CN110047015A - A kind of water total amount prediction technique merging KPCA and thinking Optimized BP Neural Network - Google Patents
A kind of water total amount prediction technique merging KPCA and thinking Optimized BP Neural Network Download PDFInfo
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Abstract
The invention discloses a kind of water total amount prediction techniques for merging KPCA and thinking Optimized BP Neural Network, include the following steps: to determine predictive factor with correlation coefficient process；Dimension-reduction treatment is carried out to predictive factor using core principle component analysis (KPCA), solves the nonlinear characteristic between data；Water total amount prediction model is established using BP neural network；Water total amount is predicted using model.The first two steps of the present invention are data predictions, it is therefore an objective to extract the useful information in water data, eliminate redundancy and interfere caused by prediction.Third step by BP neural network to water total amount prediction in, while using mind-evolution learning algorithm Optimized BP Neural Network weight and threshold value.The last one step is used for testing model effect.The method of the present invention is tested in year open count in water data of State Statistics Bureau, the results showed that, the water total amount prediction model based on KPCA and thinking Optimized BP Neural Network can predict the following water total amount well.
Description
Technical field
The present invention relates to water total amount Predicting Technique, especially a kind of use for merging KPCA and thinking Optimized BP Neural Network
Water inventory prediction technique.
Background technique
Currently, the scarcity of water resource is no longer satisfied population growth and industrial and agricultural development, serious to hinder in some areas
Therefore the Social benefit and economic benefit in area is made rational planning for water resource and is dispatched and is extremely urgent.Water total amount
Prediction work is to water resources rational distribution, scheduling and to analyze the important measure estimated under current water resource severe situation,
There is important role to Sustainable Socioeconomic Development.
Water total amount prediction is related to many aspects: industrial water consumption prediction, agricultural water consumption forecast and short-term long-term use
Water prediction.The pre- measuring angle of each aspect is different, and the predictive factor of selection is also different.Existing water total amount is pre-
Survey method is varied, common method have general tendency method, time series method, regression analysis, Grey System Model and
Neural network model.In recent years, water total amount prediction being carried out with neural network, the state that a hundred flowers blossom is presented.Document [Dan Jinlin,
Wear imposing and strange, Li Jiangtao establishes predicted city water consumption model [J] China water supply and drainage, 2001,17 (8): 61- using BP network
63.] middle using BP neural network predicted city water consumption, and water data is arranged with time series sequence, but it is this pre-
Survey method is only suitable for short-term water demands forecasting and ignores water consumption and might have uncertain factor to influence, and result is simultaneously afterwards
It is less accurate.[Sang Huiru, Wang Lixue, Chen Shaoming, et al. are needing water based on the RBF neural of principal component analysis to document
Application [J] HYDROELECTRIC ENERGY science in prediction, 2017 (7): 58-61.] in using principal component analysis to influencing water total amount
Each factor carries out dimensionality reduction, however principal component analysis is linear transformation, and water total amount factor data has non-linear, complexity, no
The features such as determining can also lose some useful information although redundancy can be got rid of by carrying out linear dimensionality reduction to it.
Summary of the invention
Goal of the invention: aiming at the problems existing in the prior art with deficiency, in order to accurately and effectively predict water total amount, this
Invention provides a kind of water total amount prediction technique for merging KPCA and thinking Optimized BP Neural Network, it overcomes between the factor
Non-linear, complexity and it is uncertain the features such as, filter out with the water total amount maximal correlation factor, while pass through thinking optimize BP mind
Weight and threshold value through network make water total amount prediction more accurate.
Technical solution: a kind of water total amount prediction technique merging KPCA and thinking Optimized BP Neural Network, including it is as follows
Step:
(1) predictive factor is determined from multiple candidate data factors for influencing water total amount with correlation coefficient process；
(2) dimension-reduction treatment is carried out to determined predictive factor using core principle component analysis；
(3) water total amount prediction model is established using BP neural network.Using mind-evolution learning algorithm optimization BP nerve
The weight and threshold value of network；
(4) water total amount is predicted using trained prediction model.
