CN110458722A - Flood interval prediction method based on multiple target random vector function connection network - Google Patents
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Abstract
The present invention relates to hydrologic forecast fields, a kind of flood interval prediction method based on multiple target random vector function connection network are disclosed, for assessing the uncertainty of flood forecasting result.To keep prediction interval mean breadth (PINAW) minimum, make prediction interval coverage rate (PICP) maximum simultaneously, coboundary and the lower boundary of the possible value of the following flood are directly forecast using dual output multiple target random vector function connection network (RVFL), by ± the 10% of the target variable initial coboundary of conduct and lower boundary, RVFL is run into ± the 0.5 of the initial weight once obtained the and threshold value feasible zone for being set as NSGA-III algorithm, using the input weight and threshold value of NSGA-III algorithm adjustment RVFL network, obtain optimal multiple target RVFL flood interval prediction model, to obtain than traditional single goal interval prediction model and based on the relatively reliable and effective flood forecasting result of multiple target ANN flood interval prediction model.
Description
Technical field
The present invention relates to hydrologic forecast field, in particular to a kind of flood based on multiple target random vector function connection network
Forecasting procedure between pool.
Background technique
Due to the influence of watershed system and mankind's activity, so that flood forecasting difficulty increases, and another aspect basin water
The required precision of flood forecasting is continuously improved in resource management and power station the safe and economic operation, and traditional point forecasting procedure is got over
To be more difficult to meet the actual demand of water resources management.In this context, probability interval forecasting procedure gradually causes hydrologist
Attention.Probability interval forecasting procedure not only can intuitively provide the variation range of flood forecasting result, can also provide mesh
Mark vector falls in the probability within the scope of prediction interval bound.
For accurately hold forecast information uncertain feature, traditional probability interval forecasting procedure have Bootstrap method,
Bayesian method and GLUE method etc..However traditional flood probability interval prediction method needs complicated mathematical computations and elder generation mostly
Distributional assumption is tested, and needs to calculate the prediction interval of flood on the basis of certainty mathematics model forecast result, it cannot be direct
Provide the probability forecast section of flood, it is difficult to meet the actual demand of power station the safe and economic operation and water resources management.
Summary of the invention
Goal of the invention: aiming at the problems existing in the prior art, the present invention provides a kind of based on multiple target random vector letter
Number connection networks flood interval prediction methods, based on LUBE interval prediction, dual output random vector function connection network and
The flood interval prediction method of NSGA-III algorithm, can provide certainly for power station the safe and economic operation and water resources management
Plan foundation.
Technical solution: the present invention provides a kind of flood interval predictions based on multiple target random vector function connection network
Method, comprising the following steps: step 1: collecting flood time series data, split data into training sample and test samples, and
By data normalization to [0,1] section；Step 2: assuming that the number of input variable is M, the small of object vector work ± 10% is disturbed
Movement is initial coboundary and the lower boundary of dual output RVFL interval prediction model, forms the RVFL or more of M input and dual output
Boundary flood interval prediction model；Step 3: input vector and object vector are inputted into the RVFL up-and-down boundary flood section
Forecasting model, and run the primary initial weight β for obtaining the RVFL up-and-down boundary flood interval prediction model0With initial threshold a0；
Step 4: the parameter of initialization NSGA-III algorithm；Step 5: by [β0- 0.5, β0+ 0.5] and [a0- 0.5, a0+ 0.5] it is arranged
For the feasible zone of the NSGA-III algorithm, NP-1 initial individuals are generated at random in feasible zone, NP-1 initial individuals add
(β0,a0) constitute the initial population of the NSGA-III algorithm；Step 6: using RVFL described in the NSGA-III algorithm optimization
The input weight and threshold value of up-and-down boundary flood interval prediction model, obtain the Pareto optimal solution set of global optimum；Step 7:
The Pareto optimal solution set and the test samples are substituted into the RVFL up-and-down boundary flood interval prediction model, examined
The interval prediction of phase is tested as a result, and calculating PINC the and PINAW index of probative term prediction interval.
