A volume-ratio index for sensitivity analysis of time-dependent models with interval uncertainty inputs

Abstract

In practical engineering, owing to the presence of physical imperfections, model inaccuracies, and structural complexities, almost all time-dependent systems have physical and geometrical uncertainties to some degree. Analyzing the effects of input uncertainties on the output of time-dependent systems is important. In this paper, we focus on sensitivity analysis for the time-dependent output with interval uncertainties. First, the interval process model is introduced to characterize the uncertainty of the time-dependent output under interval inputs. We develop an interval field model on the basis of an analysis of the interval process model. This model allows visualization of the uncertainty effect of the interval input within its interval range on the time-dependent output. Furthermore, we propose a novel sensitivity index defined by the volume ratio of the interval field model, which is designated the “volume-ratio index”. This index quantifies the contribution of interval variables to the uncertainty in the time-dependent output. Two computational strategies are developed to calculate the proposed index. At last, three examples are presented to show the validity and applicability of the developed method.