The step (1) includes:
(11) GDP, the added value of agriculture, grain yield, effective irrigation area, industrial added value, scale are chosen
The above industrial enterprise generates product, total aquatic product production, daily treatment capacity of municipal sewage, town domestic sewage discharge amount, waste water row
High-volume, thermal power output, urban green space area, aquaculture area, domestic water total amount, agricultural water total amount, with water people
Mouth, fishery value added, industrial water, grain yield, ecological water, enterprise income tax total value and individual gross income are as shadow
Ring the candidate prediction factor of water total amount；
(12) related coefficient of the measured value of each candidate prediction factor and water total amount is calculated separately out；
The calculation formula of related coefficient are as follows:
In formula, XiFor the size of the predictive factor value of the i-th sample,For the mean value of predictive factor X, YiFor i-th sample
Measured value size,For measured value mean value, M is total sample number amount；
(13) related coefficient descending is arranged, prediction of the biggish factor of k related coefficient as water total amount before choosing
The factor, k are natural number.The factor of the related coefficient greater than 0.5 may be selected in the specific implementation as the prediction for influencing water total amount
The factor.
The step (2) includes:
(21) the corresponding data of determined predictive factor are normalized, the initial factor for generating M × N inputs square
Battle array, wherein M is sample total, and N is predictive factor quantity；
(22) nuclear matrix K is sought, by kernel function by normalized data by data space projection mapping to feature space, institute
State kernel function are as follows:
In formula, xiFor all column of i-th of sample, xjFor all column of j-th of sample, a is coefficient of variation；
(23) by nuclear matrix K centralization, to correct nuclear matrix, the nuclear matrix K of centralization is obtainedc；
Kc=K-lMK-KlM+lMKlM
In formula, lMFor the matrix of M × M, each element is 1/M；
(24) nuclear matrix K is calculatedcEigenvalue λ1,…,λnWith feature vector v1,…,vn；By the arrangement of characteristic value descending and phase
The sequence of feature vector should be adjusted, n is natural number；
(25) pass through Schmidt process, orthogonalization and unitization feature vector；
(26) the contribution rate of accumulative total r of each characteristic value is calculated1,…,rn, according to given contribution rate threshold value p, if certain feature
The contribution rate of accumulative total r of valuet> contribution rate threshold value p, then t principal component before choosing, as the data after dimensionality reduction, wherein t is nature
Number.
The step (3) includes:
(31) topological structure of BP neural network is determined, BP network design is 3 layer network structures, including input layer, implicit
Layer and output layer, input layer input the predictive factor X after dimensionality reductioni, output layer output water total amount predicted value；By water total amount number
It is divided into training sample and test sample according to sample；
(32) water total amount data sequence training set and test set are inputted, by initial training iteration, obtains neural network
Initial weight and threshold value；
(33) initial population, winning sub-group and interim sub-group is randomly generated；Initial population is to be randomly generated every group to have h
The H group number of individual, population is determined as 100 here；
(34) score value of individual is sought:
Wherein, L is the quantity of training set sample,It is square of the difference of objective function and network output, ej(s)
=dj(s)-yj(s),dj(s) be objective function value, djIt (s) is network output data, s is training sample number, and j is individual
Number, Q are individual sums, whenSmaller, individual score value is better；
(35) it executes operation similartaxis and calculates each sub-group score, generate K winning sub-groups with normal distribution N (μ, Σ)
With P interim sub-groups, wherein μ is the center of normal distribution, and Σ is the covariance matrix of normal distribution, then normal state in sub-group
The coordinate of distribution center is denoted as the score i.e. weight of victor of sub-group；
(36) operation dissimilation is executed, the number that interim sub-group score is higher than winning sub-group, high interim of score are found
Sub-group replaces winning sub-group；
(37) when meeting iteration stopping condition, the optimized individual and score that output current iteration obtains are advised according to coding
Then, the optimum individual acquired is parsed, the weight and threshold value of BP neural network are generated, otherwise, return step (35)；
(38) initial weight and Threshold-training BP of the weight and threshold value as re -training of using step (37) to obtain are neural
Network model；
The utility model has the advantages that compared with the prior art, the advantages of the present invention are as follows: by KPCA and thinking Optimized BP Neural Network into
Row combined prediction water total amount, KPCA overcome non-linear, complexity between the factor and it is uncertain the features such as, to factor data
Nonlinear Dimension Reduction processing is carried out, is filtered out and the water total amount maximal correlation factor；By utilizing mind evolutionary, population is selected
Optimum individual is decoded and obtains BP neural network weight and threshold value, more accurate using water inventory prediction model, improves prediction
Precision.
