CN111310974A - Short-term water demand prediction method based on GA-ELM - Google Patents
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Abstract
The invention discloses a GA-ELM neural network short-term urban water demand prediction method, which optimizes the connection weight between an input layer and a hidden layer in an ELM model and the neuron threshold of the hidden layer by using a genetic algorithm, improves the defect of over-training fitting or hidden layer deletion of the ELM prediction model, and greatly improves the prediction accuracy. In addition, the grey correlation analysis method is used for analyzing the water use influence factors, and the characteristic value with high correlation degree is selected as input, so that the method is more scientific compared with the traditional method of using historical water data singly as input. Analysis results show that the GA-ELM prediction method provided by the invention can be used as an effective tool for urban short-term water demand prediction.
Description
Technical Field
The invention relates to a short-term water demand prediction method based on a Genetic algorithm-optimized Extreme Learning Machine (GA-ELM), and belongs to the technical field of water resource management and communication information.
Background
Water conservancy is a necessary basic element for national economy and social development, and provides important guarantee for social development and grain and ecological environment safety. With the increasing population of cities, cities have an increasing demand for water resources. The automatic operation of the urban water supply system is a development trend in the future, and the water demand prediction plays an important role in the design, planning, management and operation of the whole urban water supply system and is a key reference for water supply strategies, operation scheduling and optimization design.
At present, a great deal of research is carried out at home and abroad to try to accurately and reliably predict the water consumption of cities, and the main methods are a traditional prediction method represented by a time series method, an artificial intelligence prediction method represented by an artificial neural network and a machine learning algorithm represented by a support vector machine. An Extreme Learning Machine (ELM) is proposed by Guang-Bin Huang et al, is a learning algorithm for solving a single hidden layer feedforward neural network, has high learning speed and good generalization performance, and has the capability of efficiently processing a nonlinear data regression fitting problem. Since the ELM neural network is proposed, the ELM neural network is widely applied to the fields of short-term power load prediction, solar irradiation prediction, wind power plant anemometry data prediction and the like.
The analysis shows that the research of short-term water demand prediction by using an extreme learning machine is less, and in addition, the connection weight between an input layer and a hidden layer and the neuron threshold of the hidden layer in the traditional extreme learning machine model used in the prior art are randomly given, so that the defects that the initial network parameters with excellent global property are difficult to determine and the like may exist. In addition, in the prior art, more data of single historical water consumption are considered, only the historical water consumption is used as a training set, and the influence factor of water shortage is input into a model.
Disclosure of Invention
On the basis of the prior art, the method optimizes the connection weight between an input layer and a hidden layer in an Extreme Learning Machine (ELM) model and the neuron threshold of the hidden layer through a Genetic Algorithm (GA), establishes a GA-ELM prediction model, performs factor analysis on water-using influence factors, and takes a characteristic value with high correlation as the input of the GA-ELM model.
The effectiveness of the GA-ELM prediction method provided by the invention is simulated and verified by using 60 groups of water use data in 2019 of a water works in Beijing, the data of the highest air temperature, the lowest air temperature, the precipitation and the like in the same day are correspondingly collected, the influence factor screening analysis is carried out by using a grey correlation analysis method, the main influence factors of the water use in the Beijing city are determined and used as an input layer, the average relative error (MAPE), the average absolute error (MAE) and the Root Mean Square Error (RMSE) are used as simulation model evaluation standards, and the simulation result is compared with a BP neural network and a traditional ELM neural network prediction method. The experimental result shows that MAPE, MAE and RMSE of the GA-ELM are smaller than those of other two prediction methods, so that the GA-ELM prediction method provided by the invention is an effective tool for urban short-term water demand prediction.
The invention provides a GA-ELM-based urban short-term water demand prediction method which mainly comprises the steps of optimizing input weight and threshold of an extreme learning machine by a genetic algorithm and analyzing influence factors.
Firstly, a genetic algorithm and an extreme learning machine algorithm are combined in a nested mode, and the idea of combined optimization is as follows: and optimizing the connection weight between the input layer and the hidden layer and the neuron threshold of the hidden layer in the extreme learning machine model by using the genetic algorithm. The method solves the problems of optimal weight and threshold in the ELM water demand prediction model.
And secondly, establishing a GA-ELM short-term water demand prediction model and determining a model evaluation standard. Including data collection, data normalization processing, model training and evaluation.
