Abstract
A level crossing predictor or alarm system with prediction horizon k is said to be optimal if it, at time t detects that an upcrossing will occur at time t + k, with a certain high probability and simultaneously gives a minimum number of false alarms. For a Gaussian stationary process, the optimal level crossing predictor can be explicitly specified in terms of the predicted value of the process itself and of its derivative. To the authors knowledge this simple optimal solution has not been used to any substantial degree. In this paper it is shown how a neural network can be trained to approximate an optimal alarm system arbitrarily well. As in other methods of parametrization, the choice of model structure, as well as an appropriate representation of data, are crucial for a good result. Comparative studies are presented for two Gaussian ARMA-processes, for which the optimal predictor can be derived theoretically. These studies confirm that a properly trained neural network can indeed approximate an optimal alarm system quite well – with due attention paid to the problems of model structure and representation of data. The technique is also tested on a strongly non-Gaussian Duffing process with satisfactory results.
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Jan Holst, deceased March 3, 2006.
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Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
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Grage, H., Holst, J., Lindgren, G. et al. Level Crossing Prediction with Neural Networks. Methodol Comput Appl Probab 12, 623–645 (2010). https://doi.org/10.1007/s11009-009-9153-3
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DOI: https://doi.org/10.1007/s11009-009-9153-3
Keywords
- ARMA-process
- Detection probability
- Duffing oscillator
- False alarm
- Gaussian process
- Operating characteristic
- Optimal alarm
- Weight decay