Video-Based Vibration Analysis

• Video-based vibration analysis is a non-contact method that maps visual motion from video sensors into quantitative mechanical observables using techniques like phase-based estimation and holography.
• It employs advanced algorithms including phase-based motion estimation, deep learning, and event-based processing to extract modal parameters with sub-pixel accuracy across full-field measurements.
• Practical applications span structural health monitoring, non-destructive evaluation, and machine diagnostics, validated against traditional sensor data for precise defect detection and modal analysis.

Video-based vibration analysis is the suite of non-contact methods that quantitatively characterize vibrational phenomena in physical systems using image or event data from video sensors. This domain comprises signal acquisition (video or event stream), data-driven motion estimation (phase, optical flow, or holographic inference), frequency and modal parameter extraction, and visualization of mode shapes and operational deflection forms. The approach enables sub-pixel, full-field spatiotemporal measurement of vibratory response in macroscopic and microscopic structures—frequently surpassing contact sensor arrays in resolution, coverage, and practicality.

1. Fundamental Concepts and Measurement Modalities

Video-based vibration analysis is rooted in the mapping of visual motion—typically minute, periodic, or impulsive displacements of a structure—into time-resolved mechanical observables. The major modalities are:

• Frame-based video vibrometry: Sensors (CMOS/CCD cameras) record sequential visible frames; motion information is extracted by phase-based decomposition, Eulerian intensity analysis, or feature/keypoint tracking.
• Event-based vision sensors: Asynchronous, high-dynamic-range detectors generate a stream of pixel-wise events (ON/OFF) triggered by rapid intensity changes, with temporal resolution in the microsecond regime (Bane et al., 2024).
• Heterodyne holography: Coherent optical interferometric techniques utilize frequency-shifted reference and signal beams to reconstruct full-field vibration amplitude and phase maps at sub-nanometer sensitivity and across large bandwidth (Joud et al., 2013, Samson et al., 2011).
• Synchronous stroboscopic imaging: Illumination sources, phase-locked to vibratory excitation, "freeze" system motion at selected cycle phases for micron-level spatial mapping even at ultrasonic or RF mechanical frequencies (Linzon et al., 2011).
• Deep learning-enhanced tracking: CNN-based detection and SIFT-based subpixel matching combine for robust displacement and vibration feature extraction in challenging scenarios (markerless, low SNR, multi-object) (Bai et al., 2021).

All approaches share a common theoretical basis: the displacement field $u(x,y,t)$ under vibration modulates image intensity and/or phase, which can be algorithmically related to modal parameters (natural frequencies, mode shapes, damping ratios) via signal processing and finite element inversion (Shang et al., 2017, Sarrafi et al., 2018).

2. Phase-Based Motion Estimation and Magnification

Phase-based motion estimation (PME) employs complex steerable filter banks, typically Gabor wavelets, to extract the local phase of image intensity at each pixel and orientation (Sarrafi et al., 2018, Shang et al., 2017). The foundational sequence is:

1. Decomposition:

$$(G^\theta + i H^\theta) * I(x, y, t) = A^\theta(x, y, t) e^{i \phi^\theta(x, y, t)}$$

where $A^\theta$ is local amplitude, $\phi^\theta$ phase, and $*$ convolution.

2. Motion extraction: Phase shift $\Delta \phi$ correlates with physical displacement $\Delta x$ by:

$\Delta x(x, y) = \Delta \phi(x, y) / \omega_0$

$\omega_0$ is the filter's central spatial frequency.

1. Frequency analysis: FFT of $\phi^\theta(x, y, t)$ across time yields the motion spectrum; peaks correspond to modal resonances.
2. Motion magnification: Filtered phase at frequency $f_0$ is amplified by factor $\alpha$:

$$I_{mag}(x, y, t) = \Re \{ A(x, y, t) \exp[i(\phi(x, y, t) + \alpha \Delta\phi(x, y, t))] \}$$

yielding a video that visually emphasizes operational deflection shapes (ODS) at the target modes.

