An integrated wavelet-support vector machine for groundwater level prediction in Visakhapatnam, India
Introduction
Groundwater management has been a major cause of concern because of the ever increasing demand of water for industrial, agricultural and domestic needs. In India and in many other parts of the world, groundwater depletion has been a common cause of concern for engineers. Further, the prediction of the groundwater levels in a basin is of immense importance for the management of groundwater resources. The prediction of groundwater is very complex and highly nonlinear in nature as it depends upon many complex factors such as precipitation, evapotranspiration, soil characteristics and topography of the watershed. Nonlinear empirical models and data driven models [1], [2], [3], [4] have been used in the forecasting studies in many areas of science and engineering. In the recent decades, machine learning models are employed in modeling nonlinear processes that are complex in nature [5], particularly in problems of flow prediction where ANN has been widely used [6]. Besides neural networks, other very recent techniques such as SVM [7], [8], [9], genetic programming [10] and probabilistic graphical models such as Bayesian networks [3], [4] are found to be effective in modeling virtually any nonlinear function. Bayesian networks take into account the causal relationship between random variables statistically. Support vector machines are found to perform well compared to the other techniques [11], [12].
The concept of a support vector machine (SVM) has been developed recently by Cortes and Vapnik [13]. SVM not only possesses the strength of ANN but it also overcomes some of the major problems associated with ANN. In the context of hydrology, SVM has proved to be a promising tool. It has many applications like forecasting flood stage [14], extension of rating curve [15], forecasting future water levels [16], long term discharges [12], [17], estimation of removal efficiency of settling basins in canals [18], developing pedotransfer functions for water retention soils [19], developing probabilistic reservoir operation model [20], forecasting monthly time discharge [21], statistical downscaling [22], designing optimal insitu bioremediation [23] and so on.
In the present study, the SVR is chosen to forecast groundwater level. When making a decision regarding water management, the hydrologists consider results from many types of techniques that help them to achieve their objective. Relying on a single technique can be very risky particularly in water resources management as the results of the decision are very sensitive, effecting lives of people of a region. Combining several techniques to form a hybrid tool has become a common practice to improve the accuracy of predicted results where the unique features of all the models are combined to capture different patterns in the data. Theoretical as well as empirical findings suggest that hybrid methods can be effective and efficient in improving forecasts [24]. In the present work, SVR method coupled with the wavelet techniques is used to increase the efficiency of the model.
Wavelets are a mathematical expression which decomposes the original time series into various components. The wavelet components thus obtained are very helpful for improving the forecasting capability of a model by capturing useful information at various levels. Wavelet transforms proved to perform better compared to the traditional Fourier transforms [11]. In this study wavelet analysis is used to decompose the time series of groundwater depths into various components. The decomposed components are thus used as inputs for the SVR model.
The purpose of this paper is to investigate the performance of the wavelet-support vector regression model in predicting the ground water depths and to compare this with the performance of other existing models like Support Vector Regression model, Artificial Neural Networks and Auto Regressive Integrated Moving Average. The organization of the paper is as follows. Section 2 details the formulation of support vector machines. Section 3 describes the discrete wavelet transform. Section 4 gives the details of the study area and collected data. Section 5 deals with the details of proposed hybrid wavelet-support vector regression (WA-SVR) model. Section 6 describes the models developed for comparing forecast performance of the proposed WA-SVR model. In Section 7 results and discussions are given. Finally the summary and conclusions are presented in Section 8.
Section snippets
Support vector machines
Support Vector Machines is a data learning tool. SVM performs data regression and pattern recognition. A support vector machine constructs a set of hyper-plane in an infinite dimensional space. The SVM equations are formulated as per Vapnik׳s theory [13]. Let be assumed to be the given training data sets, where represents the input space of the sample and for represents respective target value, l denotes the number of elements in the training data set. The
Discrete wavelet transform
Wavelet transform is used in analyzing data because of it׳s capacity to extract the relevant time-frequency information from non-periodic and transient signals. Wavelets׳ decomposes the frequency components of signals. Wavelet functions disintegrate the data into different frequency components, and then study each component with a resolution matched to its scale thus overcoming the limitations of Fourier and Short-time Fourier transform. Wavelets are widely used in different fields of civil
Study area
Visakhapatnam city is located in Andhra Pradesh along the east coast of India at latitude 17°45′ North and longitude 83°16′ East. The main source of water supply in the study area is impounded water reservoirs in the city. In the recent decades, there has been a rapid industrial expansion in and around the city resulting in a significant diversion of surface water for meeting the industrial requirements. Hence groundwater is being used as an alternative source to meet the domestic water needs.
