Rethinking Gaussian-Windowed Wavelets for Damping Identification

TL;DR

This paper challenges the traditional use of Gaussian wavelets in damping estimation by exploring envelope-based estimators, proposing a data-driven optimization framework, and benchmarking against existing frequency-domain methods, revealing scenarios where non-Gaussian envelopes excel.

Contribution

It introduces a data-driven framework for optimizing envelope shapes in damping estimation and systematically compares its performance with traditional Gaussian wavelet methods and frequency-domain techniques.

Findings

Triangle and Welch windows outperform Gaussian wavelets at moderate/high SNR.

Blackman filtering is more robust under low SNR and closely spaced modes.

Optimized envelope estimators excel as SNR increases, with LSRF reliable at very low SNR.

Abstract

In modal analysis, the prevalent use of Gaussian-based wavelets (such as Morlet and Gabor) for damping estimation is rarely questioned. In this study, we challenge this conventional approach by systematically exploring envelope-based damping estimators and proposing a data-driven framework that optimizes the shape and parameters of the envelope utilizing synthetic impulse responses with known ground-truth envelopes. The performance of the resulting estimators is benchmarked across a range of scenarios and compared against frequency-domain damping estimation methods, including Least Squares Rational Function (LSRF), poly-reference Least Squares Complex Frequency-Domain (pLSCF), peak picking (PP), and the Yoshida method. Our findings indicate that Triangle and Welch windows consistently outperform or are on par with Gaussian wavelet methods in contexts of moderate to high signal-to-noise ratios (SNR). In contrast, Blackman filtering demonstrates superior robustness under low SNR conditions and scenarios involving closely spaced modes. Among the frequency-domain methods assessed, LSRF shows the most reliability at very low SNR; however, the non-Gaussian optimized envelope estimators perform exceptionally well as the SNR improves.