Quantifying the variability in Mansour nay: a stochastic approach combining vibroacoustic modelling and PCE-Kriging

The Mansour nay is a woodwind instrument made from a single piece of giant reed (Arundo donax L.). Since the body is natural and cannot be modified after construction, variability in geometry and material properties across specimens is inevitable and directly affects the instrument’s modal behaviour and pitch frequencies. Identifying which variables drive this variability is essential for luthiers selecting raw materials and determining finger hole locations. In this study, 26 Mansour nay samples manufactured from giant reeds of different ages and geographic origins are investigated through experimental modal analysis, vibroacoustic finite element modelling, and stochastic analysis. An Average Mansour Nay Model (AMNM) is constructed from the measured geometric properties of all samples and used as a reference for quantifying deviations. Polynomial chaos expansion combined with Kriging (PCE-Kriging) is employed as a surrogate modelling technique to identify the dominant sources of variability. For the structural model, the bottom diameter and mass are found to be the statistically significant variables. For the acoustic model, the top diameter and the combination of bottom diameter and mass emerge as the dominant factors, followed by finger hole distances. These results provide quantitative guidance for giant reed selection and finger hole placement in nay making, and the methodology is transferable to other instruments made of natural materials.