CN107133398B - River runoff prediction method based on complex network - Google Patents

River runoff prediction method based on complex network Download PDF

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CN107133398B
CN107133398B CN201710291000.5A CN201710291000A CN107133398B CN 107133398 B CN107133398 B CN 107133398B CN 201710291000 A CN201710291000 A CN 201710291000A CN 107133398 B CN107133398 B CN 107133398B
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吴学文
崔楠
辛嘉熙
闻昕
吴丹晖
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ANHUI JINHAIDIER INFORMATION T
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Abstract

The invention discloses a method for predicting river runoff, which mainly aims at the runoff Prediction of a data-free hydrological site (PUB). The basic principle is that the topological characteristic of a hydrological space-time sequence is mined by utilizing a complex network, and the runoff prediction is carried out on a data-free site on the basis. The method comprises the steps of constructing a runoff complex network model according to runoff data of a monitoring network site, carrying out community mining by utilizing a Newman fast algorithm (FN) on the basis, selecting candidate nodes on the basis of community mining results, selecting two types of nodes, namely common nodes and characteristic nodes, as the candidate nodes by considering the correlation between basin division and PUB, and finally predicting the runoff of the site to be predicted by utilizing a transplanting method. The invention provides a runoff prediction method for a data-free site, which considers the correlation on a runoff data topological structure and also considers the runoff data.

Description

River runoff prediction method based on complex network
Technical Field
The invention relates to the field of complex network application, in particular to a river runoff prediction method based on a complex network.
Background
Rivers play an important role in many aspects such as hydrology, water resource management, environment and ecosystem, however, the evaluation and prediction of the runoff of rivers still face many problems. As river runoff is a complex non-linear process that is interacted by climatic conditions as well as topographical features. For example, the runoff of a river is not only influenced by the distribution of rainfall over time and space, land use parameters, hydrological soil factors, geostatistical properties, and the like.
Existing research on river runoff is primarily directed to identifying the connections that exist between river runoff. However, the existing research mostly depends on specific problems and related specific elements, and a plurality of problems exist in the research on the prediction of the runoff of the river. For example, most of the existing hydrological prediction models are relatively complex, and need to rely on too many parameters and data for analysis, and meanwhile, due to the deviation of the data and the deviation of the models, the prediction of runoff is tedious and is not necessarily reliable; although some existing model correction algorithms based on deviation correction reduce prediction errors to a certain extent, the method does not help understanding the watershed hydrological mechanism; from another perspective, most of the existing models are hydrological models for a specific area, such as the model of the new anjiang river, and there is still a problem in applying them to a wider range of watersheds, so that a unified general hydrological framework system is lacking.
Therefore, it is desirable to establish the relationship of river runoff in space and time from the macroscopic view, analyze some possible relationship and influence between the river runoff and discover the relationship on the topological structure by identifying the implicit relationship between the river runoff and the corresponding climate and landform, thereby being helpful for predicting the runoff.
Disclosure of Invention
Aiming at the defects related in the background technology, the invention provides a river runoff predicting method based on a complex network, and the complex network is used for mining the topological correlation in space between river runoff data, so that the absolute dependence on the runoff data is eliminated to a certain extent; meanwhile, a river runoff network is constructed by using a complex network idea, so that research and analysis in a wide river basin are facilitated.
The invention adopts the following technical scheme for solving the technical problems:
a river runoff prediction method based on a complex network comprises the following steps:
step A), modeling river runoff space-time data by using a complex network abstraction method to form a runoff complex network model;
step B), carrying out community excavation on the runoff complex network model by using a Newman fast algorithm to complete drainage basin division;
step C), selecting common nodes and characteristic nodes based on the division of the drainage basin;
and D), predicting the runoff of the data-free hydrological site by using a transplanting method based on the selected common node and the selected characteristic node.
As a further optimization scheme of the river runoff predicting method based on the complex network, the detailed steps of the step A) are as follows:
step A.1), abstracting the geographical position of the corresponding monitoring station into nodes according to the runoff data of each hydrologic monitoring station;
step A.2), taking the correlation between the runoff sequence between the two nodes as a standard for evaluating whether a connecting edge exists between the two nodes, and establishing a runoff complex network model: if the correlation is larger than a preset correlation threshold value, the corresponding nodes are considered to have connecting edges, otherwise, the nodes are considered to have no connecting edges.
