Level crossing prediction with neural networks
Grage, Halfdan LU ; Holst, Jan LU ; Lindgren, Georg LU
and Saklak, Mietek
(2010)
In Methodology and Computing in Applied Probability
63(Online First).
p.623-645
- 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... (More)
- 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. (Less)
Please use this url to cite or link to this publication:
https://lup.lub.lu.se/record/1457411
- author
- Grage, Halfdan
LU
; Holst, Jan
LU
; Lindgren, Georg
LU
and Saklak, Mietek
- organization
- publishing date
- 2010
- type
- Contribution to journal
- publication status
- published
- subject
- keywords
- ARMA-process - Detection probability - Duffing oscillator - False alarm - Gaussian process - Operating characteristic - Optimal alarm - Weight decay
- in
- Methodology and Computing in Applied Probability
- volume
- 63
- issue
- Online First
- pages
- 623 - 645
- publisher
- Springer
- external identifiers
-
- wos:000283614400006
- scopus:77957319081
- ISSN
- 1573-7713
- DOI
- 10.1007/s11009-009-9153-3
- language
- English
- LU publication?
- yes
- additional info
- "Online First" Published online: 13 August 2009.
- id
- 27039326-1ab6-43fc-b82a-97926077061e (old id 1457411)
- date added to LUP
- 2016-04-04 08:02:16
- date last changed
- 2022-01-29 02:59:47
@article{27039326-1ab6-43fc-b82a-97926077061e,
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.}},
author = {{Grage, Halfdan and Holst, Jan and Lindgren, Georg and Saklak, Mietek}},
issn = {{1573-7713}},
keywords = {{ARMA-process - Detection probability - Duffing oscillator - False alarm - Gaussian process - Operating characteristic - Optimal alarm - Weight decay}},
language = {{eng}},
number = {{Online First}},
pages = {{623--645}},
publisher = {{Springer}},
series = {{Methodology and Computing in Applied Probability}},
title = {{Level crossing prediction with neural networks}},
url = {{http://dx.doi.org/10.1007/s11009-009-9153-3}},
doi = {{10.1007/s11009-009-9153-3}},
volume = {{63}},
year = {{2010}},
}