CN108764473A - A kind of BP neural network water demands forecasting method based on correlation analysis - Google Patents
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Abstract
The BP neural network residential communities design for commodities method based on correlation analysis that the invention discloses a kind of, water consumption influence factor is analyzed first with correlation analysis theory, it is ranked up by size is influenced, then daily water consumption sequence is analyzed with partial autocorrelation theory, correlativity existing for finding out inside daily water consumption time series, it determines the optimal delay time, and then determines input variable, establish the BP neural network community water demands forecasting model based on correlation analysis.When being trained to model, using upset daily water consumption according to chronological order arrange and formed data sequence as training set, the influence of time factor is eliminated in the limitation of break through sequence, improves the generalization ability of prediction technique.
Description
Technical field
The present invention relates to a kind of backpropagations based on correlation analysis（BP, Back Propagation）Neural network resident
Community's design for commodities method, belongs to water resources management technical field.
Background technology
Water resource is the irreplaceable important natural resources of progress of human society development, Source of life spring.Urban development
Middle industry, agricultural, life be not all the time with water, and water consumption increases year by year, and water pollution getting worse.According to statistics, at me
In 600 Duo Zuo organizational systems city of state, there are nearly 400 urban water shortages, wherein up to more than 130, National urban is annual in water shortage serious city
60 billion cubic meter of water shortage, day, water deficit was more than 1600 ten thousand steres.Water shortage is to loss caused by the urban industry output value 1200
Hundred million yuan or more, and in the gesture of growth.The shortage of water has become the important restriction factor of current economic social development.Community's water
Be city water resource consumption important component, rational community's water use forecast be regional water resources configuration, water resource it is effective
Management and the important foundation for saving water resource.
For this problem, existing technical solution is：Yan Xu et al. is in article《BP nerve nets based on genetic algorithm
Application of the network in urban water consumption prediction》In, predicted time point is closed on into moment water consumption and first 3 days in the section time
15 variables such as water consumption are elected to be input variable, bring prediction model into and predict city hourly water consumption；Mountains Chu Cheng et al. exist
Article《Water demands forecasting based on genetic algorithm and BP neural network》In, by the maximum temperature for predicting day, minimum temperature, it is averaged
Temperature, climate type and prediction 1 day maximum temperature, minimum temperature, mean temperature, climate type, daily water consumption etc. 9 a few days ago
Variable predicts municipal daily water consumption as input variable, input prediction model；Zhou Yanchun et al. is in article《Based on B
The short-term water demands forecasting in city of P Neural Network Toolbox》In, by a few days ago with the weather conditions of the previous day, max. daily temperature
It is used as input data Deng 16, brings the water consumption of model prediction day t moment into.
Invention content
Through analysis, it is found that the prior art has the disadvantage that：1）Input variable is too many, is easy to make model overfitting, shadow
Ring precision of prediction；2）Input data is complicated, and model is computationally intensive；3）Selection to input variable is advised according to history water use variation
Rule, by technical staff's subjective experience, is theoretically unsound, influences the accuracy of prediction result；4）Carrying out water demands forecasting
It is carried out in strict accordance with time series when model foundation, stringent to data demand, generalization ability is poor.
Based on this, present invention proposition is improved on the basis of BP neural network, establishes the BP based on correlation analysis
Neural network community water demands forecasting model.Water consumption influence factor is analyzed first with correlation analysis theory, by shadow
It rings size to be ranked up, then daily water consumption sequence is analyzed with partial autocorrelation theory, determines the optimal delay time, in turn
It determines input variable, when being trained to model, upsets the data order of training set at random, improve generalization ability.
The present invention uses following technical solutions：
A kind of BP neural network residential communities design for commodities method based on correlation analysis, the network are three layers of BP networks,
Including n input layer, p hidden layer neuron and 1 output layer neuron, this method comprises the following steps：First
Correlation analysis is carried out to sample data, determines input variable；Then prediction is determined using the training set for breaking strict time sequence
The parameter of model is to determine prediction model；Finally, it is predicted using the BP neural network prediction model, exports result.
Specifically, it refers to the data upset training set and formed according to chronological order arrangement to break strict time sequence
The influence of time factor is eliminated in sequence, the limitation of break through sequence.