As a further optimization scheme of the river runoff predicting method based on the complex network, the pearson coefficient is adopted as the correlation between runoff sequences between two nodes in the step a.2), and the calculation formula is as follows:
Figure GDA0002430882670000021
wherein XiRepresents a runoff time series of a node i, wherein XjRepresenting a runoff time series of a node j;
Figure GDA0002430882670000022
is a sequence XiAnd sequence XjPearson's correlation coefficient between them, cov (X)i,Xj) Is Xi，XjThe covariance of the two or more different signals,
Figure GDA0002430882670000023
is XiThe standard deviation of (a) is determined,
Figure GDA0002430882670000024
is XjStandard deviation of (2).
As a further optimization scheme of the river runoff predicting method based on the complex network, the detailed steps of the step B) are as follows:
step B.1), initializing the runoff complex network model into N communities, wherein N is the number of nodes of the runoff complex network model, namely each node is an independent community;
initialization eijAnd aiTo make it satisfy
Figure GDA0002430882670000025
ai＝ki/2m
Wherein e isijIs the ratio of the edge between the point of the community in which the node i is located and the point of the community in which the node j is located, aiIs the proportion of edges connected to the community in which node i is located, kiThe degree of the node i is, and m is the total number of edges in the network;
step B.2), merging the edge-connected community pairs to increase the modularity Q most or reduce the modularity Q least, wherein the calculation formula of the merged modularity increment delta Q is as follows:
ΔQ＝eij+eji-2aiaj＝2(eij-aiaj)
step B.3), for the corresponding element eijUpdating: e corresponding to rows and columns related to i, j communitiesijAdding as new eij；
B.4), recording the value of the current modularity Q and the corresponding community dividing structure;
step B.5), repeatedly executing the steps B.2) to B.4) until the whole runoff complex network model is merged into a community;
and B.6) selecting the community division structure corresponding to the maximum value of the modularity Q as the result of the basin division.
As a further optimization scheme of the river runoff predicting method based on the complex network, the two nodes with the largest internal connection number in each community are selected as the common nodes of the communities in the step C), and the two nodes closest to the nodes to be predicted are selected as the characteristic nodes of the nodes to be predicted.
As a further optimization scheme of the river runoff predicting method based on the complex network, two of the commonality candidate nodes and the characteristic candidate nodes are selected by the method.
As a further optimization scheme of the river runoff predicting method based on the complex network, the detailed steps of the step D) are as follows:
step D.1), setting a common factor alpha;
step D.2), distributing the weight among the common candidate nodes according to the internal connectivity of the common candidate nodes, wherein the internal connectivity of the common candidate nodes is the number of the common candidate nodes and the nodes connected in the corresponding communities, and the internal connectivity of the common candidate node o is inline _ koThen the weight w of the common candidate node ooThe calculation formula of (a) is as follows:
Figure GDA0002430882670000031
wherein k isoThe degree of the candidate node o is common,
Figure GDA0002430882670000032
the sum of the internal connection numbers of all the common candidate nodes;
step D.3), performing weight distribution on the characteristic candidate nodes by adopting an inverse distance weight distribution method, namely
Figure GDA0002430882670000033
Wherein, wqAs weights of the characteristic candidate nodes q, dqAs feature candidatesThe distance between the node q and the node to be predicted;
step D.4), adding the common part and the characteristic part to obtain a predicted value of the node to be predicted, wherein a specific calculation formula is as follows:
P＝α∑wofo+(1-α)∑wqfq
where P is the prediction result, foAnd fqThe average area unit runoff quantities of the common candidate node o and the characteristic candidate node q are respectively.
As a further optimization scheme of the river runoff prediction method based on the complex network, the commonality factor alpha is 0.2.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. universality: on one hand, the method for predicting river runoff data by using the complex network is only a specific example of predicting data by using the complex network, and can also predict various hydrological variables such as rainfall, flood characteristics, evaporation capacity and the like.
