a multi-element learning strategy to update the position information of the hydrologic site; randomly dividing the position into two parts, wherein one part is learned from the historical site positions of the current hydrological site position, and the rest is learned from the optimal position in the current hydrological site position, and the specific implementation process is as shown in an equation (24):
where j is a positive integer smaller than the market size, and j+.i; p is p j,new Representing j balding hawks in the current population; a and b are random numbers from 0 to 1; p is p best,new Is the bald eagle position of the optimal solution of the current population.
(5.6) in the dive phase, the current hydrologic sites sway from the best position of the search space to their target positions, all points also moving toward the best point, the mathematical expression of which is shown in equation (25):
wherein, c1, c 2E [1,2] increases the moving strength of the bald hawk to the optimal point and the central point.
Step 6: optimizing super parameters including the number of hidden layer nodes and learning rate of the MASTGCN model in the step 4 by utilizing UMBES, obtaining corresponding optimal parameters, and predicting the runoff condition at the future moment by utilizing the optimized MASTGCN runoff forecasting model to obtain a runoff condition forecasting result at the future moment.
And (6.1) initializing relevant parameters of the bald eagle search optimization algorithm, including population, dimension, maximum iteration number, upper and lower limits of a search space and current iteration number.
(6.2) calculation of the fused model trainingPrediction value of trainingAnd the actual value Y of the sample i The root mean square error is taken as the fitness value Fit of each individual in the BES algorithm:
and (6.3) updating the position of each bald eagle in the outgoing population according to a position updating strategy, calculating the fitness value of each individual by using a formula (26), and sequencing the fitness values.
And (6.4) calculating the individual position again by utilizing a multivariate learning strategy, calculating the individual position by utilizing a formula (24), calculating the individual fitness value by utilizing a formula (26), comparing the individual fitness value with the individual fitness value obtained in the step (6.3), and selecting the optimal position corresponding to the optimal fitness value.
And (6.5) judging whether the maximum iteration times are reached, if so, outputting an optimal solution, extracting the super parameters of the MASTGCN model from the optimal solution, and otherwise, returning to the step (6.3).
And (6.6) predicting the runoff condition at the future moment by using the optimized MASTGCN runoff prediction model to obtain a runoff condition prediction result at the future moment.

Claims (10)

1. A runoff forecasting method based on a multi-element attention space-time diagram convolution network is characterized by comprising the following steps:
(1) Acquiring hydrologic related historical data of the inner diameter of the river basin in advance, and preprocessing the historical data;
(2) Extracting topological relations of upstream and downstream stations of the river basin, and generalizing a water resource system with the effects of climate change, human activity and multi-element coupling of the underlying surface of the river basin into a graph structure;
(3) Establishing a geographic adjacency matrix based on a real space adjacency relationship, constructing a potential dependency matrix based on a non-adjacent sub-basin runoff time sequence correlation relationship, and analyzing multiple time-space dependencies of basin runoff processes on time elements, period elements, meteorological elements and space elements;
(4) Carrying out feature extraction on geographic information by adopting four-dimensional space-time convolution blocks, wherein each one-dimensional space-time convolution block comprises a layer of space-time attention mechanism and a layer of space-time diagram convolution network; wherein the spatiotemporal attention mechanism captures the dynamic correlation of the runoff sequence; the space-time diagram convolution network comprises two time gating convolution layers and a space diagram convolution layer; constructing an output layer based on time gating convolution and a fully connected neural network, and constructing a runoff forecasting model MASTGCN based on a multi-element attention space-time diagram convolution network;
(5) Initializing the initial bald eagle population position by using a uniform initialization method; introducing the improved multi-element learning into a bald eagle search optimization algorithm BES to obtain a UMBES algorithm;
(6) Optimizing super parameters including the number of hidden layer nodes and learning rate of the MASTGCN model in the step (4) by utilizing UMBES, obtaining corresponding optimal parameters, and predicting the runoff condition at the future moment by utilizing the optimized MASTGCN runoff forecasting model to obtain a runoff condition forecasting result at the future moment.
2. The method of claim 1, wherein the historical data in step (1) comprises a daily, a ten-day, a month, and a year flow data set, a geographic potential dependent data set, a proximity sequence data set, a historical meteorological element data set, and a human activity trend data set for controlling a hydrologic station.