Further, in the step 2, in the RVFL up-and-down boundary flood interval prediction model, k are given
Training sample { (xk,yk), k=1,2 ..., K, wherein X=[x1,x2,...,xK]TIndicate input vector, xk=[xk1,
xk2,...,xkM]∈RMIndicate k-th of input training sample, Y=[y1,y2,...,yK]TIndicate output vector, yk=[yk1,
yk2,...,ykN]∈RNIndicate k-th of output training sample,J=1,2 ..., J indicates kth training
The output of j-th of hidden neuron of sample, g () indicate that excitation function, j indicate the number of hidden layer node, βjIndicate input
Weight between layer and hidden layer, ajRespectively indicate the threshold value between input layer and hidden layer；The then RVFL up-and-down boundary flood
The output of k-th of training sample of interval prediction model calculates as follows:
In formula, wj, j=1,2 ..., J indicate the weight between hidden layer and output layer, wj, j=J+1, J+2 ..., J+M table
Show the weight between input layer and output layer；The nuclear mapping matrix of input layer and hidden layer to output layer is expressed as:
(2)；The matrix form of the RVFL up-and-down boundary flood interval prediction model output indicates are as follows:In formula, w=[w1,w2,...,wJ,wJ+1,...,wJ+D]T；It is exported by solving following optimization problem
Weight w:According to the solution of the available formula of regularization least square method (4):
W=(DTD+λI)-1DTY(5)；I indicates unit matrix in formula；Then the output of k-th of training sample indicates are as follows:
Preferably, in the step 4, the parameter of the NSGA-III algorithm includes: Population Size NP, greatest iteration
Number MaxIt, crossover probability pc, mutation probability pm, cross-distribution index ηcWith variation profile exponent ηm。
Further, in the step 4, the detailed process of the NSGA-III algorithm is as follows: (1) calculating reference point
Number H；(2) the number of iterations k=1 is enabled, generates the NP bodily form at random into initial population；(3) binary system crossover operator is used
Progeny population Q is generated with being recombinated and being mutated with multinomial mutation operatoro；(4) by progeny population QoIt is mixed with parent population,
Generate the population R that a size is 2NPk；(5) R is determined using non-dominated ranking algorithmkNon-dominant forward position F1,F2,...,Ft；
(6) objective function is normalized and is associated with it with reference point, offspring individual is screened using elite retention strategy and deleted
Useless reference point screens preceding NP individual in the top and generates next-generation population Pk+1；(7) if k < Gmax, stop iteration simultaneously it is defeated
Non-domination solution out；Otherwise k=k+1 setting and return step (3) are enabled.
Preferably, in step (1), the number H of the reference point is calculated by the following formula:
(7)；C indicates the number of multi-objective optimization question objective function in formula, and g indicates the segmentation section of each objective function
Number.
Preferably, in the step 6, the objective function of the RVFL up-and-down boundary flood interval prediction model is arranged
It is as follows:Wherein, PICP indicates that object vector is fallen in the upper and lower bound of prediction interval
Probability；The width of PINAW expression prediction interval.
Preferably, the PICP is defined as follows:In formula, yiIndicate i-th of number
The observation at strong point；LiAnd UiRespectively indicate the lower and upper limit of i-th of data point；The quantity of N expression training sample.
Preferably, the PINAW is defined as follows:R indicates target in formula
The range of variable, for prediction interval width to be normalized.
The utility model has the advantages that original up-and-down boundary is estimated that (LUBE) interval prediction method extends to multiple target theoretical frame by the present invention
Under, the possible value interval of runoff is directly forecast using dual output RVFL model, and using NSGA-III algorithm to dual output
The output weight of RVFL model carries out optimizing, obtains the flood forecasting section of high quality, be power station the safe and economic operation and
Water resources management provides decision-making foundation.
The present invention can only provide target variable in the single-point forecast result of future time instance for certainty Flood Forecasting Method,
Cannot assess forecast result inherent uncertainty feature and and provide its fluctuation range, the invention proposes one kind to be based on more mesh
The flood interval prediction method for marking random vector function connection network (RVFL), for assessing the uncertain of flood forecasting result
Property.It is minimum to make prediction interval mean breadth (PINAW), while keeping prediction interval coverage rate (PICP) maximum, using dual output
RVFL network directly forecasts coboundary and the lower boundary of the possible value of the following flood, will be at the beginning of ± the 10% of target variable conduct
Beginning coboundary and lower boundary, ± 0.5 that RVFL is run the initial weight once obtained and threshold value are set as NSGA-III algorithm
Feasible zone optimal multiple target RVFL flood is obtained using the input weight and threshold value of NSGA-III algorithm adjustment RVFL network
Forecasting model between pool, to obtain than traditional single goal interval prediction model and the flood section based on multiple target ANN is pre-
Report the relatively reliable and effective flood forecasting result of model.