Detailed description of the invention
Fig. 1 is the water total amount prediction structural block diagram for merging KPCA and thinking Optimized BP Neural Network.
Fig. 2 is water total amount prediction result figure in the embodiment of the present invention.
Specific embodiment
It with reference to the accompanying drawing and is embodied, the present invention is furture elucidated, it should be understood that these examples are merely to illustrate this hair
Bright rather than limit the scope of the invention, after the present invention has been read, those skilled in the art are to of the invention various etc.
The modification of valence form falls within the application range as defined in the appended claims.
Technical detail of the invention is described in conjunction with Fig. 1.In the present invention, thinking Optimized BP Neural Network is introduced into and uses water
In Prediction of Total, this method is main comprising the following three steps:
First is that carrying out the determination of predictive factor with correlation coefficient process；Second is that using core principle component analysis (KPCA) to prediction
The factor carries out dimensionality reduction；Third is that establishing water total amount prediction model using BP neural network.Mind-evolution learning algorithm is used simultaneously
The weight and threshold value of Optimized BP Neural Network；
The specific implementation process of each step described in detail below:
Step 1: the determination of predictive factor
Specifically comprise the following steps:
(11) GDP, the added value of agriculture, grain yield, effective irrigation area, industrial added value, scale are chosen
The above industrial enterprise generates product, total aquatic product production, daily treatment capacity of municipal sewage, town domestic sewage discharge amount, waste water row
High-volume, thermal power output, urban green space area, aquaculture area, domestic water total amount, agricultural water total amount, with water people
Mouth, fishery value added, industrial water, grain yield, ecological water, enterprise income tax total value and individual gross income are as shadow
Ring the candidate prediction factor of water total amount.
(12) related coefficient of the measured value of each candidate prediction factor and water total amount is calculated separately out；
The calculation formula of related coefficient are as follows:
In formula, XiFor the size of the predictive factor value of i-th of sample,For the mean value of predictive factor X, YiFor i-th of sample
Measured value size,For measured value mean value, M is total sample number amount.
(13) it is sorted from large to small according to related coefficient, then selects the biggish preceding k of related coefficient to influence as influence
The predictive factor of water total amount, k are natural number.Degree of correlation between related coefficient response variable, the bigger explanation of related coefficient
Predictive factor and the correlation of true value are bigger.
The selection of water total amount predictive factor is most important.If the input prediction factor is excessive, redundancy can be brought
Information influences predictablity rate；If the predictive factor of input is very few, it is not enough to disclose the complicated variation machine of output variable
Reason, to obtain the prediction result of inaccuracy.In the realistic case, water total amount and various aspects have relationship, such as: use water
The number of population, the number of urban green space size, GDP and effective irrigation area size etc., for the accuracy of prediction, this
Some a large amount of impact factors need all standing as far as possible also to select simultaneously with the biggish factor of water total amount correlation, because
This, these factors form multidimensional data, due to the increase of dimension, will certainly introduce redundancy and noise, the present invention uses phase
It closes Y-factor method Y to reject redundancy and noise information, these redundancies and noise information can be eliminated to the shadow of predictablity rate
It rings.
