COMPARISON OF ANN AND PCA BASED MULTIVARIATE LINEAR REGRESSION APPLIED TO PREDICT THE DAILY AVERAGE CONCENTRATION OF CO: A CASE STUDY OF TEHRAN

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NOURI ROUH ELAH; ASHRAFI KH.; AZHDARPOUR A.A.F.

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Journal: Journal of the Earth and Space Physics Year:2008 | Volume:34 | Issue:1 Page(s): 135-152

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Title

COMPARISON OF ANN AND PCA BASED MULTIVARIATE LINEAR REGRESSION APPLIED TO PREDICT THE DAILY AVERAGE CONCENTRATION OF CO: A CASE STUDY OF TEHRAN

Author(s)

NOURI ROUH ELAH | ASHRAFI KH. | AZHDARPOUR A.A.F. | Issue Writer Certificate

Keywords

PRINCIPAL COMPONENT ANALYSISQ3

ARTIFICIAL NEURAL NETWORKQ2

CARBON MONOXIDEQ3

MULTIVARIATE LINEAR REGRESSIONQ3

TEHRANQ2

Abstract

CO is the important air pollutant in TEHRAN. Two forecasting techniques are presented in this paper for prediction of average daily CO concentration. One of them, MULTIVARIATE LINEAR REGRESSION (MLR) is based on PRINCIPAL COMPONENT ANALYSIS (PCA). The other technique is ARTIFICIAL NEURAL NETWORK (ANN) model. With this regard to six pollutants, i.e., PM10, NOx, SO2, THC, CH4 and O3, and six meteorological variables, i.e., wind speed, wind direction, temperature, air pressure, humidity, solar radiation are used. These variables were measured daily throughout 2004 and 2005 at Gholhak Monitory Station, one of the eleven monitory stations in the TEHRAN area. Among all the ANNs available paradigms, a Feed-Forward Multi-Layer Perceptron (FFMLP) was considered to be the best choice for this study because it is the most popular architecture for an ANNs. Therefore, in our research, one hidden layer FFMLP was used for the average daily CO concentration prediction. The activation functions chosen were the sigmoid hyperbolic tangent function in the hidden and output layers. The error correction learning with the Levenberg–Marquardt (L–M) algorithm was chosen for training the networks.Regression model in matrix form can be shown as: Y=Xb +e (1)where b is regression coefficient matrix, e is fitting error matrix and Y is response matrix. By solving equation for b we will have:b=(X'X)-1 (XY')where X' is transpose of X.For calculating the inverse of (X'X), the independent variables should not have high relativity, because in this situation (X'X) matrix can not become inverse and we will have more error in the data and calculations. To solve this problem, we should remove the multicolinearity between independent variables with PCA approach. In this research after removing the problem of multicolinearity on independent variables by the PCA, an appropriate model (PCA-MLR) was developed for predicting CO concentration. However, in the MLR calculation, stepwise algorithm has been used. In this method, entering the variables to the MLR is step by step condition, from the most important of them to the less important of them. To achieve the best network structure for estimating CO concentration, various structures of FFMLP was investigated. Finally, a 13-22-1 architecture was selected for the best architecture of the network. Also, after removing the multicolinearity between independent variables, an appropriate PCA-MLR model was developed for prediction of CO concentration by stepwise algorithm.In this step by performing PCA from 12 Principal Components (PCs), just 8 PCs were meaningful to enter the model. It estimates the CO concentration the regard to these new input variables. Finally, a PCA-MLR model is constructed that its equation is given below:CO 4.92 0.60 (PC1)-0.57 (PC9) 0.35 (PC6)-0.29 (PC5)-0.24 (PC3) 0.24 (PC11) 0.16 (PC2) 0.13 (PC7) For better judgment and selection of one on them, the Threshold Statistic (TS) index of testing step calculated and presented. For example this index shows that Absolute Relative Error (ARE) for 75% prediction of testing stage in ANN is 20%. This value (ARE) is 25% in the PCA-MLR model. However 90% of prediction of testing stage in ANN and PCA-MLR models are ARE equal to 41% and 53% respectively. Finally, the use of FFMLP in prediction of average daily CO concentration in TEHRAN is offered.

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