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

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Abstract

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.

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Acknowledgements

The authors would like to acknowledge the East Azarbaijan Regional Water Authority for supplying the data. We wish to thank Sasha Rodrigues for improving the manuscript. Partial funding for this research was provided by an NSERC Discovery and CFI Grant held by Dr. Jan Adamowski.

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Authors and Affiliations

  1. Department of Earth Sciences, Faculty of Natural Sciences, University of Tabriz, Tabriz, Iran

    Rahim Barzegar & Asghar Asghari Moghaddam

  2. Department of Bioresource Engineering, McGill University, 21111 Lakeshore, Ste Anne de Bellevue, QC, H9X3V9, Canada

    Jan Adamowski

  3. Department of Environmental Protection and Development, Faculty of Environmental Engineering, Warsaw University of Technology, ul. Nowowiejska 20, 00-653, Warsaw, Poland

    Bogdan Ozga-Zielinski

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  1. Rahim Barzegar
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Correspondence to Rahim Barzegar.

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Barzegar, R., Asghari Moghaddam, A., Adamowski, J. et al. Multi-step water quality forecasting using a boosting ensemble multi-wavelet extreme learning machine model. Stoch Environ Res Risk Assess 32, 799–813 (2018). https://doi.org/10.1007/s00477-017-1394-z

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