Water Resources Management

, Volume 33, Issue 10, pp 3563–3577 | Cite as

Uncertainty Analysis on Hybrid Double Feedforward Neural Network Model for Sediment Load Estimation with LUBE Method

  • Xiao-Yun Chen
  • Kwok-Wing ChauEmail author


The assessment of uncertainty prediction has become a necessity for most modeling studies within the hydrology community. This paper addresses uncertainty analysis on a novel hybrid double feedforward neural network (HDFNN) model for generating the sediment load prediction interval (PI). By using the Lower Upper Bound Estimation (LUBE) method, the lower and upper bounds are directly generated as outputs of neural network based models. Coverage Width-based Criterion (CWC) is employed as an objective function for searching high quality PIs. The LUBE-based model is then applied to estimate sediment loads of Muddy Creek in Montana of USA. Results demonstrate the suitability of HDFNN-LUBE model in producing PI in both 90% and 95% confidence levels (CL). It is capable of generating appropriate lower bounds of PIs with narrow intervals. Partitioning analysis reveals consistently excellent performances of HDFNN model in constructing PI in terms of low, medium and high loads. These results therefore verify the reliability and potentiality of the HDFNN model for sediment load estimation with uncertainty. LUBE shows its efficiency in uncertainty prediction as well, which could be used to quantify total uncertainty of data-driven models.


Uncertainty analysis Hybrid double feedforward neural network Sediment load estimation Lower upper bound estimation 



This research was supported by Central Research Grant of Hong Kong Polytechnic University (4-ZZAD).


  1. Alvisi S, Creaco E, Franchini M (2012) Crisp discharge forecasts and grey uncertainty bands using data-driven models. Hydrol Res 43(5):589Google Scholar
  2. Alvisi S, Franchini M (2011) Fuzzy neural networks for water level and discharge forecasting with uncertainty. Environ Model Softw 26(4):523–537Google Scholar
  3. Browning LS, Bauder JW, Hershberger KE, Sessoms H (2005) Irrigation return flow sourcing of sediment and flow augmentation in receiving streams: a case study. J Soil Water Conserv 60(3):134–141Google Scholar
  4. Chen XY, Chau KW (2016) A hybrid double feedforward neural network for suspended sediment load estimation. Water Resour Manag 30(7):2179–2194Google Scholar
  5. Cheng CT, Chau KW (2002) Three-person multi-objective conflict decision in reservoir flood control. Eur J Oper Res 142(3):625–631Google Scholar
  6. He MY (1993) Theory, application and related problems of double parallel feedforward neural networks. Xidian University, Xi'anGoogle Scholar
  7. Khosravi A, Nahavandi S, Creighton D (2011a) Prediction interval construction and optimization for adaptive neurofuzzy inference systems. IEEE Trans Fuzzy Syst 19(5):983–988Google Scholar
  8. Khosravi A, Nahavandi S, Creighton D, Atiya AF (2011b) Lower upper bound estimation method for construction of neural network-based prediction intervals. Neural Netw IEEE Trans 22(3):337–346Google Scholar
  9. Kisi Ö, Fedakar Hİ (2014) Modeling of suspended sediment concentration carried in natural streams using fuzzy genetic approach. Computational Intelligence Techniques in Earth and Environmental Sciences (pp 175–196): SpringerGoogle Scholar
  10. Krzysztofowicz R (1999) Bayesian theory of probabilistic forecasting via deterministic hydrologic model. Water Resour Res 35(9):2739–2750Google Scholar
  11. Kuczera G, Parent E (1998) Monte Carlo assessment of parameter uncertainty in conceptual catchment models: the Metropolis algorithm. J Hydrol 211(1):69–85Google Scholar
  12. Li YT, Gu RR (2003) Modeling flow and sediment transport in a river system using an artificial neural network. Environ Manag 31(1):122–134Google Scholar
  13. Mantovan P, Todini E (2006) Hydrological forecasting uncertainty assessment: incoherence of the GLUE methodology. J Hydrol 330(1):368–381Google Scholar
  14. Maskey S, Guinot V, Price RK (2004) Treatment of precipitation uncertainty in rainfall-runoff modelling: a fuzzy set approach. Adv Water Resour 27(9):889–898Google Scholar
  15. Montanari A (2007) What do we mean by ‘uncertainty’? The need for a consistent wording about uncertainty assessment in hydrology. Hydrol Process 21(6):841–845Google Scholar
  16. Montanari A, Grossi G (2008) Estimating the uncertainty of hydrological forecasts: a statistical approach. Water Resour Res 44(12)Google Scholar
  17. Pianosi F, Lal Shrestha D, Solomatine D (2010) Uncertainty analysis of an inflow forecasting model: extension of the UNEEC machine learning-based method. EGU General Assembly Conference AbstractsGoogle Scholar
  18. Qiu L, Chen SY, Nie XT (1998) A forecast model of fuzzy recognition neural networks and its application. Adv Water Sci 9(3):258–264Google Scholar
  19. Quan H, Srinivasan D, Khosravi A (2014) Particle swarm optimization for construction of neural network-based prediction intervals. Neurocomputing 127:172–180Google Scholar
  20. Rocca P, Oliveri G, Massa A (2011) Differential evolution as applied to electromagnetics. Antennas Propag Mag IEEE 53(1):38–49Google Scholar
  21. Shrestha DL, Solomatine DP (2006) Machine learning approaches for estimation of prediction interval for the model output. Neural Netw 19(2):225–235Google Scholar
  22. Solomatine DP, Shrestha DL (2009) A novel method to estimate model uncertainty using machine learning techniques. Water Resour Res 45(12)Google Scholar
  23. Storn R, Price K (1995) Differential evolution-a simple and efficient adaptive scheme for global optimization over continuous spaces. International Computer Science Institute, BerkeleyGoogle Scholar
  24. Taormina R, Chau KW (2015) ANN-based interval forecasting of streamflow discharges using the LUBE method and MOFIPS. Eng Appl Artif Intell 45:429–440Google Scholar
  25. Thirumalaiah K, Deo MC (1998) River stage forecasting using artificial neural networks. J Hydrol Eng 3(1):26–32Google Scholar
  26. Wang YH, Wang H, Lei XH, Jiang YZ, Song XS (2011) Flood simulation using parallel genetic algorithm integrated wavelet neural networks. Neurocomputing 74(17):2734–2744Google Scholar
  27. Yang RF, Ding J, Liu GD (1998) Preliminary study of hydrology-based artificial neural network. J Hydraulics 8:23–27Google Scholar
  28. Ye L, Zhou J, Gupta HV, Zhang H, Zeng X, Chen L (2016) Efficient estimation of flood forecast prediction intervals via single- and multi-objective versions of the LUBE method. Hydrol Process 30(15):2703–2716Google Scholar
  29. Zhong SS, Ding G (2005) Research on double parallel feedforward process neural networks and its application. Control Decis 20(7):764–768Google Scholar
  30. Zou R, Lung WS, Guo HC (2002) Neural network embedded Monte Carlo approach for water quality modeling under input information uncertainty. J Comput Civ Eng 16(2):135–142Google Scholar

Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Civil and Environmental EngineeringHong Kong Polytechnic UniversityKowloonHong Kong

Personalised recommendations