Oil whip induces self-excited vibration in fluid-handling machines, and what is worse, it can cause self-excited reverse precessional full annular rub, known as "dry whip" which is a secondary phenomenon resulting from a primary cause and may lead to a catastrophic failure of machines; that is, "coincidence of oil whip and dry whip" that occurs repeatedly with constant frequency and amplitude in small clearance cases of fluid-handling machines. Early detection of rub malfunction is essential to avoid damage. Hilbert Huang Transform, which included an empirical mode decomposition and Hilbert spectral analysis, is applied. Hilbert Huang Transform is a great method for analyzing non-linear and non-stationary signals, such as rotor startup signals. Hilbert Huang Transform clearly indicates instability at its initiation stage, and energy concentration changes by different stages. Malfunctions like rub can not observe by Hilbert spectrum. Hilbert spectrum combining full spectrum is developed, as know full Hilbert spectrum, to interpret the rub. The coincidence of oil whip and dry whip is observed definitely through FHS. The advantage of the full Hilbert spectrum is to offer a faster, more efficient method to diagnose fluid-induced instability.