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Sparse-LDV Neural Reconstruction with Vibro-Acoustic Evidence Fusion for Early Bolt Preload Loss
Berkay Kullukcu, Dina Hannebauer
TL;DR
Early bolt-preload loss can produce weak, resonance-dependent changes, while dense LDV scans are costly and individual modalities can have frequency-dependent blind spots. The paper combines commissioning-baseline-assisted sparse LDV with force-normalized microphone evidence, then reports full mild-condition resonance coverage from decision-level fusion.
Problem
Dense LDV scans are costly, and early preload loss may produce weak changes that single sensing modalities miss at some frequencies.
Source: §1 · p. 1Method
The method reconstructs sparse LDV fields against a dense healthy commissioning baseline and combines hidden-node local-FRAC deficits with repeatability-normalized microphone H1 evidence at the decision level.
Source: §1 · p. 1, §3.2 · p. 2, §3.3 · p. 2Results
Takeaways & Limitations
The results support microphones as a complementary early-warning channel for resonance-dependent sparse-LDV blind spots, without pointwise fusion of separately acquired campaigns.
Source: §6 · p. 4The study uses one specimen and one healthy acoustic assembly realization, so 100% denotes commissioning-set resonance coverage rather than population detection probability.
Source: §5 · p. 4
Abstract
from arXiv · showhide
Laser Doppler vibrometry (LDV) is costly, while early bolt-preload loss may produce weak and resonance-dependent changes. We combine sparse-LDV reconstruction referenced to a dense commissioning baseline with force-normalized microphone evidence. At m = 24 measurement nodes, each single-bolt 5-Nm state is reconstructed by a neural-network fold that excludes that state from training. A late-fusion rule calibrated on the healthy baseline combines the 90th percentile of local-FRAC deficits at unmeasured nodes with microphone H1 changes normalized by impact-level repeatability. Sparse LDV alone flags 24/28 mild condition-resonance pairs (50% preload loss) and acoustic evidence flags 25/28, fusion flags all 28/28. All four LDV misses occur at RG3 (resonance group) and are recovered acoustically. Fusion remains 28/28 for repeatability-normalized acoustic thresholds from 3 to 10. The result supports complementary vibro-acoustic evidence for early preload-loss screening while avoiding pointwise fusion of separately acquired campaigns.
1. INTRODUCTION
Reduced bolt preload can alter joint behavior before gross failure, while dense LDV scans are costly and single sensing modalities can have frequency-dependent blind spots. The paper asks whether sparse LDV and separate acoustic evidence can detect an unseen single-bolt 10-to-5-Nm reduction and recover resonance windows where sparse LDV is weak.
1. INTRODUCTION
- Reduced preload can change contact stiffness, damping, and microslip before gross joint failure, motivating detection of small changes before complete loosening.Dense scanning LDV supplies spatially resolved complex FRFs but repeated scans are expensive; microphones provide a non-contact channel with frequency-dependent blind spots of their own.Source: §1 · p. 1
- The study tests sparse reconstruction of an unseen single-bolt 10-to-5-Nm reduction and whether condition-level acoustic evidence can recover weak sparse-LDV resonance windows.The LDV database includes 18 torque configurations and seven screened resonance groups, while a separate acoustic campaign includes all-tight, four single-bolt 5-Nm, and five severe states.Source: §1 · p. 1
2. RELATION TO PRIOR WORK
Prior work motivates dense-to-sparse commissioning for vibration-field recovery and complementary sound-based evidence for loosening detection. This paper retains a measured healthy field for LDV diagnostics and combines separate modality scores only at the decision level.
2. RELATION TO PRIOR WORK
- Sparse vibration recovery has advanced from graph-signal sampling and QR selection to compressed sensing and deep-learning reconstruction.Dense controlled measurements have also been used to support later sparse reconstruction; this work retains the measured healthy field as the local-FRAC reference.Source: §2 · p. 1
- Prior multimodal studies report complementary sound or sensor evidence for threaded-fastener loosening and progressive or slight damage.The present approach uses separate condition–resonance evidence scores and combines them at the decision level rather than applying resonance reweighting.Source: §2 · p. 1
- The dense commissioning scan excites the four-bolt plate near B3 and measures 51 spatial locations.This campaign supplies the dense reference for the sparse-reconstruction approach.Source: Figure 1 · p. 1, §2 · p. 1
3. METHOD
The method pairs a dense LDV commissioning reference with sparse neural reconstruction and separately acquired microphone measurements. Healthy-calibrated, decision-level fusion combines hidden-node structural evidence with repeatability-normalized acoustic evidence.
