A non-parametric approach for uncertainty quantification

Uncertainties are unavoidable in the description of real-life engineering systems. The quantification of uncertainties plays a crucial role in establishing the credibility of a numerical model. Uncertainties can be broadly divided into two categories. The first type is due to the inherent variability in the system parameters, for example, different cars manufactured from a single production line are not exactly the same. This type of uncertainty is often referred to as aleatoric uncertainty. If enough samples are present, it is possible to characterize the variability using well established statistical methods and consequently the probably density functions (pdf) of the parameters can be obtained. The second type of uncertainty is due to the lack of knowledge regarding a system, often referred to as epistemic uncertainty. This kind of uncertainty generally arise in the modelling of complex systems, for example, in the modeling of cabin noise in helicopters. Due to its very nature, it is comparatively difficult to quantify or model this type of uncertainties. In this work a new method based on the random matrix theory and the maximum entropy approach is developed to quantify this type of uncertainties. Uncertainty Quantification There are two broad approaches to quantify uncertainties in a model. The first is the parametric approach and the second is the non-parametric approach. In the parametric approach the uncertainties associates with the system parameters, such as Young’s modulus, mass density, Poisson’s ratio, damping coef-ficient and geometric parameters are quantified using statistical methods and propagated, for example, using the stochastic finit