Abstract
An investigation is presented in this paper to study the performance of Artificial Intelligence running Multiple Models (AIMM) using time series of river flows. This is a modelling strategy, which is formed by first running two Artificial Intelligence (AI) models: Support Vector Machine (SVM) and its hybrid with the Fire-Fly Algorithm (FFA) and they both form supervised learning at Level 1. The outputs of Level 1 models serve as inputs to another AI Model at Level 2. The AIMM strategy at Level 2 is run by Artificial Neural Network (MM-ANN) and this is compared with the Simple Averaging (MM-SA) of both inputs. The study of the performances of these models (SVM, SVM-FFA, MM-SA and MM-ANN) in the paper shows that the ability of SVM-FFA in matching observed values is significantly better than that of SVM and that of MM-ANN is considerably better than each SVM and/or SVM-FFA but the performances are deteriorated by using the MM-SA strategy. The results also show that the residuals of MM-ANN are less noisy than those shown by the models at Level 1 and those at Level 2 do not display any trend.
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Al-Shammari ET, Mohammadi K, Keivani A et al (2016) Prediction of daily dewpoint temperature using a model combining the support vector machine with firefly algorithm. J Irrig Drain Eng. https://doi.org/10.1061/(ASCE)IR.1943-4774.0001015
Ch S, Anand N, Panigrahi BK, Mathur S (2013) Streamflow forecasting by SVM with quantum behaved particle swarm optimization. Neurocomputing 101:18–23. https://doi.org/10.1016/j.neucom.2012.07.017
Ch S, Sohani SK, Kumar D, et al (2014) A support vector machine-firefly algorithm based forecasting model to determine malaria transmission. Neurocomputing 129:279–288. https://doi.org/10.1016/j.neucom.2013.09.030
Clemen RT (1989) Combining forecasts: a review and annotated bibliography. Int J Forecast 5(4):559–583
Collobert R, Williamson RC (2001) SVM torch: support vector Machines for Large-Scale Regression Problems. J Mach Learn Res 1:143–160. https://doi.org/10.1162/15324430152733142
Fahimi F, Yaseen ZM, El-shafie A (2016) Application of soft computing based hybrid models in hydrological variables modeling: a comprehensive review. Theor Appl Climatol:1–29. https://doi.org/10.1007/s00704-016-1735-8
Ghorbani MA, Khatibi R, Goel A et al (2016a) Modeling river discharge time series using support vector machine and artificial neural networks. Environ Earth Sci 75:685. https://doi.org/10.1007/s12665-016-5435-6
Ghorbani MA, Zadeh HA, Isazadeh M, Terzi O (2016b) A comparative study of artificial neural network (MLP, RBF) and support vector machine models for river flow prediction. Environ Earth Sci 75:476. https://doi.org/10.1007/s12665-015-5096-x
Ghorbani MA, Shamshirband S, Zare Haghi D et al (2017) Application of firefly algorithm-based support vector machines for prediction of field capacity and permanent wilting point. Soil Tillage Res 172:32–38. https://doi.org/10.1016/j.still.2017.04.009
Kadkhodaie-Ilkhchi A, Rezaee MR, Rahimpour-Bonab H, Chehrazi A (2009) Petro physical data prediction from seismic attributes using committee fuzzy interference system. Comput Geosci 35:2314–2330
Karush W (1939) Minima of Functions of Several Variables with Inequalities as Side Conditions. Masters Thesis, University of Chicago
Khatibi R, Ghorbani MA, Kashani MH, Kisi O (2011) Comparison of three artificial intelligence techniques for discharge routing. J Hydrol 403:201–212. https://doi.org/10.1016/j.jhydrol.2011.03.007
Khatibi R, Sivakumar B, Ghorbani MA, et al (2012) Investigating chaos in river stage and discharge time series. J Hydrol 414–415:108–117. doi: https://doi.org/10.1016/j.jhydrol.2011.10.026
Khatibi R, Ghorbani MA, Akhoni Pourhosseini F (2017) Stream flow predictions using nature-inspired firefly algorithms and a multiple model strategy – directions of innovation towards next generation practices. Adv Eng Inform 34:80–89. https://doi.org/10.1016/j.aei.2017.10.002
Kuhn HW, Tucker AW (1951) Nonlinear Programming. In Proceedings of the 2nd Berkley Symposium. University of California Press pp. 481–492
Nadiri AA, Fijani E, Tsai FTC, Asgharimoghaddam A (2013) Supervised committee machine with artificial intelligence for prediction of fluoride concentration. J Hydroinf 15(4):1474–1490
Nadiri A, Hassan MM, Asadi S (2015) Supervised intelligence committee machine to evaluate field performance of photocatalytic asphalt pavement for ambient air purification. Transportation Research Record: Trans Res B 2528:96–105
Nadiri AA, Gharekhani M, Khatibi R et al (2016) Groundwater vulnerability indices conditioned by supervised intelligence committee machine (SICM). Sci Total Environ 574:691–706. https://doi.org/10.1016/j.scitotenv.2016.09.093
Najah A, El-shafie A, Karim OA et al (2011) An application of different artificial intelligences techniques for water quality prediction. Int J Phys Sci 6:5298–5308. https://doi.org/10.5897/IJPS11.1180
Raheli B, Aalami MT, El-Shafie M et al (2017) Uncertainty assessment of the multilayer perceptron (MLP) neural network model with implementation of the novel hybrid MLP-FFA method for prediction of biochemical oxygen demand and dissolved oxygen: a case study of Langat River. Environ Earth Sci 76:503. https://doi.org/10.1007/s12665-017-6842-z
Rubio G, Pomares H, Rojas I, Herrera LJ (2011) A heuristic method for parameter selection in LS-SVM: application to time series prediction. Int J Forecast 27:725–739. https://doi.org/10.1016/j.ijforecast.2010.02.007
Shamshirband S, Mohammadi K, Tong CW et al (2016) A hybrid SVM-FFA method for prediction of monthly mean global solar radiation. Theor Appl Climatol 125:53–65. https://doi.org/10.1007/s00704-015-1482-2
Tayfur G, Nadiri AA, Asgharimoghaddam A (2014) Supervised intelligent committee machine method for hydraulic conductivity estimation. Water Resour Manag 28(4):1173–1184
Vapnik VN (2000) The Nature of Statistical Learning Theory. Springer New York
Wang WC, Chau KW, Cheng CT, Qiu L (2009) A comparison of performance of several artificial intelligence methods for forecasting monthly discharge time series. J Hydrol 374:294–306. https://doi.org/10.1016/j.jhydrol.2009.06.019
Willmott CJ (1981) On the validation of models. Phys Geogr 2:184–194. https://doi.org/10.1080/02723646.1981.10642213
Xiong T, Bao Y, Hu Z (2014) Multiple-output support vector regression with a firefly algorithm for interval-valued stock price index forecasting. Knowledge-Based Syst 55:87–100. https://doi.org/10.1016/j.knosys.2013.10.012
Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-inspired Comput 2(2):78–84. https://doi.org/10.1504/IJBIC.2010.032124
Yu X, Liong S, Babovic V (2004) EC-SVM approach for real-time hydrologic forecasting. J Hydroinf 3:209–223
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Ghorbani, M.A., Khatibi, R., Karimi, V. et al. Learning from Multiple Models Using Artificial Intelligence to Improve Model Prediction Accuracies: Application to River Flows. Water Resour Manage 32, 4201–4215 (2018). https://doi.org/10.1007/s11269-018-2038-x
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DOI: https://doi.org/10.1007/s11269-018-2038-x