Time synchronous averaging for the extraction of periodic waveforms is a rather common processing method for rotating machinery diagnosis. By synchronizing the signal to the rotational angle of the component of interest, e.g. by using a keyphasor reference signal, it is possible to perform the averaging in the angular domain, thus obtaining an anglesynchronous signal. Jittering of the reference signal affects the quality of the synchronous averaging process, resulting in attenuation and uncertain estimation of the extracted synchronous signal, especially in the high frequency band. In this paper, the effects of random uncertainty in the pulse arrival times of the reference signal on the synchronous averaging method are studied, with the objective of assessing the relevance of such a jitter error to the extracted waveform and the indicators derived for monitoring purposes. First, a unified framework for the computed order tracking method is presented, and then a model linking the statistics of the random jitter to the statistics of the waveform extracted through synchronous averaging in angle domain is developed. The theoretical model connects the random jitter distribution, the number of averaged periods and the ratio of the period of interest to the reference trigger period, to the distribution of the amplitudes of the synchronous frequency components in the synchronously averaged signal. Approximate analytical solutions are derived for cases of interest, allowing the prediction of the attenuation bias and variability of the extracted components amplitudes. The model is first verified against numerical simulations in order to assess consistency, and then parametric studies are presented. Experimental validation is performed on both an experimental and an operational data sets involving respectively a helicopter gearbox and a helicopter fleet.

The objective of the paper is to develop a vibration-based automated procedure dealing with early detection of mechanical degradation of helicopter drive train components using Health and Usage \mbox{Monitoring} Systems (HUMS) data. An anomaly-detection method devoted to the quantification of the degree of deviation of the mechanical state of a component from its nominal condition is developed. This method is based on an Anomaly Score (AS) formed by a combination of a set of statistical features correlated with specific damages, also known as Condition Indicators (CI), thus the operational variability is implicitly included in the model through the CI correlation. The problem of fault detection is then recast as a one-class classification problem in the space spanned by a set of CI, with the aim of a global differentiation between normal and anomalous observations, respectively related to healthy and supposedly faulty components. In this paper, a procedure based on an efficient one-class classification method that does not require any assumption on the data distribution, is used. The core of such an approach is the Support Vector Data Description (SVDD), that allows an efficient data description without the need of a significant amount of statistical data. Several analyses have been carried out in order to validate the proposed procedure, using flight vibration data collected from a H135, formerly known as EC135, servicing helicopter, for which micro-pitting damage on a gear was detected by HUMS and assessed through visual inspection. The capability of the proposed approach of providing better trade-off between false alarm rates and missed detection rates with respect to individual CI and to the AS obtained assuming jointly-Gaussian-distributed CI has been also analysed.

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