Vibration Analysis of Fluid-Filled Piping Systems with Epistemic Uncertainties

Non-determinism in numerical models of real-world systems may arise as a consequence of different sources: natural variability or scatter, which is often referred to as aleatory uncertainties, or so-called epistemic uncertainties, which arise from an absence of information, vagueness in parameter definition, subjectivity in numerical implementation, or simplification and idealization processes employed in the modeling procedure. Fuzzy arithmetic based on the transformation method can be applied to numerically represent epistemic uncertainties and to track the propagation of the uncertainties towards the output quantities of interest. In the current study, the fuzzy arithmetical approach is applied to the vibration analysis of a fluid-filled piping system with a structure attached. The investigation of this system is motivated by an automotive application, namely the brake pipes coupled to the floor panel of a car. The piping system is excited by a pressure pulsation in the fluid. Through fluid-structure interaction, this leads to a vibration of the pipes and thus of the structure attached. The uncertainties inherent to the system are of epistemic type and arise, among other things, from a lack of knowledge about the coupling elements between the pipes and the structure. Finite element simulations are performed to compute the vibration response of the system. These simulations are carried out multiple times in the framework of the fuzzy arithmetical algorithm to compute the uncertainty in the vibration response. Since a large number of simulations are needed, computational time is an important issue. In order to minimize the computational effort, substructuring in terms of the component mode synthesis (CMS) and model reduction techniques based on the Craig-Bampton method are used.