Tehran is one of the most pollutant in the world (Graedel
and Crutzen, 1994). There are many factors in polluting of Tehran that geographic
factors and pollution created by transportation are the most important factors.
Alborz Mountains in the north and northeastern block the Western winds and causing
pollution in Tehran. The existence of inversion circumstances and prevailing
of the high pressure in during of year are the physical characters in the Tehran
that we cant adjust and these circumstances. A wide variety of operational
warning systems based on empirical, causal, statistical and hybrid models have
been developed in order to start preventive action before and during episodes
(Schlink et al., 2003). Neural network models
have been used for the forecasting of a wide range of pollutants and their concentrations
at various time, with very good results (Comrie, 1997;
Gardner and Dorling, 1999; Hadjiiski
and Hopke, 2000; Kolehmainen et al., 2001).
The findings of numerous research studies also exhibit that the performance
of ANNs is generally superior in comparison to traditional statistical methods,
such as multiple regression, classification and regression trees and autoregressive
models (Yi and Prybutok, 1996; Chaloulakou
et al., 2003). In the recent years the use of ANNs has been extended
also for the prediction of particulate matter mass concentrations (Perez
et al., 2000; Chelani et al., 2002;
McKendry, 2002; Chaloulakou
et al., 2003; Ordieres et al., 2005).
The neural network models is superior in comparison with multiple linear regression
models (Grivas and Chaoulakou, 2006). The ANN has given
good results in the middle and long term forecasting of almost all the pollutants
(Viotti et al., 2002). Gradner and Dorling (1999)
also illustrated that multilayer perceptron neural networks are capable of resolving
complex patterns of source emissions without any explicit external guidance.
The aim of this study is forecasting the daily CO in the different regions of
Tehran using artificial neural networks. The artificial neural networks approach
has been explained in following. An ANN is composed of an input layer of neurons,
one or more hidden layers and an output layer. Each layer comprises multiple
units connected completely with the next layer (Fig. 1), with
an independent weight attached to each connection.
||Network model for CO forecasting
The number of nodes in the
output layer is equal to the number of values to be predicted.
One of extensively used ANN models for system modeling application is the multilayer
perceptron model based on the BP (Erb, 1993). In the
BP algorithm learning based, the initial weights of connections are randomly
chosen. Suppose we have N learning examples with each example having n inputs
and l outputs, the input vector can be described as Xj = (X1j,...,
Xnj) and the output vector as Aj = (B1j,...,
Blj), 1 = j = N. The learning process takes place using the following
two steps (Sexton et al., 1998):
Forward propagation: The input vector Xj is fed into the input layer and an output vector Oj = (O1j,..., Olj) is generated on the basis of the current weights W = (W1l, ...,Wnl). The value of Bj is compared with the actual output Aj and the output differences are summed to generate an error function E defined as:
Error back propagation: In this step, the error from Eq. 1 is back propagated by performing weights update using gradient descent as follows:
where, 0<ç<1 is a parameter controlling the convergence rate of
the algorithm. The process of forward propagation and error back propagation
continues until E converges to a predefined small value. ΔWnl is accumulated
and updated after a complete run of all the N examples for our research. The
basic BP algorithm described above is often very slow to converge in real practice.
In order to overcome the obstacles of these problems, BP algorithm has adopted
many improvement techniques. Initializing the BP weights with GA contains many
merits hence attracts the scholars and researchers interesting (Sexton
et al., 1998). And its modern form is derived mainly from Hollands
work in the 1960s. As has been shown in Fig. 2, GA is capable
to solve wide range of complex optimization problems only using three simple
genetic operations (selection, crossover and mutation) on coded solutions (strings,
chromosomes) for the parameter set, not the parameters themselves in an iterative
fashion. Genetic algorithm considers several points in the search space simultaneously,
which reduces the chance of convergence to a local optimum. At first a random
population is generated. This population feeds the population memory, which
is divided in two parts.
||Flowchart of micro algorithm genetic
The non-replaceable portion of the population memory
will never change during the entire run and is meant to provide the required
diversity for the algorithm. The initial population of the micro-GA at the beginning of each of its cycles
is taken (with a certain probability) from both portions of the population memory
as to allow a greater diversity. During each cycle, the micro-GA undergoes conventional
genetic operation: tournament selection, two-point crossover, uniform mutation
and elitism (only one nondominated vector is arbitrarily selected at each generation
and copied intact to the following one) after the micro-GA finishes one cycle
(i.e., when nominal convergence is achieved), two nondominated will chose vectors
from the final population (the first and last) and compare them with the contents
of the external memory(this memory is initially empty). If either of them (or
both) remains as nondominated after comparing against the vectors in this external
memory, then they are included there. All the dominated vectors are eliminated
from the external memory. These two vectors are also compared against two elements
from the replaceable portion of the population memory (this is done with a loop,
so that each vector is only compared against a single position of the population
memory). If either of these vectors dominates to its match in the population
memory, then it replaces it. The idea is that, over time, the replaceable part
of the population memory will tend to have more nondominated vectors. Some of
them will be used in the initial population of the micro-GA to start new evolutionary
MATERIALS AND METHODS
Study area: The city of Tehran, the capital city of Iran, is located
in Tehran province. Figure 3 shows the location of study area.
