Thermal Power Industry NOX Emissions Forecast Based on Improved Tandem Gray BP Neural Network

In this study, we build a new thermal power sector NOx emissions prediction model of tandem gray BP neural network. Firstly we use 1994-2010 years NOx emissions data to establish three gray prediction models: GM (1,1), WPGM (1,1) and pGM (1,1); Secondly, by comparison, we select the best prediction model pGM (1,1) and at the same time take NOx emissions factors as the BP neural network input, 1994-2010 year of NOx emissions data for training and testing. Lastly we proceed to predict thermal power industry NOx emissions in China in 2013 and 2020. Prediction result is: mean relative error of the improved tandem gray BP neural network prediction results is 1.92%, which is lower 0.158% than pGM (1,1) model and 0.28% than BP neural network model respectively.


INTRODUCTION
70% nitrogen oxides (NOx) discharged into the atmosphere come from the direct combustion of coal, thermal power based on coal consumption has the biggest proportion of electricity production in China, Therefore, grasping the thermal power industry NOx emissions status is the premise and basis of controlling NOx pollution (Gao et al., 2004).Because of NOx emissions restrictions by technical conditions and basic conditions, NOx emissions data statistics is quite difficult, so accurate prediction of NOx emissions of the thermal power industry is particularly important.
Relevant Chinese NOx emissions prediction research is also less.Liu (2007) had come up with several NOx emissions estimation methods in the study "Thermal Power Industry nitrogen oxides emissions estimates in China", such as emission factor method, the numerical simulation method and statistical methods and so on.However, the error of these estimates is larger, the prediction accuracy is lower; Wang et al. (2010) put forward the exponential model of the NOx emissions and the gray prediction model of NOx emissions after deep study of a high-temperature of hypoxia flame image.NO X emissions belong to the gray system of typical small sample size, poor information (Dang et al., 2009), so it is more appropriate to use the method of gray to predict emissions, however, due to the dynamic nature of the flame itself and environmental factors, they will bring some influence to the results of the prediction model.
In view of advantages and limitations of the above study, this study proposes a tandem gray BP neural network model to predict NOx emissions.First of all, substitute the original data of 1994-2010 NOx emissions into the three gray prediction model GM (1,1), WPGM (1,1) and pGM (1,1), then compare the prediction accuracy of the three models and last select the predictive results of the most accurate gray model and the main factors of impacting NOx emissions as the input of BP neural network.This method combines the strengths and weaknesses of the gray theory and artificial neural network algorithm, the results show that the relative error of predicted results of the improved tandem gray BP neural network model is smaller than the actual results, which has a good feasibility on application of NOx emissions prediction.