The RVFL flood interval prediction method that the present invention is mentioned is applied to the day flood of Upper Yangtze River basin Yichang hydrology station
In water interval prediction, compared with prior art, the present invention has the following advantages and effects:
1) value of forecasting of single goal interval prediction model is largely dependent upon penalty coefficient and confidence level
Selection.The mentioned multiple target interval prediction model of the present invention does not need to preset penalty coefficient and confidence level, and can be with one
Secondary property obtains the prediction interval under different confidence levels.
2) compared with the multiple target flood interval prediction model based on ANN, the present invention mentioned based on RVFL interval prediction
Model structure is simple, training speed is fast and Generalization Capability is more preferable.
Detailed description of the invention
Fig. 1 is dual output RVFL up-and-down boundary flood interval prediction model structure；
Fig. 2 is the flood interval prediction model flow figure based on multiple target RVFL；
Fig. 3 is the optimal forward position Pareto of training stage ANN and RVFL multiple target flood interval prediction model；
Fig. 4 is Yichang Station day flood forecasting interval diagram (1998 under 95%, 90%, 85% and 80% confidence level
Year).
Specific embodiment
The present invention is described in detail with reference to the accompanying drawing.
The present invention carries out Case Simulation, using Upper Yangtze River basin Yichang Station day flood forecasting as embodiment to verify this hair
Bright effect.Implementation steps are as follows:
Step 1: Upper Yangtze River basin Pingshan, High-Field, Li Jiawan, Bei Bei, WuLong and Yichang hydrology station point day flood are collected
Time series data.Split data into training sample and test samples, and by data normalization to [0,1] section.
Step 2: choosing Yichang Station and shift to an earlier date 1 day, and Yichang Station shifts to an earlier date 2 days, and Pingshan station shifts to an earlier date 1 day, and high station shifts to an earlier date 3 days, north
A word used in place name station shifts to an earlier date 2 days, WuLong station 2 days in advance, the gulf Li Jia station shift to an earlier date 3 days day flood time series as input variable, and to mesh
Initial coboundary and lower boundary of the microvariations of vector work ± 10% as dual output RVFL interval prediction model are marked, it is defeated to form 7
Enter the RVFL interval prediction model with 2 outputs.
The principle of RVFL up-and-down boundary flood interval prediction model:
It is a kind of stochastic neural net that random vector function, which connects network (RVFL), input weight and deviation be all with
Machine distribution, output weight is obtained using least square method.Compared with traditional neural network, the training speed of RVFL model is more
Fastly, structure is simple and Generalization Capability is more preferable.The structure of dual output RVFL up-and-down boundary flood interval prediction model is as shown in Figure 1.
K training sample { (x is given in RVFL modelk,yk), k=1,2 ..., K, wherein X=[x1,x2,...,xK]T
Indicate input vector, xk=[xk1,xk2,...,xkM]∈RMIndicate k-th of input training sample, Y=[y1,y2,...,yK]TTable
Show output vector, yk=[yk1,yk2,...,ykN]∈RNIndicate k-th of output training sample,Indicate the output of j-th of hidden neuron of k-th of training sample, g () indicates to swash
Function is encouraged, j indicates the number of hidden layer node, βjIndicate the weight between input layer and hidden layer, ajRespectively indicate input layer and
Threshold value between hidden layer.The output node of RVFL up-and-down boundary flood interval prediction model is not only connected with hidden layer node,
And directly it is connected with input layer node.One output neuron is connected with M+2 neuron in total.RVFL up-and-down boundary flood
The output of k-th of training sample of interval prediction model can calculate as follows:
In formula, w in formulaj, j=1,2 ..., J indicate the weight between hidden layer and output layer, wj, j=J+1, J+
2 ..., J+M indicates the weight between input layer and output layer.