Step 2: core principle component analysis (KPCA) dimensionality reduction
Specifically comprise the following steps:
(21) the corresponding data of identified predictive factor are normalized, eliminate the shadow of predictive factor dimension
It rings, generates the initial factor input matrix of M × N, wherein M is sample total, and N is predictive factor quantity；
(22) nuclear matrix K is sought, is realized using kernel function by the data after normalizing by data space map to feature
Space；The kernel function used is Radial basis kernel function, formula are as follows:
In formula, xiFor all column of i-th of sample, xjFor all column of j-th of sample, a is coefficient of variation；
(23) centralization nuclear matrix Kc, for correcting nuclear matrix, formula are as follows:
Kc=K-lMK-KlM+lMKlM
Wherein, lMFor the matrix of M × M；
(24) calculating matrix KCEigenvalue λ1,…,λnAnd corresponding feature vector is v1,…,vn.Characteristic value is bigger
The useful information that can be extracted is more, therefore obtains λ ' by characteristic value descending sort1> ... > λ 'n, feature vector accordingly adjusts v
'1,…,v'n。
(25) by Schmidt process, orthogonalization and unitization feature vector, a is obtained1,…,an。
(26) contribution rate of accumulative total of characteristic value is calculatedAccording to given contribution rate threshold value p, such as
Fruit rt> p, then t principal component amount a before choosing1,…,at, as the input factor variable after dimensionality reduction.
Due to having non-linear behavior with water fugacity, the present invention is reflected the nonlinear principal component of original input space using KPCA
The linear pivot being mapped in High-dimensional Linear feature space, not only increases arithmetic speed, and eliminate interference information, can be effective
Improve water total amount accuracy rate.
KPCA method is a kind of Via Nonlinear Principal Component Analysis method, can extract the nonlinear characteristic in original sample, mainly
Thought: input vector X is mapped to a High-dimensional Linear feature space F by the nonlinear mapping function Ф selected in advance using certain
Among, then pivot ingredient is calculated using PCA method in the F of space.
Step 3: thinking optimization is in conjunction with BP neural network
Specifically comprise the following steps:
(31) topological structure of BP neural network is determined, BP network design is 3 layer network structures, including input layer, implicit
Layer and output layer.If water total amount data sequence is (Xi, Yi), wherein i=1,2 ..., M.Input layer inputs the prediction after dimensionality reduction
Factor Xi, output layer is water total amount predicted value yi, Yi is water total amount actual value.Water total amount data sample is divided into training
Sample and test sample, input node is 3 in this example, and implying node is 12, and output node is 1；
(32) water total amount data sequence training set and test set are inputted, by initial training iteration, obtains neural network
Initial weight and threshold value；
(33) initial population, winning sub-group and interim sub-group are generated；Initial population is to be randomly generated every group in this example
There is the H group number of h individual, population is determined as 100 here；
(34) score value of individual is sought:
Wherein, L is the quantity of training set sample,It is square of the difference of objective function and network output, ej(s)
=dj(s)-yj(s),dj(s) be objective function value, djIt (s) is network output data, s is training sample number, and j is individual
Number, Q are individual sums, whenSmaller, individual score value is better；
(35) it executes operation similartaxis and calculates each sub-group score, generate K winning sub-groups with normal distribution N (μ, Σ)
With P interim sub-groups, wherein μ is the center of normal distribution, and Σ is the covariance matrix of normal distribution, then in the sub-group just
The coordinate of state distribution center is denoted as the score i.e. weight of victor of the sub-group, when each denapon is mutually indepedent, winning subgroup
Body and interim sub-group are 6；
(36) operation dissimilation is executed, the number that interim sub-group score is higher than winning sub-group, high interim of score are found
Sub-group replaces winning sub-group；
(37) (e.g., meet setting the number of iterations when meeting iteration stopping condition or find the high sub-group of score), it is defeated
Optimized individual and score that current iteration obtains out parse the optimum individual acquired according to coding rule, generate BP nerve net
The weight and threshold value of network, otherwise, return step (35)；
(38) initial weight and Threshold-training BP of the weight and threshold value as re -training of using step (37) to obtain are neural
Network model.
