Journal
IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS
Volume 26, Issue 11, Pages 2787-2800Publisher
IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC
DOI: 10.1109/TNNLS.2015.2396933
Keywords
Interval-valued neural networks (NNs); multi-objective genetic algorithm (MOGA); prediction intervals (PIs); short-term wind speed forecasting; uncertainty
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We consider the task of performing prediction with neural networks (NNs) on the basis of uncertain input data expressed in the form of intervals. We aim at quantifying the uncertainty in the prediction arising from both the input data and the prediction model. A multilayer perceptron NN is trained to map interval-valued input data onto interval outputs, representing the prediction intervals (PIs) of the real target values. The NN training is performed by nondominated sorting genetic algorithm-II, so that the PIs are optimized both in terms of accuracy (coverage probability) and dimension (width). Demonstration of the proposed method is given in two case studies: 1) a synthetic case study, in which the data have been generated with a 5-min time frequency from an autoregressive moving average model with either Gaussian or Chi-squared innovation distribution and 2) a real case study, in which experimental data consist of wind speed measurements with a time step of 1 h. Comparisons are given with a crisp (single-valued) approach. The results show that the crisp approach is less reliable than the interval-valued input approach in terms of capturing the variability in input.
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