The nuclear mapping matrix of input layer and hidden layer to output layer can indicate are as follows:
The matrix form of RVFL up-and-down boundary flood interval prediction model output can indicate are as follows:
In formula, w=[w1,w2,...,wJ,wJ+1,...,wJ+D]T。
After hidden layer weight and threshold value is randomly generated, the target of RVFL up-and-down boundary flood interval prediction model is exactly to find
Most suitable w, so that network exportsError between target output Y is minimum.It can be obtained by solving following optimization problem
Export weight w:
According to the solution of the available formula of regularization least square method (4):
W=(DTD+λI)-1DTY (5)
I indicates unit matrix in formula.
Then the output of k-th of training sample can indicate are as follows:
Step 3: inputting RVFL model for input vector and object vector, and runs the primary initial power for obtaining RVFL model
Value β0With initial threshold a0；
Step 4: the parameter of initialization NSGA-III algorithm, setting Population Size NP are 100, maximum number of iterations MaxIt
For 200, crossover probability pcFor 0.7, mutation probability pmFor 0.3, cross-distribution index ηcFor 20 and variation profile exponent ηmIt is 20；
NSGA-III algorithm principle:
NSGA-III algorithm is a kind of new non-dominated ranking multi-objective genetic algorithm based on reference point, Integral Thought
It is similar with classical NSGA-II with theoretical frame.Different from crowding distance operator used in NSGA-II, NSGA-III is utilized
Make the optimal forward position distribution of Pareto of algorithm more uniform based on reference point mechanism.
The detailed process of NSGA-III algorithm is as follows:
(1) the number H of calculating reference point:
C indicates the number of multi-objective optimization question objective function in formula, and g is that the segmentation number of segment of each objective function (works as C=
15) the number H of 3 and g=4, reference point are calculated as；
(2) the number of iterations k=1 is enabled, individual is generated at random and forms initial population；
(3) it uses binary system crossover operator and is recombinated and be mutated with multinomial mutation operator and generate progeny population Qo；
(4) by progeny population QoIt is mixed with parent population, generates the population R that a size is 2NPk；
(5) R is determined using non-dominated ranking algorithmkNon-dominant forward position F1,F2,...,Ft；
(6) objective function is normalized and is associated with it with reference point, using the screening filial generation of elite retention strategy
Body simultaneously deletes useless reference point, screens preceding NP individual in the top and generates next-generation population Pk+1；
(7) if k < Gmax, stop iteration and export non-domination solution；Otherwise k=k+1 setting and return step (3) are enabled.
Step 5: by [β0- 0.5, β0+ 0.5] and [a0- 0.5, a0+ 0.5] it is set as the feasible zone of NSGA-III algorithm.In
NP-1 initial individuals are generated in feasible zone at random, NP-1 individual adds (β0,a0) constitute NSGA-III algorithm initial population；
Step 6: it using the input weight and threshold value of NSGA-III algorithm optimization RVFL flood interval prediction model, obtains
The objective function of the Pareto optimal solution set of global optimum, RVFL up-and-down boundary flood interval prediction model is provided that
PICP indicates that object vector falls in the probability in the upper and lower bound of prediction interval.PICP is bigger, in prediction interval
Number of targets strong point it is more, forecast interval it is more reliable.PICP can be defined as follows:
In formula, yiIndicate the observation of i-th of data point；LiAnd UiRespectively indicate the lower and upper limit of i-th of data point；N
Indicate the quantity of training sample.
PINAW can effectively describe the width of prediction interval.PINAW is smaller, and the information that forecast interval includes is more,
Prediction interval is more effective.PINAW is defined as follows:
R indicates the range of target variable in formula, for prediction interval width to be normalized.
Step 7: it is pre- that Pareto optimal solution set obtained by step 6 and test samples are substituted into RVFL up-and-down boundary flood section
Model is reported, obtains the interval prediction of probative term as a result, and calculating PINC the and PINAW index of probative term prediction interval.
Flood interval prediction method flow diagram based on multiple target random vector function connection network is as shown in Figure 2.
