Comparison of ARIMA and NNAR Models for Forecasting Water Treatment Plant's Influent Characteristics

  • Afshin Maleki
  • Simin Nasseri
  • Mehri Solaimany Aminabad
  • Mahdi Hadi
Environmental Engineering
First Online:
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Abstract

A reliable forecasting model for each Water Treatment Plant (WTP) influent characteristics is useful for controlling the plant's operation. In this paper Auto-Regressive Integrated Moving Average (ARIMA) and Neural Network Auto-Regressive (NNAR) modeling techniques were applied on a WTP's influent water characteristics time series to make some models for short-term period (to seven days ahead) forecasting. The ARIMA and NNAR models both provided acceptable generalization capability with R2s ranged from 0.44 to 0.91 and 0.45 to 0.92, respectively, for chloride and temperature. Although a more prediction performance was observed for NNAR in comparison with ARIMA for all studied series, the forecasting performance of models was further examined using Time Series Cross-Validation (TSCV) and Diebold-Mariano test. The results showed ARIMA is more accurate than NNAR for forecasting the horizon-daily values for CO2, Cl and Ca time-series. Therefore, despite of the good predictive performance of NNAR, ARIMA may still stands as better alternative for forecasting task of aforementioned series. Thus, as a general rule, not only the predictive performance using R2 statistic but also the forecasting performance of a model using TSCV, are need to be examined and compared for selecting an appropriate forecasting model for WTP's influent characteristics.

Keywords

time series analysis neural network auto-regressive model auto-regressive integrated moving average model water treatment plant forecasting 
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References