Mind evolutionary is applied in the tune ginseng problem of BP neural network recurrence, water total amount is predicted, it can
To improve predictablity rate.
Step 4: water total amount is predicted.By predictive factor data progress KPCA dimensionality reduction obtain 3 principal components composition column to
Principal component column vector is inputted in thinking Optimizing BP Network water total amount prediction model, obtains water total amount prediction result by amount.
In order to verify prediction effect of the present invention, chooses official website, State Statistics Bureau and distinguish province's data annually as research
Object is chosen the annual GDP of 31 provinces, autonomous regions and municipalities of 2007-2016, the added value of agriculture, grain and is produced
Amount etc. 22 influences the data factors of water total amount as data collection indirectly, using 2007-2015 totally 248 groups of data as
Training sample, 31 groups of data in 2016 establish the total with water of fusion KPCA and thinking Optimized BP Neural Network as test sample
Measure prediction model.
1 related-factors analysis coefficient of table
Table 1 is the related coefficient between predictive factor and water total amount, due to related coefficient greater than 0.5 the factor and use water
Total amount correlation is very big, therefore 12 related coefficients of model final choice are greater than 0.5 predictive factor.
The comparison of the different dimensionality reduction mode water total amount prediction results of table 2
Table 2 is the comparison of water total amount prediction result under different dimensionality reduction modes, it will thus be seen that for nonlinear total with water
Data are measured, after KPCA dimensionality reduction, prediction result is got well than with the result of PCA dimensionality reduction.Because KPCA it overcome between the factor
Non-linear, complexity and it is uncertain the features such as, although and PCA is also reduction of the dimension of data, it is linear transformation, right
In nonlinear data, the useful information of the initial data factor can be lost, reduces the accuracy rate of prediction.
Fig. 2 is the result figure of national 31 provinces, autonomous regions and municipalities' water total amounts prediction in 2016, can from figure
Out, it merges KPCA and the water total amount prediction model of thinking Optimized BP Neural Network can be very good prediction water.To water resource
Reasonable distribution, scheduling and analysis, which are estimated, to point the direction, and has important role to Sustainable Socioeconomic Development.
Claims (5)
1. a kind of water total amount prediction technique for merging KPCA and thinking Optimized BP Neural Network, which is characterized in that including as follows
Step:
(1) predictive factor is determined from multiple candidate data factors for influencing water total amount with correlation coefficient process；
(2) dimension-reduction treatment is carried out to identified predictive factor using core principle component analysis；
(3) water total amount prediction model is established using BP neural network, using mind-evolution learning algorithm Optimized BP Neural Network
Weight and threshold value；
(4) water total amount is predicted using trained prediction model.
2. the water total amount prediction technique of fusion KPCA and thinking Optimized BP Neural Network according to claim 1, special
Sign is that the step (1) includes:
(11) choose GDP, the added value of agriculture, grain yield, effective irrigation area, industrial added value, it is more than scale
Industrial enterprise generate product, total aquatic product production, daily treatment capacity of municipal sewage, town domestic sewage discharge amount, wastewater discharge,
Thermal power output, urban green space area, aquaculture area, domestic water total amount, agricultural water total amount, with water population, fishing
Industry value added, industrial water, grain yield, ecological water, enterprise income tax total value and individual gross income are used as influence
The candidate prediction factor of water inventory；
(12) related coefficient of the measured value of each candidate prediction factor and water total amount is calculated separately out；
The calculation formula of related coefficient are as follows:
In formula, XiFor the size of the predictive factor value of i-th of sample,For the mean value of predictive factor, YiFor the reality of i-th of sample
Measured value size,For measured value mean value, M is total sample number amount；
(13) related coefficient descending is arranged, the biggish factor of k related coefficient is as the prediction for influencing water total amount before choosing
The factor, k are natural number.
