3. Identifying and classifying design variables
Before a single run of the DOE matrix can be generated, the restraint engineer must convert an ambiguous requirement — "make the occupant protection more robust" — into a finite, typed, and bounded set of design variables. LS-DYNA restraint models are expensive to run (a full frontal sled or vehicle model with a detailed dummy may take 30 minutes to several hours per run), so the cost of a poorly specified variable set is paid twice: once in wasted runs, and again in a matrix that cannot be interpreted. This chapter establishes a disciplined classification scheme and applies it to the specific constraints that restraint systems impose.
Three orthogonal classifications
Every candidate variable should be tagged along three independent axes. The axes are orthogonal: a variable can be continuous and controllable, discrete and controllable, or continuous and noisy, and each combination has different implications for the matrix design.
Axis 1 — Continuous vs. discrete. A continuous variable can take any value within its range: pretensioner trigger time (ms), seat belt anchor height (mm), airbag vent diameter (mm), inflator mass flow scaling factor. A discrete variable takes values from a finite, often unordered set: airbag module part number, retractor type (load-limiting profile A/B/C), seat track position (fore/aft detent), buckle stalk variant, or a categorical on/off flag such as "adaptive load limiter enabled." Discrete variables with more than two levels cannot be handled by a two-level screening design without collapsing levels, so they must be identified early.
Axis 2 — Controllable vs. noise. Controllable (design) factors are those the engineering team can set and hold during production: geometry, material grade, trigger thresholds, vent size. Noise factors are those that vary in service or in the test environment and cannot be economically controlled: occupant size and posture, ambient temperature, belt routing and slack, production tolerance on the retractor, crash pulse variation between vehicles of the same build. Noise factors belong in a robust-design (Taguchi-style) inner/outer array or in a Monte Carlo layer, not in the primary screening matrix. Mixing them into the main array inflates run count and destroys the clean main-effect estimates that screening depends on.
Axis 3 — Constraint status. A variable may be free within its range, or it may be coupled to another variable by a physical or regulatory constraint. Constraint status determines whether the matrix can be generated as a full factorial or must be filtered, and whether the design space is a box or a manifold.
Applying the classification to a frontal restraint model
Consider a driver-side frontal restraint system in an LS-DYNA sled model. A typical candidate list, classified, looks like this:
| Variable | Type | Role | Range / Levels | Constraint |
|---|---|---|---|---|
| Pretensioner trigger time | Continuous | Controllable | 8–20 ms | Free |
| Load limiter force level | Continuous | Controllable | 2.5–4.5 kN | Coupled to belt geometry |
| Airbag vent diameter | Continuous | Controllable | 25–45 mm | Free |
| Retractor profile | Discrete | Controllable | A / B / C | Free |
| Adaptive LL enabled | Discrete (binary) | Controllable | 0 / 1 | Free |
| Occupant stature (5th/50th/95th) | Discrete | Noise | 3 dummies | Outer array |
| Ambient temperature | Continuous | Noise | -35 to +85 °C | Outer array |
| Belt anchor position (regulatory) | Continuous | Controllable | Fixed by FMVSS 208 | Excluded |
Two entries in this table deserve emphasis. First, the load limiter force level is coupled to belt geometry: a higher force level is only physically meaningful if the belt payout path and anchor geometry can sustain it without spool-out. In practice this means the matrix cannot treat the two as independent — either the belt geometry is fixed at a nominal value and the LL force is swept, or the pair is treated as a constrained 2D design space and infeasible combinations are filtered out before run submission. Second, the belt anchor position is controllable in the model but fixed by regulation in the vehicle; it must be excluded from the matrix, not because it is unimportant, but because varying it produces runs that cannot be certified.
Restraint-specific constraints
Restraint systems impose constraints that generic DOE tools do not know about. The engineer must encode them explicitly, either as bounds in the design table or as post-generation filters.
- Regulatory bounds. FMVSS 208, ECE R94/R95, and C-NCAP specify dummy injury thresholds (HIC, chest deflection, neck Nij, femur load) and, in some cases, prescribe the test configuration itself. Any variable that is fixed by the regulation — anchor location, belt webbing stiffness class, dummy type — is not a design variable for the matrix; it is a boundary condition.
- Physical coupling. Pretensioner trigger time and load limiter force interact strongly: a late trigger with a high LL force produces a different belt force history than an early trigger with the same force. If the DOE is a screening design, this interaction must be estimable, which means the resolution of the design must be high enough (Resolution IV or better) to avoid aliasing the two-factor interaction with main effects.
- Packaging and geometry limits. Airbag vent diameter is bounded above by module packaging and below by the minimum inflation performance required to meet out-of-position (OOP) criteria. These bounds are not symmetric and should be entered as explicit lower/upper limits, not as ±10% of nominal.
- Discrete-level feasibility. A retractor profile C may not be compatible with a particular buckle stalk variant. Such combinations must be removed from the design table before the matrix is generated, otherwise the solver will either error out or silently substitute a default.
From classification to a variable register
The output of this chapter is a variable register — a single table that the matrix generator consumes. Each row records the variable name as it appears in the LS-DYNA keyword deck (for example *MAT_ELASTIC card field, *DEFINE_CURVE abscissa, or a *PARAMETER name), its type, its role, its range or level set, its constraint status, and the keyword card or parameter it maps to. The register is the contract between the restraint engineer and the DOE tool: if a variable is not in the register, it does not enter the matrix, and if it is in the register with the wrong type, the matrix will be wrong regardless of how sophisticated the sampling algorithm is.
A minimal register entry for the pretensioner trigger time might read: name PT_TRIG, continuous, controllable, range 8–20 ms, free, mapped to the abscissa of the pretensioner force curve in *DEFINE_CURVE. The load limiter force level would read: name LL_FORCE, continuous, controllable, range 2.5–4.5 kN, coupled to BELT_GEOM, mapped to the ordinate plateau of the retractor force curve. Once every candidate has been entered in this form, the classification work is complete and the matrix generation step can proceed with a design space that is finite, typed, and physically meaningful.