3. Test data acquisition for correlation

Correlation between CAE predictions and physical tests is only as trustworthy as the measurement data feeding it. A model calibrated against noisy, poorly placed, or inadequately documented test data will reproduce the test's errors rather than the structure's true behavior. This chapter addresses the three decisions that determine whether test data is fit for correlation: which sensors to use and where to place them, how to quantify and propagate measurement uncertainty, and how to assess data quality before it enters the calibration loop.

Sensor Selection: Matching Transducer Physics to the Correlation Target

Sensor selection begins with the quantity the correlation will actually compare. If the CAE output is a strain field at a weld toe, an accelerometer mounted 200 mm away provides little value regardless of its accuracy. The selection process should work backward from the model response of interest to the physical quantity, then to the transducer that measures it with acceptable fidelity in the test environment.

For structural dynamics correlation, the dominant choices are piezoelectric accelerometers, strain gauges, and laser vibrometers. Accelerometers are selected primarily by sensitivity, frequency range, mass loading, and mounting method. A common practical rule is that the sensor mass should not exceed roughly one-tenth of the effective modal mass of the structure at the measurement point; exceeding this shifts the local resonance and biases the modal frequencies being correlated. Mounting method matters as much as the sensor: a stud-mounted accelerometer may have a usable range to 10 kHz, while the same sensor attached with petro-wax or a magnetic base may roll off below 2 kHz. The mounting resonance should be documented, because it appears directly in the measured FRF.

Strain gauges are chosen by gauge length relative to the strain gradient. In a region with a steep gradient—near a notch or a load introduction point—a long gauge averages the peak strain and under-reports it. Rosette configurations (0°/45°/90°) are required wherever principal strain direction is unknown, which is typical for correlation points not aligned with the load axis. Temperature compensation and lead-wire resistance must be recorded, since a quarter-bridge circuit with long unshielded leads will pick up both thermal drift and electromagnetic noise.

For lightweight or compliant structures where mass loading is unacceptable, laser vibrometers or scanning LDV provide non-contact velocity measurement. Their limitation is line-of-sight access and sensitivity to surface finish; a retroreflective tape target is usually needed on machined or painted surfaces.

Measurement Uncertainty: Sources and Propagation

Measurement uncertainty in a correlation context is not a single number but a budget assembled from independent contributions. For a typical accelerometer channel, the dominant terms are:

• Calibration uncertainty — typically 1–3% for a factory calibration, reducible to below 1% with a accredited recalibration.
• Mounting and mass-loading error — can exceed 5% in frequency near a mounting resonance or on light structures.
• Signal conditioning and digitization — amplifier gain error, anti-alias filter roll-off, and ADC quantization; usually small but must be bounded.
• Environmental effects — temperature drift, base strain, cable triboelectric noise, and acoustic pickup.
• Positioning error — the difference between the nominal and actual sensor location, which for mode shape correlation can dominate at high spatial gradients.

These contributions combine in root-sum-square fashion when independent. A representative budget for a modal test accelerometer channel might yield a combined standard uncertainty of about 3–4% in amplitude and 0.5–1° in phase over the correlation band. That figure should be carried forward: when a CAE mode frequency differs from test by 4%, and the test frequency uncertainty is 0.5%, the discrepancy is attributable to the model, not the measurement. When the discrepancy is 1% and the uncertainty is 1.5%, the correlation is inconclusive and the model should not be tuned on that basis.

Uncertainty also propagates through derived quantities. Modal damping estimated by half-power bandwidth is far more sensitive to noise than modal frequency; a 3% amplitude uncertainty can produce 20–30% scatter in damping estimates. Similarly, strain-derived stress at a notch amplifies both gauge placement error and gauge-length averaging. Calibration targets should therefore be weighted by the uncertainty of the underlying measurement, not treated as equally reliable.

Data Quality Assessment Before Calibration

Data quality assessment is a gate, not a formality. The following checks should be completed and documented before any parameter is adjusted in the CAE model.

Signal-level and saturation checks. Verify that peak amplitudes sit within the linear range of sensor, amplifier, and ADC—typically 30–70% of full scale. A channel that clipped during a random excitation run will show a flattened peak and elevated harmonics; coherence will drop at the affected frequencies. Clipping is often invisible in a time-history overview and must be checked per channel.

Coherence and signal-to-noise. For random excitation, ordinary coherence between excitation and response should exceed 0.9 across the correlation band. Dips in coherence indicate low excitation energy at those frequencies, leakage, or nonlinearity. Do not average coherence away; inspect it frequency by frequency, because a narrowband dip at a mode of interest invalidates the FRF there.

Reciprocity and repeatability. Where the structure is expected to be linear, measure at least one reciprocal pair (excite at A, measure at B; then excite at B, measure at A). A reciprocity deviation above roughly 5% in magnitude signals nonlinearity, a loose joint, or a mounting problem. Repeat a subset of measurements after re-mounting to bound mounting variability.

Rigid-body and boundary-condition verification. For a free-free modal test, the six rigid-body modes should appear below roughly 5–10% of the first elastic mode. If they do not, the suspension is too stiff and the boundary condition assumed in the CAE model is not reproduced. This is one of the most common and most consequential correlation errors.

Geometry and channel mapping. Confirm that every measurement DOF maps to the correct node and direction in the test geometry, and that the test geometry aligns with the CAE coordinate system. A sign error in a single channel will corrupt MAC values and mode shape comparison in ways that are easy to misattribute to the model.

Practical Example: Assessing a Modal Test Dataset

Consider a free-free modal test on a 4.2 kg aluminum bracket, instrumented with 24 uniaxial accelerometers (sensitivity 100 mV/g, ±5% factory calibration) and excited by an instrumented modal hammer at 6 drive points. The correlation target is the first five elastic modes between 80 Hz and 900 Hz.

During assessment, the following observations are made. The rigid-body modes appear at 1.8, 2.1, and 2.4 Hz, well below 10% of the first elastic mode at 84 Hz, so the suspension is acceptable. Coherence exceeds 0.95 across the band except for a dip to 0.72 between 610 and 640 Hz at two response channels; the hammer spectrum shows low energy in that range, indicating insufficient excitation rather than a structural problem. Reciprocity between drive point 3 and response channel 11 deviates by 3.1% in magnitude, within the 5% threshold. One channel shows a peak at 92% of full scale during the highest-energy hit, which is close enough to the ADC limit to warrant re-ranging that channel and repeating the run.

The combined uncertainty budget for this setup is estimated at 3.5% in amplitude and 0.8° in phase, dominated by calibration (2.5%) and mounting variability (2%). The first elastic mode is measured at 84.0 Hz; the CAE model predicts 87.6 Hz, a 4.1% difference. Because the test frequency uncertainty is well below 1%, the 4.1% discrepancy is attributable to the model—most plausibly the bracket-to-fixture joint stiffness—and is a legitimate calibration target. A second mode shows a 1.2% difference, which is comparable to the uncertainty and should not be used to drive parameter changes.

The output of this stage is a documented, uncertainty-quantified dataset with an explicit list of which response features are eligible as calibration targets and which are not. That dataset—not the raw time histories—is the input to the parameter calibration and correlation workflow that follows.