WA-SVR model development
The wavelet support vector machine (WA-SVR) model is developed for predicting the groundwater depth for the three observation wells located at Sivajipalem, Madhurawada and Gullalapalem. The details of the wavelet decomposition time series and details regarding the input parameters are discussed briefly in this section.
WA-SVR models are formed by combining the decomposing capabilities of wavelet with support vector machines. MATLAB Wavelet toolbox [33] is used in this study. The input data of
Models for comparing forecast performance
The prediction accuracy of the proposed WA-SVR model is compared with the normal Support Vector Regression (SVR) model, Artificial Neural Networks (ANN) model and also with traditional Auto Regressive Integrated Moving Average (ARIMA) model.
Results and discussion
The input combinations of best WA-SVR model are different for different wells. For Sivajipalem well, the best WA-SVR model is a function of the monthly precipitation, maximum temperature and groundwater levels from the current month (t) and previous month (t−1). For Madhurawada and Gullalapalem wells, the best WA-SVR model is a function of the monthly precipitation, maximum temperature and groundwater levels from the current month (t), previous month (t−1) and 2 months earlier (t−2). The models
Summary and conclusions
In the present study, the prediction capability of an Integrating model with Discrete Wavelet Transform and Support Vector Regression has been investigated to predict the monthly groundwater levels at three observation wells in the Visakhapatnam city viz, Sivajipalem, Madhurawada and Gullalapalem observation wells. To study the accuracy of WA-SVR model, other models such as SVR, ANN and ARIMA are developed. The multivariate time series analysis is performed by considering the various
Acknowledgments
The authors wish to thank the Directors and other authorities of A.P. State Groundwater Board and Indian Meteorological Department for providing necessary data for carrying out this work. We also acknowledge the support rendered by Mr. K.S. Sastry, Deputy Director, State Groundwater Board–Visakhapatnam during this work. We also thank the reviewers of this paper whose comments have significantly improved its quality.
Ch. Suryanarayana received his M.Tech in Water Resources Engineering from Indian Institute of Technology, Delhi. Currently he is pursuing his Ph.D. from Andhra University College of Engineering, Visakhapatnam, India. He is working as an Assistant Professor in Civil Engineering Department, G.V.P. College of Engineering, Visakhapatnam. His research interests include groundwater modeling and optimization of water resource management.
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Ch. Suryanarayana received his M.Tech in Water Resources Engineering from Indian Institute of Technology, Delhi. Currently he is pursuing his Ph.D. from Andhra University College of Engineering, Visakhapatnam, India. He is working as an Assistant Professor in Civil Engineering Department, G.V.P. College of Engineering, Visakhapatnam. His research interests include groundwater modeling and optimization of water resource management.
Ch. Sudheer received his Ph.D. in Water resources from Indian Institute of Technology Delhi. Currently he is a Senior Project Scientist in Civil engineering Department at IIT Delhi. His research interests include Groundwater Contamination, Bioremediation of Soils, Design of landfills, Developing mathematical models for Malaria transmission.
Vazeer Mahammood is a professor of Civil Engineering in Andhra University College of Engineering, Visakhapatnam, India. He has Master of Engineering in Hydraulics, Coastal & Harbour engineering. He has also done M.Tech in Remote Sensing & GIS from CSSTEAP (affiliated to United Nations) and Ph.D. in Water Resources Engineering. He is guiding research works in water resources engineering and applied remote sensing & GIS. He has done major research projects funded by UGC. He is consultant for many governmental civil engineering works.
B.K. Panigrahi is an Associate Professor with the Department of Electrical Engineering, Indian Institute of Technology (IIT), New Delhi. His main research focuses on the development of advanced DSP tools and machine intelligence techniques for power quality studies, protection of power systems, etc. He also works in the area of application of evolutionary computing techniques to solve the problems related to power system planning, operation, and control.