Nonlinearity Detection in Dynamical Systems

Abstract

A method to detect the presence of nonlinearity in dynamical systems is proposed. The method quantifies nonlinearity as a statistical variance from a system's response when linearised. For a given input signal, bounds are defined by an F-score statistical significance test. If the variance of the system's output compared to an ideal linear response exceeds those bounds, linearity is very unlikely and cannot be assumed for the system. The proposed method has use in selecting model structures for system identification and for controller design. The effectiveness of the proposed technique is demonstrated on three single-input single-output (SISO) benchmark systems: a linear spring-damper system, a nonlinear pendulum and nonlinear Duffing oscillator. Each model is driven with inputs of varying amplitude, showing how the effect of nonlinearity in the system dynamics increases as the input amplitude increases. This also demonstrates that, for the same input signals, some of the systems' responses behave more nonlinearly than others. The method is also applied to a published multiple-input-multiple-output (MIMO) nonlinear diesel engine air-path model to show relevance for real applications.