Accelerometer Aliasing Vibration Measurement Case Study

This case study follows a vibration measurement that appeared to show a serious rotating-machinery fault. The spectral peak was real in the recorded data, but it was not real in the machine. It was created by a measurement chain that sampled too slowly while allowing high-frequency acceleration to reach the analog-to-digital converter.

The useful lesson is that a clean FFT peak is not automatically physical evidence. In a sampled measurement system, the engineering evidence begins before the FFT: sensor mounting, analog bandwidth, anti-alias filtering, sample rate, clock stability, record length, and validation tests define whether the spectrum can be trusted.

The central question is:

Did the accelerometer data reveal a mechanical fault, or did the acquisition system fold out-of-band vibration into the diagnostic band?

The answer is that the original acquisition was not valid for release. A high-frequency vibration component near the sensor mounting resonance was aliased into the band used for machine acceptance.

Case Summary

Item	Engineering relevance
System	Variable-speed test stand with accelerometer-based vibration acceptance.
Sensor	Piezoelectric accelerometer on a bearing housing.
Interface	Charge amplifier, analog low-pass filter, 16 bit data acquisition, FFT-based acceptance report.
Original objective	Verify vibration content from shaft speed through low-order harmonics.
Failure observed	A strong spectral peak appeared near 4x shaft speed.
Hidden weakness	The analog filter did not sufficiently attenuate content above Nyquist.
Main consequence	The acceptance report classified an acquisition artifact as a possible mechanical fault.
Corrective action	Reacquire with a justified sample rate and anti-alias filter, perform sample-rate sensitivity tests, and release only data with measurement-chain evidence.

The machine was nearly pulled from test for a suspected fault. The data deserved suspicion first.

Measurement Setup

The test stand recorded vibration during a controlled run at:

The shaft frequency was therefore:

The acceptance report was interested in low-order vibration through roughly:

The acquisition configuration was:

Quantity	Symbol	Value
sample rate	f_s	1024\ \text{Hz}
Nyquist frequency	f_N	512\ \text{Hz}
analog filter type		single-pole low-pass
analog filter cutoff	f_c	700\ \text{Hz}
ADC range		\pm10\ \text{V}
ADC resolution		16 bit
suspicious FFT peak	f_p	114\ \text{Hz}
independent high-rate reference peak	f_h	910\ \text{Hz}

The suspicious peak was:

so it looked like a 4x shaft-speed component. That made it easy to interpret as a mechanical fault involving looseness, rub, modulation, or a secondary rotating feature.

Why the Original Spectrum Looked Plausible

The report was plausible because the suspicious peak was:

1. narrow in frequency;
2. repeatable over several records;
3. near an integer shaft-speed multiple;
4. above the local noise floor;
5. large enough to trigger review.

None of those facts proves that the peak is physical. A sampled system can produce a stable, repeatable, narrow false peak if a stable out-of-band component aliases into the recorded band.

The first diagnostic rule was:

A spectral feature must be tested against the acquisition chain before it is assigned to the machine.

Step 1: Check Nyquist Frequency

For a sample rate:

the Nyquist frequency is:

Any analog content above:

must be sufficiently attenuated before the ADC. If it reaches the converter, it can fold into the recorded spectrum.

The independent reference acquisition, sampled at a much higher rate with a steeper front-end filter, showed a strong component near:

That frequency is above the original Nyquist frequency:

so the original acquisition was vulnerable to aliasing unless the analog filter removed that component before sampling.

Engineering Comment

The nominal measurement band was only 0 to 200\ \text{Hz}, but the sensor did not stop sensing above 200\ \text{Hz}. Mechanical mounting resonance, local housing modes, acoustic excitation, cable motion, and piezoelectric sensor dynamics can all create out-of-band acceleration. The analog front end must control what reaches the ADC, not only what the engineer plans to interpret.

Step 2: Predict the Alias Frequency

A practical alias relation is:

where n is the integer that brings the apparent frequency into the recorded band.

For the high-frequency component:

with:

choose:

Then:

This exactly matches the suspicious FFT peak:

and:

Engineering Comment

The dangerous detail is that the alias landed on an apparently meaningful machine order. That coincidence can push engineers toward a mechanical diagnosis before checking the acquisition system. Aliasing is especially deceptive when the false frequency resembles an order, a bearing feature, a control oscillation, or a structural mode.

Step 3: Check Original Anti-Alias Attenuation

The original analog filter was a single-pole low-pass filter with:

A first-order low-pass magnitude is:

At:

the magnitude is:

In decibels:

If the high-frequency component at the accelerometer was approximately:

the component reaching the ADC after this filter was still about:

Engineering Comment

A cutoff above Nyquist is not an anti-alias strategy. A single-pole filter at 700\ \text{Hz} attenuates the 910\ \text{Hz} component only modestly, so the ADC still samples enough out-of-band energy to create a visible false in-band peak. Digital filtering after the ADC cannot remove this error, because the 114\ \text{Hz} alias is already inside the sampled record.

Step 4: Validate by Changing Sample Rate

The team repeated the acquisition with the same sensor and mounting but changed the sample rate while also recording a high-rate reference channel.