2. Robustness: and discovering the characteristics of the runoff space sequences on the topological structure by using a complex network community mining method. When runoff prediction is carried out, topological structure characteristics are taken into consideration, and therefore a certain guiding effect is achieved on hydrological characteristic analysis and research of a watershed. At present, weather changes and human activities affect the effect of hydrology and water resources and the effect of hydrology and water circulation, water environment and water disasters, so certain errors are certainly brought to river runoff prediction if only data values are used for prediction depending on historical data, and topological structure characteristics implied by the data are not considered.
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FIG. 1 shows an overall algorithm flow diagram of the present invention;
FIG. 2 illustrates a flow chart of the construction of a runoff complex network of the present invention;
FIG. 3 illustrates a flowchart of the basin partitioning, Newman's community mining algorithm, of the present invention;
FIG. 4 illustrates a candidate node type graph of the present invention;
FIG. 5 illustrates a migration prediction flow diagram of the present invention.
Detailed Description
The technical scheme of the invention is further explained in detail by combining the attached drawings:
fig. 1 shows the general algorithm flow chart of the present invention. The runoff prediction method based on the complex network basically comprises four basic steps: the method comprises the steps of runoff complex network construction, Newman rapid algorithm, candidate node selection and river runoff prediction by using a transplantation method. The input of the algorithm is a plurality of known river runoff time sequences, and the output is the unknown runoff data of the site to be predicted.
Fig. 2 shows a flow path complex network building block diagram of the present invention. The method comprises the following specific steps:
step 1: selecting proper hydrological data
And selecting appropriate hydrological data of the monitoring station meeting the requirements from the database according to the requirements, wherein the selected standard is the age range of the runoff data and the time length of the runoff sequence. Assuming that N runoff monitoring stations meeting the requirements are selected, and the runoff time sequence corresponding to each runoff monitoring station is represented as X ═ (X)1,x2,x3,……xT)。
Step 2: node abstraction
The abstraction of the nodes in the invention is that the geographical position of the monitoring station corresponding to the runoff time sequence is taken as the node, and N nodes are total and correspond to X nodes1,X2,X3……XN。
And step 3: calculating a correlation coefficient R
The correlation measurement standard selected in the invention is the Pearson coefficient:
Figure GDA0002430882670000051
wherein XiRepresents a runoff time series of a node i, wherein XjRepresenting a runoff time series of a node j; for each node XiAnd respectively calculating the Pearson correlation coefficients of the nodes and the other N-1 nodes, wherein the calculation formula is as the above formula.
And 4, step 4: setting a correlation threshold TS
The correlation threshold TS is set in consideration of the edge density ρ (t):
Figure GDA0002430882670000052
where n (t) represents the number of network edges when TS is t, if the threshold TS is set too large, n (t) is too small, resulting in many isolated nodes, and if the threshold TS is set too small, n (t) is too large, resulting in a network that is almost a complete network, which are useless for network research and node analysis, so that a density distribution map of correlation coefficients is drawn according to the correlation coefficients calculated in step 2, and a suitable TS value range is selected.
Meanwhile, the selection of the correlation threshold TS also needs to consider the existence of the remote correlation related edges, so-called remote correlation refers to the nodes with high correlation even if the nodes are located far away from each other. Care should be taken not to lose these edges during the threshold selection process.
And 5: abstraction of edges
For node i, j, if it is
Figure GDA0002430882670000053
And considering that a connecting edge exists between the two nodes, namely the corresponding position of the adjacency matrix A is 1, otherwise, the corresponding position is 0. Namely, it is
Figure GDA0002430882670000054
And finishing the construction of the runoff complex network model.
According to the consistency between community mining and basin partitioning, community mining is used for carrying out community partitioning on the complex network model of the radial flow, and as a result of the community mining, the connection between nodes in each group is relatively very tight, but the connection between the groups is relatively sparse, so that the basin partitioning is carried out by using the community mining method.
The Newman fast algorithm is used for carrying out community division, and the method is a cohesive algorithm based on the greedy algorithm idea. Firstly, each node is considered as a community, then the nodes are gradually merged into a community, the merging principle is towards the direction of maximum increase or minimum decrease of the community modularity, and the community partition with the maximum modularity corresponds to the optimal community partition, namely the result of basin partition.
