Data-driven Modeling of Chinese Gong Based on Sparse Identification of Nonlinear Dynamics

Abstract

Abstract Gong is widely employed in Chinese folk bands, but its sound mechanism and mathematical model is still not fully resolved. This work employs MEMS gyroscope to collect the vibration angular rate of two types of Hand Gong including median pitch and high pitch Gongs. This paper further employs Sparse Nonlinear Dynamics Identification (SINDy) [1] to identify a reduced order model of Gong. The model is using angular velocity as state variable and candidate library of nonlinearity is chosen up to fifth-order polynomial. The results indicate that the nonlinearity is prominent up to the third order (cubic) and the cubic nonlinearity is not appearing for the rotation around the axis perpendicular to Gong surface. These results confirm previous observations that the oscillator with a cubic nonlinearity is able to well characterize the nonlinear vibration behavior of Gong [2]. One potential application of this work is on musical psychology.