Uncertainty analysis of mechanical dynamics by combining response surface method with signal decomposition technique

Abstract

Studying multibody dynamic systems, a common way to evaluate the effects of uncertainty parameters is the response surface method, which works by building a polynomial surrogate model at each time instant through a set of input and corresponding output responses. However, a dynamic response always becomes a more and more complicated function of uncertainty parameters with the increase of time; as a result, the fitted surrogate model often fails to provide an accurate approximation at later time instants. This paper suggests that a dynamic response is composed of several vibration components and one trend component. Therefore, it is better to decompose the response into its multiple components, and then fit the amplitude and phase of each vibration component, as well as the trend component, using polynomial functions. By combining the response surface method with signal decomposition techniques, such as Hilbert-Huang transform and local mean decomposition, this study proposes a novel methodology to develop a high-accuracy surrogate model for interval uncertainty analysis. The proposed methodology will degenerate to the conventional response surface method when the dynamic response is a trend component. Three mechanical systems – a Duffing oscillator, a single pendulum and a slider-crank model – are used to confirm the effectiveness of the proposed methodology. This methodology provides a new technical pathway to improve the accuracy of dynamical uncertainty analysis.