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In this paper two of the main sources of non-stationary dynamics, namely the timevariability and the presence of nonlinearity, are analyzed through the analytical and experimental study of a time-varying inertia pendulum. The pendulum undergoes large swinging amplitudes, so that its equation of motion is definitely nonlinear, and hence becomes a nonlinear time-varying system. The analysis is carried out through two subspace-based techniques for the identification of both the linear time-varying system and the nonlinear system.The flexural and the nonlinear swinging motions of the pendulum are uncoupled and are considered separately: for each of them an analytical model is built for comparisons and the identification procedures are developed. The results demonstrate that a good agreement 2 between the predicted and the identified frequencies can be achieved, for both the considered motions. In particular, the estimates of the swinging frequency are very accurate for the entire domain of possible configurations, in terms of swinging amplitude and mass position.

In many engineering applications the dynamics may significantly be affected by nonlinear effects, which must be accounted for in order to accurately understand and robustly model the dynamics. From a practical point of view, it is very important to solve theinverse problemrelated to system identification and output prediction. In this paper the recently developed Nonlinear Subspace Identification (NSI) method is presented and applied to an oscillator described by the Duffing equation, with different types of excitation including random forces, which are demonstrated to be very suitable for the identification process. The estimates of system parameters are excellent and, as a consequence, the behaviour of the system, including the jump phenomena, is reconstructed to a high level of fidelity. In addition, the possible memory limitations affecting the method are overcome by the development of a novel algorithm, based on a specific computation of the QR factorisation.

The experimental study of damping in a time-varying inertia pendulum is presented. The system consists of a disk travelling along an oscillating pendulum: large swinging angles are reached, so that its equation of motion is not only time-varying but also nonlinear. Signals are acquired from a rotary sensor, but some remarks are also proposed as regards signals measured by piezoelectric or capacitive accelerometers. Time-varying inertia due to the relative motion of the mass is associated with the Coriolis-type effects appearing in the system, which can reduce and also amplify the oscillations. The analytical model of the pendulum is introduced and an equivalent damping ratio is estimated by applying energy considerations. An accurate model is obtained by updating the viscous damping coefficient in accordance with the experimental data. The system is analysed through the application of a subspace-based technique devoted to the identification of linear time-varying systems: the so-called short-time stochastic subspace identification (ST-SSI). This is a very simple method recently adopted for estimating the instantaneous frequencies of a system. In this paper, the ST-SSI method is demonstrated to be capable of accurately estimating damping ratios, even in the challenging cases when damping may turn to negative due to the Coriolis-type effects, thus causing amplifications of the system response.

Abstract.A fundamental aspect when dealing with rolling element bearings, which often represent a key component in rotating machineries, consists in correctly identifying a degraded behaviour of a bearing with a reasonable level of confidence. This is one of the main requirements a health and usage monitoring system (HUMS) should have. This paper introduces a monitoring technique for the diagnosis of bearing faults based on Principal Component Analysis (PCA). This method overcomes the problem of acquiring data under different environmental conditions (hardly biasing the data) and allows accurate damage recognition, also assuring a rather low number of False Alarms (FA). In addition, a novel criterion is proposed in order to isolate the area in which the faulty bearing stands. Another useful feature of this PCA-based method concerns the capability to observe an increasing trend in the evolution of bearing degradation. The described technique is tested on an industrial rig (designed by Avio S.p.A.), consisting of a full size aeroengine gearbox. Healthy and variously damaged bearings, such as with an inner or rolling element fault, are set up and vibration signals are collected and processed in order to properly detect a fault. Finally, data collected from a test rig assembled by the Dynamics & Identification Research Group (DIRG) are used to demonstrate that the proposed method is able to correctly detect and to classify different levels of the same type of fault and also to localise it.