Fault Detection in Dynamic Systems Using the Largest Lyapunov Exponent

Abstract

A complete method for calculating the largest Lyapunov exponent is developed in this thesis. For phase space reconstruction, a time delay estimator based on the average mutual information is discussed first. Then, embedding dimension is evaluated according to the False Nearest Neighbors algorithm. To obtain the parameters of all of the sub-functions and their derivatives, a multilayer feedforward neural network is applied to the time series data, after the time delay and embedding dimension are fixed. The Lyapunov exponents can be estimated using the Jacobian matrix and the QR decomposition. The possible applications of this method are then explored for various chaotic systems. Finally, the method is applied to some real world data to demonstrate the general relationship between the onset and progression of faults and changes in the largest Lyapunov exponent of a nonlinear system.