4. Key correlation metrics

Correlation between a physical crash test and its PAM-CRASH model is never judged by a single number. Five response channels form the backbone of almost every correlation report: acceleration, velocity, displacement, intrusion, and energy absorption. They are not independent — they are successive integrals and products of the same measured signal — so an error in one channel propagates predictably into the others. Understanding that chain is what lets you decide which channel to trust and where to start calibrating.

The integration chain and why it matters

Acceleration is the raw measurement. Velocity is its time integral, displacement is the integral of velocity, and intrusion is a displacement measured at a specific structural point relative to a reference. Energy absorption is the work done by the contact force, i.e. the integral of force over displacement. In PAM-CRASH these relationships are available directly through the /TH/ACCEL, /TH/VEL, /TH/DISP, and /TH/ENERGY time-history requests, but the physical coupling is what drives your debugging strategy.

Because integration amplifies low-frequency error and differentiation amplifies high-frequency noise, the same physical discrepancy looks different in each channel. A constant offset in acceleration produces a linear drift in velocity and a quadratic drift in displacement. A high-frequency ringing artifact that is barely visible in displacement can dominate the acceleration peak. This is why a model that "looks good" in displacement can still fail badly in acceleration correlation.

Acceleration: the most sensitive, least forgiving channel

Acceleration is usually the first channel compared because it is the direct output of the sensor and the most sensitive to model detail. In practice you compare the filtered acceleration time history at a defined location — for example a B-pillar base accelerometer or a tunnel-mounted sensor — against the corresponding PAM-CRASH node or rigid-body output. The standard practice is to apply the same SAE J211 channel filter class (typically CFC 60 for structural, CFC 180 for occupant-relevant locations) to both signals before comparison, otherwise you are comparing filter artifacts rather than physics.

Key quantitative metrics for acceleration correlation include peak value, time of peak, pulse duration, and the cross-correlation coefficient or normalized integral square error. A useful working target in body-structure correlation is a peak acceleration within ±10% and a peak timing within ±2 ms. If the model peak is early and high, the structure is too stiff locally; if it is late and low, the load path is too compliant or a joint is releasing too early.

Velocity and displacement: checking the integration

Velocity and displacement are rarely measured directly in a full-scale crash test — they are derived from accelerometer integration, often with a high-pass or baseline correction to remove drift. When you compare them, you are really validating that the area under the acceleration curve matches. A model that matches acceleration peaks but diverges in velocity indicates a systematic difference in pulse shape rather than peak magnitude.

Displacement is the most intuitive channel for engineers and the easiest to communicate. It is also the most forgiving, because integration smooths out high-frequency discrepancies. A common trap is to declare correlation "good" based on displacement alone. Always check displacement and acceleration together: matching displacement with mismatched acceleration means the total energy is right but the load distribution is wrong.

Intrusion: the occupant-relevant metric

Intrusion is a displacement measured at a specific structural point relative to a fixed reference, typically the undeformed occupant compartment. It is the metric that connects structural correlation to occupant safety. In PAM-CRASH you extract intrusion by tracking the relative displacement between a node on the deforming structure (e.g. door inner panel, footwell, steering column) and a reference node on the rigid occupant cell.

Intrusion correlation is judged by maximum intrusion depth, the time at which it occurs, and the intrusion rate. A typical passenger-car side-impact target might be a maximum door intrusion of 300 mm at 60 ms; the model should reproduce this within ±15 mm and ±3 ms. Intrusion is sensitive to local material failure, spot-weld rupture, and contact definitions, so it is often the channel that reveals modelling errors that acceleration and displacement hide.

Energy absorption: the global balance check

Energy absorption is the integral of contact force over displacement, and in PAM-CRASH it is available as internal energy, kinetic energy, and contact energy through the /TH/ENERGY output. The global check is simple: total initial kinetic energy must equal the sum of absorbed energy plus residual kinetic energy at the end of the event. If the model's internal energy at 100 ms is 15% higher than the test-derived value, the structure is absorbing too much energy — usually because of overly stiff materials, missing failure, or incorrect contact friction.

Energy correlation is best presented as a time-history plot of cumulative absorbed energy, with the test curve derived from measured force and displacement. The slope of this curve is the instantaneous crush force, so a steeper model slope points directly to a local stiffness problem.

Practical correlation workflow

A reproducible correlation sequence for a frontal offset case might look like this:

1. Extract test signals: filter accelerometers at CFC 60, integrate to velocity and displacement with baseline correction.
2. Extract PAM-CRASH time histories at matching nodes using /TH/ACCEL and /TH/DISP, applying the same filter.
3. Compare acceleration first — identify peak magnitude and timing errors.
4. Check velocity and displacement to confirm the pulse area is correct.
5. Compare intrusion at the occupant-relevant points.
6. Validate the global energy balance.

Summary of target tolerances

These five metrics form a hierarchy: acceleration tells you when and how hard, velocity and displacement tell you how much, intrusion tells you where it matters for the occupant, and energy tells you whether the whole system balances. Calibrating in that order — from the most sensitive to the most global — keeps the correlation effort focused and prevents chasing errors that are actually integration artifacts.