The concept of cyclic sound intensity and its application to acoustical imaging

This paper demonstrates how to take advantage of the cyclostationarity property of engine signals to define a new acoustical quantity, the cyclic sound intensity, which displays the instantaneous flux of acoustical energy in the angle-frequency domain during an average engine cycle. This quantity is attractive in that it possesses the ability of being instantaneous and averaged at the same time, thus reconciling two conflicting properties into a rigourous and unambiguous framework. Cyclic sound intensity is a rich concept with several original ramifications. Among other things, it returns a unique decomposition into instantaneous active and reactive parts. Associated to acoustical imaging techniques, it allows the construction of sound radiation movies that evolve within the engine cycle and whose each frame is a sound intensity map calculated at a specific time - or crankshaft angle - in the engine cycle. This enables the accurate localisation of sources in space, in frequency and in time (crankshaft angle). Furthermore, associated to cyclic Wiener filtering, this methodology makes it possible to decompose the overall radiated sound into several noise source contributions whose cyclic sound intensities can then be analysed independently.