About the modelling of dispersed vibroacoustic frequency response functions of serial production vehicles

Since todays design process of manufactured objects mainly relies on simulations, the relevance of models -ie their capability to foresee real objects properties, including dispersion of these properties- is a crucial engineering issue. When making a reproducibility test (same experiment on numerous samples), it appears that industrial objects -cars for example- measured vibroacoustic FRFs show huge dispersion. Thus, dispersed FRFs exhibit some characteristics patterns. These characteristic behaviors suggest the modeling of dynamic systems uncertainties should be possible in a rather generic manner.
Among many possible methods, a maximum of entropy non-parametric modeling –based on a random matrix theory- is preferred since it does not require any detailed knowledge of the object's uncertainties. Uncertainties are considered as a whole, whatever their root causes: modeling uncertainties, data uncertainties (material and geometry), object diversity, manufacturing process or measurement errors. Amount of uncertainties is controlled through the variance of physically consistent mass, stiffness and damping matrices. These variances may be set a priori or identified a posteriori. The theory is numerically well fitted for dynamic and vibroacoustic problems when using generalized coordinates (modes) in order to compute solutions.
The stochastic model may be built from current FE models, and independent realizations are performed during a Monte-Carlo simulation. Statistics of the dynamic responses (modes, FRFs, energies…) can then be performed. Various use of the stochastic vibroacoustic modeling in an industrial context will finally be presented: model assessment, design assessment against targets, design sensitivity analysis.