Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter
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TY - CHAP
T1 - Identification and representation of state dependent non-linearities in flood forecasting using the DBM methodology
AU - Beven, Keith
AU - Leedal, David
AU - Smith, Paul
AU - Young, Peter
PY - 2012
Y1 - 2012
N2 - This paper addresses the issue of identifying a state dependent input nonlinearity in a Data Based Mechanistic (DBM) flood forecasting model based on the data rather than some prior conceptualisation of nonlinearity in the system response. Four forms of nonlinear function are presented. A power law may be useful when the input non-linearity is simple. The Radial Basis Function (RBF) network method is appropriate for systems that exhibit well defined but complex input non-linearities. The Piecewise Cubic Hermite Data Interpolation (PCHIP) method also provides the flexibility to map complex input non-linearity shapes while providing the ability to maintain a natural curve. Overfit to the calibration data is a risk in both RBF and PCHIP methods when a large number of knots are used. The Takagi-Sugeno Fuzzy Inference method, together with interactive tuning, provides an alternative approach that allows human-in-the-loop interaction during the parameter estimation process but is not optimal in any statistical sense. Future work will explore the use of these methods with continuous time transfer functions and optimisation of the nonlinear function at the same time as the transfer function.
AB - This paper addresses the issue of identifying a state dependent input nonlinearity in a Data Based Mechanistic (DBM) flood forecasting model based on the data rather than some prior conceptualisation of nonlinearity in the system response. Four forms of nonlinear function are presented. A power law may be useful when the input non-linearity is simple. The Radial Basis Function (RBF) network method is appropriate for systems that exhibit well defined but complex input non-linearities. The Piecewise Cubic Hermite Data Interpolation (PCHIP) method also provides the flexibility to map complex input non-linearity shapes while providing the ability to maintain a natural curve. Overfit to the calibration data is a risk in both RBF and PCHIP methods when a large number of knots are used. The Takagi-Sugeno Fuzzy Inference method, together with interactive tuning, provides an alternative approach that allows human-in-the-loop interaction during the parameter estimation process but is not optimal in any statistical sense. Future work will explore the use of these methods with continuous time transfer functions and optimisation of the nonlinear function at the same time as the transfer function.
U2 - 10.1007/978-0-85729-974-1_17
DO - 10.1007/978-0-85729-974-1_17
M3 - Chapter
SN - 978-0-85729-973-4
SP - 341
EP - 366
BT - System Identification, Environmental Modelling and Control Systems Design
A2 - Wang, Liuping
A2 - Garnier, Hugues
PB - Springer Verlag
CY - London
ER -