THE GRAY BP NEURAL NETWORK MODEL
Gray thoery prediction model: The basic idea of the gray system theory is to take the system of small sample size, poor information and the uncertainty based on partial information known and some of the information unknown as the research object, extract valuable information mainly through the generation and development of the part known information, make sure the correct description and effective monitoring to the system running behavior and the evolution (Xiao et al., 2005).In this study we select three gray forecasting model GM (1,1), WPGM (1,1) and pGM (1,1) to predict the thermal power industry NOX emissions.
Set â as a be estimated parameters vector, ˆ( ) a a = µ , which can be solved by the least squares method, the solution is:, in which: (1) (1) (2) (3) Solve the differential equations, then we can obtain Discrete-time response function of gray prediction: Is the accumulating prediction value, restore the predictive value, we can see the gray prediction model: ˆ(1) (1) (3) WPGM (1,1)model: If the original data is an index sequence, that is: Its one time accumulated generating sequence: (1) (1 )/(1 e ) k=1,2 Using the GM (1,1) to build a model, we obtain: After derivation available: The ultimate simulation result is: By ( 12), we can get: Use the GM (1,1) model parameters â , û to express the parameters of the original data sequence.Assume the established model on index sequence is: If, then ' ˆ= a a , At this point ( 14) is the no deviation model of (5).
pGM (1,1) model: Set the original data sequence is, . Its one time accumulated generating sequence, In which the albino value of gray parameters.β = [a, u] T Determine the optimal weights and generate background value sequence: Using the least squares method to calculate β , then: Substitute the obtained gray parameters into (15) and then find the solution of differential equations: ˆt x + is the model calculated value, tired less generate it, you can get the analog value of the model, ˆˆˆ( 1)( ) (18) and ( 19) is a specific formula for calculating pGM (1,1) model.
BP neural network prediction model: BP network has a three-tier structure, namely the input layer, the hidden layer and the output layer, which are fully connected.Set the input layer is i , the hidden layer is h and the output layer is j , the number of nodes of three layers respectively are ni , nh , nj , the threshold value of the hidden layer nodes and output layer nodes respectively are h θ and j θ , the wiring weight between the input layer nodes and the hidden layer node is, the wiring weight of hidden layer nodes and output layer nodes is, each node input is x .
• Normalize the input and output samples • The initialization.Assume the input and output samples after normalized are: Taken to a random value in the interval (-0.1，0.1)• Set 1 k = , provide the input and output samples to the network • Calculate the input and output of each node of the hidden layer ( 1, 2, ) • Calculate the input and output of each node of the output layer ( 1, 2, ) The calculation of the change rate of the total input changes the output layer node receives a single sample error.
, ( 1)( ) ( 1, 2, ) The calculation of the change rate of the total input changes the Hidden layer node receives a single sample error.
The correction of the connection weights and thresholds.
1 1 ( ) In which correction number is, Learning rate, momentum factor, algorithm converges is slowly while is smaller, algorithm converges is faster while is larger, but it is instable, may shock and the function of is opposite.Set, k = k+1 provide (x k,i , d k, j ) to the network, then go to step 4), until all the samples are completely trained.
Repeate steps 3) to 9), until the network global error function.
Learning frequency is bigger than the pre-set value or less than a smaller value of the pre-set.

Improved tandem gray BP neural network model:
Tandem gray BP neural network is to take the results of gray prediction model as input of neural network, utilizing the non-linear fitting ability to obtain the final predicted value.But this approach ignores the impact of the other main factors to results prediction, based on which, we put forward a Improved tandem gray BP neural network model to predict thermal power NOX emissions In this study, that is: select a best forecast model among GM (1,1), WPGM (1,1) and pGM (1,1), at the same time take the main factors of effecting nitrogen oxide emissions as the input of the neural network to achieve the best fit.As shown in Fig. 1:

NOX EMISSIONS PROJECTIONS OF THERMAL POWER BASED ON SERIES GRAY BP NEURAL NETWORK MODEL
The selection of the basic data: Neural network and gray neural network model need some data including NOX emissions data, the coal consumption, installed capacity, power generation as well as GDP.The raw data of the study sample is selected from annual NOx emissions of the thermal power industry from 1994 to 2010 (Ministry of Environmental Protection of the People's Republic of China, 2010;Zhu et al., 2004), the coal consumption (National Bureau of Statistics, 2008), the installed capacity (China Electric Power Yearbook Editorial Board, 2009), power generation, the GDP (National Bureau of Statistics, 2008), the specific data is shown in Table 1.

The gray model selection of NOX emissions:
According to the original sample data in Table 1, we establish gray prediction model GM (1,1), WPGM (1,1), pGM (1,1), program Three models using MATLAB language and forecast NOX emissions from 1994 to 2010, the predicted results are shown in Table 2. Relative error is used as an explanation for the accuracy of the prediction model: In the formula, x(h) means the actual value, ˆ( ) x h means the predictive value.

