Rethinking Gaussian-Windowed Wavelets for Damping Identification

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.

💡 Research Summary

This paper presents a critical re-evaluation and data-driven enhancement of damping identification methods in experimental modal analysis. It challenges the conventional reliance on Gaussian-windowed wavelets (like Morlet and Gabor) for estimating damping ratios from impulse responses, arguing that their optimal time-frequency localization does not necessarily translate to optimal damping estimation accuracy.

The core of the work is a proposed data-driven framework for optimizing envelope estimators. Recognizing that damping ratio estimation fundamentally relies on accurately extracting the exponential decay envelope of individual modal responses, the authors focus on optimizing this specific linear transformation step. Since true modal envelopes are unknown in real experiments, the framework leverages synthetic data generation. Impulse responses are synthesized from Linear Time-Invariant (LTI) mechanical models with proportional damping, for which the modal parameters (natural frequencies, damping ratios, and thus the true envelopes) are precisely known. A wide range of window functions (Gaussian, Triangle, Hann, Hamming, Blackman, Welch, etc.) and their parameters are then systematically applied as filters to estimate the envelope from the synthetic signals. The optimization process aims to minimize the error between the estimated envelope and the known ground-truth envelope.

The performance of these optimized envelope estimators is rigorously benchmarked against established Gaussian-wavelet methods and several advanced frequency-domain techniques, including Least Squares Rational Function (LSRF), poly-reference Least Squares Complex Frequency-Domain (pLSCF), peak picking, and the Yoshida method. Evaluations are conducted across a comprehensive set of scenarios: single-mode and double-mode systems, with varying levels of signal-to-noise ratio (SNR) from very low to high, and including cases with closely-spaced modes.

The key findings reveal a significant dependency of optimal estimator performance on the measurement context. For moderate to high SNR conditions, optimized estimators using simple window shapes like Triangle and Welch consistently matched or outperformed the traditional Gaussian-wavelet methods. In contrast, under very low SNR conditions and in scenarios involving closely-spaced modes, the Blackman window demonstrated superior robustness, attributed to its excellent sidelobe suppression which effectively mitigates noise and spectral leakage from adjacent modes. Among the frequency-domain methods, LSRF proved to be the most reliable at extremely low SNRs. However, as the SNR improved, the performance of the data-driven, non-Gaussian optimized envelope estimators became exceptionally strong.

In conclusion, the study successfully demonstrates that moving beyond the default Gaussian wavelet paradigm can yield substantial improvements in damping estimation accuracy. By adopting a context-aware, data-driven approach to select or optimize the envelope estimation filter based on the specific signal conditions (SNR, mode spacing), practitioners in modal analysis can achieve more reliable and precise damping identification, with direct benefits for structural health monitoring and dynamic analysis.