Applied Digital Signal Processing

Abstract

This chapter contains a broad discussion of digital signal processing techniques as applied to the solution of mechanical problems, primarily by analyzing the vibration responses of a machine or structure. Such responses are always a combination of a set of excitation functions and structural response or transfer functions, and the aim of the analyst is usually to separate them and learn their characteristics, for purposes such as structural analysis, primarily concerned with changes in the latter, and machine condition monitoring and diagnostics, primarily concerned with changes in the former, but possibly in both. Since a number of other chapters are mainly concerned with structural analysis, the reader is referred to those for some specialized treatments. The chapter first introduces a number of idealized signal types, including their definitions and basic analysis methods, then gives a guide to the optimum choice of such models to apply in practical situations, such as for modal analysis and condition monitoring. A very important section deals with the two types of blind separation required for complete analysis; first the separation of the various independent sources acting on the machine or structure, and then the identification of the different transfer functions by which the responses to these different sources are modified at the various measurement points. Topics include separation by filtering, blind extraction, blind deconvolution, and separation of responses to different sources, including those distinguished by different characteristics (e.g. deterministic or random), or by virtue of statistical independence. There is a comprehensive discussion of analysis in different domains, or domain pairs, such as time, frequency, and joint time-frequency, but also the recognition that with variable speed machines, it is often best to represent “time” as rotation angle, with corresponding “frequency” in terms of harmonic order. A topic that has become much more important in recent years is the recognition that many machine signals are stochastic, but with random carrier signals that are modulated by deterministic modulation functions, usually linked to machine speed, which can be extracted and identified, even though seemingly hidden in normal signal representations. With constant speed machines, such signals are “cyclostationary”, but with varying speed are termed “cyclo-non-stationary”. Most of these approaches are demonstrated by applying them to three quite different, but very important examples of machine diagnostics, namely for rolling element bearings, gears and reciprocating machines and engines. Finally, a topic which is not widely known, cepstrum analysis, is presented in some detail, because of its very powerful properties in both source separation and structural analysis, with examples of application to machine diagnostics and modal analysis.