Uncertainty Quantification of Sound Transmission Measurement Procedures Based on the Gaussian Orthogonal Ensemble

The sound insulation of a partitioning structure is subject to uncertainty as it depends on the properties of the acoustic rooms it connects, the properties of the structure, and the measurement setup. The combined effect of these parameters is quantified using a probabilistic framework, constructing their joint probability distribution by means of a maximum entropy approach. Once the joint probability distribution of all parameters has been determined, the uncertainty of the predicted sound insulation values is obtained by Monte Carlo simulation. In this way, it is possible to carry out virtual round robin testing, i.e. to assess the inherent uncertainty of a given measurement procedure. In order to efficiently quantify the uncertainty for the mid- and high-frequency range, a new nonparametric probabilistic method is presented based on the Gaussian Orthogonal Ensemble (GOE). This method is computationally efficient because the random subsystems are modeled with only a few degrees of freedom and because the natural frequencies and mode shapes of these subsystems are directly drawn from universal probability distributions. The method furthermore permits computing any statistic of interest, including confidence intervals and joint probabilities.