Uncertainty quantification of diffuse sound insulation values

The sound transmission loss of a partitioning structure depends on the nature of the sound fields in the source and receiver spaces. In an indoor setting, both sound fields are often taken to be diffuse. A diffuse field may represent the sound field of a conceptual ensemble of rooms with the same volume and reverberation time, but otherwise any possible arrangement of boundaries and small objects that have a wave scattering effect. Uncertainty due to random wave scattering is therefore inherently present in the diffuse transmission loss values. In this paper, closed-form expressions are derived for quantifying this uncertainty, such that it becomes possible to estimate by how much the transmission loss of a particular room-wall-room system may deviate from the nominal, ensemble-averaged diffuse value which corresponds to omni-directional incidence and halfspace radiation. First, an exact expression is derived for the harmonic or band-averaged diffuse transmission loss variance, based on hybrid deterministic- statistical energy analysis theory. Its evaluation requires knowledge of the dynamic stiffness of the partitioning structure and of the radiation impedances of the surrounding fluids. Subsequently, an approximate expression is derived, which depends on energy-related quantities only, making it also applicable in an experimental setting. Furthermore, it is demonstrated that the diffuse transmission loss is approximately normally distributed, such that a complete uncertainty quantification is possible from the mean and variance values. The expressions are verified in a Monte-Carlo simulation study involving a single wall and then validated with experimental data of double-leaf plasterboard walls containing flexible steel studs.