3. CORA methodology overview

CORA (Correlation and Analysis) is a standardized objective rating method used to quantify how well a CAE-simulated occupant restraint curve matches its corresponding physical test curve. In airbag and occupant restraint development, engineers routinely compare time-history signals such as head acceleration, chest acceleration, chest deflection, belt force, and airbag pressure. CORA converts these subjective "looks close" judgments into a reproducible numeric score, typically expressed on a 0–1 scale, where 1.0 indicates perfect agreement. Understanding the score's internal decomposition is essential, because a single CORA value hides which physical characteristic actually failed — and that distinction drives the corrective engineering action.

Decomposition of the CORA Score

CORA evaluates a curve pair through two independent sub-scores: a corridor score and a cross-correlation score. The overall CORA value is a weighted combination of these two, and each sub-score itself aggregates several evaluation criteria.

The corridor score measures amplitude agreement. Two corridors are constructed around the reference (test) curve: an inner corridor and an outer corridor, whose widths are defined by a percentage of the reference signal's range (commonly 2%–5% for the inner and 10%–20% for the outer corridor, configurable per signal). At each time sample, the deviation between the simulation curve and the reference curve is rated: inside the inner corridor earns full credit, between inner and outer corridors earns partial credit with a linear or progressive falloff, and outside the outer corridor earns zero. The corridor score is the time-weighted average of these sample ratings, so a brief excursion is penalized less than a sustained one.

The cross-correlation score captures phase and shape agreement, independent of pure amplitude. It is computed from the normalized cross-correlation function between the two signals, and it rewards curves that rise, peak, and decay at the same times. A simulation that matches peak amplitude but lags the test by 8 ms will score well on corridor amplitude yet poorly on cross-correlation — a classic signature of a timing error such as an incorrect airbag trigger delay or belt slack model.

Each sub-score is further broken down into phase and shape components in the standard CORA formulation. Phase evaluates the temporal offset of corresponding features (peak locations, zero crossings, gradient changes), while shape evaluates the progression of the signal between those features. The aggregation uses weighting factors that the analyst sets per signal type; for restraint curves, phase weighting is often raised because occupant loading timing is physically critical.

The Overall Rating Workflow

Rating a restraint system is not a single curve comparison; it is a structured workflow applied across a defined signal set. The typical sequence is:

1. Define the signal set and weighting. Select the channels that represent occupant injury relevance — for a frontal impact this might be head resultant acceleration, chest resultant acceleration, chest deflection, upper belt force, and airbag internal pressure. Assign relative weights reflecting their importance to the occupant outcome (for example, head and chest acceleration weighted higher than belt force).
2. Preprocess both curves. Apply consistent filtering (commonly CFC 60 or CFC 180 per SAE J211 for accelerations), align the time origin to a defined event (e.g., bumper contact or trigger), and resample to a common time base. Inconsistent filtering is one of the most common causes of spurious low scores.
3. Compute sub-scores per channel. Run the corridor and cross-correlation evaluation for each signal pair, producing per-channel corridor, phase, and shape values.
4. Aggregate to a channel score, then to a system score. Combine sub-scores per channel using the configured weights, then combine channel scores using the signal-set weights to obtain the overall CORA rating.
5. Interpret and act. Compare the result against the project's acceptance threshold (commonly 0.7–0.8 for occupant safety sign-off, though thresholds are program-specific) and, more importantly, inspect the per-channel breakdown to locate the physical cause of any deficiency.

The following diagram illustrates the decomposition and aggregation path from raw curve pair to final rating, including the diagnostic split between amplitude and timing failures.

Worked Example: Interpreting a Mid-Range Rating

Consider a frontal impact sled model rated against a physical test. Suppose the signal set contains five channels with weights: head resultant acceleration 0.30, chest resultant acceleration 0.25, chest deflection 0.20, upper belt force 0.15, and airbag pressure 0.10. After preprocessing at CFC 60 and aligning t0 to trigger, the per-channel CORA values come out as 0.82, 0.78, 0.71, 0.88, and 0.65 respectively. The weighted system score is:

System CORA = 0.30(0.82) + 0.25(0.78) + 0.20(0.71) + 0.15(0.88) + 0.10(0.65)
            = 0.246 + 0.195 + 0.142 + 0.132 + 0.065
            = 0.780

Against a 0.75 threshold this passes, but the airbag pressure channel at 0.65 is the weakest link. Inspecting its sub-scores: corridor 0.80 but cross-correlation 0.48. The high corridor score says the peak pressure magnitude is roughly right; the low cross-correlation says the pressure rise is late relative to the test. The physical hypothesis is a delayed inflator mass-flow ramp or an over-stiff fabric model that delays chamber pressurization. The corrective action is to adjust the inflator mass-flow curve timing or the airbag fabric permeability, then re-run and re-rate — not to tune the head acceleration channel, which is already acceptable. This example is illustrative and uses assumed values; actual project thresholds and weights are set by the program's correlation plan.

Practical Considerations for Reliable Ratings

• Consistency of preprocessing dominates reproducibility. Filter class, time-zero definition, and resampling must be identical for test and simulation. A CFC mismatch alone can shift a corridor score by several hundredths.
• Corridor widths should reflect signal physics. A high-frequency, noisy signal such as head acceleration tolerates wider corridors than a smooth belt force trace; setting widths per channel avoids over-penalizing noise.
• Weights encode engineering judgment. Document the weighting rationale in the correlation plan so that a score is comparable across builds and reviewers.
• Never report only the aggregate. The per-channel and per-sub-score breakdown is the actionable output; the single number is a summary for gate reviews.
• Beware of over-fitting to one curve. A high CORA on a single test does not guarantee robustness; rate across the full load case matrix before drawing conclusions.

CORA thus provides a transparent, decomposable metric: the corridor score answers "is the amplitude right?", the cross-correlation score answers "is the timing and shape right?", and the weighted aggregation answers "does the whole restraint system correlate well enough to sign off?" Reading the breakdown, not just the total, is what turns a rating into an engineering decision.