Determine that prediction model includes：
（1）Parameter initialization；
（2）Training set data is inputted, each layer output is calculated；
（3）Calculate output layer error；
（4）Judge whether to reach error precision,
（5）If not reaching error precision, according to each layer weights of output layer error transfer factor and threshold value, return to step（2）；
（6）If reaching error precision, it is determined that BP neural network prediction model.
Further, correlation analysis includes determining whether each influence factor such as weather conditions, festivals or holidays to residential communities water consumption
Influence, using related-coefficient test method carry out correlation analysis, according to correlation analysis theoretical calculation resident's daily water consumption Y with influence
Correlation coefficient r between factor X：
Wherein xiAnd yiRespectively influence factor X and residential communities i-th day numerical value of water consumption Y,WithRespectively X's and Y
Mean value, i=1,2 ... n.
Determine that input variable includes measuring residential communities daily water consumption with partial Correlation Analysis theoretical calculation PARCOR coefficients
Correlativity existing for inside time series.Water consumption sample set is Y (t)=y1, y2, y3..., yn, PARCOR coefficients are
In formula, k is delay time, i.e. time interval, k=1,2 ..., m；For mean value；rkFor PARCOR coefficients.
Determine rkCorresponding k values are the optimal delay time when first time zero crossing；For the r when delay time is very bigk?
Level off to zero the case where, optimum delay time takes rkIt is less than for the first timeWhen corresponding k values.
If the threshold value of j-th of neuron of hidden layer is θj, then the input of j-th of neuron of hidden layer is
In formula, WijIt is the connection weight of i-th of input neuron and j-th of hidden layer neuron；ziWhen being inputted for input variable
The input value of i-th of neuron；The output of j-th of neuron of hidden layer is bj=f（sj）, j=1,2 ..., p, f is excitation function,
Form is：
The threshold value of daily water consumption output layer neuron is γ, and the input of the neuron of daily water consumption output is：
In formula, VjIt is j-th of hidden layer neuron and the connection weight of output neuron；
Daily water consumption output is Cr=f (L).
Output layer error calculation is
Wherein,For training set number of samples, ydWithThe respectively measured value and predicted value of training sample.
One aspect of the present invention can accurately determine input variable according to theory analysis, avoid model overfitting, calculate again
Miscellaneous and artificial subjective factor influences, and improves precision of prediction；On the other hand suitable according to time order and function by using daily water consumption is upset
Sequence arranges and time factor is eliminated in training set of the data sequence of formation as model foundation, the limitation of break through sequence
It influences, improves model generalization ability.
Description of the drawings
Fig. 1 show three layers of BP neural network topological structure schematic diagram；
Fig. 2 show the flow chart of model prediction；
Fig. 3 show daily water consumption partial autocorrelation figure；
Fig. 4 shows the comparison of BP neural network predicted value and measured value；
Fig. 5 shows the comparison of different BP neural network model predication values and measured value；
Fig. 6 shows the comparison of the BP neural network model and LSSVM model prediction results of foundation；And
Fig. 7 shows the comparison of different model relative error results.
Specific implementation mode
In the design for commodities of residential communities, the influence factor selection of input is very few, can influence the accurate of prediction result
Property；The influence factor of input is excessive, and local optimum may be absorbed in while increasing computation complexity.It is preferable pre- in order to obtain
Survey determines input variable as a result, reasonable selection influence factor, most important.
1.1 daily water consumption influence factor correlation analyses
In order to judge influence of each influence factor such as weather conditions, festivals or holidays to residential communities water consumption, examined using related coefficient
It tests method and carries out correlation analysis.It examines the correlativity between resident's daily water consumption Y and influence factor X whether notable, exactly examines
Examine the size of correlation coefficient r.According to correlation analysis theory, the calculation formula of the correlation coefficient r of X and Y is as follows：
（1）
In formula：xiAnd yiRespectively influence factor X and residential communities i-th day numerical value of water consumption Y,WithRespectively X's and Y
Mean value, i=1,2 ... n.
Work as r>When 0, Y and X is referred to as positive correlation；Work as r<When 0, Y and X is referred to as negatively correlated.If the absolute value very little of correlation coefficient r
（Close to 0）When, then show that the correlativity between Y and X is not notable.When the absolute value of correlation coefficient r is larger（Close to 1）
When, just show that correlativity is notable between Y and X.
