Source-linked AI summary
Screening bolt loosening in a four-bolt plate with global FRF correlation and local FRAC maps from full-field laser Doppler vibrometry
Berkay Kullukcu, Robin Pianowski, Mehmet Sait Özer, Ercan Altinsoy, Dina Hannebauer
TL;DR
The paper addresses how bolt loosening can be detected through dense, spatially resolved changes in structural FRFs without relying on specimen-specific mode labels or a trained classifier. It applies a full-field LDV screening workflow to a four-bolt plate, retaining seven resonance groups and comparing global amplitude/phase dissimilarities with local FRAC maps. The groups separate into low-, intermediate-, and high-distortion responses, while hotspot maps distinguish compact joint-centered changes from broader FRF redistribution.
Problem
Bolt-loosening methods provide damage-sensitive variables but do not necessarily measure dense maps of how structural response changes across an inspected surface, and raw frequency labels are specimen-specific.
Method
The study selects seven trackable resonance groups from the all-tight spatial RMS spectrum, then combines amplitude-only and complex global FRF dissimilarities with local FRAC-deficit maps and normalized hotspot-area fractions.
Results
RG1−RG3 form a low-distortion set, RG4 is intermediate, and RG5−RG7 show the largest response-field changes, with local maps distinguishing compact hotspots from broader redistribution.
Takeaways & Limitations
Global complex dissimilarity and normalized hotspot area should be interpreted together with complete local maps because the area descriptor does not replace global dissimilarity or identify the full response-field change.
Takeaways & Limitations
The study is limited to one plate, four 0 N m cases, approximate free-free support, overlapping high-frequency tracking windows, and an analyst-selected fixed 0.75 threshold.
Abstract
from arXiv · showhide
Full-field laser Doppler vibrometry (LDV) can reveal how bolt torque loss redistributes a frequency response function (FRF) over an entire structure rather than only at a few sensor positions. This work presents a screening procedure for a four-bolt aluminum plate using pointwise amplitude and phase exports of scanned H1 FRFs. Candidate resonances were selected from the all-tight spatial RMS spectrum and tracked in four single-bolt 0 Nm cases. Seven baseline responses remained trackable within prescribed group-specific search windows and were retained as experimental resonance groups RG1-RG7; a dimensionless plate-frequency coefficient was reported alongside each measured frequency. Global changes were quantified using amplitude-only and complex, phase-retaining modal-assurance dissimilarities, and local changes were evaluated using matched-window FRAC-deficit maps and a normalized hotspot-area fraction. The retained groups separate into low-, intermediate-, and high-distortion responses, while the local maps distinguish compact joint-centered changes from distributed FRF redistribution. The workflow therefore links global FRF distortion with spatially resolved interpretation without relying on a trained classifier or specimen-specific node labels.
1. Introduction
Bolted-joint degradation changes structural vibration through coupled contact, preload, and stiffness effects, motivating dense spatial measurements. The study addresses transferability by combining experimental resonance-group labels with a plate-normalized frequency coefficient and complementary global and local FRF comparisons.
- Joint friction, preload-dependent nonlinearity, and assembly conditions can alter resonance frequencies, damping, higher-order FRF behavior, effective stiffness, and measured vibration response.
- Full-field LDV provides non-contact vibration measurements with high spatial sampling density, supporting comparison of response changes across an inspected surface.
- A raw frequency label is specimen-specific, while assigning an FRF peak a mode number requires modal-parameter identification rather than peak picking alone.
- The workflow uses ordered experimental resonance-group labels and reports a dimensionless plate-frequency coefficient alongside each measured frequency to separate response identity from scaled frequency information.
- The contribution links resonance-group selection with amplitude-only and complex global FRF comparison and local FRAC-based spatial interpretation.
2. Experimental setup and analysis workflow
The study combines full-field LDV measurements with resonance-group tracking, global FRF dissimilarities, and local FRAC-based maps to screen bolt loosening in a four-bolt plate. Seven trackable responses are indexed with experimental group labels and plate-normalized frequency descriptors, while matched analysis windows and fixed hotspot criteria support comparison across torque states.
- Resonance-group selection and tracking: Seven resonance groups are selected from the all-tight spatial RMS spectrum and retained only when corresponding peaks remain trackable in all four loose-bolt cases.Candidate selection uses smoothed-spectrum maxima, prominence and width criteria, de-duplication, and group-specific search windows.
- Specimen and measurements: The experiment uses a 100 × 150 × 7 mm aluminum plate, four M6 bolts, an all-tight 10 N m reference, and four single-bolt 0 N m cases.The plate was measured under soft-sponged, approximately free-free conditions using scanned H1 displacement-to-force FRFs up to 20 kHz.
- Specimen and measurements: The analysis compares 51 LDV coordinates common to amplitude and phase exports across all analyzed states.The complete scan contained 79 measured positions, of which 51 were retained for comparisons.
- Resonance-group selection and tracking: RG1–RG7 are ordered by increasing all-tight frequency, with each group paired with a geometry- and material-normalized plate-frequency coefficient.The coefficient uses representative material properties because the alloy grade was not documented; the measured FRF metrics do not depend on these assumptions.
- Global and local screening metrics: Global screening uses amplitude-only 1 − MAC_a and phase-retaining 1 − CMAC dissimilarities, averaged across the four single-bolt cases with exhaustive-bootstrap intervals.The complex metric retains measured phase information, whereas the amplitude-only metric compares spatial amplitude vectors.