As has been shown in Tehran has 22 administrative regions and 11 pollution measure
stations. This city having more than 7 million people is the most populated
city in the country. The city is surrounded by Alborz Mountains in the Northeast.
Data used: In this study, CO data obtained from Tehran air quality control center based on SPI (Standard Pollution Index) in different days months, days, year and regions in during 2002-2005.
Method: The neural network has one input layer, one or two hidden and one output layer with one neuron. The input parameters are the concentration of pollutants. The number of autoregression components is determined by the correlation coefficients between the predicted value and its previous values persistence of the predicted variable. The goal is now to forecast one step ahead. The number of neurons in the first and second layers is determined by the criterion of the minimum squared error and the highest correlation coefficient between the observed and predicted data sets. When several neural networks were selected by this criteria, the best is chosen by the lowest percent of distribution of the observed versus the predicted concentrations in the vicinity of the Limit of Admissible Concentration (LAC).
In this study, at first CO data classified per regions, days, months. Day, month, year and regions as input parameters and pollution (CO) as output parameter identified. To accuracy, the combination of artificial neural network with Genetic algorithm was used. Because of vary confounding in classification, we used multiple perceptron and created a 3 layers model that contained input layer, output layer and hidden layer.
||The map of 22 administrative regions and pollution stations
||Network parameters are trained after train and error
TanhAxon function that is a most important function in BP method is used as irritate function. Neural solutions software is used for training artificial network. To reduce forecasting error, train and error on the network parameters carried out and at the end parameters arranged. The best parameter that has lowest error and presents the best results has been shown in Table 1. The model that used for this research is multilayer perceptron with 4 hidden layer and DeltaBarDelta as Training method. Irritate function (transfer) assigned for running model was TanhAxon with step size 0/1 and 1000 epochs. Momentum is one of the main parameters in training that illustrate the fraction of before weights effect to new weights that in this study 0/7 considered. Neuron is smallest processing unit of hidden layer and learning coefficient control the speed of collation the weights among neurons.
RESULTS AND DISCUSSION
Two models in accordance with the methods of determining the connection weights of BP and hybrid of GA-BP are compared with the real experimental results. The results of network training with arranged samples showed that doesnt present a logical results rather than samples that selected by chance. Thus, after selection data by chance, network was trained and the results showed in Fig. 4.
There is a good coordination between real data (CO) with ANN forecast after selection data by chance. There is a nonlinear correlation between daily CO concentration in the months and regions that is one of the reasons of increase artificial networks accuracy rather than classic models such as regression models that are linear (Fig. 4).
Minimum training error of network after training equal to 0/02 and maximum error is 35/64 that shows network accuracy. Correlation coefficient presents relation rate between network outputs with real data (CO). Correlation coefficient equal to 1, shows fulfill coordination between real data (CO) with ANN forecast and -1 show no coordination between them. Figure 5 shows correlation and adjust coefficient between real data (CO) with ANN forecast for three variable days, month and regions that equal to 0/91 and 0/84, respectively.
||Comparing amount of real data (CO) with ANN forecast
||Correlation between real data (CO) with ANN forecast
||Comparing amount of real data (CO) in combination with ANN-GA
As described above the basic BP algorithm is often very slow to converge in
real practice. In order to overcome the obstacles of these problems, the BP
weights with GA was used.
As has been shown in Fig. 6 the combination of artificial
neural networks with Genetic algorithm result in reducing error. In other word
the real data and forecasted data closer together.
||Correlation between real data (CO) in combination with ANN-GA
In addition to the speed
of calculation will be higher. Minimum training error of network rate after
training equal to 0/02 and maximum error is 34/22 that means maximum error reduce
1/42 rather before situation.
Figure 7 shows correlation between real data (CO) with combination ANN-GA forecast that equal to 0/92 and adjust coefficient increase to 0/85.
Artificial neural networks can model time series successfully and are employed
when the using classic methods arent effective (Chakraborty
et al., 1992; Grivas and Chaloulakou, 2006).
Also, the results of this study showed that the artificial neural network can
better forecasts air pollution rather than other statistical methods. There
is a nonlinear trend between CO and time factor. Thus using of these models
for nonlinear trends increase mistake rate (Chelani et
al., 2002). The evaluation of model results shows that the degree of
success in forecasting CO concentration is promising.
The aim of this study is forecasting air pollution with artificial neural networks. The results after testing network with hidden layers and different learning coefficients showed that using artificial neural networks with one perceptron with 4 hidden layers, 0/1 learning coefficient and 0/7 momentum result in a relative better model and after retraining and testing network with different hidden layers and learning coefficients in combination with genetic algorithm cause decrease error and increase the speed of calculations and present a better model. Artificial network forecasts the nonlinear correlation between CO concentration related to day, season and different regions. For forecasting, Network training with accident data has a better accuracy rather than arranged data. The combination of algorithm genetic with artificial network increases the speed of analyzing and processing accuracy and decrease error rate.