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.

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The German Aerospace Center (DLR) is currently studying different technologies for reusable launch vehicles (RLVs) to evaluate and compare their benefits. The project CALLISTO (Cooperative Action Leading to Launcher Innovation in Stage Toss-back Operations) investigates a VTVL (vertical takeoff, vertical landing) concept. In the DLR project ReFEx (reusability flight experiment), in the context of which this paper is presented, a winged VTHL (vertical takeoff, horizontal landing) concept is investigated to develop the key technologies for future winged RLV applications, culminating in a flight experiment to demonstrate the capability of controlled autonomous return flight from supersonic to subsonic speeds. In this paper, analysis of stability and controllability is used on a three-dimensional envelope of points to derive a suitable flight corridor for the re-entry. Second, a controller concept based on inversion of the rotational equations of motion is derived. The validity of the presented controller concept is shown on a preliminary level via comparison of open-loop and closed-loop dynamics at two representative flight points and a time simulation which includes a segment of the planned mission.