1.2 daily water consumption partial autocorrelations are analyzed
In the case where other influence factors are invariable, with partial Correlation Analysis theoretical research residential communities daily water consumption time sequence
Arrange correlativity existing for inside, the true degree of correlation reflected between water consumption inside.PARCOR coefficients are measured partially from phase
The index of pass degree.Water consumption sample set is Y (t)=y1, y2, y3..., yn, then its PARCOR coefficients be
（2）
In formula:K is delay time, i.e. time interval, k=1,2 ..., m；For mean value；rkFor PARCOR coefficients, value model
It encloses for [- 1,1].
There are two ways to the general determining optimal delay time：①rkCorresponding k values when first time zero crossing；2. for
The r when delay time is very bigkJust level off to zero the case where, optimum delay time can use rkIt is less than for the first timeWhen corresponding k
Value.
1.3 BP neural network design for commodities models
BP neural network is a kind of Multi-layered Feedforward Networks having hidden layer.Its basic principle is gradient steepest descent method, it
Central idea, which is adjustment weights, keeps network overall error minimum, that is, uses gradient search technology, to keep the reality of network defeated
The error mean square value for going out value and desired output is minimum.Network learning procedure is that a kind of error corrects power system in back-propagation
Several processes.Three layers of BP network topology structures schematic diagram are as shown in Figure 1, include n input layer, p hidden layer nerve
Member and 1 output layer neuron.
By Fig. 1, the threshold value of j-th of neuron of hidden layer can be set as θj, then the input of j-th of neuron of hidden layer is
（3）
In formula：WijIt is the connection weight of i-th of input neuron and j-th of hidden layer neuron；ziWhen being inputted for input variable
The input value of i-th of neuron；N is the neuron number of input layer.The output of j-th of neuron of hidden layer is bj=f（sj）,j=
1,2 ..., p, p are hidden layer neuron number, and f is excitation function, and form is：
（4）
The effect of excitation function f is to simulate the nonlinear characteristic of biological neuron.
If the threshold value of daily water consumption output layer neuron is γ, then the input of the neuron of daily water consumption output is：
（5）
In formula：VjIt is j-th of hidden layer neuron and the connection weight of output neuron.
Daily water consumption output is Cr=f (L).It is complete primary along communication process that here it is an input patterns.Work as civil water
Measure output valve（Predicted value）With desired output（Measured value）When differing, there are output layer error Es, i.e.,
（6）
In formula：For training set number of samples, in the present embodiment=80, ydWithThe respectively measured value of instruction sample and pre-
Measured value.
Weights and threshold value, the i.e. inverse communication process of error are adjusted according to output layer error size.Network training is exactly to pass through
Pattern saequential transmission broadcasts the alternately and repeatedly progress with error Back-Propagation, until error is met the requirements.
So far, by carrying out analysis and with partial autocorrelation theory to day to daily water consumption influence factor with correlation analysis theory
Time series of water consumption is analyzed, and is established the BP neural network prediction model based on correlation analysis, be may be implemented to resident society
Area's daily water consumption is effectively predicted.
To make the objectives, technical solutions, and advantages of the present invention clearer, below in conjunction with specific embodiment, and reference
Attached drawing, the present invention is described in more detail.
Residential communities daily water consumption is carried out using the BP neural network model based on correlation analysis as shown in Fig. 2, determining
Prediction.Correlation analysis is carried out to sample data first, the major influence factors of community's daily water consumption is determined, determines input variable；
Then determine prediction model parameter to determine prediction model, finally, by input variable bring into BP neural network prediction model into
Row prediction, exports result.
The determination of wherein prediction model includes：Parameter initialization；Training set data is inputted, each layer output is calculated；It calculates defeated
Go out a layer error；Judge whether to reach error precision, if not reaching error precision, be weighed according to each layer of output layer error transfer factor
Training set data is re-entered in value and threshold, return；If reaching error precision, it is determined that BP neural network prediction model.
2.1 data source
Data used herein come from the online water detection platform of Hebei University Of Engineering, using resident Families Home April 1 in 2016
The real community water consumption data in day to July 9.
