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The potential for obtaining scaled separated forcing functions and scaled transfer functions...

All measured vibrations are the combined effect of forcing functions and transfer functions, the latter representing the structural dynamic (i.e. modal) properties of the structure. In order to fully understand them, under operational conditions, two types of blind separation are required:
1) A blind separation at each measurement point of the responses to each of a (possibly unknown) number of individual excitations.
2) A blind separation of each response into its forcing function and transfer function components, these being convolved in the time domain.

This paper discusses the potential for performing these separations, and even extracting scaled modal properties and scaled forcing functions, which should allow much better prediction of responses under somewhat different conditions, e.g. different speed, or after modifications are made to the structure or forces. This should also allow better predictions of future developments, once the forcing functions are better understood.

Determination of the structural dynamic properties falls under the topic of Operational Modal Analysis (OMA), which is already rather well developed for structures such as bridges, buildings and wind turbine assemblies, and where they are largely independent of the forcing functions, which are typically ambient excitations such as wind, waves, and road traffic. OMA forms a large part of the field of Structural Health Monitoring (SHM), since information about structural health mainly resides in these modal properties, and if they do change with factors such as tidal height or wind strength, this is in a reasonably systematic way.

Things are much more complicated with machine health monitoring (MHM), since the situation is almost reversed in that fault indicators are probably 70% given by changes in forcing functions, which are much more complicated and vastly different for different components, for example rolling element bearings and gears. Recent advances in cepstral methods of OMA have demonstrated that even though they are unlikely to replace conventional methods for OMA of static structures, they do have considerable potential for rotating machines, because they assist in both types of separation; blind separation of the sources, and for the separate sources, blind separation of forcing and transfer function. For example, in cases of variable speed machines, the forcing functions normally vary with the speed, but resonant response frequencies remain fixed independent of speed, and these effects can be separated. A number of other blind source separation methods, often based on higher order statistical analysis, or cyclostationary analysis, can be combined with the cepstral methods. Related matrix decomposition methods will also be discussed as a promising future approach.

Even though being developed for MHM, these techniques should have applications in other areas as well, for example variations in noise radiation under different operating conditions, or because of differences from one unit to another.

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