Level Crossing Prediction with Neural Networks

Halfdan Grage, Jan Holst, Georg Lindgren () and Mietek Saklak
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Halfdan Grage: Novo Nordisk A/S
Jan Holst: Lund University
Georg Lindgren: Lund University
Mietek Saklak: Visma Software AB

Methodology and Computing in Applied Probability, 2010, vol. 12, issue 4, 623-645

Abstract: 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.

Keywords: ARMA-process; Detection probability; Duffing oscillator; False alarm; Gaussian process; Operating characteristic; Optimal alarm; Weight decay; Primary 62M45; Secondary 60G25; 60G70; 62M20 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1007/s11009-009-9153-3

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