Issue 78

C. Vendittozzi et alii, Fracture and Structural Integrity, 78 (2026) 519-540; DOI: 10.3221/IGF-ESIS.78.30

 FAST Hann STFT. To improve time localization around brief high-energy event transitions, a a shorter-window configuration was applied at the same acquisition frequency (1.0 kHz) with L=1024 samples (1.024 s) and H=256 samples (0.256 s), maintaining 75% overlap. This variant provides a higher update rate (  3.906 Hz) at the expense of coarser frequency resolution ( Δ f  0.977 Hz).  Thomson multitaper variant. To reduce estimator variance and spectral leakage without changing the nominal frame duration or update rate, a Thomson multitaper formulation was applied using DPSS tapers with (NW=3) and (K=5). The same (L=2048) and (H=512) values used for the main Hann configuration were retained, so that the comparison reflected the effect of tapering strategy rather than a change in time–frequency discretization. The (L=2048) configuration was not intended to identify an instantaneous touchdown time. At 1.0 s f  kHz, this configuration corresponds to a 2.048 s analysis frame and was selected to obtain stable spectral-family descriptors over event-centered windows. Transitions occurring over shorter time scales may therefore be temporally smeared within a frame, because pre-event and post-event responses can contribute to the same local spectrum. When finer localization of brief transitions is required, the (L=1024), (H=256) configuration provides improved time localization, although at reduced frequency resolution. For this reason, the main multitaper maps are interpreted as descriptors of evolving spectral families rather than as instantaneous modal snapshots or independently validated touchdown markers. For all estimators, spectrograms were limited to the 9–500 Hz band in order to exclude residual low-frequency drift while retaining the main spectral components observed in the analyzed records. Outputs included two-dimensional spectrograms and three dimensional waterfall representations to support both quantitative descriptor extraction and qualitative assessment of ridge persistence and evolution across event-centered windows. In a single-taper STFT, each frame yields one spectral estimate, whereas in the Thomson multitaper approach the same frame yields multiple tapered estimates that are subsequently averaged. This averaging does not introduce additional physical information; rather, it reduces estimator variance and spectral leakage, improving the stability of persistent narrowband components. Under matched frame length and hop, the Thomson multitaper estimate was therefore adopted as the reference representation for ridge extraction. Ridge tracking and dominant-line extraction Ridge trajectories were extracted by selecting, for each accepted time frame, the frequency bin of maximum spectral power within the 9–500 Hz band of the multitaper spectrogram, after masking low-SNR frames and frames exceeding the interpolation-fraction threshold. The resulting ridge tracks provide a single-curve summary per sensor and event-centered window, facilitating comparison across events and supporting subsequent descriptor extraction. Ridge trajectories were exported to CSV to enable post-processing and the computation of summary statistics across sensors within the same event and across the two analyzed datasets. The ridge trajectory is interpreted here as a dominant spectral descriptor, not as direct modal identification. When several spectral families have comparable amplitudes, the ridge may switch from one family to another. Similarly, during rapid changes in boundary conditions, the same analysis frame may contain contributions from both pre-event and post-event response states. For this reason, ridge trajectories are used to summarize the evolution of dominant frequency content, but they are not treated as independently validated modal tracks or touchdown markers. For graphical representation of the ridge-family overlays, consecutive ridge points separated by excessively steep frame-to-frame frequency jumps were not connected. This operation was used only to avoid visually misleading near-vertical line segments and did not alter the extracted ridge frequencies or the quantitative descriptors computed from them. Event-level descriptor extraction The quantitative analysis was restricted to event-level descriptors derived from the multitaper spectrograms: ridge median frequency, ridge interquartile range (IQR), ridge persistence within selected frequency bands, and band-limited RMS. These quantities summarize the dominant spectral families observed in each event window and allow comparison across sensors and recordings without relying on damage labels, hard-landing classes, or independently identified operational phases. The frequency bands used for descriptor extraction were 20–60 Hz, 60–120 Hz, 120–220 Hz, and 350–500 Hz. Ridge persistence was defined as the percentage of accepted frames within an event-centered window for which the ridge frequency fell within a selected band. Band-limited RMS was used to indicate the frequency interval in which the response energy was preferentially concentrated during the same event window. The ridge median frequency and the RMS-dominant band describe related but distinct aspects of the response. The ridge median represents the central tendency of the maximum power ridge trajectory, whereas the RMS-dominant band identifies the predefined frequency interval with the largest band limited RMS contribution within the same event-centered window. Ridge persistence is then computed as the percentage of accepted ridge points falling inside that RMS-dominant band. These quantities may differ when broadband content or competing spectral families are present within the same event-centered window, as observed for Dataset B, sensor S3, Event

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