3. the water total amount prediction technique of fusion KPCA and thinking Optimized BP Neural Network according to claim 2, special
Sign is, selects the factor of the related coefficient greater than 0.5 as the predictive factor for influencing water total amount.
4. the water total amount prediction technique of fusion KPCA and thinking Optimized BP Neural Network according to claim 1, special
Sign is that the step (2) includes:
(21) the corresponding data of determined predictive factor are normalized, generate the initial factor input matrix of M × N,
Wherein M is sample total, and N is predictive factor quantity；
(22) nuclear matrix K is sought, it is described by kernel function by the data after normalization by data space projection mapping to feature space
Kernel function are as follows:
In formula, xiFor all column of i-th of sample, xjFor all column of j-th of sample, a is coefficient of variation；
(23) by nuclear matrix K centralization, to correct nuclear matrix, the nuclear matrix K of centralization is obtainedc；
Kc=K-lMK-KlM+lMKlM
In formula, lMFor the matrix of M × M, each element is 1/M；
(24) nuclear matrix K is calculatedcEigenvalue λ1,…,λnWith feature vector v1,…,vn, characteristic value descending is arranged and is accordingly adjusted
The sequence of whole feature vector, n are natural number；
(25) pass through Schmidt process, orthogonalization and unitization feature vector；
(26) the contribution rate of accumulative total r of each characteristic value is calculated1,…,rn, according to given contribution rate threshold value p, if certain characteristic value
Contribution rate of accumulative total rt> contribution rate threshold value p, then t principal component before choosing, as the data after dimensionality reduction, wherein t is natural number.
5. the water total amount prediction technique of fusion KPCA and thinking Optimized BP Neural Network according to claim 4, special
Sign is that the step (3) includes:
(31) determine the topological structure of BP neural network, BP network design is 3 layer network structures, including input layer, hidden layer and
Output layer, input layer input the predictive factor after dimensionality reduction, and output layer exports water total amount predicted value；By water total amount data sample
It is divided into training sample and test sample；
(32) water total amount data sequence training set and test set are inputted, by initial training iteration, it is initial to obtain neural network
Weight and threshold value；
(33) initial population, winning sub-group and interim sub-group is randomly generated；
(34) score value of individual is sought:
Wherein, L is the quantity of training set sample,It is square of the difference of objective function and network output, ej(s)=dj
(s)-yj(s),dj(s) be objective function value, djIt (s) is network output data, s is training sample number, and j is individual number,
Q is individual sum, whenSmaller, individual score value is better；
(35) it executes operation similartaxis and calculates each sub-group score, generate K winning sub-groups and P with normal distribution N (μ, Σ)
A interim sub-group, wherein μ is the center of normal distribution, and Σ is the covariance matrix of normal distribution, then normal state point in sub-group
The coordinate at cloth center is denoted as the score of sub-group；
(36) operation dissimilation is executed, the number that interim sub-group score is higher than winning sub-group, the high interim subgroup of score are found
Body replaces winning sub-group；
(37) when meeting iteration stopping condition, the optimized individual and score that output current iteration obtains, according to coding rule, solution
The optimum individual acquired is analysed, the weight and threshold value of BP neural network are generated, otherwise, return step (35)；
(38) initial weight and Threshold-training BP neural network of the weight of using step (37) to obtain and threshold value as re -training
Model.
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| CN111008735B (en) * | 2019-11-27 | 2023-06-02 | 巴斯夫新材料有限公司 | Predictive emissions management system and method |
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| CN111598435A (en) * | 2020-05-14 | 2020-08-28 | 北京工业大学 | Quality trend prediction method based on adaptive feature selection and improved thought evolution algorithm |
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