3. Design space definition for crash CAE

In crash CAE design optimization, the design space is the mathematical domain over which the response surface will be constructed. If the design space is defined poorly, no amount of surrogate modeling sophistication will recover a useful optimum: the true optimum may lie outside the sampled region, the response surface may be dominated by noise from irrelevant variables, or the design of experiments (DOE) budget may be wasted on parameters that barely influence the crash responses. This chapter addresses three coupled decisions: which parameters to include, how wide to set their bounds, and how to screen the candidate set down to a tractable, physically meaningful subset before committing to a DOE.

From CAD and CAE model to candidate parameters

Parameter selection begins with a systematic inventory of the crash model rather than with the optimizer. A practical workflow is to walk the finite element model by subsystem and record every dimension, thickness, material property, and connection attribute that a design engineer could legitimately change. For a typical frontal impact model this inventory includes:

  • Geometric parameters: front rail section width and height, crash box length, bumper beam curvature, shotgun profile, dash panel inclination.
  • Gauge parameters: thickness of rails, crash boxes, bumper beam, shotgun, floor cross members, B-pillar reinforcement.
  • Material parameters: yield strength and hardening exponent of DP590/DP780 grades, bake-hardening level, strain-rate sensitivity coefficient.
  • Connection parameters: spot weld pitch, adhesive bead width, number of weld nuggets at critical joints.
  • Topology/position parameters: bead or rib placement, trigger notch location, load-path bracket position.

Each candidate should be tagged with its owning subsystem, its nominal value, its manufacturing tolerance, and the crash responses it is expected to influence (e.g., intrusion, peak acceleration, energy absorption, mass). This tagging is not administrative overhead — it is the raw material for the screening step later. Parameters that cannot be manufactured within tolerance, or that are frozen by package or styling constraints, should be removed at this stage rather than carried into the DOE.

Setting bounds: physics, manufacturing, and packaging

Bounds are the most consequential and least formalized part of design space definition. Three constraints must be reconciled simultaneously:

  1. Physical validity. A rail thickness of 0.4 mm or a crash box length of 5 mm is not a design — it is a numerical artifact. Bounds must keep every sample inside a region where the FE model remains representative of a real structure.
  2. Manufacturing feasibility. Gauge bounds should respect the steel supplier's standard thickness series (e.g., 1.0, 1.2, 1.4, 1.6, 1.8, 2.0 mm) and the forming window of the chosen grade. A bound that forces a 1.35 mm gauge is technically valid but practically unusable.
  3. Packaging and interface. Geometric parameters are usually bounded by adjacent components: the rail cannot grow taller than the powertrain clearance, the crash box cannot be longer than the bumper-to-rail offset.

A defensible default is to set bounds at roughly ±20–30% of nominal for gauges and ±10–15% for geometric dimensions, then tighten any bound that violates the constraints above. Bounds that are too narrow produce a response surface that is locally accurate but globally misleading; bounds that are too wide introduce strong nonlinearity and even mesh-distortion failures in the crash model. The width should also be checked against the expected curvature of the response: peak acceleration is typically far more sensitive to gauge than intrusion is, so the acceleration-relevant parameters may warrant narrower bounds to keep the surface smooth.

Before running any DOE, verify that the corner points of the box (all parameters at their lower or upper bounds simultaneously) still solve cleanly. Corner-point runs that terminate on negative volume or excessive hourglassing indicate that the design space extends beyond the model's robust region, and the offending bounds should be pulled in.

Screening with engineering judgment and sensitivity analysis

With a candidate list of 20–40 parameters, a full-factorial or even a moderate-resolution DOE is infeasible. Screening reduces the set to the 6–12 parameters that actually drive the responses of interest. Two complementary tools are used: engineering judgment first, then quantitative sensitivity analysis.

Engineering judgment screening removes parameters whose influence is structurally obvious. A floor cross-member gauge will not meaningfully change frontal peak acceleration; a bumper beam curvature will not change rear intrusion. This step is fast and prevents the sensitivity study from being diluted by irrelevant variables, but it must be documented — a parameter removed by judgment should be recorded with the reason, so that the decision can be revisited if the response surface later shows unexplained lack of fit.

