Analyzing symmetry-based techniques to reduce the computation time of sound power estimates obtained from vibration measurements

Two significant drawbacks have been identified in an emerging vibration-based sound power (VBSP) method when compared to its pressure andintensity-based competitors. Firstly, the measurement time increases significantly when dealing with large structures or higher frequencies. Secondly, sound power is computed through the matrix triple product veH(ω)R(ω)ve(ω) which has expensive temporal costs as the structure becomes more complex and for dense scans. This work focuses on the latter concern pertaining to the computation time of the R matrix. Previous research has shown that leveraging the inherent symmetries arising from reciprocity between element radiators across the surface of a structure expedites the construction of the R matrix. Additionally, theoretical work has revealed further symmetries in unbaffled structures, offering potential improvements in computational efficiency. To demonstrate this reduced computation time, simple case studies implementing the R matrix symmetries were conducted using experimental data from various unbaffled geometries. Furthermore, approaches to reducing the temporal costs of this specific matrix triple product, which exhibits these symmetries, will be investigated to enable real-time results within minutes after conducting dense scans. Reducing the computation time will contribute to the VBSP method becoming an efficient and reliable technique for measuring sound power in various applications. [Funding for this work was partially provided by the National Science Foundation (NSF).]