This allows for robust visualization of structure mode shapes, identification of defects via ODS modulation or frequency shifts, and quantitative estimation of frequency and damping parameters to within $<3\%$ of ground truth for a variety of structures, including wind turbine blades and bioprinted hydrogels (Rahman et al., 31 Dec 2025, Sarrafi et al., 2018).

3. Full-Field Holographic and Stroboscopic Techniques

Heterodyne holography extends conventional video-based methods using coherent optical interferometry. By introducing a controlled frequency shift $\Delta \omega$ to a reference beam, the interference against the phase-modulated object beam encodes vibration information in optical sidebands (Joud et al., 2013, Samson et al., 2011). The Bessel-function sideband expansion:

$$E_\text{signal}(t) = E_0 \sum_{n=-\infty}^\infty J_n(A) \exp[i (\omega_0 + n \Omega) t]$$

permits selective imaging of amplitude and phase at each pixel for a given vibration mode. The amplitude is retrieved via inverse lookup on $|J_n(A)|$, while phase demodulation yields the local mechanical phase. Stroboscopic methods synchronize pulsed illumination with the vibrational cycle, freezing complex vibration profiles at GHz frequencies and enabling extraction of nonlinear mode shapes in MEMS/NEMS via time-resolved movies or peak amplitude mapping (Linzon et al., 2011).

Advantages include nanometer-to-micrometer amplitude sensitivity, full-field acquisition, tunable dynamic range, and direct recovery of spatially continuous amplitude and phase maps beyond the reach of high-speed cameras (Joud et al., 2013, Samson et al., 2011).

4. Event-Based Vibrometry and Advanced Sensing Architectures

Event cameras (DVS, DAVIS, Prophesee, etc.) generate data only on rapid intensity changes, making them ideally suited for analyzing high-frequency or low-amplitude vibration (Bane et al., 2024, Cai et al., 4 Jul 2025). Frequency mapping can be performed using:

• Hypertransition counting: Record ON$\rightarrow$OFF transition timestamps at each pixel, compute intervals $\Delta t_k$, derive local frequency $f_\text{vib} = 1 / \bar T$.
• Global spectral estimation: Bin event counts over time windows, apply DFT for spectrum; vibration frequency is at the dominant peak.
• Motion-magnification via hybrid pipeline: Reconstruct intensity frames from event streams (e.g., E2VID RNN) and apply phase-based magnification via steerable pyramids.

Event-based sensing supports real-time operation (latency $<$10 ms), high frequency bandwidth ($>$10 kHz), and large dynamic range with minimal power and bandwidth requirements. Limitations include oversmoothing in intensity reconstruction, sensitivity to camera motion/scene flicker, and computational expense for real-time pyramid decompositions (Bane et al., 2024, Cai et al., 4 Jul 2025).

5. Applications: Structural Health Monitoring and Non-Destructive Evaluation

Video-based vibration analysis is widely adopted for:

• Structural health monitoring (SHM): Detecting damage, defect localization, and quantifying mass/stiffness anomalies in wind turbine blades, bridges, bioprinted constructs, and other engineered components by spectral deviation and direct ODS comparison (Rahman et al., 31 Dec 2025, Shang et al., 2017, Sarrafi et al., 2018).
• Non-destructive testing (NDT): Infer internal material heterogeneity (Young's modulus, density) and defect presence without invasive actuation or physical contact, often validated by finite element simulations (Rahman et al., 31 Dec 2025).
• Machine diagnostics: RF-assisted strobe systems fuse radar-based frequency estimation with video and LED-stroboscopic imaging for rapid, multi-point vibration assessment of rotating machinery, with amplitude sensitivities $\sim$0.1 mm and sub-percent frequency error (Roy et al., 2020).
• Micro/Nano-mechanical systems: Synchronous imaging and holographic methods acquire GHz-mode vibration profiles and nonlinear dynamics for MEMS/NEMS resonators (Linzon et al., 2011).

