Multi-step water quality forecasting using a boosting ensemble multi-wavelet extreme learning machine model

The use of electrical conductivity (EC) as a water quality indicator is useful for estimating the mineralization and salinity of water. The objectives of this study were to explore, for the first time, extreme learning machine (ELM) and wavelet-extreme learning machine hybrid (WA-ELM) models to forecast multi-step-ahead EC and to employ an integrated method to combine the advantages of WA-ELM models, which utilized the boosting ensemble method. For comparative purposes, an adaptive neuro-fuzzy inference system (ANFIS) model, and a WA-ANFIS model, were also developed. The study area was the Aji-Chay River at the Akhula hydrometric station in Northwestern Iran. A total of 315 monthly EC (µS/cm) datasets (1984–2011) were used, in which the first 284 datasets (90% of total datasets) were considered for training and the remaining 31 (10% of total datasets) were used for model testing. Autocorrelation function (ACF) and partial autocorrelation function (PACF) demonstrated that the 6-month lags were potential input time lags. The results illustrated that the single ELM and ANFIS models were unable to forecast the multi-step-ahead EC in terms of root mean square error (RMSE), coefficient of determination (R2) and Nash–Sutcliffe model efficiency coefficient (NSC). To develop the hybrid WA-ELM and WA-ANFIS models, the original time series of lags as inputs, and time series of 1, 2 and 3 month-step-ahead EC values as outputs, were decomposed into several sub-time series using different maximal overlap discrete wavelet transform (MODWT) functions, namely Daubechies, Symlet, Haar and Coiflet of different orders at level three. These sub-time series were then used in the ELM and ANFIS models as an input dataset to forecast the multi-step-ahead EC. The results indicated that single WA-ELM and WA-ANFIS models performed better than any ELM and ANFIS models. Also, WA-ELM models outperformed WA-ANFIS models. To develop the boosting multi-WA-ELM and multi-WA-ANFIS ensemble models, a least squares boosting (LSBoost) algorithm was used. The results showed that boosting multi-WA-ELM and multi-WA-ANFIS ensemble models outperformed the individual WA-ELM and WA-ANFIS models.

[1]  R. Deo,et al.  Forecasting effective drought index using a wavelet extreme learning machine (W-ELM) model , 2017, Stochastic Environmental Research and Risk Assessment.

[2]  Rahim Barzegar,et al.  Assessment of heavy metals concentrations with emphasis on arsenic in the Tabriz plain aquifers, Iran , 2015, Environmental Earth Sciences.

[3]  Christopher Heil,et al.  Continuous and Discrete Wavelet Transforms , 1989, SIAM Rev..

[4]  Rahim Barzegar,et al.  Combining the advantages of neural networks using the concept of committee machine in the groundwater salinity prediction , 2016, Modeling Earth Systems and Environment.

[5]  J. Adamowski,et al.  A wavelet neural network conjunction model for groundwater level forecasting , 2011 .

[6]  Yunqian Ma,et al.  Another look at statistical learning theory and regularization , 2009, Neural Networks.

[7]  E. Tziritis,et al.  Assessing the hydrogeochemistry and water quality of the Aji-Chay River, northwest of Iran , 2016, Environmental Earth Sciences.

[8]  Jan Adamowski,et al.  Using discrete wavelet transforms to analyze trends in streamflow and precipitation in Quebec and Ontario (1954–2008) , 2012 .

[9]  J. Adamowski.  Development of a short-term river flood forecasting method for snowmelt driven floods based on wavelet and cross-wavelet analysis , 2008 .

[10]  A. Walden,et al.  Wavelet Methods for Time Series Analysis , 2000 .

[11]  R. Schapire.  The Strength of Weak Learnability , 1990, Machine Learning.

[12]  Mahmud Güngör,et al.  Monthly total sediment forecasting using adaptive neuro fuzzy inference system , 2010 .

[13]  ChunTian Cheng,et al.  Monthly discharge forecasting using wavelet neural networks with extreme learning machine , 2014, Science China Technological Sciences.

[14]  R. Maheswaran,et al.  Wavelet–Volterra coupled model for monthly stream flow forecasting , 2012 .

[15]  Daoliang Li,et al.  A hybrid approach of support vector regression with genetic algorithm optimization for aquaculture water quality prediction , 2013, Math. Comput. Model..

[16]  Mohamad Javad Alizadeh,et al.  Development of wavelet-ANN models to predict water quality parameters in Hilo Bay, Pacific Ocean. , 2015, Marine pollution bulletin.

[17]  Jan Adamowski,et al.  Short-term SPI drought forecasting in the Awash River Basin in Ethiopia using wavelet transforms and machine learning methods , 2016, Sustainable Water Resources Management.

[18]  S. Mallat.  A wavelet tour of signal processing , 1998 .

[19]  G. Visconti,et al.  A Neural Network Approach to Real-Time Rainfall Estimation for Africa Using Satellite Data , 2003 .

[20]  Jan Adamowski,et al.  Multiscale streamflow forecasting using a new Bayesian Model Average based ensemble multi-wavelet Volterra nonlinear method , 2013 .

[21]  Mahmut Firat,et al.  Adaptive Neuro-Fuzzy Inference System for drought forecasting , 2009 .

[22]  T. Ouarda,et al.  Estimation of water quality characteristics at ungauged sites using artificial neural networks and canonical correlation analysis , 2011 .

[23]  Yu Lei,et al.  Prediction of length-of-day using extreme learning machine , 2015 .

[24]  Mohd Tahir Ismail,et al.  A Comparative Study between Discrete Wavelet Transform and Maximal Overlap Discrete Wavelet Transform for Testing Stationarity , 2013 .