FIG. 3 shows a flowchart of the Newman fast algorithm of the present invention. The method comprises the following steps:
step 1: initialization
The network is initialized to N communities, namely each node is an independent community. Initialization eijAnd aiSatisfy the requirement of
Figure GDA0002430882670000061
ai＝ki/2m
Wherein k isiM is the total number of edges in the network, which is the degree of node i.
Step 2: merging networks
Merging the edge-connected community pairs at one time, and calculating the modularity increment after merging:
ΔQ＝eij+eji-2aiaj＝2(eij-aiaj)
according to the principle of greedy algorithm, each merge should be done in a direction that increases Q the most or decreases Q the least. Each timeAfter the second combination, for the corresponding element eijUpdating: e corresponding to rows and columns related to i, j communitiesijAdding as new eij。
And repeating the step, and continuously merging the communities until the whole network is merged into a community.
And step 3: selecting an optimal community division result
In the process of merging communities, each merged community corresponds to a community division result, and a community division corresponding to a local maximum Q value is selected and corresponds to an optimal network community structure.
FIG. 4 illustrates a candidate node type diagram of the present invention. The selection of the candidate node takes two factors into consideration: a commonality candidate node and a characteristic candidate node. The common candidate node is a representative node of a watershed in a highly relevant community in a certain watershed, and two nodes with the largest internal connection number in each community are selected as common nodes of the community. Because for a network node, the degree of the node represents the relevance of the node to other nodes, if the degree of one node is larger, the more important the node is proved to be in the community; the characteristic node is selected according to the fact that similar things are always similar, therefore, the selected standard is the distance between the characteristic node and the node to be predicted, the closer the distance is, the more similar the characteristic node is considered to be to the node to be predicted, and the two nodes closest to the node to be predicted are selected as the characteristic node of the node to be predicted.
Fig. 5 shows a prediction flow chart of the transplantation method of the present invention. The method comprises the following specific steps:
step 1: setting a commonality factor
Since the commonality candidate node and the characteristic candidate node are selected, the commonality factor is first set, typically 0.2.
Step 2: weight distribution among common candidate nodes
The distribution of weights among the common candidate nodes is divided according to the importance degree of the common candidate nodes in the community, namely
Distributing the weight among the common candidate nodes according to the internal connectivity of the common candidate nodes, and obtaining the common candidate nodesThe internal connection number of the nodes is the number of the common candidate nodes and the nodes connected in the corresponding communities, and the internal connection number of the common candidate node o is made to be inline _ koThen the weight w of the common candidate node ooThe calculation formula of (a) is as follows:
Figure GDA0002430882670000071
wherein k isoThe degree of the candidate node o is common,
Figure GDA0002430882670000072
is the sum of the number of internal connections of all the commonality candidate nodes.
And step 3: feature candidate inter-node weight assignment
The weight distribution basis of the characteristic candidate nodes is that the closer the distance is, the more important the characteristic candidate nodes are in prediction, and an inverse distance weight distribution method is adopted, namely
Figure GDA0002430882670000073
Wherein, wqAs weights of the characteristic candidate nodes q, dqThe distance between the characteristic candidate node q and the node to be predicted.
And 4, step 4: additive computation
And adding the common part and the characteristic part to obtain a predicted value of the node to be predicted. The specific calculation formula is as follows:
P＝α∑wofo+(1-α)∑wqfq
where P is the prediction result, foAnd fqThe average area unit runoff quantities of the common candidate node o and the characteristic candidate node q are respectively.