  1. Akaike, H. (1974). “A new look at the statistical model identification.” Automatic Control, IEEE Transactions on, Vol. 19, No. 6, pp. 716–723, DOI: 10.1109/TAC.1974.1100705.MathSciNetCrossRefMATHGoogle Scholar
  2. Battiti, R. (1992). “First-and second-order methods for learning: Between steepest descent and Newton's method.” Neural Computation, Vol. 4, No. 2, pp. 141–166, DOI: 10.1162/neco.1992.4.2.141.CrossRefGoogle Scholar
  3. Box, G. E. and Cox, D. R. (1964). “An analysis of transformations.” Journal of the Royal Statistical Society. Series B (Methodological), Vol. 26, No. 2, pp. 211–252.MathSciNetMATHGoogle Scholar
  4. Box, G. E., Jenkins, G. M., and Reinsel, G. C. (2013). Time series analysis: Forecasting and control, John Wiley & Sons, DOI: 10.1002/9781118619193.MATHGoogle Scholar
  5. Diebold, F. X. and Mariano, R. S. (1995). “Comparing predictive accuracy.” Journal of Business & Economic Statistics, Vol. 13, pp. 253–265, DOI: 10.1198/073500102753410444.Google Scholar
  6. Durbin, J. and Watson G. S. (1950). “Testing for serial correlation in least squares regression: I.” Biometrika, Vol. 37, Nos. 3-4, pp. 409–428, DOI: 10.2307/2332391.MathSciNetCrossRefMATHGoogle Scholar
  7. Field, A. (2009). Discovering statistics using SPSS:(and sex and drugs and rock ‘n’roll). 3rd ed, Sage, Los Angeles.Google Scholar
  8. Hadi, M., Mesdaghinia, A., Yunesian, M., Nasseri, S., Nodehi, R. N., Tashauoei, H., Jalilzadeh, E., and Zarinnejad, R. (2016). “Contribution of environmental media to cryptosporidiosis and giardiasis prevalence in Tehran: a focus on surface waters.” Environmental Science and Pollution Research, Vol. 23, No. 19, pp. 19317–19329, DOI: 10.1007/s11356-016-7055-9.CrossRefGoogle Scholar
  9. Hagan, M. T., Demuth, H. B., and Beale, M. H. (1996). Neural network design, Thomson Learning, Singapore.Google Scholar
  10. Hill, T., Marquez, L., O'Connor, M., and Remus, W. (1994). “Artificial neural network models for forecasting and decision making.” International Journal of Forecasting, Vol. 10, No. 1, pp. 5–15, DOI: 10.1016/0169-2070(94)90045-0.CrossRefGoogle Scholar
  11. Ho, S. L., Xie, M., and Goh, T. N. (2002). “A comparative study of neural network and Box-Jenkins ARIMA modeling in time series prediction.” Computers & Industrial Engineering, Vol. 42, Nos. 2-4, pp. 371–375, DOI: 10.1016/S0360-8352(02)00036-0.CrossRefGoogle Scholar
  12. Hosseini, H. G., Luo, D., and Reynolds, K. J. (2006). “The comparison of different feed forward neural network architectures for ECG signal diagnosis.” Medical Engineering & Physics, Vol. 28, No. 4, pp. 372–378, DOI: 10.1016/j.medengphy.2005.06.006.CrossRefGoogle Scholar
  13. Howard, D. and Mark, B. (2000). Neural Network Toolbox For Use with MATLAB: Computation Visualization, Programming, User’s Guide Version 4, MathWorks, Inc.Google Scholar
  14. Hyndman, R. J. and Khandakar, Y. (2007). “Automatic time series for forecasting: The forecast package for R.” Journal of Statistical Softwore, Vol. 27, No. 3, DOI: 10.18637/jss.vo27.i03.Google Scholar
  15. Hyndman, R. J. and Koehler A. B. (2006). “Another look at measures of forecast accuracy.” International Journal of Forecasting, Vol. 22, No. 4, pp. 679–88, DOI: 10.1016/j.ijforecast.2006.03.001.CrossRefGoogle Scholar
  16. Franses, P. H. (2016). “A note on the mean absolute scaled error.” International Journal of Forecasting, Vol. 32, No. 1, pp. 20–22, DOI: 10.1016/j.ijforecast.2015.03.008.CrossRefGoogle Scholar
  17. Jafari Mansoorian, H., Karimaeec, M., Hadi, M., Jame Porazmey, E., Barati, F., and Baziar, M. (2017). “Feed forward artificial neural network model to estimate the TPH removal efficiency in soil washing process.” Archives of Hygiene Sciences, Vol. 6, No. 1, pp. 69–104.Google Scholar
  18. Khashei, M. and Bijari, M. (2010). “An artificial neural network (p, d, q) model for timeseries forecasting.” Expert Systems with Applications, Vol. 37, No. 1, 479–489, DOI: 10.1016/j.eswa.2009.05.044.CrossRefMATHGoogle Scholar
  19. Khodadadi, M., Mesdaghinia, A., Nasseri, S., Ghaneian, M. T., Ehrampoush, M. H., and Hadi, M. (2016). “Prediction of the waste stabilization pond performance using linear multiple regression and multi-layer perceptron neural network: A case study of Birjand.” Iran. Environmental Health Engineering and Management Journal, Vol. 3, pp. 81–89.CrossRefGoogle Scholar
  20. Khashei, M. and Bijari, M. (2011). “A novel hybridization of artificial neural networks and ARIMA models for time series forecasting.” Applied Soft Computing, Vol. 11, No. 2, pp. 2664–2675, DOI: 10.1016/j.asoc.2010.10.015.CrossRefGoogle Scholar
  21. Kusiak, A., Verma, A., and Wei, X. (2012). “A data-mining approach to predict influent quality.” Environmental Monitoring and Assessment, Vol. 185, pp. 2197–2210, DOI: 10.1007/s10661-012-2701-2.CrossRefGoogle Scholar
  22. Ljung, G. M. and Box, G. E. (1978). “On a measure of lack of fit in time series models.” Biometrika, Vol. 65, No. 2, pp. 297–303, DOI: 10.1093/biomet/65.2.297.CrossRefMATHGoogle Scholar
