Path sensitivity and uncertainty propagation in SEA

This work addresses the differentiation of the inverse coupling matrix with respect to a coupling or damping loss factor. It applies to two central questions in conjunction with statistical energy analysis (SEA). The first concerns optimization problems for which a sensitivity factor is proposed, based on a simple Taylor series. The factor shows the sensitivity of the vibrational energy flow to a certain coupling loss factor and hence the associated path.The second question where the differentiated inverse coupling matrix applies is the investigation of the propagation of uncertainties in input quantities in a statistical energy analysis. This enables a variance calculation for primary the energies of the subsystems. The approach can be used to establish a variation range for the results from an SEA analysis.Generic configurations with different transmission paths are investigated employing numerical implementations of the approaches. Both procedures are applicable for systems of arbitrary size.