3. The runoff forecasting method based on the multi-element attention space-time diagram convolution network according to claim 1, wherein the implementation process of the step (2) is as follows:
dividing a river basin into different sub-river basins, determining outlet control sites of the sub-river basins, abstracting a spatial relationship among the sub-river basins into an undirected and weight-free graph G= (V, E, A), displaying a physical relationship between a river basin water system and hydrologic sites, wherein V represents a set of all sub-river basin control sites, and each sub-river basin control siteIs a node in graph G; e represents the edge set in FIG. G, representing a watershed main or tributary; a= { A for adjacency matrix between sub-basin control sites geo ,A rel Represented by (A), where A geo ∈R n×n Is a geographic adjacency matrix, A rel ∈R n×n An adjacency matrix for potential spatial dependencies;
the whole watershed shares |v|=n sub-watershed, then the sub-watershed control site set is defined as:
V＝{v 1 ,...,v n ,...,v N } (1)
wherein n refers to an nth sub-basin site;
order theRepresenting the runoff value of the sub-basin n at the time T (1.ltoreq.t), the set of runoff values of all the sub-basins at the time T is represented as:
order theA historical meteorological element sequence P representing the value of a meteorological element of a sub-basin n at the time t t The method comprises the following steps:
based on the historical time sequence of all node runoffs and meteorological elements on the graph G, the time length of the sub-basin control site in the future is T p The prediction of the radial flow value in the time period of (2) is as follows:
Y＝(y 1 ,y 2 ,...,y N ) (4)
in the method, in the process of the invention,representing the sub-basin n from time l+1 to time l+T p And h is the forecast period of the runoff forecast.
4. The runoff forecasting method based on the multi-element attention space-time diagram convolution network according to claim 1, wherein the implementation process of the step (3) is as follows:
establishing a geographic adjacency matrix based on a real space adjacency relation by considering that larger runoff mobility exists between spatially adjacent sub-watershed, and describing the local spatial dependence of peripheral sub-watershed runoffs on a target vector; specifically, for any two different sub-watershed i and j, its geographic adjacency matrix is represented as follows:
in the method, in the process of the invention,representing sub-watershed i and j as adjacent sub-watershed +.>Representing non-adjacency;
constructing a potential dependency matrix based on non-adjacent sub-drainage basin runoff time sequence correlation, and describing potential dependency relations between upstream and downstream non-adjacent sub-drainage basins; specifically, for any two different sub-watershed i and j, its potential dependency matrix is represented as follows:
adopting a chaos phase space reconstruction theory and Copula entropy correlation analysis to quantify the time correlation and dependence of the basin runoff process on time elements, period elements and meteorological elements;
respectively utilizing chaotic phase space reconstructionQuantitative analysis of time dependence of basin runoff process on periodicity and nearby moment by theoretical and Copula entropy correlation analysis, and cutting off subscripts T along time axis h And T p Is the input of two components of the model at the moment of approach and the moment of periodical repetition, t 0 The two sets of sequences at time are denoted as:
the Copula entropy correlation analysis is further utilized to intercept the subscript as T m Historical meteorological elements of (a).
5. The runoff forecasting method based on the multi-element attention space-time diagram convolutional network according to claim 1, wherein the dynamic correlation implementation process of capturing the runoff sequence by adopting a space-time attention mechanism in the step (4) is as follows:
the space-time attention mechanism is used for adaptively capturing dynamic correlations between different space-time dimension nodes, and comprises a space attention mechanism and a time attention mechanism which are respectively used for capturing the dynamic correlations of the mutual influence of runoff sequences of different sites and the correlations between runoff processes of different times of the same site; the spatial attention matrix H for the example of the adjacent sequence is expressed as:
H＝U m ·δ((X h W 1 )W 2 (W 3 X h ) T +b m ) (9)
in the process, data is inputWherein N, C in T represents the number of top points, the number of input channels and the length of the input data time dimension respectively; u (U) m ,b m ∈R N×N ，W 1 ∈R T ，/>Representing the learned parameters; delta (·) represents the activation function; h i,j Representing the attention coefficient of node i to node j; h'. i,j Representing the normalized attention coefficient, and further obtaining a normalized spatial attention matrix H';
proximity sequence X h The time attention matrix T of (1) is expressed as:
T＝U n ·δ(((X h ) T V 1 )V 2 (V 3 X h )+b n ) (11)
in U n ,b n ∈R T×T ，V 1 ∈R N ,Representing the learned parameters; delta (·) represents the activation function; t (T) i,j Representing the attention coefficient of node i to node j; t'. i,j Representing the normalized attention coefficient, and further obtaining a normalized time attention matrix T'; the normalized time and space attention moment array is applied to the current input data to obtain the adjusted input data:
and then carrying out space-time feature mining based on the adjusted input data.
6. The runoff forecasting method based on the multi-element attention space-time graph convolution network according to claim 1, wherein the time gating convolution layer in the step (4) is composed of a one-dimensional convolution neural network and a gating linear unit and is used for extracting characteristics of hydrological meteorological elements in a time dimension; the calculation formula is as follows:
where tconv (·) represents a one-dimensional convolution function;denoted by length L w For inputting data +.>Mapping to a single output; />Wherein Y is 1 ,Y 2 Is of the same dimension and has a reduced length T-L w +1；
Y obtained by dividing by adopting gating linear unit 1 ,Processing is performed to improve the nonlinear learning ability of the MASTGCN model to obtain the output S of the time-gated convolutional layer.
