Poly-Reference Least-Square Complex Frequency Identification Revised to Improve Damping Estimation

The Poly-Reference Least-Square Complex Frequency (p-LSCF) identification method is a well-established method currently available in commercial software. It is known to deliver clear stabilization diagrams in which spurious poles can hopefully be separated from physical ones. It is shown in the literature [1] that this property is achieved thanks to an appropriate choice of constraints for the least-square (LS) problem to be solved. It is also demonstrated that, in case of low signal to noise ratio, the extracted damping ratio value is usually underestimated, the discrepancy being worse in situations in which the damping level is high. Solutions have been proposed to improve the damping estimation such as the frequency-domain maximum likelihood estimation. However, this type of identification method is iterative and particularly time consuming and therefore not suitable in many industrial cases.
In this paper, a solution is proposed to tackle damping underestimation and to improve pole identification. The developed methodology solves two subsequent least-square problems: one for each of the two opposite choices of constraints. The stabilization diagram is then built according to the p-LSCF method, but the damping ratios are computed solving the second LS problem on the paired poles.
The first part of the paper describes the method and the implementation in an in-house modal analysis software.
In the second part, the methodology is applied to two meaningful test cases to assess the improvement achieved. First, a finite element model of a clamped beam is considered to explore the sensitivity of the proposed damping estimation with respect to the noise level. If the noise level becomes too high, the proposed method behaves similarly to the LSCE method but with a cleaned stabilization diagram which improves identification of the poles. The relative error on the damping ratio estimation remains low while it becomes significant if the p-LSCF method is used. The method is then applied to an industrial test case and the results are compared and discussed.