On the Calculation of Confidence Levels of the Experimentally Derived Internal and Coupling Loss Factors

This paper deals with the statistical aspects of the Power Injection Method (PIM), a well-established technique to experimentally derive the SEA loss factor model. It is outlined how the variances of the energies measured in the power injection process can be obtained and how approximate analytical expressions describing the propagation of the energy variances through the loss factor calculation can be derived based on a first order Taylor expansion. The expressions giving the loss factor variances as functions of the energy variances offer the practical advantage that they can be quickly evaluated during the acquisition process. Subsequently, it is discussed how the confidence levels of the SEA predictions can be obtained. The practical usefulness and limitations of the derived analytical expressions are investigated based on a Monte-Carlo variability analysis. The statistical theory is then applied to a railway carriage of a high-speed train, illustrating how the effectiveness of loss factor modifications can be evaluated in terms of confidence levels.