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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)
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author
organization
publishing date
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
Kluwer
external identifiers
  • wos:000283614400006
  • scopus:77957319081
ISSN
1573-7713
DOI
10.1007/s11009-009-9153-3
language
English
LU publication?
yes
id
27039326-1ab6-43fc-b82a-97926077061e (old id 1457411)
date added to LUP
2009-08-18 14:01:16
date last changed
2018-06-24 04:47:12
@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},
  keyword      = {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    = {Kluwer},
  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},
  volume       = {63},
  year         = {2010},
}