Sparse stability diagrams of LSCF method via strategic pole destabilization using orthogonal matching pursuit

Abstract

In various engineering fields including mechanical, aerospace, and civil engineering, the identification of modal parameters, including natural frequencies, damping ratios, and mode shapes, is crucial for determining the vibration characteristics of engineered structures. A common method for identifying the modal parameters of structures involves experimental modal analysis using frequency response functions (FRFs) obtained from forced vibration tests. The least squares complex frequency (LSCF) domain method is a widely-used frequency-domain curve-fitting method for the FRFs using the polynomials of high order, which can extract modal parameters with high accuracy. However, increasing the polynomial order tends to result in the generation of non-physical spurious poles that need to be eliminated from the stability diagrams. To overcome this issue, we propose a method that strategically destabilize the stable yet spurious poles of the characteristic polynomials by making their coefficients as sparse as possible, via orthogonal matching pursuit (OMP). This results in sparse stability diagrams because unstable poles can be eliminated from the diagrams. In this paper, the proposed method is first applied to a numerically-obtained FRFs of a rectangular plate using finite element model, and its validity is discussed. Then, the method is applied to experimentally-obtained FRFs of rectangular plates with low-damping and with high-damping. Furthermore, to confirm its applicability to industrial applications with realistic complexity, it has also been applied to the FRFs of the electric machine's stator core used for electric vehicles. Based on the results, we have confirmed that the spurious roots can be eliminated from the stability diagrams without compromising accuracy for the cases considered.