Uncertainty Quantification in Hierarchical Development of Computational Models

Computational models for large systems are sometimes built in a hierarchical way from simple components to subsystems made from a collection of components and finally to the full system. In general, individual component data is more readily available then full system data more often than not due to economic reasons (components are cheaper than the full system). This lack of system data requires the use of modeling and simulation to study a particular behavior of the system. Simulation-based certification requires quantification and propagation of uncertainty to the predicted response of the system model in order to establish the confidence in representing the actual system behavior. Sources of uncertainty arise from (1) physical variability, (2) the coupling of various components, (3) from data collection, (4) modeling assumptions and (5) model approximations. This paper proposes a framework that allows quantification of uncertainty in a hierarchical system model prediction and uses the available data at multiple levels of complexity (i.e. components, subsystem, etc). Propagation of uncertainty to a system level prediction is achieved via Bayes networks. In this work, only sources of aleatoric uncertainty are included in such quantification. Nomenclature Klin = linear stiffness of joint Knon = non-linear stiffness of joint npow = degree of non linearity of joint ρ = density of foam E = modulus of elasticity of foam θ = model parameters ε = Error term I