Mechanical Systems and Signal Processing (2001) 15(5), 945}962 doi:10.1006/mssp.2001.1415, available online at http://www.idealibrary.com on THE RELATIONSHIP BETWEEN SPECTRAL CORRELATION AND ENVELOPE ANALYSIS IN THE DIAGNOSTICS OF BEARING FAULTS AND OTHER CYCLOSTATIONARY MACHINE SIGNALS R. B. RANDALL School of Mechanical and Manufacturing Engineering, The University of New South Wales, Sydney 2052, Australia J. ANTONI Laboratoire d 'Analyse des Signaux et des Processus Industriels (LASPI), IUT de Roanne, 42334 Roanne, France AND S. CHOBSAARD Department of Engineering Development, Royal Thai Naval Dockyard, Thailand In recent years there has been an increasing interest in applying cyclostationary analysis to the diagnostics of machine vibration signals. This is because some machine signals, while being almost periodic, are not exactly phase-locked to shaft speeds, and thus even after compensation for speed #uctuation cannot be extracted by synchronous averaging. Typical examples are the combustion events in IC engines, which vary from cycle to cycle, and impulsive signals from faults in rolling element bearings, which are a!ected by minor but randomly varying slip. Two main tools for the analysis of cyclostationary signals are the two-dimensional autocorrelation function vs central time on the one axis and time displace- ment around the central time on the other, and its two-dimensional Fourier transform known as the spectral correlation. The latter can be quite complex to interpret, so some authors have suggested integrating it over all frequencies to obtain a Fourier series spectrum vs cyclic frequency. In this paper, it is shown that this gives the same result as a Fourier transform of the average squared envelope of the signal, which is much easier to obtain directly. Not only that, envelope analysis has long been used in the diagnostics of rolling element bearing signals, and some of the experience gained can be carried over to spectral correlation analysis. There is a possibility that the full spectral correlation may still give some advantage in distinguishing between modulation e!ects due to gear rotations and bearing inner race rotations (even at the same speed) by virtue of the di!erent amounts of randomness associated with each.  2001 Academic Press 1. INTRODUCTION Many machine signals are periodic or quasi-periodic (mixtures of non-commensurable periodic signals) with frequency components which are phase-locked to the various shaft speeds and their harmonics, such as gearmesh frequencies. Others, such as bearing fault signals, are tied to shaft speeds, but not strictly phase-locked because of variable slip between the bearing components. The latter can be explained by the fact that the kinematic formulae for the various fault frequencies contain a term cos , where  is the load angle 0888}3270/01/050945#18 $35.00/0  2001 Academic Press