Liquid rocket engine turbopumps operate under severe non-stationary conditions, making it challenging for traditional vibration signal analysis methods to effectively extract fault features. To address this challenge, the cyclostationary random signal model is extended and a generalized cyclostationary analysis framework is established. This framework preserves the advantages of cyclostationary methods in fault diagnosis while broadening their applicability to non-stationary operating regimes. Focusing on vibration signal modeling, fault feature extraction, and characterization, a comprehensive generalized cyclostationary analysis framework specifically for rocket turbopump fault diagnosis is proposed. The superiority and validity of the established theoreical system are demonstrated through a cryogenic bearing operation experiment on a rocket turbopump and a cavitation fault simulation test on a centrifugal pump. Results indicate that vibration signals from rotating machinery can be regarded as approximately cyclostationary processes subject to time warping, which can be further transformed into modulated cyclostationary signals. In the rocket turbopump cryogenic bearing operation experiment, fault feature signals are extracted using the proposed blind adaptive cyclostationary-nonstationary signal extraction method. Its order-frequency spectral correlation map clearly detects spectral lines corresponding to the fundamental train frequency (0.42 Hz) and the ball pass frequency outer race (5.08 Hz). In the centrifugal pump cavitation fault simulation experiment, the proposed high-precision reassigned spectral correlation estimation technique enhances the localization of the blade-pass frequency (197 Hz) in the spectral correlation map. Furthermore, it reliably identifies fault features even under severe noise induced by increasing cavitation levels.