3.1. Experimental Setups
- The four-bolt aluminum plate is hammer-excited near B3, with complex displacement-to-force FRFs measured at 51 common locations across seven tracked resonance windows.The separate acoustic campaign uses two microphones 30 mm from the bolt pairs, with sample-synchronous microphone and hammer-force recordings and pressure-to-force calibration in Pa/N.Source: §3.1 · pp. 1–2, Figure 2 · p. 2
3.2. Sparse Reconstruction and Diagnostic Maps
- Pivoted QR selection on a four-nearest-neighbor graph chooses fixed sparse measurement nodes, whose observations initialize a residual-MLP reconstruction with exact measured-row consistency.Each 5-Nm state is evaluated by a fold that excludes it from training; complete- and multi-bolt-loose states are excluded from fitting. Map fidelity uses Pearson correlation, including a hidden-node metric that omits the 24 measured locations.Source: §3.2 · p. 2
3.3. Healthy-Calibrated Vibro-Acoustic Evidence Fusion
- Structural evidence is the 90th percentile of reconstructed local-FRAC deficits over hidden nodes, with its threshold calibrated only from reconstructed healthy commissioning; acoustic evidence measures baseline-relative RMS change in force-normalized H1 within the same ±60-Hz band.The acoustic change is normalized by impact-level repeatability; the primary threshold is 5 pooled-SD units, fixed without optimizing on mild states, with 3 and 10 as sensitivity checks.Source: §3.3 · p. 2
4. RESULTS
With 24 LDV nodes, decision-level fusion of sparse-LDV diagnostics and hammer-normalized microphone evidence flags all 28 mild resonance windows, recovering every LDV miss.
4. RESULTS
- At m = 24, repeated LDV acquisition falls from 51 to 24 locations (52.9%), with median full-map and hidden-node correlations of r = 0.940 and 0.870 across 28 out-of-fold mild maps.The four single-bolt 5-Nm states are evaluated by folds that exclude each state from training.Source: §4 · p. 2
- Table 1 reports median dense-reference residual-DNN performance across 91 unseen severe condition–resonance samples, with columns for m, NMSE, phase, rfull, and rhid.The caption identifies the table scope and metrics but does not provide cell values.Source: Table 1 · p. 2
- The workflow expands repeated sparse LDV measurements into a 51-point FRF field and combines LDV diagnostics with parallel hammer-normalized two-microphone evidence.The dense all-tight commissioning scan supplies the reference for reconstruction.Source: Figure 3 · p. 3
- Figure 4 compares the dense measured B2-loose RG5 local-FRAC deficit field with reconstructions from progressively larger sparse sets, all referenced to the same healthy 51-point map.Source: Figure 4 · p. 3
- The acoustic input passes 58 impacts, with median target-band coherence of 0.9947 and median complex FRAC of 0.9991 against exported transfer functions.A healthy-state leave-one-impact-out check gives a maximum absolute band-RMS change of 0.983 dB.Source: §4 · p. 3
- 28/28 mild resonance windows are flagged by fusion, versus 24/28 by sparse LDV and 25/28 by microphones alone.All four LDV misses occur at RG3 and are recovered acoustically; fused coverage stays 28/28 from 3σ to 10σ.Source: §4 · p. 3
- At m = 24, the structural basis is strongest for early-loss fusion while removing more than half of repeated scan locations.Source: §4 · p. 3
5. DISCUSSION
Fusion maintains full mild-window coverage across tested acoustic thresholds, recovering sparse LDV misses concentrated at RG3. The discussion distinguishes this decision-level complementarity from pointwise fusion and limits the result to commissioning-set coverage.
5. DISCUSSION
- 28/28 mild resonance windows remain covered by fusion across acoustic thresholds from 3 to 10 pooled-SD units.Sparse LDV alone covers 85.7% of the mild windows.Source: §5 · p. 4, Figure 5 · p. 4
- All four sparse-LDV misses cluster at RG3, where force-normalized acoustic evidence is strong and recovers those windows without training on mild states.The hidden-node 90th percentile targets hotspot-like FRAC changes while avoiding the sensitivity of a maximum to one reconstructed node.Source: §5 · p. 4
- The study retains a spatial LDV diagnostic field and fuses normalized evidence at the condition–resonance level because the campaigns are separate realizations.This differs from pointwise multimodal regression and aligns with late/confidence fusion and evidence aggregation for slight damage.Source: §5 · p. 4
- Coverage is commissioning-set resonance coverage, not a population detection probability, given one specimen, one healthy acoustic assembly, and four mild physical conditions.The study also lacks multi-bolt 5-Nm acoustic states and cannot quantify assembly-to-assembly false alarms; repeated synchronized reassemblies are needed for calibrated sensitivity and specificity.Source: §5 · p. 4
- Figure 6 compares retained LDV budgets using hidden-node complex NMSE and FRAC-map correlation.Its caption distinguishes dense-reference full and hidden maps from the sparse-reference protocol.Source: Figure 6 · p. 4
6. CONCLUSION
With 24 of 51 LDV locations, the method retains high spatial map fidelity for four unseen single-bolt 5-Nm states. Decision-level fusion covers all 28 mild resonance windows, with every LDV miss recovered acoustically.
6. CONCLUSION
- 24/28 mild windows are covered by sparse LDV alone and 25/28 by acoustic evidence, while fusion covers 28/28.All four LDV misses are recovered acoustically, and fusion remains at 28/28 for thresholds from 3 to 10 pooled standard deviations.Source: §6 · p. 4
- Using 24 of 51 LDV locations, four unseen single-bolt 5-Nm states retain high spatial map fidelity; at a conservative 5σ acoustic criterion, fusion covers all 28/28 mild resonance windows.Source: §6 · p. 4
- The results support microphones as a complementary early-warning channel for resonance-dependent sparse-LDV blind spots, while population-level claims require larger repeated and synchronized experiments.Source: §6 · p. 4