4. CAE model fidelity management

In occupant restraint virtual validation, a CAE model is only as trustworthy as its demonstrated agreement with physical test data. Model fidelity management is the discipline that keeps that trust measurable, traceable, and repeatable across the program lifecycle. For restraint components — airbags, seat belts, retractors, pretensioners, load limiters, and steering-wheel modules — fidelity management covers four tightly coupled activities: defining correlation metrics, updating the model against test evidence, proving mesh convergence, and validating material cards. This chapter explains what each activity requires and how to execute it in practice.

Correlation Metrics: Turning "Looks Close" into a Number

Correlation metrics quantify the difference between simulation and test responses. For restraint systems, the most common responses are sled pulse acceleration, belt force at the retractor and anchor, airbag internal pressure, and occupant injury criteria such as HIC and chest deflection. Three metric families are widely used:

• Peak and timing metrics — peak value error, time-to-peak error, and pulse duration error. These are intuitive and map directly to injury-criterion sensitivity.
• Integral metrics — normalized integral difference (e.g., the ISO/TR 9790-style corridor or the Sprague–Geers magnitude and phase error). These capture the whole history, not just the peak.
• Statistical metrics — CORA (CORrelation and Analysis) rating, which combines corridor, phase, and magnitude scores into a single 0–1 value. A CORA rating above 0.86 is commonly treated as "good" for restraint responses, 0.7–0.86 as "acceptable with justification," and below 0.7 as requiring model update.

The metric must be chosen before the model is built, not after the results are known. A practical rule: use peak/timing metrics for pass/fail gates on injury criteria, and CORA for the underlying physical channels (belt force, pressure, acceleration) that drive those criteria. Always document the time window, filtering (e.g., SAE J211 CFC 60 for acceleration, CFC 600 for belt force), and the test channel used as reference.

Model Updating: From Mismatch to Justified Change

Model updating is the controlled adjustment of parameters to reduce correlation error. It is not arbitrary tuning. The workflow is: identify the dominant mismatch, select parameters that are physically uncertain (not those that are merely convenient), bound them within manufacturing or test tolerance, and re-run.

For a driver airbag module, a typical mismatch is early pressure rise being too fast. Candidate parameters and their justified bounds might be:

Update one parameter family at a time and record the sensitivity. If a 5% change in mass flow rate moves peak pressure by 8% but a 20% change in permeability moves it by 2%, the mass flow rate is the dominant lever and should be updated first. Stop when the metric target is met and all parameters remain inside their justified bounds. A model that correlates only with out-of-tolerance parameters is not validated — it is overfit.

Mesh Convergence: Proving the Discretization Is Not the Answer

Mesh convergence demonstrates that further refinement does not change the result beyond an acceptable tolerance. For restraint components, the critical regions are the airbag fabric, the belt webbing, and any component undergoing large deformation or contact.

A practical convergence study for an airbag model uses a sequence of characteristic element sizes, for example 20 mm, 15 mm, 10 mm, and 8 mm on the bag fabric. Track peak pressure, peak bag volume, and occupant HIC at each refinement. Convergence is declared when the change between successive refinements is below 5% for the quantities of interest. If the 10 mm and 8 mm results differ by less than 5%, the 10 mm mesh is adequate and the 8 mm mesh is unnecessary cost.

Refinement   Element size   Peak pressure (kPa)   Δ vs previous
M1           20 mm          245                   —
M2           15 mm          262                   6.9%
M3           10 mm          271                   3.4%
M4            8 mm          274                   1.1%   ← converged

Note that convergence must be checked per quantity. A mesh may be converged for pressure but not for a local strain used in fabric rupture. Report the convergence table in the model documentation and state the selected mesh with its justification.

Material Card Validation: The Foundation Under Everything

Material cards for restraint components are unusually sensitive because the materials are rate-dependent, anisotropic, and often modeled with simplified constitutive laws. Validation means reproducing the coupon or component test that the card is intended to represent.

For belt webbing, a common approach is a orthotropic elastic–plastic card calibrated to tensile tests at 0.1/s, 1/s, and 10/s. Validation steps:

1. Build a single-element or small coupon model with the proposed card.
2. Apply the same strain rates and boundary conditions as the physical test.
3. Compare force–displacement and failure strain. Target: peak force within 5%, failure strain within 10%.
4. If the card fails, adjust only parameters with physical meaning (modulus, yield, hardening, failure strain) and re-check all rates.

For airbag fabric, a common failure mode is that a card calibrated at quasi-static rate under-predicts stiffness at deployment rates. The fix is to include rate dependence explicitly, not to scale the modulus globally. For inflator output, the "material" is really a gas source; validate it against tank pressure–time data before it enters the occupant model.

Integrating the Four Activities

These four activities are not sequential; they interact. A mesh that is too coarse can mask a material card error. A material card updated to compensate for a coarse mesh will fail when the mesh is refined. The correct order is: converge the mesh first with a nominal material card, then validate the material card on the converged mesh, then update model parameters, then compute correlation metrics on the final configuration.

The workflow above is iterative, not linear. After the correlation step, if a target is missed, the engineer returns to the dominant parameter identified by sensitivity analysis, re-checks that the mesh and material card are still valid, and repeats. Each iteration is logged. The final deliverable is a model fidelity report containing the convergence table, the validated material cards with their independent-test evidence, the parameter update log with justifications, and the correlation metric summary against the reference sled tests. That report is what allows a restraint CAE model to be used for design decisions and regulatory submissions with confidence.