Analyzing Vibration Isolation Telemetry

Given a telemetry dataset (accelerometer/displacement sensors on isolated platform + ground reference), immediately:

1. Compute transmissibility: T(f) = |X_platform(f)| / |X_ground(f)| via FFT of both channels over matching time windows
2. Identify natural frequency f_n (transmissibility peak) and compare to design spec (typically 1-5 Hz for pneumatic/active isolation)
3. Check isolation ratio at operating frequencies of concern (building HVAC ~5-50 Hz, foot traffic ~1-3 Hz, rotating machinery harmonics)
4. Flag any transmissibility > 1 (amplification) in the equipment's sensitive frequency band (e.g., for e-beam lithography: 1-100 Hz; for AFM/STM: 1-200 Hz)

Python
import numpy as np
from scipy import signal

f_platform, Pxx_platform = signal.welch(platform_accel, fs=fs, nperseg=4096)
f_ground, Pxx_ground = signal.welch(ground_accel, fs=fs, nperseg=4096)
transmissibility = np.sqrt(Pxx_platform / Pxx_ground)
f_resonance = f_platform[np.argmax(transmissibility)]

Progress:

• Step 1: Validate telemetry quality (sample rate, sensor calibration, clipping, dropouts)
• Step 2: Compute PSD and transmissibility curves for each axis (X, Y, Z, and tilt if available)
• Step 3: Identify resonance frequencies and compare against isolator design parameters
• Step 4: Correlate anomalies with environmental/operational context (time of day, nearby equipment, temperature)
• Step 5: Classify root cause (mechanical wear, air spring leak, control loop instability, structural coupling, payload change)
• Step 6: Quantify impact on equipment performance metric (overlay error, image blur, positioning repeatability)
• Step 7: Recommend corrective action and define re-validation criteria

Step 1 — Telemetry Validation

• Confirm sample rate ≥ 10x highest frequency of interest (Nyquist margin, not just Nyquist limit)
• Check for ADC clipping (values pinned at sensor range limits)
• Check for gaps/dropouts that would corrupt FFT — flag any window with >1% missing samples
• Verify accelerometer units and sensitivity against datasheet; a wrong scale factor silently invalidates all downstream analysis

Step 2 — Frequency Domain Analysis

• Use Welch's method (averaged periodograms) over raw FFT to reduce variance — window length trades frequency resolution vs. noise
• Compute per-axis AND cross-axis coupling (e.g., vertical excitation causing horizontal response indicates misalignment or worn isolator)
• Generate waterfall/spectrogram plots if data spans hours+ to catch time-varying behavior (thermal drift, intermittent faults)

Step 3 — Resonance & Isolator Health

• Active isolation systems: resonance peak should be low (~0.5-2 Hz) and well-damped (Q factor < 2); a sharpening peak over time = failing damper or feedback loop
• Passive pneumatic isolators: check for shift in natural frequency over weeks/months — indicates air spring pressure drift or payload mass change
• Compare current transmissibility curve against baseline/commissioning curve — overlay plots, compute RMS deviation per decade of frequency

Step 4 — Contextual Correlation

• Cross-reference anomaly timestamps with: HVAC cycling schedule, nearby crane/forklift operation, building occupancy, facility construction logs
• Check for correlation with ambient temperature (thermal expansion changes isolator stiffness) and with payload/tool state (idle vs. active processing)

Step 5 — Root Cause Classification

Step 6 — Impact Quantification

• Translate vibration spec violation into equipment-specific metric: overlay error (nm) for lithography, image resolution loss for microscopy, positioning repeatability (nm/µm) for metrology tools
• Use equipment manufacturer's vibration specification curve (often given as acceleration PSD limit vs. frequency) as pass/fail reference

Step 7 — Recommendations

• Specify concrete action: re-level isolator, replenish air spring pressure, replace damper, re-tune active control gains, relocate equipment away from vibration source
• Define re-test protocol: duration, conditions (idle vs. operating), acceptance threshold matching original commissioning spec

Example 1: Input: Telemetry from an active vibration isolation platform under a semiconductor metrology tool shows transmissibility rising from 0.3 to 1.8 at 3.2 Hz over the past 6 weeks, with Q factor increasing from 1.1 to 4.5. Output: Diagnosis: active control loop losing damping authority, likely actuator or sensor feedback degradation (not passive mechanical issue, since passive natural frequency would shift rather than sharpen in isolation). Recommend: check actuator current draw vs. command, inspect position sensor noise floor, verify control loop gains against commissioning values. Impact: measurement repeatability likely degraded ~3-5x at 3.2 Hz band; flag tool for recalibration if 3.2 Hz coincides with known disturbance source (check facility vibration survey).

Example 2: Input: Passive pneumatic isolators under a TEM show a slow downward drift of natural frequency from 2.0 Hz to 1.4 Hz over 3 months, uniform across all 4 legs. Output: Diagnosis: air spring pressure loss (slow leak) or gradual payload increase (e.g., added shielding/accessories) — uniform drift across legs points to systemic cause rather than single-leg failure. Recommend: verify air supply pressure and leak-test pneumatic lines; confirm no equipment additions; re-level and re-pressurize to restore 2.0 Hz design point; re-baseline transmissibility curve post-service.