Uncertainty analysis of developed ANN and ANFIS models in prediction of carbon monoxide daily concentration

Abstract

This study aims to predict daily carbon monoxide (CO) concentration in the atmosphere of Tehran by means of developed artificial neural network (ANN) and adaptive neuro-fuzzy inference system (ANFIS) models. Forward selection (FS) and Gamma test (GT) methods are used for selecting input variables and developing hybrid models with ANN and ANFIS. From 12 input candidates, 7 and 9 variables are selected using FS and GT, respectively. Evaluation of developed hybrid models and its comparison with ANN and ANFIS models fed with all input variables shows that both FS and GT techniques reduce not only the output error, but also computational cost due to less inputs. FS–ANN and FS–ANFIS models are selected as the best models considering R², mean absolute error and also developed discrepancy ratio statistics. It is also shown that these two models are superior in predicting pollution episodes. Finally, uncertainty analysis based on Monte-Carlo simulation is carried out for FS–ANN and FS–ANFIS models which shows that FS–ANN model has less uncertainty; i.e. it is the best model which forecasts satisfactorily the trends in daily CO concentration levels.

Introduction

In recent years, artificial intelligence (AI) based methods have been proposed as alternatives to traditional statistical ones in many scientific disciplines. The literature demonstrates that AI models such as ANN and neuro-fuzzy techniques are successfully used for air pollution modeling (Nunnari et al., 2004, Perez-Roaa et al., 2006) and forecasting (Perez et al., 2000, Gautama et al., 2008). Moseholm et al. (1996) investigated the relationships between traffic and carbon monoxide (CO) concentrations using ANN model measured near an intersection which was sheltered from the wind by multi-story buildings. They compared ANN and MLR models and reported ANN as the superior model. Viotti et al. (2002) used an ANN model with a hidden layer to predict short-term and medium-term air pollutant concentrations (CO, ozone and benzene) in an urban area of Perugia city. Martin et al. (2008) used ANN and k-nearest neighbors classifiers as predictive tool in order to predicting future peaks of CO. Noori et al. (2008) compared use of ANN and PCA-MLR models in forecasting CO daily concentration in atmosphere of Tehran and reported ANN as the superior model. Modeling and controlling CO concentration using a neuro-fuzzy technique have been used by Tanaka et al. (1995) in a large city of Japan. Prediction results show that the fuzzy model is much better than the linear model. Yildirim and Bayramoglu (2006) proposed adaptive neuro-fuzzy inference system (ANFIS) to estimate the impact of meteorological factors on SO₂ and total suspended particular matter pollution levels over an urban area in Turkey. Carnevale et al. (2009) presented the application of neural network and neuro-fuzzy models to estimate nonlinear source–receptor relationships between precursor emission and pollutant concentrations (ozone and PM₁₀) in Northern Italy. The results show that, despite a large advantage in terms of computational costs, the selected source–receptor models are able to accurately reproduce the simulation of the 3D modeling system.

Input selection is a crucial step in ANN and ANFIS implementation. These techniques are not engineered to eliminate superfluous inputs. In the case of a high number of input variables, irrelevant, redundant, and noisy variables might be included in the data set, simultaneously; meaningful variables could be hidden (Seasholtz and Kowalski, 1993, Noori et al., 2009a). Therefore, reducing input variables is recommended. There are different methods for reducing the number of input variables such as forward selection (FS) (Chen et al., 1989, Wang et al., 2006) and Gamma test (GT) techniques (Corcoran et al., 2003, Moghaddamnia et al., 2009). In comparison with other statistical models, another important subject which rarely has been observed in ANN and ANFIS is uncertainty analysis of results. It is obvious that predictions are not certain; therefore, uncertainty analysis can be effective in application of results. Literature shows that just a few methods proposed for determination of uncertainty in ANN and ANFIS. Some of them are bootstrap and sandwich estimator (Tibshirani, 1994), maximum likelihood and Bayesian inference (Dybowski, 1997) and Mont-Carlo method proposed by Marce et al. (2004). In this research, Mont-Carlo simulation, which is based on locating the models in a Mont-Carlo random sampling process, is selected, because it has not only better performance but also more novelty. Aqil et al. (2007) applied this uncertainty analysis method for evaluating outputs of ANFIS to predict weekly stream flow in the river and reported that it is appropriate for ANFIS model. Noori et al. (2009b) used Mont-Carlo method for uncertainty analysis of solid waste generation forecasting by means of wavelet transform-ANFIS and wavelet transform-ANN.

In this study, two techniques of input selection (FS and GT) have been applied in order to building hybrid models with ANN and ANFIS (FS–ANN, FS–ANFIS, GT–ANN, and GT–ANFIS), then have been compared with ANN and ANFIS fed with all input data. Finally, uncertainty analysis is done for two best models and the superior model is reported.