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This paper investigates the accelerating up transient vibrations of a rotor system under both the random and uncertain-but-bounded uncertainties. The Polynomial Chaos Expansion (PCE) coupled with the Chebyshev surrogate method is used to analyses the propagations of the two categorizes of uncertainties. The output responses will possess the characteristics of both bounded quantities and statistical moments. As a hybrid non-intrusive uncertainty quantification (UQ) procedure, the deterministic rotor model is taken as a black box and will only be executed at specific parameter points. A number of uncertain physical parameters are studied and the corresponding transient responses are presented. The accuracy and efficiency are verified by the Monte Carlo simulations (MCS) in combination with the scanning scheme and also other hybrid analysis framework. It will provide guidance for the accurate transient dynamic analysis of engineering problems with hybrid uncertainties.

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Bearings are used as the most important load-carrying transmission components in various machines, thus subjecting to a number of faults including wear, fatigue pitting, cracks and so on. Fault detection and diagnosis of bearings can effectively prevent the machine from such typical failures and subsequent consequences. The faults in bearings can lead to the vibration signals that exhibit cyclostationary characteristics due to the inevitably random phase noise (or slippage between bearing components). In this article, a phase linearisation–based modulation signal bispectrum is proposed to tune up the cyclostationary bearing signal into a periodic waveform by linearizing the instantaneous phase of the narrow frequency band signals. In this way, the signal becomes more deterministic and modulation signal bispectrum can be effectively applied to suppression noise and obtain accurate and robust diagnosis results. As a result, this fault detector can achieve high performance in characterising the nonstationary bearing vibration signals and hence diagnose the bearing faults even in the case of extremely low signal-to-noise ratio (<−20 dB), which is benchmarked by the method of conventional modulation signal bispectrum in both simulation and experiment studies.