A variety of alternative schemes to dissect and analyse the properties of non-stationary signals have been developed to improve the description of their frequency domain content. Each of these techniques have their own particular domain of focus, and address certain problems, but not all, encountered in the analysis of non-stationary signals. Investigations are to include angle domain analysis, parametric spectral estimation and time-frequency analysis. A comparison of these techniques is presented below, including some practical examples illustrating how they can be used to assist in the analysis of vibration data.
Classes of Non-Stationary Signals
Before attempting to develop a general framework for the analysis of non-stationary machine vibrations, it is necessary to categorise the classes of non-stationary signals confronted in machine condition monitoring. Two major classes have been identified, evolutionary harmonic signals and transient signals[LEUR94]. A third class, evolutionary broad band signals also exists, however this form of non-stationary signal is rarely confronted in machine condition monitoring.
Evolutionary Narrow Band (Harmonic) Signals
Evolutionary harmonic signals consist of several non-stationary narrow band tones, superimposed on a background of random noise. These signals are usually a result of the vibrations being related to some underlying periodic time-varying phenomenon, such as the rotational speed of a motor. Some typical examples include variable speed machinery, engine start ups, and cam driven rotary systems. Further complications arise when a signal consists of a combination of stationary and non-stationary harmonic signal components, or involves varying signal amplitude with time.
Evolutionary Broad Band Signals
An evolutionary broad band signal is one whose spectral density covers a broad band of frequencies, which are of a time varying nature. Evolutionary broad band signals are more commonly associated with structural vibrations, and thus will not be considered in detail. The approach usually adopted when analysing signals of an evolutionary broad band nature is to minimise the observation period while maintaining a reasonable spectral resolution, thus enabling analysis over an essentially stationary segment of the signal. A method that has proven useful in analysing signals of this form is auto-regressive modelling, which accentuates the most prominent features, while attenuating the less prominent components.
Transient vibrations are short time events, whose time behaviour
cannot be predicted and are totally varying in nature. Transient
vibrations are usually a result of impactive loading or variable
transmission paths, both common dilemmas in machine condition
monitoring. Some examples of machines which exhibit transient
vibrations are cranes, excavators, and rock crushers. Helicopter
gear transmission systems and internal combustion engines also
display vibrations of a transitory nature within one operational
cycle due to their variable transmission path.