- Global and local screening metrics: Local screening compares equal-width matched frequency windows with FRAC-deficit maps and a normalized high-deficit area fraction.The hotspot-area calculation uses the common LDV-coordinate hull and a fixed descriptive threshold τ = 0.75 rather than a dataset-optimized threshold.
3. Results
The seven retained resonance groups separate by both global FRF distortion and spatial redistribution. Lower-frequency groups show consistent upward peak shifts and low distortion, while higher-frequency groups exhibit bidirectional relocation, larger complex dissimilarity, and broader or contrasting local deficit patterns.
- Tracked resonance groups: RG1−RG4 shift upward in all four loose-bolt cases, whereas RG5−RG7 show bidirectional changes from approximately Δf = −180 to +180 Hz.The lower-frequency shifts are 74−85 Hz for RG1, 134−169 Hz for RG2, 71−96 Hz for RG3, and 124−177 Hz for RG4.
- Global screening: RG1−RG3 form a low-distortion set, with mean 1−MAC_a values of 0.049−0.052 and 1−CMAC values of 0.066−0.073.
- Global screening: RG4 is intermediate, with 1−MAC_a = 0.146 and 1−CMAC = 0.185, while RG5−RG7 have amplitude dissimilarities of 0.276, 0.335, and 0.288.
- Global screening: Phase-aware dissimilarities reach 0.624, 0.599, and 0.608 for RG5−RG7, indicating complex spatial FRF redistribution beyond resonance relocation.The uncertainty intervals also broaden for the high-frequency groups, particularly for 1−CMAC.
- Local screening: RG3 has the clearest compact joint-centered field, with an L_g ≥ 0.75 core occupying 1.49% of the scanned area, while RG1 and RG2 occupy 2.87% and 2.01%.Despite similarly low global dissimilarities, RG1−RG3 do not exhibit equivalent local behavior.
- Local screening: RG4−RG6 have normalized high-deficit areas of 9.63%, 9.91%, and 7.98%, whereas RG7 has a 0.81% thresholded core despite 1−CMAC = 0.608.The full local map remains necessary because thresholded area does not describe absolute magnitude, position, or the remainder of the response field.
4. Discussion
The discussion separates resonance groups using global phase-aware FRF distortion and local hotspot extent, showing that these descriptors capture complementary aspects of response change. It also identifies tracking overlap, case dependence, and study-design constraints that limit interpretation.
- Global distortion: RG1−RG3 show low global distortion, while RG5−RG7 show much larger phase-aware changes; phase retention increases mean dissimilarity by 0.0183 versus 0.3107 across these regimes.The corresponding mean 1−CMAC values are 0.0690 and 0.6103, respectively.
- Limitations: High-frequency uncertainty is strongly case dependent: the mean 95% 1−CMAC interval width is 0.032 for RG1−RG3 and 0.642 for RG5−RG7.With four bolt locations resampled, these intervals represent bolt-location variability rather than population-level uncertainty.
- Local spatial extent: RG1−RG3 have a mean hotspot area of 2.12%, whereas RG4−RG6 average 9.17%, indicating broader multi-region redistribution in the latter group.RG4−RG6 therefore average 4.32 times the RG1−RG3 hotspot area.
- Complementary descriptors: RG7 demonstrates that global dissimilarity and hotspot extent are not monotonic: its 1−CMAC is 0.608, but its hotspot core is only 0.81%.RG4 and RG5 have nearly identical hotspot areas despite markedly different global dissimilarities.
- Complementary descriptors: The pair (1−CMAC, η0.75) should be interpreted with the complete local map because the hotspot fraction measures relative core area, not absolute FRAC-deficit magnitude.The map additionally identifies hotspot location and fragmentation.
- Limitations: The study is constrained by one plate, four 0 N m cases, approximate free-free support, overlapping high-frequency windows, asymmetric excitation during symmetry averaging, and an analyst-selected 0.75 threshold.Future work should test additional geometries, preload levels, bolt layouts, boundary conditions, and tracking or threshold sensitivities.
5. Conclusion
The study applies full-field LDV screening to a four-bolt plate and combines global amplitude and phase correlation with local FRAC mapping. Seven experimental resonance groups separate into distortion regimes, while local maps distinguish compact joint-centered hotspots from broader redistribution.
- Workflow: Seven trackable resonance groups were selected from the spatial RMS spectrum and reported with one plate-normalized frequency coefficient.The analysis used an all-tight reference and four single-bolt 0 N m cases.
- Findings: RG1−RG3 form a low-distortion set, RG4 an intermediate response, and RG5−RG7 a strongly phase-aware distorted set.Local FRAC maps identify RG3 as the clearest compact joint-centered hotspot, while RG4−RG6 show broader high-deficit regions.
- Implication: The normalized hotspot-area fraction complements, but does not replace, global dissimilarity measures.Together, the workflow links resonance selection, global correlation, and local FRF mapping without a trained classifier or specimen-specific node labels.
Data availability
The experimental database and its supporting materials are publicly available through Zenodo.
- Data availability: The repository contains measurement data, metadata, supporting documentation, and analysis scripts associated with the experiments.A companion data-descriptor manuscript has been submitted for publication.
CRediT authorship contribution statement
The authors contributed across conceptualization, methodology, software, analysis, supervision, resources, and manuscript preparation.
- Contributions: Kullukcu led conceptualization, methodology, software, formal analysis, and the original draft, with Pianowski contributing to methodology, analysis, and writing.Özer contributed to formal analysis and writing.
- Contributions: Altinsoy and Hannebauer provided supervision and resources, with Hannebauer also contributing to review and editing.