[25]  Ercan Kahya,et al.  Daily precipitation predictions using three different wavelet neural network algorithms by meteorological data , 2015, Stochastic Environmental Research and Risk Assessment.

[26]  Shahaboddin Shamshirband,et al.  The use of ELM-WT (extreme learning machine with wavelet transform algorithm) to predict exergetic performance of a DI diesel engine running on diesel/biodiesel blends containing polymer waste , 2016 .

[27]  Wensheng Wang,et al.  Wavelet Network Model and Its Application to the Prediction of Hydrology , 2003 .

[28]  Yi Wang,et al.  Monthly water quality forecasting and uncertainty assessment via bootstrapped wavelet neural networks under missing data for Harbin, China , 2013, Environmental Science and Pollution Research.

[29]  W M Davis.  THE CACHAR EARTHQUAKE OF 1869. , 1883, Science.

[30]  Vladimir Novotny,et al.  Water Quality Management , 1980 .

[31]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[32]  Durdu Ömer Faruk.  A hybrid neural network and ARIMA model for water quality time series prediction , 2010, Eng. Appl. Artif. Intell..

[33]  Cui Dong-wen.  Application of extreme learning machine to total phosphorus and total nitrogen forecast in lakes and reservoirs , 2013 .

[34]  O. Kisi,et al.  Wavelet and neuro-fuzzy conjunction model for precipitation forecasting , 2007 .

[35]  John R. Olson,et al.  The reference condition: predicting benchmarks for ecological and water-quality assessments , 2010, Journal of the North American Benthological Society.

[36]  Santosh Kumar Nanda,et al.  A Cascaded Fuzzy Inference System for Indian river water quality prediction , 2011, Adv. Eng. Softw..

[37]  Jan Adamowski,et al.  Trend detection in surface air temperature in Ontario and Quebec, Canada during 1967–2006 using the discrete wavelet transform , 2013 .

[38]  Z. Zeng,et al.  Extreme learning machine for the displacement prediction of landslide under rainfall and reservoir level , 2014, Stochastic Environmental Research and Risk Assessment.

[39]  Michiel C. van Wezel,et al.  A support system for predicting eBay end prices , 2008, Decis. Support Syst..

[40]  J. Adamowski,et al.  Application of wavelet-artificial intelligence hybrid models for water quality prediction: a case study in Aji-Chay River, Iran , 2016, Stochastic Environmental Research and Risk Assessment.

[41]  Jan Adamowski,et al.  Urban water demand forecasting and uncertainty assessment using ensemble wavelet‐bootstrap‐neural network models , 2013 .

[42]  O. Kisi.  Wavelet Regression Model as an Alternative to Neural Networks for River Stage Forecasting , 2011 .

[43]  Ozgur Kisi,et al.  Wavelet regression model as an alternative to neural networks for monthly streamflow forecasting , 2009 .

[44]  R. Barzegar,et al.  Comparative evaluation of artificial intelligence models for prediction of uniaxial compressive strength of travertine rocks, Case study: Azarshahr area, NW Iran , 2016, Modeling Earth Systems and Environment.

[45]  Victor C. M. Leung,et al.  Applying a new localized generalization error model to design neural networks trained with extreme learning machine , 2014, Neural Computing and Applications.

[46]  Shuangyin Liu,et al.  Study of short-term water quality prediction model based on wavelet neural network , 2013, Math. Comput. Model..

[47]  Chee Kheong Siew,et al.  Extreme learning machine: Theory and applications , 2006, Neurocomputing.

[48]  Guoyin Wang,et al.  An Improved Hybrid ARIMA and Support Vector Machine Model for Water Quality Prediction , 2014, RSKT.

[49]  Shengli Wu,et al.  Effective Neural Network Ensemble Approach for Improving Generalization Performance , 2013, IEEE Transactions on Neural Networks and Learning Systems.

[50]  Jian Zhang,et al.  A wavelet extreme learning machine , 2015, Neural Computing and Applications.

[51]  Hongjian Zhang,et al.  A Hybrid Methodology for Salinity Time Series Forecasting Based on Wavelet Transform and NARX Neural Networks , 2014, Arabian Journal for Science and Engineering.

[52]  Yoav Freund,et al.  Experiments with a New Boosting Algorithm , 1996, ICML.

[53]  Jan Adamowski,et al.  Development of a coupled wavelet transform and neural network method for flow forecasting of non-perennial rivers in semi-arid watersheds. , 2010 .

[54]  Mohammad H. Aminfar,et al.  A combined neural-wavelet model for prediction of Ligvanchai watershed precipitation , 2009, Eng. Appl. Artif. Intell..

[55]  Asghar Asghari Moghaddam,et al.  A supervised committee machine artificial intelligent for improving DRASTIC method to assess groundwater contamination risk: a case study from Tabriz plain aquifer, Iran , 2016, Stochastic Environmental Research and Risk Assessment.

[56]  Sanaz Imen.  Drinking Water Infrastructure Assessment with Teleconnection Signals, Satellite Data Fusion and Mining , 2015 .

[57]  Junfei Qiao,et al.  An efficient self-organizing RBF neural network for water quality prediction , 2011, Neural Networks.

[58]  雛元 孝夫,et al.  ウェーブレット変換の基礎 = Wavelets made easy , 2000 .

[59]  Barnali M. Dixon,et al.  Optimization of DRASTIC method by supervised committee machine artificial intelligence to assess groundwater vulnerability for Maragheh–Bonab plain aquifer, Iran , 2013 .

[60]  K. P. Sudheer,et al.  A data‐driven algorithm for constructing artificial neural network rainfall‐runoff models , 2002 .

[61]  Rathinasamy Maheswaran,et al.  Comparative study of different wavelets for hydrologic forecasting , 2012, Comput. Geosci..