4. Characterizing input variability

Crash CAE predictions are only as credible as the distributions that feed them. A frontal impact model may reproduce a physical test within 5% on peak deceleration, yet the same model, when run across a production population, can show a 20–30% spread in occupant injury metrics. That spread does not come from solver noise; it comes from the fact that every input to the model — yield stress, sheet thickness, flange position, impact angle, and velocity — is itself a random variable. This chapter addresses how to characterize those input variables from two complementary data sources: controlled experiments and production records.

The central discipline is to treat each input as a random variable with a defined distribution type, mean, and dispersion, and to justify each of those three choices with data rather than convenience. A common failure mode in industrial practice is to assign a coefficient of variation (CoV) "because that is what we always use," without checking whether the underlying data support a normal, lognormal, or Weibull form. The sections below work through the four input families in the order they typically enter a crash model: material, thickness, geometry, and loading.

Material properties: separating batch-to-batch from specimen-to-specimen scatter

For crash-relevant metals — mild steel, DP590/DP780, 6xxx-series aluminum — the properties that matter most are yield strength, ultimate tensile strength, uniform elongation, and, for forming-sensitive grades, the strain-hardening exponent n. Experimental data usually arrive as tensile test records: a set of specimens per heat, several heats per coil, several coils per supplier. This nested structure matters because the variance components are not interchangeable. Specimen-to-specimen scatter within a single heat reflects local microstructure and test repeatability; heat-to-heat scatter reflects chemistry and processing drift; supplier-to-supplier scatter reflects different mill practices.

A defensible characterization therefore begins with a variance-component analysis rather than pooling all coupons into one histogram. In practice, a one-way random-effects ANOVA on yield strength grouped by heat gives the within-heat and between-heat variance; the total variance is their sum, and the CoV reported to the CAE team should be the total. For a typical DP780 dataset of, say, 8 heats × 5 specimens, one commonly observes within-heat CoV near 1.5–2.5% and between-heat CoV near 3–5%, giving a total CoV around 4–6%. These figures are illustrative of typical automotive sheet grades, not measured values from a specific program, and should be replaced by project data.

Distribution choice deserves explicit attention. Yield strength is bounded below by zero and mildly right-skewed, so a lognormal or a three-parameter Weibull often fits better than a normal, particularly when the CoV exceeds about 8%. A quick Anderson–Darling or Kolmogorov–Smirnov test on the pooled sample, plus a probability plot, is sufficient to justify the choice. Where data are sparse — fewer than about 20 observations — a normal fit with a conservative CoV is acceptable, but the assumption should be documented.

Thickness: from coil certificates to formed-part measurements

Sheet thickness variability has two distinct sources that are often conflated. The first is incoming coil thickness tolerance, governed by standards such as EN 10131 or the equivalent OEM specification; a nominal 1.2 mm cold-rolled sheet typically carries a tolerance of ±0.05 to ±0.09 mm depending on width and grade. The second is thinning during forming: a drawn pillar or a hydroformed rail may lose 10–20% of its thickness at critical radii. Crash models built from nominal CAD thickness miss both effects.

The practical approach is to build a thickness distribution per formed region, not per part. Ultrasonic or eddy-current thickness gauging at a grid of points on a formed coupon or a sectioned production part yields a spatial map; the distribution of thickness within a crash-critical zone (a bend, a spot-weld nugget vicinity, a fold initiator) is what enters the model. For a typical B-pillar inner, one might find a mean of 1.14 mm against a 1.20 mm nominal, with a standard deviation of 0.04 mm — a CoV near 3.5%. Again, these are representative magnitudes for illustration.

Two cautions apply. First, thickness and material strength are often negatively correlated in production because mills roll to the lower thickness limit when the grade is running strong; ignoring this correlation overstates the joint probability of thin-and-weak sections. Second, thickness measurements taken on the flat blank do not represent the formed part; the correlation between blank thickness and formed thickness at a critical radius is typically 0.6–0.8, not unity.

Geometry: manufacturing variation beyond nominal CAD

Geometric variability in crash models arises from stamping springback, assembly tolerance stack-up, and weld distortion. The variables that most affect crash response are flange angles, bend radii, spot-weld positions, and the relative position of mating parts at joints. Characterizing these requires dimensional data — either from a coordinate measuring machine (CMM) on production parts or, increasingly, from in-line optical scanning of a sample of parts per shift.

The workflow is to reduce the high-dimensional scan data to a small set of scalar features that the CAE model can accept. For a front rail, for example, the features might be the flange angle at the crush initiator, the longitudinal position of the first weld, and the offset of the bumper attachment face. A principal component analysis on the scan data typically shows that the first two or three modes explain 80–90% of the geometric variance; those modes, scaled by their eigenvalues, become the random variables. This is far more efficient than perturbing every node, and it preserves the physically correlated deformation patterns that pure random nodal perturbation destroys.

Loading conditions: test-to-test and fleet variability

Loading variability enters through impact velocity, impact angle, barrier alignment, and, for side impacts, the striking vehicle's mass and stiffness. Regulatory tests are tightly controlled — a 50 km/h frontal impact has a tolerance of roughly ±1 km/h and ±1° in yaw — but real-world crashes are not. Field data from accident databases (for example, NASS-CDS or GIDAS) give the distribution of delta-v and impact angle for the crash mode of interest. A typical offset frontal population might show delta-v with a mean near 45 km/h and a standard deviation of 8–10 km/h, with impact angle approximately normal about zero and a standard deviation of 5–8°.

For regulatory and consumer-rating load cases, the loading variability is small and can often be treated as deterministic; for robustness studies aimed at real-world performance, it must be sampled. The distinction should be stated explicitly in the model documentation, because mixing the two in a single Monte Carlo run produces results that are neither a compliance prediction nor a field-performance prediction.

Putting the four families together: correlation and sampling

Once each family has a marginal distribution, the remaining task is to define the dependence structure before sampling. Three correlations are commonly material in crash work: thickness versus yield strength (negative, as noted), flange angle versus weld position (positive, both driven by the same stamping die), and impact velocity versus impact angle (weakly dependent in field data, often treated as independent). Ignoring a correlation of −0.4 between thickness and strength can shift the predicted 95th-percentile intrusion by several millimeters, because the joint tail of thin-and-weak is under-sampled.

A practical workflow is to assemble a correlation matrix from the available data, complete it with engineering judgment where data are absent, and then use a Gaussian copula or a Nataf transformation to generate correlated samples from the marginals. The Latin hypercube design with 200–500 samples is usually sufficient for a crash model with 6–10 input variables; convergence should be checked by comparing the 5th and 95th percentiles of the output across two independent sample sets.

Documentation and traceability

Every distribution used in a crash CAE robustness study should be traceable to a data source, a sample size, and a stated assumption. A compact input-variability register — one row per variable, with columns for nominal value, distribution type, mean, CoV or standard deviation, data source, sample size, and correlation partners — is sufficient and is far more useful than a prose description buried in a report. The register becomes the single point of truth when the model is re-run for a new program or when a supplier changes.

The quality of the output distribution is bounded by the quality of this register. A model with well-characterized inputs and a modest sample size will generally outperform a model with nominal inputs and a large sample size, because the latter is precisely sampling the wrong thing. Characterizing input variability is therefore not a preliminary chore before the "real" analysis; it is the analysis.