Sensitivity analysis then quantifies what judgment cannot. The standard approach for crash CAE is a Plackett–Burman or fractional-factorial screening design, which estimates main effects with a small number of runs (typically 12–24 for 10–20 parameters). Each parameter is run at two levels (its bounds), and the main effect on each response is computed as the difference in mean response between the high and low levels. Parameters whose standardized effect falls below a threshold — commonly |effect| < 2–3 standard errors, or a contribution below roughly 5% of total response variance — are candidates for removal.

For crash responses, main-effect screening alone is often insufficient because interactions between gauges and geometry are strong. A useful refinement is to retain any parameter that shows a large main effect on any response, and to retain pairs known from engineering experience to interact (e.g., rail gauge × rail section height). The output of screening is a reduced parameter set with documented bounds, ready for the response surface DOE.

1. Candidate Inventory Geometry · Gauge · Material Connections · Topology Tag: subsystem, nominal, tolerance, target response 20–40 parameters 2. Bound Setting Physical validity Manufacturing feasibility Packaging / interface Gauge ±20–30% · Geom ±10–15% Corner-point check 3. Judgment Screen Remove structurally irrelevant parameters Document reason for each removal 4. Sensitivity Plackett–Burman 12–24 runs Main effects |effect| threshold Retain interactions Reduced Parameter Set 6–12 parameters with documented bounds → ready for response surface DOE Example: standardized main effects on peak acceleration (illustrative) 0 2 4 6 8 threshold ≈ 3 Rail gauge Crash box length Bumper beam curvature Shotgun gauge Weld pitch standardized effect magnitude

Worked example: frontal impact design space

Consider a frontal impact model with 28 candidate parameters. After judgment screening, 16 remain: six gauges (front rail, crash box, bumper beam, shotgun, floor cross member, B-pillar reinforcement), four geometric dimensions (rail section width, rail section height, crash box length, bumper beam curvature), three material properties (rail yield strength, crash box hardening exponent, strain-rate coefficient), two connection parameters (rail weld pitch, bumper-to-rail adhesive width), and one topology parameter (trigger notch location).

A Plackett–Burman design with 20 runs is executed at the parameter bounds. The standardized main effects on peak acceleration are shown in the accompanying figure: rail gauge and crash box length dominate, bumper beam curvature is moderate, shotgun gauge and weld pitch fall below the threshold. The same screening design is evaluated for intrusion and mass, and the union of parameters exceeding the threshold on any response is retained. The result is a reduced set of nine parameters — rail gauge, crash box length, crash box gauge, bumper beam curvature, rail section height, rail yield strength, crash box hardening exponent, adhesive width, and trigger notch location — with bounds documented and corner points verified to solve cleanly.

Screening is not a one-time gate. If the response surface built on the reduced set later shows systematic lack of fit in a region of the design space, the removed parameters should be re-examined — particularly those removed by judgment rather than by measured effect. A parameter that appeared irrelevant at the screening levels can become significant once the dominant parameters move the structure into a different deformation mode.

Practical checks before committing to the DOE

Three checks are worth running before the design space is frozen. First, confirm that every retained parameter has a documented nominal value, lower bound, upper bound, and unit, and that the bounds are consistent with the manufacturing and packaging constraints recorded during inventory. Second, run the corner points and a small number of interior points to confirm that the FE model remains stable across the full box; record any run that terminates abnormally and adjust the offending bound rather than the solver settings. Third, verify that the reduced set still spans the responses of interest: if a response has no retained parameter with a meaningful effect, either the response is not design-sensitive or a relevant parameter was screened out prematurely, and the screening should be revisited.

The output of this chapter is a frozen design space: a reduced parameter list with bounds, units, and documented screening rationale, validated at its corners. This is the input to the response surface DOE, and its quality determines whether the surrogate model that follows is a faithful representation of the crash behavior or an expensive interpolation of noise.

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