Numerical conditioning and stability of PRCE and ERA methods

Document Type

Conference Proceeding

Date of Original Version



The poly-reference complex exponential (PRCE) and eigensystem realization algorithm (ERA) methods are two popular time-domain methods for experimental modal analysis (EMA): PRCE based on a high order polynomial model and ERA simply a first order matrix model. As PRCE and ERA methods are modelled differently with distinct solution algorithms, implementing these two methods would have different conditioning and stability, even using extremely clean measured signals. The objective of this paper is to provide rigorous comparison of the numerical conditioning and stability, and thus the modal parameter estimation, between PRCE and ERA methods. The numerical study uses an impulse response signal from a 6-DOF dynamic system, which features the followings: six modes with wide frequency range, damping ranging from low to relatively high levels, two weak modes, and a pair of closely spaced modes. Using a clean signal, it is found that PRCE method is very sensitive to both sampling rate and round-off error, and using PRCE cannot correctly estimate modal frequencies when the sampling rate is too high. In contrast, ERA method is very tolerant to both sampling rate and round-off error. When a noisy impulse response signal is used, the stabilization diagram of ERA is much more clean and stable than that of PRCE.

Publication Title, e.g., Journal

5th International Operational Modal Analysis Conference, IOMAC 2013

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