Level crossing prediction with neural networks
(2010) In Methodology and Computing in Applied Probability 63(Online First). p.623645 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 ARMAprocesses, 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 nonGaussian Duffing process with satisfactory results. (Less)
Please use this url to cite or link to this publication:
http://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
 ARMAprocess  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
 15737713
 DOI
 10.1007/s1100900991533
 language
 English
 LU publication?
 yes
 id
 270393261ab643fcb82a97926077061e (old id 1457411)
 date added to LUP
 20090818 14:01:16
 date last changed
 20190308 03:04:27
@article{270393261ab643fcb82a97926077061e, 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 ARMAprocesses, 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 nonGaussian Duffing process with satisfactory results.}, author = {Grage, Halfdan and Holst, Jan and Lindgren, Georg and Saklak, Mietek}, issn = {15737713}, keyword = {ARMAprocess  Detection probability  Duffing oscillator  False alarm  Gaussian process  Operating characteristic  Optimal alarm  Weight decay}, language = {eng}, number = {Online First}, pages = {623645}, publisher = {Kluwer}, series = {Methodology and Computing in Applied Probability}, title = {Level crossing prediction with neural networks}, url = {http://dx.doi.org/10.1007/s1100900991533}, volume = {63}, year = {2010}, }