Acquisition	Sample rate	Expected result for a real 114 Hz vibration	Observed result
Original	1024\ \text{Hz}	Peak stays at 114\ \text{Hz}	Peak at 114\ \text{Hz}
High-rate reference	4096\ \text{Hz}	Peak stays at 114\ \text{Hz}	Dominant peak at 910\ \text{Hz}
Diagnostic resample	1500\ \text{Hz}	Peak stays at 114\ \text{Hz}	Apparent peak near 590\ \text{Hz}
Steeper filtered setup	1024\ \text{Hz} with stronger analog filtering	Real 114\ \text{Hz} peak remains	Peak nearly disappears

For the diagnostic resample:

and:

The same physical 910\ \text{Hz} component aliases to:

That movement is strong evidence that the original 114\ \text{Hz} peak was not a physical 4x shaft-speed vibration.

Engineering Comment

A real mechanical peak should remain at the same physical frequency when the sample rate changes, subject to speed variation and order tracking. An alias generally moves when the sample rate changes. This is one of the fastest diagnostic tests for suspected aliasing, provided the machine operating condition is stable and the acquisition chain is otherwise controlled.

Step 5: Redesign the Measurement Boundary

The release objective was not to measure every possible vibration feature. It was to validate low-order vibration through:

The corrected setup used:

1. the same accelerometer location after mounting verification;
2. a documented valid band of 0 to 200\ \text{Hz};
3. a fourth-order low-pass analog anti-alias filter with:

4. sample rate:

For an ideal fourth-order low-pass magnitude approximation:

At the top of the desired band:

the magnitude is:

so the desired band is only weakly attenuated.

At the high-frequency disturbance:

the magnitude is:

The 2.4g_{\text{pk}} out-of-band component is reduced to:

Engineering Comment

This filter is not universal. It is appropriate only if the accepted measurement band is really 0 to 200\ \text{Hz}. If bearing diagnostics, gear-mesh analysis, acoustic resonance, impact detection, or high-frequency envelope analysis is required, the measurement boundary must be redesigned with a higher sample rate, different filter, and validated sensor mounting bandwidth.

Release Decision

The original data package should not be used for machine release. It contains a false in-band peak caused by an invalid acquisition setup. The machine should not be cleared or rejected from that evidence alone.

The corrected release decision is:

1. mark the original report as measurement-chain invalid for spectral acceptance;
2. reacquire data with the documented valid band, sample rate, analog filter, sensor mounting, and clock settings;
3. verify that the suspicious peak does not persist under the corrected anti-alias boundary;
4. if a real in-band peak remains, diagnose it as a machine issue using speed, phase, order tracking, sensor relocation, and mechanical inspection;
5. keep the high-frequency 910\ \text{Hz} feature as a separate observation, not as evidence of a 4x shaft-speed fault.

After reacquisition, the 114\ \text{Hz} peak disappeared below the release threshold. The high-frequency component remained visible only on the high-rate reference channel and was traced to local fixture resonance near the accelerometer mount. The machine release was accepted for the low-order vibration requirement, with a follow-up action to improve fixture stiffness and update the acquisition standard.

Validation Evidence Required

A defensible measurement release package should include:

Evidence	Purpose
Stated valid frequency band	Prevents using the data outside the designed measurement boundary.
Sensor and mounting check	Confirms that local resonance and mounting stiffness are understood.
Analog filter specification	Shows cutoff, order, attenuation, tolerance, and phase implications.
Sample rate and clock settings	Defines Nyquist frequency and timing reliability.
Out-of-band injection or reference comparison	Demonstrates that alias-prone content is controlled.
Sample-rate sensitivity test	Shows whether suspicious peaks move with sample rate.
Raw waveform retention	Allows clipping, transients, dropout, and timing issues to be checked.
Tachometer or speed reference	Separates true machine orders from acquisition artifacts.

The evidence does not need to be elaborate for every measurement. It must be proportionate to the decision. Acceptance, certification, root-cause analysis, alarm tuning, and safety-related monitoring require stronger evidence than a screening trend.

Common Mistakes

• Treating sensor bandwidth as equivalent to anti-alias protection.
• Setting the low-pass cutoff above Nyquist and calling it an anti-alias filter.
• Trusting a narrow FFT peak before checking how it changes with sample rate.
• Interpreting a peak as a machine order because it lands near an integer multiple of speed.
• Applying digital smoothing after sampling and assuming aliasing has been removed.
• Reporting a valid frequency range without stating filter order, sample rate, or attenuation.
• Using the same acquisition setup for low-order vibration trending and high-frequency fault diagnostics.

Transferable Lessons

Aliasing is not only a signal-processing topic. It is a measurement-integrity failure. The false peak came from a real physical vibration, a real sensor, a real ADC, and a real FFT, but the inferred low-frequency machine fault was not real.

Good engineering practice is to define the measurement boundary before interpreting the data. State the frequency band, sample rate, analog filter, sensor mounting, uncertainty contributors, and validation test. If a spectral feature moves when the sample rate changes, changes when the analog filter changes, or disappears under a higher-quality reference channel, the measurement chain deserves the diagnosis before the machine does.