CAIMS*SCMAI Doctoral Dissertation Award 2004
Winner and Abstract

Ovidiu Voitcu, Department of Mathematics, University of Alberta:

Neural Network Approach for Nonlinear Dynamics Prediction and Feature Extraction

In this thesis, the use of artificial neural networks (ANNs) for long-term prediction of nonlinear oscillations is investigated. Our objective is to predict an accurate long-term behaviour when only a limited data set, representing the transient state of a given nonlinear dynamical system, is known. An ANN is employed to model the underlying dynamics based on the known data set and to subsequently reconstruct the asymptotic state of the system by a multi-step prediction process. A theoretical justification of the proposed approach is provided, showing that, under certain conditions, the omega-limit sets of the original trajectory and of the predicted signal are close to each other. Original ANN architectures with features that control the propagation of the prediction errors are designed. The developed ANNs were tested on both numerically generated signals and real-life experimental data sets representing oscillations of a nonlinear aeroelastic system. Methods for consistently choosing the number of network inputs and hidden layer neurons, as well as appropriate initial weights for training, are also reported. A detailed comparison of 12 combinations of neural network architectural and training algorithm features is performed in order to identify the method that extracts the maximum amount of information from the training set using the minimum number of neurons, while providing robustness in the presence of noise and of variations in different network parameters. The best combination has proven to be a two-layer feedforward ANN with normalized second layer weights, trained with a constant learning rate, and for which the first layer weights were initialized with normalized segments of the training signal. The present study also demonstrates that the ANN approach is capable of predicting the nonlinear behavior of a highly complex dynamical system and of efficiently extracting important features, such as the frequency and damping coefficients of a simulated aerodynamic data set. ANNs thus prove to be useful tools in long-term prediction and feature extraction.