Multi-output Gaussian process regression for uncertainty-aware sound insulation prediction in mass timber floors

Reliable analysis of sound insulation of mass timber floors requires extensive and time-consuming measurements. Such multi-layer assemblies exhibit a complex insulation behavior under both airborne and structure-borne excitation, governed by the interactions between individual layers. In addition, there are uncertainties associated with timber as a building material, its processing, and measurement of the built assemblies. In order to reduce the measurement effort in the long term, a prediction approach that both accounts for these uncertainties in the model and quantifies them in its predictions is required. This study introduces multi-output Gaussian process regression models for the prediction of airborne and impact sound insulation spectra from 50 Hz to 5 kHz. Single-number quantities are derived from the prediction distributions using a Monte Carlo method. The models are developed on a curated dataset of laboratory measurements of mass timber floor assemblies. To also account for nominal inputs, the models are augmented by embeddings that are trained end-to-end with the remaining model parameters under a common objective, the negative log marginal likelihood. The predictions distinguish aleatoric, i.e. measurement-related uncertainty, from epistemic uncertainty that additional knowledge could reduce. Averaged over the frequency bands, the predictions reach mean absolute errors of 2.1 dB for airborne and 3.9 dB for impact sound insulation, while the derived single-number quantities are predicted to within 1.4 dB and 2.2 dB, respectively.