Model order determination and noise removal for modal parameter estimation

Abstract

Given a noisy impulsive response function (IRF) that has been contributed by an unknown number of modes, this article proposes a different approach from the traditional methods for estimating modal parameters from this noisy IRF. The major difference lies in the way of handling noise and choosing the computational model order. Whereas the traditional approach accommodates noise by purposely increasing the computational model order, the proposed approach uses the actual system order as the computational model order and rejects noise prior to performing the modal parameter estimation. The proposed approach includes three steps: (1) model order (or number of modes) determination from the measured IRF—by finding the rank of a Hankel matrix constructed from the measured IRF, (2) noise removal from the measured IRF to obtain a filtered IRF—by implementing Cadzow's algorithm for the structured low rank approximation (SLRA) on the Hankel matrix, and (3) modal parameters estimation from the filtered IRF—by using the complex exponential method (Prony's method). Numerical studies include both synthesized and experimental data. While measured IRFs with mild and strong noise levels are simulated for a 5 degree-of-freedom mass-spring-dashpot system, the modal parameter estimations based on the filtered IRFs are very good for both noise levels. While experimental data are measured from two accelerometers mounted at a cantilever beam, the modal parameters estimated from the filtered IRFs of the two accelerometers are in excellent agreement.