Modal parameter estimation by combining stochastic and deterministic frequency-domain approaches

The poly-reference Least squares Complex Frequency-domain (pLSCF) estimator—commercially known as the LMS PolyMAX estimator—is used intensively in modal analysis applications nowadays. pLSCF is non-iterative (deterministic) and relatively accurate modal parameter estimation algorithm. This algorithm has several advantages: it is polyreference, fast, numerically stable for large-bandwidth with high-model order analysis, and yields very clear stabilization diagrams even with highly noisy FRFs measurements. One drawback of the pLSCF-estimator is that it yields a poor damping estimates especially for highly damped and weakly excited modes when the FRFs are very noisy.

In this contribution, an approach will be proposed to improve the accuracy of pLSCF estimator and in particular, the damping estimates in case of high noise level. The new proposed approach is a combined stochastic-deterministic frequency-domain algorithm. In this approach, a 2-step procedure is introduced to improve the damping estimates while maintaining the very clear stabilization diagrams. In the first step, a parametric Maximum Likelihood smoothing approach, which is the stochastic part, is used to remove the noise from the data and in the second step, the pLSCF estimator, which is the deterministic part, is applied to the smoothed data resulting in improved (damping) estimates.

The presented algorithm is able to maintain the benefits of pLSCF and at the same time leads to an improvement of the damping estimates in highly damped and very noisy cases. In addition, the new procedure properly deals with uncertainty on the measurements where the data variance due to measurement noise is taken into account.

The procedure is illustrated and tested by using simulated as well as experimental data. The presented procedure to process a highly damped noisy vibration data leads to very accurate estimates in comparison to the traditional pLSCF estimator.