Thirdly, aiming at the collected urban water use data and the influence factors, screening the influence factors with higher association degree by utilizing grey association analysis, and taking the influence factors as the input of a prediction model, thereby effectively improving the prediction precision of the model.
And finally, carrying out simulation verification, and comparing the prediction result of the GA-ELM with the BP neural network and the traditional ELM neural network.
The invention adopts the following technical scheme: a short-term water demand prediction method based on GA-ELM is characterized in that: and optimizing the ELM neural network by adopting a genetic algorithm, analyzing water use influence factors by adopting a grey correlation analysis method, finding out main factors as input of the optimized ELM neural network, and predicting water demand.
The processing of the original data comprises that all the data are represented by numerical values, all the original data are processed with equivalence and orderliness by adopting a processing method of interval value, the original data are converted into a range of [0,1] to obtain a new sequence, one sequence is used as a reference sequence, and the other sequences are used as comparison sequences. And further, solving the grey correlation coefficient and the correlation degree, solving the correlation degree of the comparison sequence corresponding to each factor and the reference sequence, sequencing the correlation degree, and finding out the main factors influencing water consumption.
Optimizing the connection weight and the threshold of an input layer and a hidden layer of the ELM neural network by adopting a genetic algorithm, and specifically comprising the following steps:
(1) inputting daily water consumption data and influencing factors as training samples;
(2) an ELM neural network for randomly generating a connection weight and a threshold is established according to input training data;
(3) setting population number and an optimization target of a genetic algorithm; selecting errors as fitness functions, and optimizing the target to achieve the target errors;
(4) binary coding is carried out on the connection weight value and the hidden layer threshold value of the input layer and the hidden layer of the ELM model;
(5) training the population and calculating the fitness value of each individual in the population;
(6) selecting, crossing and varying the population according to the fitness value to generate a sub population, inserting the individuals of the sub population into the parent population to replace the individuals with the minimum fitness value in the parent population to obtain a new population, and adding 1 to the iteration number;
(7) judging whether the end condition is met, if so, performing the step (8), otherwise, returning to the step (5); the ending condition is set to reach the optimization target or the maximum iteration times;
(8) and decoding the parameters, and updating the GA-ELM model according to the obtained connection weight of the optimal input layer and the hidden layer and the node threshold of the hidden layer.
Initial parameters of the GA were set as: the population size S is 30; cross probability pc0.9; mutation rate pm0.01; the number of individuals transmitting the next generation is 4; maximum overlap of GAThe generation number is 120; the optimization target is set to mean square error of 1 × 10-4。
Drawings
FIG. 1 shows the relative trend of daily water consumption in Beijing and the highest and lowest air temperatures;
FIG. 2 is a diagram of an ELM neural network architecture;
FIG. 3 is a flow chart of GA-ELM model optimization;
FIG. 4 is a comparison of the predicted results of three different predictive models; and
FIG. 5 is a graph of absolute percentage error comparisons for three different prediction models.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to specific embodiments and the accompanying drawings.
Fig. 1 shows the relative trend of daily water consumption in Beijing and the highest and lowest air temperatures. There are many complex factors that affect city water usage, such as holidays, the highest temperature on the day, the lowest temperature, weather, etc. The method of the invention uses grey correlation analysis, which mainly comprises the following steps:
1. the raw data is processed. The original data comprises water consumption, the highest temperature of the day, the lowest temperature of the day, holidays and weather, all the data are represented by numerical values, all the original data are subjected to equivalence and orderliness processing by adopting an interval valued processing method, the original data are converted into a range of [0,1], 5 new sequences are obtained, namely 5 sequences of the water consumption, the highest temperature, the lowest temperature, the weather and holidays are used as reference sequences, and other sequences are used as comparison sequences.
Let the original data sequence be x ═ (x (1), x (2), … x (m)), and the interval operator be N2，xN2For sequences after segmentation, then xN2＝(x(1)n2,x(2)n2,x(3)n2,…x(m)n2) And then:
inspection of the characteristic value:
small expected eigenvalue:
wherein the content of the first and second substances,
for the minimum value in each of the sequences,
is the maximum value in each sequence, m is the sequence length, and x (i) is each value in the original sequence of numbers.
That is, a new sequence x '(1), x' (2), x '(3), …, x' (m)) is obtained.
2. And then solving the grey correlation coefficient and the correlation degree to obtain the correlation degree between the comparison sequence corresponding to each factor and the reference sequence.
