Contributed by the Technical Committee on Vibration and Sound for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received Feb. 1999; revised Aug. 2001. Associate Editor: A. F. Vakakis.

Proper orthogonal decomposition (POD) is a useful experimental tool in dynamics and vibration. A common application of POD to structures involves sensed displacements, x1t,x2t,,xMt, at M locations on the structure. When the displacements are sampled N times at a fixed sampling rate, we can form displacement-history arrays, such that xi=(xit1,xit2,,xitN)T, for i=1,,M. The mean values are often subtracted from the displacement histories. These displacement histories are used to form an N×M ensemble matrix,
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