The determination of 2.2 prediction model input variables
The many because being known as of residential communities water consumption are influenced, the application mainly considers maximum temperature, weather conditions, festivals or holidays feelings
Condition and previous daily water consumption, according to correlation analysis theory, formula（1）Between each influence factor and residential communities water consumption
Related coefficient calculated, as a result such as table 1.
The related coefficient result of table 1 residential communities daily water consumption and each influence factor
As shown in Table 1, influence size cases of each influence factor to urbanite water consumption amount are：Previous daily water consumption>Maximum temperature>It
Vaporous condition>Festivals or holidays situation, wherein previous daily water consumption, maximum temperature and festivals or holidays situation are positive correlation on water requirement influence,
Weather conditions are negatively correlated on water requirement influence.
When the input variable of a model is too many, details in the learning training data that the model of foundation may be excessive and
Noise so that model shows very poor, generation " over-fitting " phenomenon in new data, and then causes the precision of prediction of model to become
Low, Generalization Capability is deteriorated.So we generally under the premise of meeting precision of prediction, reduce mode input variable to the greatest extent.We
Case only selects to influence maximum previous daily water consumption.
Formula is used again（2）It calculates daily water consumption PARCOR coefficients and determines the historical data of daily water consumption and practical civil water
The correlativity of amount, wherein n=100, m=16, the results are shown in Figure 3.
From the figure 3, it may be seen that rkIn r2When just already less than 0, there is no delay time it is very big when rkIt just levels off to and zero to ask
Topic, therefore this programme selection first method determines the daily water consumption optimal delay time, it is clear that the daily water consumption optimal delay time is
One day, there are highly relevant relationships with previous daily water consumption for daily water consumption, weaker with other days correlativities.
The correlation analysis result of calculation presented by table 1 and Fig. 3, determines with strongest previous with daily water consumption correlativity
Daily water consumption predicts residential communities daily water consumption it is pre- to establish BP neural network using previous daily water consumption as input variable
Survey model.
2.3 BP neural network design for commodities
Break stringent time series data according to the input variable of above-mentioned determination in order to make model that there is better practicability,
99 day datas of acquisition are divided into two parts, with wherein arbitrary 80 days for training set, establish model；It was survey with other 19 days
Examination collection, tests to constructed model.Data are normalized before modeling, eliminate the dimension shadow different with unit
It rings, prevents " decimal eats big number " problem from occurring.Then it is modeled using MATLAB softwares.First BP nerves are determined with trial and error procedure
The parameters such as hidden layer neuron number, error precision, frequency of training and the learning rate of network model, the evaluation criterion of prediction result
Using relative error（）And average relative error（MAPE）, calculation formula is：
In formula：N is test set number of samples, in the present embodiment n=19, yiWithThe respectively measured value of test sample and pre-
Measured value.
By being adjusted repeatedly to parameter with trial and error procedure, finally obtained optimal model parameters are：Hidden layer neuron
Number be 6, error precision 0.004, frequency of training 100, learning rate 0.1.
Technical solution of the present invention prediction result is shown in Fig. 4, relative error（）It is 6.87%, average relative error（MAPE）For
2.21%。
In order to verify the effect of technical solution of the present invention, the application is established respectively without the input variable Jing Guo correlation analysis
For the BP neural network model of previous daily water consumption and maximum temperature（2 input BP neural network models）, before input variable is
One daily water consumption, maximum temperature and the BP neural network of weather conditions model（3 input BP neural network models）, input variable
For the BP neural network model of previous daily water consumption, maximum temperature, weather conditions and festivals or holidays situation（4 input BP nerve nets
Network model）With the least square method supporting vector machine model that input variable is previous daily water consumption（LSSVM models）, other in guarantee
Sample data is trained and is predicted in the case that condition is constant.Prediction result and the input variable established herein are proxima luce (prox. luc)
The BP neural network model of water consumption（1 input BP neural network model）It compares and analyzes, as a result respectively such as Fig. 5 and Fig. 6
Shown, prediction result is evaluated as shown in Fig. 7 and table 2.
The different model design for commodities precision evaluations of table 2
By Fig. 4, Fig. 5, Fig. 6, Fig. 7 and table 2 it is found that measured value that prediction technique difference input variable of the same race obtains and predicted value
Error is different, and the error for the measured value and predicted value that input variable difference prediction technique of the same race obtains also is different.This
Application is established determines input variable, and then the predicted value tendency predicted with BP neural network model based on correlation analysis theory
It is almost the same with measured value tendency, and numerical value is very close, and error is smaller, and accuracy is high.