The flood interval prediction model based on RVFL is mentioned using the present invention to carry out the day flood time series of Yichang Station
Forecast, Pareto optimal forward position of the Fig. 3 for training stage ANN and RVFL multiple target flood interval prediction model, Fig. 4 95%,
RVFL model flood forecasting interval diagram under 90%, 85% and 80% confidence level, table 1 are 95%, 90%, 85% and 80%
Multiple target RVFL model (NSGAIII-RVFL) flood interval prediction error under confidence level.
From the figure 3, it may be seen that multiple target interval prediction model can disposably obtain under different confidence levels (PINC)
Pareto optimal solution compares NSGAIII-ANN and NSGAIII- to obtain the flood forecasting section under different confidence levels
It is found that when PICP is greater than 0.56, the optimal forward position the Pareto of multiple target RVFL model is distributed in the optimal forward position the Pareto of RVFL
Slightly it is better than the optimal forward position Pareto of multiple target ANN model.
As shown in Figure 4, apply the present invention in Upper Yangtze River basin Yichang Station day flood interval prediction, the value of forecasting is good
It is good.
Table 1 is RVFL interval prediction model prediction error under 95%, 90%, 85% and 80% confidence level.
Table 1
The technical concepts and features of above embodiment only to illustrate the invention, its object is to allow be familiar with technique
People cans understand the content of the present invention and implement it accordingly, and it is not intended to limit the scope of the present invention.It is all according to the present invention
The equivalent transformation or modification that Spirit Essence is done, should be covered by the protection scope of the present invention.
Claims (8)
1. it is a kind of based on multiple target random vector function connection network flood interval prediction method, which is characterized in that including with
Lower step:
Step 1: flood time series data is collected, splits data into training sample and test samples, and extremely by data normalization
[0,1] section；
Step 2: assuming that the number of input variable be M, to object vector make ± 10% microvariations as the section dual output RVFL
The initial coboundary of forecasting model and lower boundary form the RVFL up-and-down boundary flood interval prediction model of M input and dual output；
Step 3: input vector and object vector are inputted into the RVFL up-and-down boundary flood interval prediction model, and run one
The secondary initial weight β for obtaining the RVFL up-and-down boundary flood interval prediction model0With initial threshold a0；
Step 4: the parameter of initialization NSGA-III algorithm；
Step 5: by [β0- 0.5, β0+ 0.5] and [a0- 0.5, a0+ 0.5] feasible zone of the NSGA-III algorithm, In are set as
NP-1 initial individuals are generated in feasible zone at random, NP-1 initial individuals add (β0,a0) constitute the initial of the NSGA-III algorithm
Population；
Step 6: using the input weight of RVFL up-and-down boundary flood interval prediction model described in the NSGA-III algorithm optimization
And threshold value, obtain the Pareto optimal solution set of global optimum；
Step 7: the Pareto optimal solution set and the test samples are substituted into the RVFL up-and-down boundary flood interval prediction
Model obtains the interval prediction of probative term as a result, and calculating PINC the and PINAW index of probative term prediction interval.