  23. Maest, A. S., Kuipers J., Travers C. L., and Atkins D. A. (2005). Predicting Water Quality at Hardrock Mines: Methods and Models, Uncertainties and State-of-the-art, Earthworks, Washington, DC.Google Scholar
  24. Matalas, N. (1967). “Time series analysis.” Water Resources Research, Vol. 3, No. 3, pp. 817–829, DOI: 10.1029/WR003i003p00817.CrossRefGoogle Scholar
  25. Pankratz, A. (2009). Forecasting with univariate Box-Jenkins models: Concepts and cases, John Wiley & Sons, New Jersey.Google Scholar
  26. Panno, S. V., Keith, C. H., Hwang, H. H., Greenberg, S., Krapac, I. G., Landsberger, S., and O'Kelly, D. J. (2002). “Source identification of sodium and chloride contamination in natural waters: Preliminary results.” In Proceedings, 12th Annual Illinois Groundwater Consortium Symposium, Illinois Groundwater Consortium.Google Scholar
  27. Plazl, I., Pipus, G., Drolka, M., and Koloini, T. (1999). “Parametric sensitivity and evaluation of dynamic model for single-stage wastewater treatment plant.” Acta Chimica Slovenica, Vol. 46, No. 2, pp. 289–300.Google Scholar
  28. R Core Team (2016). R: A language and environment for statistical computing, R Foundation for Statistical Computing, Vienna, Austria. URL: https://www.R-project.org.Google Scholar
  29. Rostami Fasih, Z., Mesdaghinia, A., Nadafi, K., Nabizadeh Nodehi, R., Mahvi, A. H., and Hadi, M. (2015). “Forecasting the air quality index based on meteorological variables and autocorrelation terms using artificial neural network.” Razi Journal of Medical Sciences, Vol. 22, No. 137, pp. 31–43.Google Scholar
  30. Rumelhart, D. E. and McClelland, J. L. (1986). Parallel distributed processing: Explorations in the microstructure of cognition: Foundations, MIT Press Cambridge, MA, USA.Google Scholar
  31. Salas, J. D. Obeysekera J. (1982). “ARMA model identification of hydrologic time series.” Water Resources Research, Vol. 18, No. 4, pp. 1011–1021, DOI: 10.1029/WR018i004p01011.CrossRefGoogle Scholar
  32. Salas, J. D. (1980). Applied modeling of hydrologic time series, Water Resources Publication.Google Scholar
  33. Salas, J. D., Boes, D. C., and Smith, R. A. (1982). “Estimation of ARMA models with seasonal parameters.” Water Resources Research, Vol. 18, No. 4, pp. 1006–1010, DOI: 10.1029/WR018i004p01006.CrossRefGoogle Scholar
  34. Solaimany-Aminabad, M., Maleki, A., and Hadi, M. (2013). “Application of Artificial Neural Network (ANN) for the prediction of water treatment plant influent characteristics.” Journal of Advances in Environmental Health Research, Vol. 1, No. 2, pp. 89–100, DOI: 10.22102/jaehr.2013.40130.Google Scholar
  35. Thoplan, R. (2014). “Simple v/s sophisticated methods of forecasting for mauritius monthly tourist arrival data.” International Journal of Statistics and Applications, Vol. 4, No. 5, pp. 217–223, DOI: 10.5923/j.statistics.20140405.01.Google Scholar
  36. Valipour, M., Banihabib, M. E., and Behbahani, S. M. R. (2013). “Comparison of the ARMA, ARIMA, and the autoregressive artificial neural network models in forecasting the monthly inflow of Dez dam reservoir.” Journal of Hydrology, Vol. 476, pp. 433–441, DOI: 10.1016/j.jhydrol.2012.11.017.CrossRefGoogle Scholar
  37. Wu, G.-D. and Lo, S.-L. (2008). “Predicting real-time coagulant dosage in water treatment by artificial neural networks and adaptive networkbased fuzzy inference system.” Engineering Applications of Artificial Intelligence, Vol. 21, No. 8, pp. 1189–1195, DOI: 10.1016/j.engappai. 2008.03.015.CrossRefGoogle Scholar
  38. Wu, G.-D. and Lo, S.-L. (2010). “Effects of data normalization and inherentfactor on decision of optimal coagulant dosage in water treatment by artificial neural network.” Expert Systems with Applications, Vol. 37, No. 7, pp. 4974–4983, DOI: 10.1016/j.eswa.2009.12.016.CrossRefGoogle Scholar
  39. Zhang, G., Eddy Patuwo, B. Y and Hu M. (1998). “Forecasting with artificial neural networks: The state of the art.” International Journal of Forecasting, Vol. 14, No. 1, pp. 35–62, DOI: 10.1016/S0169-2070(97)00044-7.CrossRefGoogle Scholar
  40. Zhang, G. P. (2003). “Time series forecasting using a hybrid ARIMA and neural network model.” Neurocomputing, Vol. 50, pp.159–175, DOI: 10.1016/S0925-2312(01)00702-0.CrossRefMATHGoogle Scholar
  41. Zhang, G. P. and Qi, M. (2005). “Neural network forecasting for seasonal and trend time series.” European Journal of Operational Research, Vol. 160, No. 2, pp. 501–514, DOI: 10.1016/j.ejor.2003.08.037.CrossRefMATHGoogle Scholar

Copyright information

© Korean Society of Civil Engineers 2018

Authors and Affiliations

  • Afshin Maleki
    • 1
  • Simin Nasseri
    • 2
    • 3
  • Mehri Solaimany Aminabad
    • 1
  • Mahdi Hadi
    • 2
  1. 1.Dept. of Environmental Health Engineering, Environmental Health Research CenterKurdistan University of Medical SciencesSanandajIran
  2. 2.Center for Water Quality Research (CWQR), Institute for Environmental Research (IER)Tehran University of Medical SciencesTehranIran
  3. 3.Dept. of Environmental Health Engineering, School of Public HealthTehran University of Medical SciencesTehranIran

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