Particular embodiments described above has carried out further in detail the purpose of the present invention, technical solution and advantageous effect
Describe in detail bright, it should be understood that the above is only a specific embodiment of the present invention, is not intended to restrict the invention, it is all
Within the spirit and principles in the present invention, any modification, equivalent substitution, improvement and etc. done should be included in the protection of the present invention
Within the scope of.
Claims (10)
1. a kind of backpropagation based on correlation analysis（BP, Back Propagation）Neural network residential communities daily water consumption
Prediction technique, the BP neural network are three layers of BP networks, including n input layer, p hidden layer neuron and 1
Output layer neuron, this method comprises the following steps：Correlation analysis is carried out to sample data first, determines input variable；Then
Determine the parameter of prediction model to determine prediction model using the training set for breaking strict time sequence；Finally, BP god is utilized
It is predicted through Network Prediction Model, exports result.
2. according to the method described in claim 1, the strict time sequence of breaking refers to upsetting training set according to time order and function
The influence of time factor is eliminated in the data sequence for being ranked sequentially and being formed, the limitation of break through sequence.
3. according to the method described in claim 2, wherein determining that prediction model includes：
（1）Parameter initialization；
（2）Training set data is inputted, each layer output is calculated；
（3）Calculate output layer error；
（4）Judge whether to reach error precision,
（5）If not reaching error precision, according to each layer weights of output layer error transfer factor and threshold value, return to step（2）；
（6）If reaching error precision, it is determined that BP neural network prediction model.
4. according to the method described in claim 3, the correlation analysis includes determining whether each influence factor such as weather conditions, festivals or holidays
Influence to residential communities water consumption carries out correlation analysis using related-coefficient test method.
5. according to the method described in claim 4, the correlation analysis includes according to correlation analysis theoretical calculation resident's civil water
Measure the correlation coefficient r between Y and influence factor X：
Wherein xiAnd yiRespectively influence factor X and residential communities i-th day numerical value of water consumption Y,WithRespectively X's and Y is equal
Value, i=1,2 ... n.
6. according to the method described in claim 5, the determining input variable includes using partial Correlation Analysis theoretical calculation partially from phase
Relationship measures correlativity existing for the daily water consumption time series inside of residential communities several times.
7. according to the method described in claim 6, water consumption sample set is Y (t)=y1, y2, y3..., yn, PARCOR coefficients
For
In formula, k is delay time, i.e. time interval, k=1,2 ..., m；For mean value；rkFor PARCOR coefficients.
8. according to the method described in claim 7, determining rkCorresponding k values are the optimal delay time when first time zero crossing；It is right
The r when very big when delay timekJust level off to zero the case where, optimum delay time takes rkIt is less than for the first timeWhen corresponding k
Value.
9. according to the method described in claim 1, setting the threshold value of j-th of neuron of hidden layer as θj, then j-th of hidden layer nerve
Member input be
In formula, WijIt is the connection weight of i-th of input neuron and j-th of hidden layer neuron；ziWhen being inputted for input variable
The input value of i-th of neuron；The output of j-th of neuron of hidden layer is bj=f（sj）, j=1,2 ..., p, f is excitation function,
Form is：
The threshold value of daily water consumption output layer neuron is γ, and the input of the neuron of daily water consumption output is：
In formula, VjIt is j-th of hidden layer neuron and the connection weight of output neuron；
Daily water consumption output is Cr=f (L).
10. according to method any one of in claim 3-9, the output layer error calculation is
Wherein,For training set number of samples, ydWithThe respectively measured value and predicted value of training sample.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN109993354A (en) * | 2019-03-24 | 2019-07-09 | 北京工业大学 | A method of it is predicted for energy consumption |
| CN110136014A (en) * | 2019-05-23 | 2019-08-16 | 王为光 | A kind of medical insurance data analysing method based on big data |
| CN110674985A (en) * | 2019-09-20 | 2020-01-10 | 北京建筑大学 | Urban resident domestic water consumption prediction method and application thereof |
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