It will be understood by those skilled in the art that, unless otherwise defined, all terms (including technical and scientific terms) used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this invention belongs. It will be further understood that terms, such as those defined in commonly used dictionaries, should be interpreted as having a meaning that is consistent with their meaning in the context of the prior art and will not be interpreted in an idealized or overly formal sense unless expressly so defined herein.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only illustrative of the present invention and are not intended to limit the present invention, and any modifications, equivalents, improvements and the like made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (5)

1. A river runoff predicting method based on a complex network is characterized by comprising the following steps:
step A), modeling river runoff space-time data by using a complex network abstraction method to form a runoff complex network model;
step B), carrying out community excavation on the runoff complex network model by using a Newman fast algorithm to complete drainage basin division;
step C), selecting common nodes and characteristic nodes on the basis of division of a drainage basin, namely selecting two nodes with the largest internal connection number in each community as the common nodes of the community, and selecting two nodes closest to the nodes to be predicted as the characteristic nodes of the nodes to be predicted;
step D), predicting the runoff of the data-free hydrological site by using a transplanting method based on the selected common nodes and the selected characteristic nodes;
the detailed steps of the step D) are as follows:
step D.1), setting a common factor alpha;
step D.2), distributing the weight among the common nodes according to the internal connectivity of the common nodes, wherein the internal connectivity of the common nodes is the number of the common nodes and the nodes connected in the corresponding communities, and the internal connectivity of the common node o is the inline _ koThe weight w of the common node ooThe calculation formula of (a) is as follows:
Figure FDA0002579145570000011
wherein k isoIs the degree of the common node o,
Figure FDA0002579145570000012
the sum of the internal connection numbers of all the common nodes;
step D.3), performing weight distribution on the characteristic nodes by adopting an inverse distance weight distribution method, namely
Figure FDA0002579145570000013
Wherein, wqAs weights of the characteristic nodes q, dqThe distance between the characteristic node q and the node to be predicted is obtained;
step D.4), adding the common part and the characteristic part to obtain a predicted value of the node to be predicted, wherein a specific calculation formula is as follows:
P＝α∑wofo+(1-α)∑wqfq
where P is the prediction result, foAnd fqThe average area unit runoff of the common node o and the characteristic node q are respectively.
2. The method for predicting river runoff based on a complex network as claimed in claim 1, wherein the detailed steps of the step a) are as follows:
step A.1), abstracting the geographical position of the corresponding monitoring station into nodes according to the runoff data of each hydrologic monitoring station;
step A.2), taking the correlation between the runoff sequence between the two nodes as a standard for evaluating whether a connecting edge exists between the two nodes, and establishing a runoff complex network model: if the correlation is larger than a preset correlation threshold value, the corresponding nodes are considered to have connecting edges, otherwise, the nodes are considered to have no connecting edges.
3. The river runoff predicting method based on the complex network as recited in claim 2, wherein the pearson coefficient is used as the correlation between the runoff sequence between two nodes in the step a.2), and the calculation formula is as follows:
Figure FDA0002579145570000021
wherein XiRepresents a runoff time series of a node i, wherein XjRepresenting a runoff time series of a node j;
Figure FDA0002579145570000022
is a sequence XiAnd sequence XjPearson's correlation coefficient between them, cov (X)i,Xj) Is Xi，XjThe covariance of the two or more different signals,
Figure FDA0002579145570000023
is XiThe standard deviation of (a) is determined,
Figure FDA0002579145570000024
is XjStandard deviation of (2).
4. The method for predicting river runoff based on a complex network as claimed in claim 3, wherein the detailed steps of the step B) are as follows:
step B.1), initializing the runoff complex network model into N communities, wherein N is the number of nodes of the runoff complex network model, namely each node is an independent community;
initialization eijAnd aiTo make it satisfy
Figure FDA0002579145570000025
ai＝ki/2m
Wherein e isijIs the ratio of the edge between the point of the community in which the node i is located and the point of the community in which the node j is located, aiIs the proportion of edges connected to the community in which node i is located, kiThe degree of the node i is, and m is the total number of edges in the network;
step B.2), merging the edge-connected community pairs to increase the modularity Q most or reduce the modularity Q least, wherein the calculation formula of the merged modularity increment delta Q is as follows:
ΔQ＝eij+eji-2aiaj＝2(eij-aiaj)
step B.3), for the corresponding element eijUpdating: e corresponding to rows and columns related to i, j communitiesijAdding as new eij；
B.4), recording the value of the current modularity Q and the corresponding community dividing structure;
step B.5), repeatedly executing the steps B.2) to B.4) until the whole runoff complex network model is merged into a community;
and B.6) selecting the community division structure corresponding to the maximum value of the modularity Q as the result of the basin division.
5. The method for predicting river runoff flow based on a complex network as claimed in claim 1, wherein said commonality factor α is 0.2.
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