Generalized Random Decrement Method for Analysis of Vibration Data

The Random Decrement method used in system identification for analysis of random vibration data is considered from a rigorous mathematical perspective. It is shown that the Random Decrement signature deviates from the system free vibration curve of an associated linear system, unless the corresponding input excitation is white. The error induced by approximating the system excitation by a white noise process is examined. Further, a generalized Random Decrement signature is introduced; it is used to estimate efficiently the auto-correlation function of an ergodic Gaussian random process. Several examples are discussed to elucidate the theoretical developments.