7. The runoff forecasting method based on the multi-element attention space-time diagram convolution network, which is characterized in that the space-diagram convolution layer in the step (4) excavates the space characteristics of the runoff process of the flow domain and applies a layer of time-gating convolution layer to realize the rapid propagation of the state of the space-convolution layer; the space diagram convolution layer adopts a K-order chebyshev polynomial to carry out approximate calculation on the Laplacian matrix L of the diagram so as to capture the space dependence among the diagram structure data, and the calculation formula of the output F of the space diagram convolution layer is as follows:
wherein gconv (·) represents a space diagram convolution function; k is a super parameter;is a k-order chebyshev polynomial, θ k As coefficients thereof; θ max Is the maximum eigenvalue of matrix L;
after obtaining the output F of the space diagram convolution layer, a layer of time gating convolution layer is applied again to realize the rapid propagation of the state of the space convolution layer, so as to obtain the output of the space-time convolution blockFor adjacent sequence X h The result of the space-time convolution block processing is as follows:
X h '＝tconv(gonv(tconv(H'X h T'))) (19)。
8. the runoff forecasting method based on the multi-element attention space-time graph convolutional network according to claim 1, wherein the output layer implementation process based on the time-gated convolutional and fully-connected neural network is built in the step (4) as follows:
for data X after space-time convolution block processing h ' potential space-time expression of adjacent sequences is obtained by adopting output layer processing based on time gating convolution and fully connected neural networkSimilarly, obtaining potential space-time expression of the rest space-time sequences after being processed by the space-time convolution block and the output layer; fusing the forecast values of different sequences, wherein the final forecast result is expressed as:
wherein, the ". As used herein, the Hadamard product is the multiplication of the corresponding elements in the matrix; w (W) g ，W h ，W p ，W m Respectively represent the parameters learned by four different time space convolution block components, reflecting the geographic potential dependency sequence X g Adjacent sequence X h Periodically repeating sequence X p Historical meteorological element sequence X m The degree of influence on the target sequence;respectively representing the forecast values of the four groups of sequences.
9. The runoff forecasting method based on the multi-element attention space-time diagram convolution network according to claim 1, wherein the implementation process of the step (5) is as follows:
(51) Setting an objective function of a BES algorithm as a runoff prediction accuracy rate, and determining the population size, the iteration number, the dimension size and the upper and lower limits of a search space;
(52) And initializing the initial bald eagle position by adopting a uniform initializing method, wherein the formula of the improved initializing mode is as follows:
P i ＝P i L +r(P i U -P i L ) (21)
wherein P is i Representing the initial position of the ith hydrological site, L is the lower boundary of a search interval, U is the upper boundary of the search interval, and r is [0,1]A uniform random number therebetween;
(53) Calculating a fitness value by taking the runoff prediction accuracy as an objective function, and obtaining an optimal solution according to the calculated fitness;
(54) A selection phase, in which the hydrologic site identifies and selects the best region in the selected search space:
P new,i ＝P best +α*r(P mean -P i ) (22)
where α is a parameter controlling the change of position, P best Is the current optimal position, P mean Information indicating the utilization of all the previous points;
in the searching stage, each hydrologic site searches for new relevant position information in the selected searching space and moves in different directions in the spiral space so as to speed up the searching speed:
wherein θ (i) and r (i) are the polar angle and the polar diameter of the spiral equation when a search relation is established between the ith hydrological site and the neighbor site; a and R are parameters for controlling the spiral track, and the variation ranges are (5, 10) and (0.5, 2) respectively; rand is a random number in (0, 1), and x (i) and y (i) represent the position of the ith hydrological site in polar coordinates;
(55) Introducing a multi-element learning strategy to update the position information of the hydrologic site; the position is randomly divided into two parts, one part is learned from the historical site position of the current hydrological site position, the other parts are learned from the optimal position in the current hydrological site position, and the specific implementation process is as follows:
wherein j is a positive integer less than i; p is p j,new Representing j hydrologic sites in the current population; a and b are random numbers from 0 to 1; p is p best,new The position of the hydrological site which is the optimal solution of the current population;
(56) In the dive phase, the current hydrologic sites sway from the best position of the search space to their target positions, all points also moving toward the best point, the mathematical expression of which is shown in equation (25):
wherein c1, c2 e [1,2] increases the moving strength of the historical hydrologic site to the optimal point and the central point.
10. The runoff forecasting method based on the multi-element attention space-time diagram convolution network according to claim 1, wherein the implementation process of the step (6) is as follows:
(61) Initializing relevant parameters of the BES algorithm, including population, dimension, maximum iteration number, upper and lower limits of a search space and current iteration number;
(62) Calculating predicted values trained by fusion modelsAnd the actual value Y of the sample i The root mean square error is taken as the fitness value Fit of each individual in the BES algorithm:
(63) According to a position updating strategy, updating the position of each bald eagle in the population, calculating the fitness value of each individual, and sequencing the fitness values;
(64) Calculating the individual position again by utilizing a multivariate learning strategy, calculating the individual position and the individual fitness value, comparing the individual position and the individual fitness value obtained in the step (63), and selecting an optimal position corresponding to the optimal fitness value;
(65) Judging whether the maximum iteration times are reached, if so, outputting an optimal solution, extracting the super parameters of the MASTGCN model, and otherwise, returning to the step (63).
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