Blind Identification of Operational Deflection Shapes from Continuous Scanning Laser Doppler Vibrometry Data

Abstract

Continuous Scanning Laser Doppler Vibrometry (CSLDV) is a well known technique that makes it possible to extract the Operational Deflection Shapes (ODSs) of a vibrating structure in a very fast and efficient way. The spatial evolution of the ODS with respect to the scanned path determines an amplitude modulation effect on CSLDV vibration data: this effect causes the presence of sidebands with respect to the ODS resonance frequency (central frequency) spaced by integer multiple of the scanning frequency used to sweep the laser spot over the target. However, depending on the structure under analysis and on the testing condition, the spectrum measured might present unclear patterns of sidebands, therefore an extraction of ODSs using a standard peak peaking approach can provide erroneous results. This paper aims at presenting a blind approach for recovery ODSs in these challenging situations. The algorithm is based on the solution, in least square sense, of a set of linear equation defining the relations between the contributions of each cluster of frequencies (central frequency + sidebands) potentially defining the spectral pattern of a certain ODS to the complex spectrum measured. Results on a virtual experiment involving a cantilever beam having its first three modes within a very narrow bandwidth (3 Hz) are presented and discussed.