2. Uncertainty sources in occupant CAE

An occupant CAE model is a chain of approximations: sheet-metal thicknesses are nominal, material cards are fitted to coupon tests, the restraint system is positioned within drawing tolerances, and the crash pulse comes from a vehicle model that is itself an approximation. When a sled or full-vehicle result is used to certify a restraint system, the question is no longer "what is the dummy reading?" but "how much of that reading is attributable to factors we did not control?" This chapter classifies the four dominant uncertainty sources in occupant CAE — material variability, geometry tolerances, loading conditions, and model form uncertainty — and shows how each is characterized, quantified, and propagated in practice.

Material Variability

Material variability enters occupant CAE at two levels. The first is batch-to-batch and within-batch scatter of the physical material: yield strength, ultimate tensile strength, elongation, and strain-rate sensitivity of the body and restraint materials. For a typical dual-phase steel used in a seat frame or a B-pillar, the yield strength may be specified as 600 ± 40 MPa, and the hardening curve derived from tensile tests carries additional scatter in the post-uniform region. The second level is modeling variability: the choice of constitutive law, the calibration procedure, and the extrapolation of the hardening curve beyond the measured strain range.

In practice, material uncertainty is represented by a set of calibrated material cards rather than a single nominal card. A defensible workflow is:

1. Collect coupon test data (tensile, shear, and where relevant high-rate tests) across at least three heats or batches.
2. Fit a hardening law (for example, a Swift or Voce combination) to each batch, and record the fitted parameters rather than only the raw curves.
3. Treat the fitted parameters as random variables with a mean vector and covariance matrix estimated from the batch fits.
4. Generate a sample set (Latin hypercube or Sobol) of material parameter vectors, and run the occupant model once per sample.

For restraint materials such as webbing and airbag fabric, the dominant variability is often in the force–elongation characteristic and the friction coefficient at the slip interface, not in the elastic modulus. A webbing elongation tolerance of ±5% can shift chest deflection by several millimeters in a frontal impact, which is comparable to the margin between a pass and a marginal result.

Geometry Tolerances

Geometry uncertainty in occupant CAE comes from three distinct sources: manufacturing tolerances on the parts that define the occupant environment (seat frame, cushion, belt anchorages, steering column), assembly variation (weld and rivet positions, hemming, gap and flush), and positioning uncertainty of the dummy and the restraint system relative to the vehicle.

The most consequential geometry parameters are rarely the ones with the largest tolerance. In a frontal sled model, the following typically dominate:

• Seat cushion angle and cushion height — affect pelvis position and hence belt fit; a 2° cushion angle change can move the H-point by 5–10 mm.
• Belt anchorage locations — the D-ring and buckle positions control the belt path over the shoulder and pelvis; ±10 mm in the D-ring fore-aft position changes the shoulder belt angle and the chest loading.
• Steering column rake and telescope — affect the airbag-to-driver distance and the chin/chest interaction.
• Dummy positioning — the H-point and pelvis angle tolerances specified in the relevant regulation or protocol (for example, a ±5 mm H-point tolerance and a ±1° pelvis angle tolerance) are themselves a source of scatter that must be included, not assumed away.

A practical way to handle geometry is to parameterize the model with a small set of morphing or parametric variables (seat angle, D-ring x/z, column rake, dummy H-point x/z), assign tolerances from the drawing or the positioning protocol, and sample within those bounds. The key discipline is to keep the parameter set small — typically 5–10 variables — so that the sample size remains tractable and the sensitivity results remain interpretable.

Loading Conditions

Loading uncertainty is the source most often underestimated in occupant CAE, because the crash pulse is usually treated as a fixed input. In reality, the pulse delivered to the occupant compartment varies with vehicle-to-vehicle differences, barrier alignment, impact speed, and the occupant model's own boundary conditions.

Three loading parameters deserve explicit treatment:

• Impact speed and pulse shape — a ±2 km/h variation in impact speed, or a change in pulse rise time from 25 ms to 35 ms, alters the occupant's forward excursion and the timing of airbag contact.
• Pulse duration and the secondary pulse — the deceleration after the primary peak affects rebound and the belt-to-occupant interaction.
• Boundary conditions of the sled or body model — seat mounting stiffness, floor deformation, and the presence or absence of a pre-crash braking phase.

For a frontal occupant model, a defensible loading uncertainty set might include impact speed (e.g., 48–52 km/h), pulse rise time (25–35 ms), and a seat-mount stiffness multiplier (0.8–1.2). These are sampled jointly with the material and geometry variables, not varied one at a time, because the occupant response is strongly nonlinear and the interactions matter.

Model Form Uncertainty

Model form uncertainty is the discrepancy between the model's structure and the real physics — not the scatter of its inputs. It includes the choice of dummy model (finite-element vs. rigid-body), the contact definition between belt and dummy, the airbag gas model, the friction law at the belt–clothing interface, and the treatment of strain-rate effects in the restraint system.

Model form uncertainty is the hardest to quantify because it cannot be sampled from a distribution in the same way as material scatter. The practical approaches are:

• Model comparison — run the same load case with two or three defensible modeling choices (e.g., two dummy models, or two belt contact formulations) and treat the spread as a lower bound on model form uncertainty.
• Validation against test — compare the model prediction with sled or vehicle test data at the same nominal inputs; the residual is an estimate of the combined model form and calibration error.
• Expert elicitation — where test data are unavailable, structured expert judgment can provide a bounded estimate, provided the basis is documented.

How the Sources Combine

The four sources are not independent in their effect on the occupant response. Material softening in the seat frame changes the occupant kinematics, which changes the belt path, which changes the chest loading — so material and geometry uncertainties interact. Loading uncertainty modulates all of them. The figure below shows the propagation structure: each source enters the occupant model through a specific set of parameters, and the output metrics (HIC, chest deflection, belt force, head excursion) respond with different sensitivities.

The practical consequence of this structure is that a one-at-a-time sensitivity study is insufficient. If material softening and seat-angle variation both push the occupant forward, their combined effect on chest deflection can exceed the sum of their individual effects. A joint sampling scheme — Latin hypercube across all four source groups, with model form handled as a separate scenario set — is the minimum defensible approach for a UQ study intended to support a design decision.

Documenting the Uncertainty Budget

A useful deliverable at the end of this characterization step is an uncertainty budget table that records, for each source, the parameter, its distribution or bound, the basis (test data, drawing tolerance, protocol, expert judgment), and the expected effect on the key response metrics. The table below is an illustrative example for a frontal occupant sled model; the values are representative assumptions, not measured results.

Two disciplines make this budget useful rather than decorative. First, every row must have a stated basis; a bound without a source is an assumption, and assumptions must be labeled as such. Second, the budget should be reviewed against the sensitivity results: if a parameter with a wide bound turns out to have negligible effect on the response, it can be fixed at its nominal value in later studies, which reduces the sampling dimension and the computational cost. Conversely, a parameter with a narrow bound but high sensitivity deserves more careful characterization, because the model's prediction is riding on it.

With the sources characterized and the budget documented, the next step is to choose the propagation method — Monte Carlo, Latin hypercube, or a surrogate-assisted approach — and to define the response metrics and acceptance criteria that the UQ study will report against. The quality of that downstream analysis is bounded by the quality of this source characterization: an elegant sampling scheme applied to poorly justified input distributions produces a precise but meaningless answer.