(1) The correlation coefficient is as follows:
ξ thereinoj(k) Denotes the jth comparison sequence xjWith reference sequence x0The correlation coefficient for the kth value. Wherein, the jth comparison sequence xjThe k point on the curve and the reference sequence x0The absolute difference at the kth point on the curve, denoted Δoj(k)；Δoj(k) The minimum value of (d) is denoted as Δ (min) and the maximum value is denoted as Δ (max). Rho is a resolution coefficient, generally between 0 and 1, and is taken as 0.5 in the application.
(2) Calculating the degree of association roj
The formula is as follows:
wherein m is the length of a reference sequence, and 60 is taken in the application.
3. And (4) sorting the degrees of association, wherein the larger the numerical value is, the deeper the influence degree is, and the main factors influencing urban water consumption can be found out from the table 1, namely the lowest air temperature and the highest air temperature in the day.
TABLE 1 correlation coefficient of influencing factors
2 Water demand prediction using optimized extreme learning machine
2.1 extreme learning machine principle
An Extreme Learning Machine (ELM) is a novel algorithm for a single hidden layer feedforward neural network, and consists of an input layer, a hidden layer and an output layer, and has the advantages of being easy to implement in engineering, high in training speed, strong in generalization capability and the like. The structure of the ELM neural network used in the present invention is shown in FIG. 2.
Although ELM has improved performance over traditional neural networks, there are still some areas to be improved: the main factor influencing the performance of the single hidden layer feedforward neural network (SLFNs) is the connection weight between nodes, and for ELM, the connection weight and the threshold of the input layer and the hidden layer are generated randomly, so that the network structure is poor in stability and easy to generate an overfitting phenomenon to a certain extent, and the generalization performance of the neural network is influenced. Therefore, the invention optimizes the neural network according to the connection weight and the threshold of the input layer and the hidden layer.
2.2 genetic Algorithm optimization extreme learning machine neural network
The invention adopts the genetic algorithm to carry out optimization selection on the connection weight and each layer of threshold value of the ELM neural network, the genetic algorithm takes the variable code as an operation object, the genetic algorithm is different from the traditional algorithm which directly acts on the actual value of the parameter, the genetic algorithm has wide applicability, and the multi-point information searching mode of the genetic algorithm ensures that the genetic algorithm has good global searching property and parallel searching property.
FIG. 3 is a flowchart illustrating GA-ELM model optimization. The method comprises the following steps:
the method comprises the following steps: daily water consumption data and influencing factors are used as training sample input.
Step two: and establishing an ELM neural network for randomly generating a connection weight and a threshold according to the input training data.
Step three: and setting the population number and the optimization target of the genetic algorithm. Preferably, the error is selected as a fitness function, and the optimization goal is to achieve the target error.
Step four: and carrying out binary coding on the connection weight value and the hidden layer threshold value of the input layer and the hidden layer of the ELM model.
Step five: training the population and calculating the fitness value of each individual in the population.
Step six: and selecting, crossing and mutating the population according to the fitness value to generate a sub population, inserting the individuals of the sub population into the parent population to replace the individuals with the minimum fitness value in the parent population to obtain a new population, and adding 1 to the iteration number.
Step seven: and judging whether the ending condition is met. And if so, performing the step eight, otherwise, returning to the step five. The end condition is set to reach the optimization goal or to reach the maximum number of iterations.
Step eight: and decoding the parameters, and updating the GA-ELM model according to the obtained connection weight of the optimal input layer and the hidden layer and the node threshold of the hidden layer.
The initial parameters of the GA in this application are set as: the population size S is 30; cross probability pc0.9; mutation rate pm0.01; the number of individuals transmitting the next generation is 4; the maximum iteration number of the GA is 120; target error (mean square error MSE) of 1 × 10-4。
The parameters of the GA-ELM short-term water demand prediction model are set as follows:
TABLE 2 GA-ELM short-term prediction model parameter set-up
And inputting the influence factors into the optimized GA-ELM prediction model to obtain a water demand prediction result.
The accuracy of the prediction model needs to be judged by some error evaluation standards, and the evaluation standards used in the method are mean relative error (MAPE), Mean Absolute Error (MAE) and Root Mean Square Error (RMSE).
Where C is the test set sample size, ynIs the actual water consumption of the nth day,
the corresponding predicted water usage.
