Modeling and Forecast Biological Oxygen Demand (BOD) using Combination Support Vector Machine with Wavelet Transform

Chemical pollution of surface water is one of the serious issues that threaten the quality of water. This would be more important when the surface waters used for human drinking supply. One of the key parameters used to measure water pollution is BOD. Because many variables affect the water quality parameters and a complex nonlinear relationship between them is established conventional methods can not solve the problem of quality management of water resources. For years, the Artificial Intelligence methods were used for prediction of nonlinear time series and a good performance of them has been reported. Recently, the wavelet transform that is a signal processing method, has shown good performance in hydrological modeling and is widely used. Extensive research has been globally provided in use of Artificial Neural Network and Adaptive Neural Fuzzy Inference System models to forecast the BOD. But support vector machine has not yet been extensively studied. For this purpose, in this study the ability of support vector machine to predict the monthly BOD parameter based on the available data, temperature, river flow, DO and BOD was evaluated.
SVM was introduced in 1992 by Vapnik that was a Russian mathematician. This method has been built based on the statistical learning theory. In recent years the use of SVM, is highly taken into consideration. SVM was used in applications such as handwriting recognition, face recognition and has good results. Linear SVM is simplest type of SVM, consists of a hyperplane that dataset of positive and negative is separated with maximum distance. The suitable separator has maximum distance from every one of two dataset. So about this machine that its output groups label (here -1 to ), the aim is to obtain the maximum distance between categories. This is interpreted to have a maximum margin. Wavelet transform is one of methods in the mathematical science that its main idea was given from Fourier transform that was introduced in the nineteenth-century. Overall, concept of wavelet transform for current theory was presented by Morlet and a team under the supervision of Alex Grossman at the Research Center for Theoretical Physics Marcel in France. After the parameters decomposition using wavelet analysis and using principal component analysis (PCA), the main components were determined. These components are then used as input to the support vector machine model to obtain a hybrid model of Wavelet-SVM (WSVM). For this study, a series of monthly of BOD in Karun River in Molasani station and auxiliary variables dissolved oxygen (DO), temperature and monthly river flow in a 13 years period (2002-2014) were used.
To run the SVM model, seven different combinations were evaluated. Combination 6 which was contained of 4 parameters including BOD, dissolved oxygen (DO), temperature and monthly river flow with a time lag have best performance. The best structure had RMSE equal to 0.0338 and the coefficient of determination equal to 0.84. For achieving the results of the WSVM, the wavelet transform and input parameters were decomposed to sub-signal, then this sub-signals were studied with Principal component analysis (PCA) method and important components were entered as inputs to SVM model to obtain the hybrid model WSVM. After numerous run this program in certain modes and compare them with each other, the results was obtained. One of the key points about the choice of the mother wavelet is the time series. So, the patterns of the mother wavelet functions that can better adapt to diagram curved of time series can do the mappings operation and therefore will have better results. In this study, according to different wavelet tests and according to the above note, four types of mother wavelet functions Haar, Db2, Db7 and Sym3 were selected.
Compare the results of the monthly modeling indicate that the use of wavelet transforms can increase the performance about 5%. Different structures and sensitivity analysis showed that the most important parameter which used in this study was parameter BOD, and then flow, DO and temperature were important. This means that the most effective BOD and temperature with minimum impact. Also between different kernels types, RBF kernel showed the best performance. So, combined wavelet with support vector machine is a new idea to predict BOD value in the Karun River.