Motion magnification, multi-point feature extraction, and enhanced data-driven band selection further enable robust field deployment on large, complex structures.

6. Data Processing, Calibration, and Experimental Validation

Precise calibration and processing pipelines are essential for rigorous video-based vibration analysis:

• Pixel-to-metric conversion: Relate measured displacement (pixels or phase shift) to physical units (mm, μm) via controlled scale markers or camera pinhole models (Bai et al., 2021, Shang et al., 2017).
• Role of filtering: Butterworth, Savitzky–Golay, and narrowband temporal filters suppress aliasing, improve SNR, and isolate modal behavior.
• Machine learning-based localization: Mask R-CNN (HRNet backbone) segmentation coupled with SIFT keypoint refinement achieves sub-pixel placement and tracks motion with $<$0.005" MAE versus ground truth (Bai et al., 2021).
• Validation against contact sensors: Modal frequencies and shapes extracted from video are cross-validated with accelerometers/LVDTs; frequency error is typically $<$3 %, spatial MAC $>$0.85 for modes (Sarrafi et al., 2018, Shang et al., 2017).
• Limitations: Lens distortion, perspective error, imaging frame rate, and surface reflectivity/setups must be addressed for accurate measurement. Methods often require manual annotation, ROI selection, and specific best-practices (e.g., rigid tripod mounting, high-contrast markers) (Bai et al., 2021, Shang et al., 2017).

7. Limitations, Challenges, and Future Directions

Technical challenges persist:

• Illumination and scene stability: Robust phase/motion extraction is undermined by nonuniform lighting, camera shake, and specular surfaces. Event cameras demand strict scene design to avoid flicker-induced false positives (Bane et al., 2024, Cai et al., 4 Jul 2025).
• Frame rate constraints: Modal aliasing occurs if the sensor frame rate does not meet $f_s \ge 2 f_{\max}$.
• Reconstruction algorithms: Event-based intensity mapping is susceptible to oversmoothing except under ideal conditions; phase-magnification at the event-domain level remains open.
• Computational efficiency: Dense multi-point extraction and real-time video processing require significant GPU/CPU resources and optimized algorithms for steerable pyramid filtering and FFT.
• Calibration completeness: Current practice often omits multi-view geometric calibration and lens distortion correction, potentially limiting accuracy.

A plausible implication is that adaptive real-world datasets, FPGA-based pyramid implementations, and direct event-domain phase-extraction algorithms will further expand the applicability and precision of video-based vibration analysis across emerging fields such as bioprinting, large-scale civil infrastructure, and ultrafast MEMS diagnostics.

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Key References:

• Heterodyne Holography: Joud et al. ("Vibration motions studied by Heterodyne Holography" (Joud et al., 2013)), Leclerc et al. ("Video-rate laser Doppler vibrometry by heterodyne holography" (Samson et al., 2011)).
• Phase-based Eulerian Magnification: Sarrafi et al. ("Vibration-Based Damage Detection in Wind Turbine Blades" (Sarrafi et al., 2018)), Zhang & Sattar ("Multi-point Vibration Measurement for Mode Identification…" (Shang et al., 2017)).
• Event-Based Vibrometry: "Non-Invasive Qualitative Vibration Analysis using Event Camera" (Bane et al., 2024), "Event2Audio: Event-Based Optical Vibration Sensing" (Cai et al., 4 Jul 2025).
• Deep Learning Tracking: Bai et al. ("Automatic Displacement and Vibration Measurement…” (Bai et al., 2021)).
• SHM Applications: Guo et al. ("Non-Contact and Non-Destructive Detection...” (Rahman et al., 31 Dec 2025)).
• Stroboscopic/Hybrid Sensing: Fathollahi ("A Novel RF-assisted-Strobe System…” (Roy et al., 2020)).
• Synchronous Imaging: Kozinsky et al. ("Synchronous imaging for rapid visualization…” (Linzon et al., 2011)).