The simulation software used in the method is MATLAB R2016(b), the traditional BP neural network, the unmodified ELM neural network and the GA-ELM neural network are respectively used for predicting the daily water consumption in Beijing urban areas, and FIG. 4 is a comparison graph of prediction results of the three prediction methods. As can be seen from FIG. 4, the GA-ELM prediction model is closest to the actual daily water consumption curve, and has obvious advantages compared with the traditional BP neural network and ELM, and FIG. 5 is a daily absolute percentage error curve graph of the three models, and it can be seen that the precision of the GA-ELM neural network is much higher than that of the other two neural network models.
Error pair ratio is as follows:
TABLE 3 prediction error result comparison
As can be seen from the table:
(1) the average error of the GA-ELM predicted value (MAE) is the lowest compared with the other two prediction models, and under the huge million cubic water consumption data, the average error is an objective figure at 71758.878 cubic meters.
(2) The prediction accuracy of the model is the highest GA-ELM accuracy, and the advantages of the traditional ELM prediction model compared with the traditional BP neural network prediction model are not obvious.
(3) The loss of the GA-ELM prediction model is minimal relative to the other two models, as can be seen by the Root Mean Square Error (RMSE).
The invention provides a GA-ELM neural network short-term urban water demand prediction method, which utilizes the advantages of high training speed, good generalization value and no need of parameter adjustment of the ELM neural network, optimizes the input weight and the hidden layer neuron threshold value by using a genetic algorithm, improves the defects of over-training fitting or hidden layer deletion of an ELM prediction model, greatly improves the prediction precision, and compares the prediction result of the prediction method with the results of other prediction methods. Analysis results show that the prediction precision of the GA-ELM prediction method is higher than that of an ELM neural network prediction method and a BP neural network prediction method.
In addition, the grey correlation analysis method is used for analyzing the water use influence factors, and the characteristic value with high correlation degree is selected as input, so that the method is more scientific compared with the traditional method of using historical water data singly as input.
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are only exemplary embodiments 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 (8)
1. A short-term water demand prediction method based on GA-ELM is characterized in that: and optimizing the ELM neural network by adopting a genetic algorithm, analyzing water use influence factors by adopting a grey correlation analysis method, finding out main factors as input of the optimized ELM neural network, and predicting water demand.
2. The method of claim 1, wherein the processing of the raw data comprises numerically representing all the raw data, performing equivalence and identity processing on all the raw data by interval-valued processing, transforming the raw data into the range of [0,1] to obtain new sequences, and using one of the sequences as a reference sequence and the other sequences as comparison sequences.
3. The method of claim 2, further comprising solving for the grey correlation coefficient and the degree of correlation, finding the degree of correlation between the comparison sequence corresponding to each factor and the reference sequence, ranking the degrees of correlation, and finding out the main factors affecting water use.
4. The method according to any one of claims 1-3, wherein genetic algorithm is used to optimize the connection weights and thresholds of the input layer and the hidden layer of the ELM neural network.
5. The method according to claim 4, wherein the optimization comprises the following steps:
(1) inputting daily water consumption data and influencing factors as training samples;
(2) an ELM neural network for randomly generating a connection weight and a threshold is established according to input training data;
(3) setting population number and an optimization target of a genetic algorithm;
(4) binary coding is carried out on the connection weight value and the hidden layer threshold value of the input layer and the hidden layer of the ELM model;
(5) training the population and calculating the fitness value of each individual in the population;
(6) selecting, crossing and varying the population according to the fitness value to generate a sub population, inserting the individuals of the sub population into the parent population to replace the individuals with the minimum fitness value in the parent population to obtain a new population, and adding 1 to the iteration number;
(7) judging whether the end condition is met, if so, performing the step (8), otherwise, returning to the step (5);
(8) and decoding the parameters, and updating the GA-ELM model according to the obtained connection weight of the optimal input layer and the hidden layer and the node threshold of the hidden layer.
6. The method of claim 5, wherein the error in step (3) is selected as a fitness function, and the optimization objective is to achieve a target error.
7. The method of claim 6, the termination condition in step (7) being set to achieve an optimization goal or to achieve a maximum number of iterations.
8. The method of claim 7, wherein the initial parameters of the GA are set as: the population size S is 30; cross probability pc0.9; mutation rate pm0.01; the number of individuals transmitting the next generation is 4; the maximum iteration number of the GA is 120; the optimization target is set to mean square error of 1 × 10-4。
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