A contribution to the probabilistic road noise simulation using a Non-Parametric Variability Modeling

An application of a Non-Parametric Variability Modeling (NPVM), as introduced by Pr. Soize, of a full vehicle road noise simulation, is an opportunity to highlight some applicative issues of such a stochastic approach. First, the convergence of the stochastic computations is considered by introducing the probabilistic modal density of the considered model as an indicator of the system intrinsic dynamic behavior. Since the probabilistic model induces a spread of modal frequencies, the upper range shows a lack of modes, deviating from the actual system modal density. The study of this deviation leads to the modal truncation criterion required to achieve a relevant probabilistic modal density in a targeted frequency range. The required margin in order to achieve a proper convergence of the probabilistic problems appears larger than expected. Then, using appropriate parameters, road noise simulation is investigated in the framework of the stochastic modeling. After the capability of the NPVM to handle the random loads requested for road noise, an FRF Based Sub-structuring approach is used to investigate different options for the loads application. Indeed, the complex behavior of the rotating tire/wheel system with the road is often handled by computing (or measuring) blocked forces or interface forces of a source sub-system (chassis) applied to a receiving sub-system (trimmed body). Cases where the receiving subsystems variability only, or both subsystems variability are considered, are investigated. It appears that, when variability applies to the full vehicle, using deterministic blocked forces may lead to erroneous results. When the trimmed body only is subject to uncertainties, deterministic interfaces forces lead to a reasonable approximation of probabilistic results. In both parts, theoretical derivations are illustrated by the results obtained from actual industrial models.