4. Measurement system analysis for crash simulation

Before a DMAIC team can attribute a crash-simulation discrepancy to a design change, a material model, or a solver setting, it must first prove that the measurement system itself is trustworthy. In a crashworthiness program the "measurement system" is not a single gauge — it is a chain of three distinct links: the finite element solver that produces predicted responses, the physical instrumentation that produces test responses, and the correlation metrics that compare the two. Measurement system analysis (MSA) in this context means quantifying the error and repeatability of each link, so that any observed gap between simulation and test can be decomposed into measurement noise versus genuine physical disagreement.

A useful framing is to treat the total observed discrepancy as a sum of contributions. If the solver is deterministic but sensitive to discretization, the instrumentation has sensor and DAQ error, and the correlation metric has its own sensitivity to time alignment and filtering, then a discrepancy of, say, 12% in peak intrusion may be dominated by any one of these. MSA is the discipline of bounding each contribution before drawing conclusions.

Validating the solver as a measurement device

The solver link is often overlooked because engineers assume a deterministic code produces a deterministic answer. In practice, crash solvers exhibit run-to-run variation from parallel decomposition, contact sorting, and floating-point reduction order, and they exhibit discretization sensitivity that behaves like measurement bias. A defensible solver MSA has three parts.

First, establish repeatability: run the identical deck three to five times with the same core count and confirm that key responses (peak intrusion, peak acceleration, HIC, section force) vary by less than a pre-agreed threshold — commonly 0.5% for peak values and 1% for integrated quantities. If variation exceeds this, the discrepancy budget is already consumed before any correlation is attempted.

Second, establish reproducibility across numerical settings: vary mesh density (e.g., 8 mm, 6 mm, 5 mm in the occupant-compartment region), time step, and mass-scaling factor, and record how each response moves. A response that shifts 6% between 8 mm and 5 mm mesh is not a reliable measurement of the physical quantity; it is a measurement whose uncertainty band is ±3%. That band must be carried into the correlation discussion.

Third, confirm determinism of the post-processing: the same binary output read by the same extraction script must yield identical curves. Version drift in the extraction script or a changed filtering default is a classic source of phantom discrepancies.

# Example solver repeatability check (illustrative)
run_id   peak_intrusion_mm   peak_accel_g   HIC15
run_01   142.3               68.4           412
run_02   142.1               68.6           410
run_03   142.4               68.3           413
# spread: intrusion 0.3 mm (0.21%), accel 0.3 g (0.44%), HIC 3 (0.7%)
# verdict: repeatability acceptable for correlation use

Validating instrumentation data

On the test side, the MSA question is whether the recorded signal faithfully represents the physical response at the sensor location. Three checks matter most for crash data. Calibration and range: an accelerometer with a ±500 g range and a 10 kHz mounted resonance is adequate for a chest accelerometer but marginal for a B-pillar sensor seeing 800 g spikes; range clipping silently truncates peaks. Filtering compliance: SAE J211 specifies channel frequency classes (CFC 60 for many occupant channels, CFC 180 or 1000 for structural channels). Applying the wrong CFC changes peak values by several percent and shifts phase — a discrepancy that has nothing to do with the design. Mounting integrity: a sensor that resonates on its bracket produces a high-frequency artifact that a correlation metric will penalize even though the underlying structure matched.

A practical instrumentation MSA is a channel-by-channel audit table. For each channel record the sensor model, range, sensitivity, calibration date and drift, DAQ sample rate, anti-alias setting, and applied CFC. Then compute the expected uncertainty contribution and compare it with the observed simulation–test gap for that channel. Channels whose uncertainty band is comparable to the gap cannot support a root-cause conclusion and must be flagged.

Validating the correlation metric itself

The third link is the metric. CORA, ISO/TS 18571, and similar composite scores combine magnitude, phase, and shape terms with weighting factors. These metrics are not neutral observers: they have their own sensitivity to time alignment, to the filtering applied before scoring, and to the evaluation window. An MSA of the metric asks: if the same two curves are shifted by 2 ms, or filtered at a different CFC, how much does the score move? If a 2 ms shift changes a CORA score from 0.82 to 0.71, then a 0.05 difference between two design variants is not meaningful.

Establish metric repeatability by scoring a fixed reference pair of curves multiple times with controlled perturbations (time shift ±1 ms, ±2 ms; CFC variation; window truncation) and recording the score spread. Use that spread as the resolution limit of the metric. Only differences larger than the resolution limit should be treated as real.

The output of this MSA is a discrepancy budget: a documented allocation of the observed simulation–test gap to solver noise, instrumentation uncertainty, and metric resolution, with the residual attributed to genuine model or design differences. That residual is the only quantity the rest of the DMAIC investigation should attempt to explain. When the budget shows the residual is small relative to the measurement bands, the correct conclusion is that the correlation is already within measurement capability and further model tuning would be fitting noise. When the residual is large and clearly outside all three bands, the team has earned the right to proceed to root-cause analysis with confidence that the signal is real.