2. the flood interval prediction method according to claim 1 based on multiple target random vector function connection network,
It is characterized in that, in the step 2, in the RVFL up-and-down boundary flood interval prediction model, gives k training sample
{(xk,yk), k=1,2 ..., K, wherein X=[x1,x2,...,xK]TIndicate input vector, xk=[xk1,xk2,...,xkM]∈
RMIndicate k-th of input training sample, Y=[y1,y2,...,yK]TIndicate output vector, yk=[yk1,yk2,...,ykN]∈RN
Indicate k-th of output training sample,J=1,2 ..., J indicates j-th of hidden layer of k-th of training sample
The output of neuron, g () indicate that excitation function, j indicate the number of hidden layer node, βjIt indicates between input layer and hidden layer
Weight, ajRespectively indicate the threshold value between input layer and hidden layer；
Then the output of described RVFL up-and-down boundary flood interval prediction k-th of training sample of model calculates as follows:
In formula, wj, j=1,2 ..., J indicate the weight between hidden layer and output layer, wj, j=J+1, J+2 ..., J+M is indicated
Weight between input layer and output layer；
The nuclear mapping matrix of input layer and hidden layer to output layer is expressed as:
The matrix form of the RVFL up-and-down boundary flood interval prediction model output indicates are as follows:
In formula, w=[w1,w2,...,wJ,wJ+1,...,wJ+D]T。
Output weight w is obtained by solving following optimization problem:
According to the solution of the available formula of regularization least square method (4):
W=(DTD+λI)-1DTY (5)
I indicates unit matrix in formula；
Then the output of k-th of training sample indicates are as follows:
3. the flood interval prediction method according to claim 1 based on multiple target random vector function connection network,
It is characterized in that, in the step 4, the parameter of the NSGA-III algorithm includes:
Population Size NP, maximum number of iterations MaxIt, crossover probability pc, mutation probability pm, cross-distribution index ηcWith variation point
Cloth index ηm。
4. the flood interval prediction method according to claim 1 based on multiple target random vector function connection network,
It is characterized in that, in the step 4, the detailed process of the NSGA-III algorithm is as follows:
(1) the number H of calculating reference point；
(2) the number of iterations k=1 is enabled, generates the NP bodily form at random into initial population；
(3) it uses binary system crossover operator and is recombinated and be mutated with multinomial mutation operator and generate progeny population Qo；
(4) by progeny population QoIt is mixed with parent population, generates the population R that a size is 2NPk；
(5) R is determined using non-dominated ranking algorithmkNon-dominant forward position F1,F2,...,Ft；
(6) objective function is normalized and is associated with it with reference point, simultaneously using elite retention strategy screening offspring individual
Useless reference point is deleted, preceding NP individual in the top is screened and generates next-generation population Pk+1；
(7) if k < Gmax, stop iteration and export non-domination solution；Otherwise k=k+1 setting and return step (3) are enabled.
5. the flood interval prediction method according to claim 4 based on multiple target random vector function connection network,
It is characterized in that, in step (1), the number H of the reference point is calculated by the following formula:
C indicates the number of multi-objective optimization question objective function in formula, and g indicates the segmentation number of segment of each objective function.
6. the flood interval prediction method according to claim 1 based on multiple target random vector function connection network,
It is characterized in that, in the step 6, the objective function of the RVFL up-and-down boundary flood interval prediction model is provided that
Wherein, PICP indicates that object vector falls in the probability in the upper and lower bound of prediction interval；PINAW indicates prediction interval
Width.
7. the flood interval prediction method according to claim 6 based on multiple target random vector function connection network,
It is characterized in that, the PICP is defined as follows:
In formula, yiIndicate the observation of i-th of data point；LiAnd UiRespectively indicate the lower and upper limit of i-th of data point；N is indicated
The quantity of training sample.
8. the flood interval prediction method according to claim 6 based on multiple target random vector function connection network,
It is characterized in that, the PINAW is defined as follows:
R indicates the range of target variable in formula, for prediction interval width to be normalized.
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Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112036649A (en) * | 2020-09-03 | 2020-12-04 | 合肥工业大学 | Hydropower station risk assessment method based on multi-core parallel runoff probability density prediction |
| CN113468803A (en) * | 2021-06-09 | 2021-10-01 | 淮阴工学院 | Improved WOA-GRU-based flood flow prediction method and system |
| CN117273200A (en) * | 2023-08-31 | 2023-12-22 | 淮阴工学院 | Runoff interval forecasting method based on convolution optimization algorithm and Pyraformer neural network |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN112036649A (en) * | 2020-09-03 | 2020-12-04 | 合肥工业大学 | Hydropower station risk assessment method based on multi-core parallel runoff probability density prediction |
| CN112036649B (en) * | 2020-09-03 | 2022-09-13 | 合肥工业大学 | Hydropower station risk assessment method based on multi-core parallel runoff probability density prediction |
| CN113468803A (en) * | 2021-06-09 | 2021-10-01 | 淮阴工学院 | Improved WOA-GRU-based flood flow prediction method and system |
| CN113468803B (en) * | 2021-06-09 | 2023-09-26 | 淮阴工学院 | WOA-GRU flood flow prediction method and system based on improvement |
| CN117273200A (en) * | 2023-08-31 | 2023-12-22 | 淮阴工学院 | Runoff interval forecasting method based on convolution optimization algorithm and Pyraformer neural network |
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