2. Injury prediction landscape

Occupant injury prediction sits at the intersection of biomechanics, regulation, and numerical simulation. Before any uncertainty can be quantified, we must be precise about what is being predicted and how the prediction is produced. This section maps the three layers that every UQ study must respect: the injury metrics that define the output quantities of interest, the regulatory and consumer test protocols that anchor those metrics to physical loading conditions, and the CAE model chain that transforms a crash pulse into a predicted injury value. Understanding these layers is what allows us to later attribute uncertainty to the correct source — material scatter, boundary conditions, dummy variation, or model form error.

Injury metrics as quantities of interest

Injury criteria are scalar reductions of complex time histories. They are deliberately simple so that regulators, OEMs, and suppliers can compare results, but that simplicity hides assumptions that matter for UQ.

Head Injury Criterion (HIC). HIC is computed from the resultant translational acceleration at the head center of gravity:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
subject to t2 - t1 ≤ 15 ms

The 2.5 exponent makes HIC highly sensitive to peak acceleration, and the 15 ms window means the metric is dominated by short, sharp events. For UQ this is critical: small timing shifts in the acceleration trace can move the maximizing window and produce discontinuous HIC changes. A Monte Carlo study that treats HIC as a smooth function of inputs will underestimate its variance.

Brain Injury Criterion (BrIC). Rotational motion drives diffuse axonal injury, which HIC cannot capture. BrIC uses peak angular velocity components:

BrIC = max( |ωx|/ωx_crit , |ωy|/ωy_crit , |ωz|/ωz_crit )
with ωx_crit = 66.25 rad/s, ωy_crit = 56.45 rad/s, ωz_crit = 42.87 rad/s

BrIC is a normalized maximum, so it is piecewise linear in the angular velocity components and switches governing axis as loading direction changes. This axis-switching is a common source of non-smooth response surfaces in DOE studies.

Chest deflection and viscous criterion. Thoracic injury is characterized by chest compression and compression rate. Chest deflection is typically reported as absolute compression (mm) or normalized deflection (fraction of chest depth). The viscous criterion VC combines both:

VC = max over t of [ (D(t) * dD(t)/dt) ]   (m/s)

where D(t) is the normalized chest deflection. Because VC multiplies deflection by rate, it is sensitive to both the magnitude and the phase of the deflection signal — a subtle point when comparing simulations with different damping assumptions.

Regulatory and consumer test protocols

Metrics only become meaningful when tied to a loading condition. The principal protocols are:

Two features of these protocols drive UQ design. First, the test conditions are fixed but the tolerance on those conditions is not zero: barrier speed, impact angle, dummy positioning, and restraint timing all carry manufacturing and setup variation. Second, consumer protocols increasingly score continuous metrics rather than applying binary limits, which means the full distribution of the predicted metric matters, not just whether it crosses a threshold.

The CAE model chain for occupants

A frontal occupant simulation is not a single model but a chain of coupled submodels. Each link introduces its own uncertainty, and errors propagate forward. The figure below shows the chain and the dominant uncertainty sources at each stage.

The chain begins with the crash pulse, usually a sled acceleration trace derived from vehicle testing or full-vehicle CAE. Pulse shape, duration, and filtering convention all affect the occupant response. Next, the restraint system model captures belt geometry, pretensioner firing, load limiter force, and airbag inflation. These are among the most uncertain inputs because they depend on pyrotechnic and fabric behavior that is difficult to characterize repeatably. The occupant model — an Anthropomorphic Test Device (ATD) finite element model or a human body model — introduces variability through joint stiffness, mass distribution, and initial posture. The contact and kinematics stage governs how forces transfer between restraint, occupant, and interior; friction coefficients and contact stiffness are common calibration knobs. Finally, the injury metric stage reduces the simulated response to a scalar, introducing its own sensitivity through filtering and window selection.

From chain to UQ strategy

The practical consequence of this chain structure is that uncertainty sources are not interchangeable. Upstream sources — pulse scatter and restraint timing — typically dominate the variance of HIC and chest deflection, because they change the entire loading history. Downstream sources — contact parameters and metric post-processing — more often introduce bias and non-smoothness. A well-designed UQ campaign therefore stratifies inputs by their position in the chain and their physical interpretability, rather than treating all parameters as a flat list.

As a concrete example, consider a frontal sled study with a 50th-percentile Hybrid III driver. A reasonable first-pass input set might assign: pulse scaling factor (normal, σ = 3%), pretensioner trigger time (uniform, ±2 ms), belt load limiter force (normal, σ = 5%), airbag inflator mass flow (normal, σ = 4%), and ATD hip joint stiffness (uniform, ±10%). Running a Latin hypercube design of 200 samples and computing HIC15, BrIC, and peak chest deflection for each yields a response dataset suitable for variance decomposition. The expected finding — consistent with published sensitivity studies — is that pulse scaling and limiter force together explain the majority of HIC variance, while BrIC is more sensitive to initial head position and airbag interaction. These are illustrative expectations, not measured results; the actual ranking must be established from the specific model and design.

The next step in any UQ workflow is to decide which of these chain links to treat as random, which as fixed, and which as model-form uncertainty to be calibrated against test data. That decision depends on the available evidence — component test data for restraints, certification data for ATDs, and vehicle-level crash tests for the pulse — and it is the bridge between the landscape described here and the formal uncertainty quantification methods that follow.