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Titel |
Fuzzy Neural Networks for water level and discharge forecasting |
VerfasserIn |
Stefano Alvisi, Marco Franchini |
Konferenz |
EGU General Assembly 2010
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Medientyp |
Artikel
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Sprache |
Englisch
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Digitales Dokument |
PDF |
Erschienen |
In: GRA - Volume 12 (2010) |
Datensatznummer |
250033508
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Zusammenfassung |
A new procedure for water level (or discharge) forecasting under uncertainty using artificial
neural networks is proposed: uncertainty is expressed in the form of a fuzzy number. For this
purpose, the parameters of the neural network, namely, the weights and biases, are
represented by fuzzy numbers rather than crisp numbers. Through the application of the
extension principle, the fuzzy number representative of the output variable (water level or
discharge) is then calculated at each time step on the basis of a set of crisp inputs and fuzzy
parameters of the neural network.
The proposed neural network thus allows uncertainty to be taken into account at the
forecasting stage not providing only deterministic or crisp predictions, but rather predictions
in terms of “the discharge (or level) will fall between two values, indicated according to the
level of credibility considered, whereas it will take on a certain value when the level of
credibility is maximum”.
The fuzzy parameters of the neural network are estimated using a calibration procedure
that imposes a constraint whereby for an assigned h-level the envelope of the
corresponding intervals representing the outputs (forecasted levels or discharges,
calculated at different points in time) must include a prefixed percentage of observed
values.
The proposed model is applied to two different case studies. Specifically, the data related
to the first case study are used to develop and test a flood event-based water level
forecasting model, whereas the data related to the latter are used for continuous discharge
forecasting.
The results obtained are compared with those provided by other data-driven models -
Bayesian neural networks (Neal, R.M. 1992, Bayesian training of backpropagation networks
by the hybrid Monte Carlo method. Tech. Rep. CRG-TR-92-1, Dep. of Comput. Sci., Univ. of
Toronto, Toronto, Ont., Canada.) and the Local Uncertainty Estimation Model (Shrestha D.L.
and Solomatine D.P. 2006, Machine learning approaches for estimation of prediction interval
for the model output. Neural Networks, 19(2), 225-235.). The comparison shows the
effectiveness of the fuzzy neural network forecasting model in estimating water levels or
discharges under uncertainty. In particular, the fuzzy neural network enables us to define
bands that describe, for an assigned h-level, the range of variability of the predicted
variable. An analysis of the results obtained reveals that these bands generally have
a slightly smaller width compared to the bands obtained using other data-driven
models, the percentage of observed values contained within the bands being equal. |
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