4. Design of experiments for occupant injury sensitivity

Sensitivity analysis in occupant safety is only as trustworthy as the design of experiments (DOE) that feeds it. A restraint system model may contain dozens of parameters—belt anchor positions, pretensioner timing, airbag vent size, seat friction, padding stiffness—yet only a handful materially influence the injury criteria we care about. The DOE stage is where we decide which factors to vary, over what ranges, with what sampling structure, and against which scalar responses. Get these four decisions right and the subsequent ranking (main effects, interactions, Sobol indices) becomes interpretable; get them wrong and the analysis will confidently rank noise.

Factor selection: from model inventory to a defensible shortlist

Begin with a complete parameter inventory extracted from the CAE model, not from memory. For a frontal 50 km/h sled or full-vehicle model this typically includes restraint geometry (D-ring height, buckle stalk angle, anchor fore-aft position), restraint characteristics (retractor force-limiting level, pretensioner stroke and fire time, load-limiter profile), airbag parameters (vent diameter, inflator mass flow, tether length, module standoff), and occupant/contact parameters (seat cushion stiffness, friction coefficient, initial posture offsets). Record each parameter with its nominal value, its plausible engineering range, and the physical mechanism by which it could affect injury.

Then apply three filters. First, controllability: a factor that cannot be adjusted in the physical system (e.g., occupant stature in a fixed 50th-percentile study) is a noise variable, not a design factor—handle it by stratification or by fixing it. Second, range plausibility: a ±40 mm anchor shift may be numerically convenient but physically unbuildable; ranges should reflect tolerance stack-up, package constraints, and manufacturing capability. Third, mechanism relevance: retain factors with a credible causal path to the response. A useful discipline is to write one sentence per factor linking it to a load path—for example, "lower load-limiter force reduces chest deflection but increases head excursion, therefore interacts with airbag standoff."

For a typical frontal study, a workable shortlist is 8–12 factors. Beyond that, screening cost grows and factor effects become confounded with noise unless the design is carefully chosen. Document the excluded factors and the reason for exclusion; this record is essential when a reviewer asks why a known-sensitive parameter was omitted.

Levels and ranges: encoding the physics, not just the numbers

Two-level designs are the workhorse of screening, but the choice of low and high values deserves more thought than a symmetric ±10% rule. Set levels from the engineering tolerance band, then verify that the extremes remain physically realizable and numerically stable. If a factor's response is known to be nonlinear—airbag vent area versus head acceleration, for instance—a two-level screen will fit a linear surrogate that may mislead. In such cases either narrow the range around the nominal so linearity is a fair approximation, or reserve the factor for a later response-surface stage with three or more levels.

Encode factors to dimensionless form before building the matrix: x = (X − X₀) / ΔX, where X₀ is the nominal and ΔX the half-range. This makes main effects directly comparable across factors with different units and lets you read a coefficient as "change in response per half-range." Keep a decoding table so every coded column maps back to a physical setting.

Example values above are illustrative teaching parameters, not measured data. Always derive ranges from your own tolerance and package studies.

Screening designs: choosing the matrix that fits the budget

With 8–12 factors and an expensive explicit model (often 4–12 h per run), a full factorial is out of reach. The standard screening choice is a fractional factorial, typically a Resolution IV design such as a 2⁽⁸⁻⁴⁾ or 2⁽¹⁰⁻⁵⁾, which estimates all main effects clear of two-factor interactions, at the cost of aliasing two-factor interactions with each other. If interaction structure matters—and in restraint systems it usually does—a Plackett–Burman design offers similar economy but with heavier aliasing, so it is best reserved for a first pass to eliminate clearly inert factors.

For sensitivity ranking specifically, space-filling designs are often a better fit than classical factorial screens. A Latin hypercube sample of 60–120 runs over the full factor ranges supports variance-based global sensitivity analysis (Sobol indices) and captures nonlinearity and interaction without assuming a polynomial form. The trade-off is that LHS gives no replicated center points, so run-to-run numerical noise must be assessed separately—typically by repeating the nominal configuration three times and checking that the coefficient of variation in the response is well below the smallest effect you intend to rank.

A practical hybrid is common in industry: run a 2-level fractional factorial (16–32 runs) to screen out inert factors, then build a 40–80 run Latin hypercube on the surviving 5–7 factors for quantitative ranking. This two-stage structure keeps total cost near 100 runs while giving both a defensible screening record and a statistically sound sensitivity estimate.

Response definition: one scalar per injury criterion, never a blended score

The response is the dependent variable of the entire study, and ambiguity here is the most common source of unusable sensitivity results. Each run must yield a well-defined scalar per injury criterion, extracted by a fixed, automated post-processing script so that no analyst judgment enters between runs. Typical responses for a frontal occupant study are HIC15, 3 ms chest clip, maximum chest deflection, Nij, and peak femur force; for side impact, add rib deflection and pelvic force. Define the extraction window explicitly—for example, HIC15 computed over the interval that maximizes the value within 0–150 ms after the defined time zero—and freeze that definition for every run.

Two rules prevent subtle errors. First, do not average or weight injury criteria into a single composite response for sensitivity analysis. A factor that reduces chest deflection while raising head excursion will cancel in a blended score, hiding exactly the trade-off the ranking is meant to reveal. Analyse each criterion separately and compare rankings across criteria. Second, filter the response for numerical noise: if the model uses a time-step or contact algorithm that produces small run-to-run variation, quantify it with repeated nominal runs and discard factors whose apparent effect falls below that floor. A factor whose main effect is smaller than the noise band should be reported as "not distinguishable from noise," not ranked.

Finally, verify the response pipeline before committing to the full matrix. Run the nominal configuration, confirm each extracted scalar matches the value reported by the standard occupant-safety post-processor, and check that the extraction script handles the full range of factor settings without clipping or missing channels. A screening study built on a mis-specified response is worse than no study, because it produces a confident and wrong ranking.