Uncertainty bounds of energies predicted by MODal ENergy Analysis method

The MODal ENergy Analysis (MODENA) has been developed in the same framework as Statistical modal Energy distribution Analysis (SmEdA) to predict the energy flow between modes of coupled subsystems excited at pure tone. These so-called "energy methods" are useful to condense information obtained from finite element softwares and to give analysis tools for NVH engineers. Contrary to SmEdA, MODENA is based on power balance expressed for pure tone excitation and takes into account non-resonant contribution of modes. In some circumstances, for Transmission Loss computation for example, the non-resonant contribution is not negligible. It has been previously demonstrated that MODENA gives satisfactory results compared to exact computation even if some discrepancies can appear, in particular for non-directly excited subsystems. This is mainly due to the assumption of uncorrelated forces applied on modal "oscillators". At pure tone, this assumption is fulfilled when the phase between modal forces is random. However, it is very difficult to ensure that modal forces have randomly distributed phases in real industrial applications. The present study aims at providing energy uncertainty bounds for MODENA applications. Derived in a general case, these uncertainty bounds permit to quantify the error due to MODENA when the assumption of uncorrelated modal forces is not verified. In the present paper, the derivation of the uncertainty bounds is detailed and an application to a plate/cavity test case is shown. The uncertainty bounds prove that the errors mainly appear on the response of the non-directly exited subsystem while the energy response of the excited subsystem is almost exact.