Amplitude-Identifiable MUSIC (Aid-MUSIC) for Asynchronous Frequency in Blade Tip Timing

Multiple signal classification (MUSIC) has gained prominence in frequency estimation with the virtue of overcoming the undersampling problem of blade tip timing (BTT). However, as a crucial vibration feature, the amplitude cannot be estimated by MUSIC. Existing amplitude extraction methods for MUSIC are performed as postprocessing methods not related to MUSIC. Additionally, existing derivations of MUSIC for real signals use Euler's formula to transform real signals into complex exponential signals. Therefore, this article rederives MUSIC based solely on real signals and further proposes an amplitude-identifiable MUSIC (Aid-MUSIC) approach to recover the amplitude information hidden in the eigenvalue decomposition of MUSIC. Combined with the proposed formulaic explanation of MUSIC's asynchronous-pass ability, Aid-MUSIC is adapted according to the characteristics of BTT signal. The simulations and experiments show that Aid-MUSIC can achieve the simultaneous and stable extraction of amplitude and frequency for asynchronous frequency components without the interference of synchronous frequency components.