A Mathematical Basis for the Random Decrement Vibration Signature Analysis Technique

The mathematical basis for the Random Decrement Technique of vibration signature analysis is established. The general relationship between the autocorrelation function of a random process and the Randomdec signature is derived. For the particular case of a linear time invariant system excited by a zero-mean, stationary, Gaussian random process, a Randomdec signature of the output is shown to be proportional to the auto-correlation of the output. Example Randomdec signatures are computed from acceleration response time histories from an offshore platform.