Measurement of the best linear time-invariant approximation of linear time-periodic systems
Faculty of Applied Engineering Sciences
Heverlee :Katholieke Univ Leuven, Dept. Werktuigkunde, 2014
International Conference on Noise and Vibration Engineering (ISMA), SEP 15-17, 2014, Leuven, Belgium
Time-periodic (TP) phenomena occurring, for instance, in wind turbines, helicopters, anisotropic shaft-bearing systems, reciprocating engines, ... are often not addressed when classical frequency response function (FRF) measurements are performed. As the traditional FRF concept is based on the linear time-invariant (LTI) system theory, it is only approximately valid for systems with varying dynamics. Accordingly, the quantification of any deviation from this ideal LTI framework is more than welcome. The "measure of deviation" allows us to define the notion of the best LTI (BLTI) approximation, which yields the best - in mean square sense - LTI description of a linear time-periodic LTP system. By taking into consideration the TP effects, it is shown in this paper that the variability of the BLTI measurement can be reduced significantly compared with that of classical FRF estimators. The theory presented is supported by a numerical example.