The accuracy validation of nox emissions projections model based on improved series gray bp neural network:
NOx emissions factor is the input of NOx emissions projections network, in theory, the number of impact factors is the number of input layer neurons, Coal consumption, electricity generation, installed capacity and GDP are selected as the input, therefore, input nodes of NOx emissions artificial neural network model are four.Based on trial and error method, a hidden layer has 13 neurons according to empirical formula of node algorithm, the network training adopts the Levenberg-Marquardt algorithm.
After training the data from 1994 to 2005 using above neural network model, predicted results of NOx emissions are shown in Table 5 from 2006 to 2010.
According to above analysis, pGM (1,1) is compared to GM (1,1) and WPGM (1,1) whose predictive effect is better, pGM (1,1) model prediction results is taken as the input of improved series gray neural network model.Combined with the above trained neural network structure, we can see the structure of the improved series gray neural network model: The input layer 5 neurons: pGM (1,1) model prediction results, coal consumption, power generation, installed capacity and GDP, Output layer has one neuron, hidden layer has 13 neurons, network training   6 and in Fig. 3.
Mean relative error of this prediction results is 1.586%, which is smaller for 4.179% than pGM1,1model and for 2.608% than neural network model.Therefore improved series gray neural network can be used to predict NOx emissions of the thermal power industry in China from 2013 to 2020.

NOX emissions forecast of China's thermal power industry:
We can find GDP, coal consumption, installed capacity, power generation data from 2009 to 2011 from China Statistical Yearbook, China Electric Power Yearbook and other relevant information.As is known from the content, prediction effect of pGM (1, 1) is best, so through the pGM (1, 1) model, forecast the data of all the factors in 2012 and 2020 on the basis of historical data.Specific results are shown in Table 7: Use 1998-2008 NOX emission data modeling pGM (1,1), forecast NOX emissions for 2012 and 2020,the results respectively are 879.3621ten thousand tons and 982.1435 ten thousand tons.
Input vector in 2012 and 2020 of improved tandem gray BP neural network model respectively are: {509527.2,181935.6,94217,32164.5,879.3621} and {821469.4,284636.2,131525,41132.5,982.1435}Transporting two sets of vectors to the improved tandem gray BP neural network, we can obtain NOX emissions of the thermal power industry in China in 2012 and 2020: 894.3113 ten thousand tons and 1000.804ten thousand tons.

CONCLUSION
The study sets up a newly improved series gray neural network model for NOx emissions projections of the thermal power, with the problems that there are not enough long-term forecasting data for NOx emissions, we established three gray prediction models which include pGM(1,1), GM(1,1), WPGM(1,1) using time series of NOx emissions from 1994 to 2010.Combining the advantages and disadvantages of gray theory and neural network algorithm, a new model that the best accuracy PGM (1,1) model, GDP, coal consumption, installed capacity as well as power generations are all taken as the input of neural network is constructed.Then the new model is put to test the NOx emissions from 2006 to 2010, the average relative error of the predicted results is 1.586% which is smaller than pGM (1,1) model for 4.179% and is also smaller than neural network model for 2.608%.Finally, we make a forecasting for NOx emissions of the china thermal power in 2013 and in 2020.Therefore, the newly improved series gray neural network model has a higher prediction accuracy that can be regarded as an effective way for thermal power NOX emissions projections.
Fig. 1: Overall framework of NO X emissions prediction model

Table 1 :
(Zhu et al., 2004)e data Thermal power NOx emissions data from 1994 to 2002 come from fahua Zhu's paper in 2004(Zhu et al., 2004); NOx emissions data from 2003 to 2010 is from the statistics of the State Environmental Protection Department (Ministry of Environmental Protection of the People's Republic of China, 2010); Coal consumption, electricity generation, and GDP data are from the website of the National Bureau of Statistics of the People's Republic of China (National Bureau of Statistics, 2008); The installed capacity data come from the power industry statistics of the China Electricity Council (China Electric Power Yearbook Editorial Board, 2009).

Table 3 :
Analog performance of the three models

Table 7 :
The determination of input vector in 2012 and 2020