3. Exploratory data analysis for occupant CAE outputs

Before any correlation coefficient or regression fit is computed, the occupant CAE dataset must be understood on its own terms. Exploratory data analysis (EDA) is the stage where response distributions, variable relationships, and anomalous runs are characterized so that later modeling decisions rest on evidence rather than assumption. In occupant safety work the stakes are concrete: a single mislabeled sled run, a unit inconsistency between acceleration channels, or a non-physical HIC value can dominate a regression and produce a restraint tuning recommendation that fails in hardware. This section covers the four core EDA instruments — histograms, boxplots, scatterplot matrices, and outlier screening — and how to apply them to occupant CAE outputs such as HIC15, chest deflection, neck injury criterion (Nij), femur force, and head excursion.

Establishing the analysis dataset

A typical occupant CAE study for a frontal impact program might contain 60–200 runs generated by a DOE over restraint design variables (belt anchor height, pretensioner force, airbag vent size, seat pan angle) with responses extracted from the dummy model at each run. The EDA table should be assembled as one row per run and one column per response, with run identifiers, DOE factor values, and a model-version tag retained. Two practical rules apply before plotting: confirm units and sign conventions per channel (for example, chest deflection reported as positive compression in millimeters, head acceleration in g with the SAE J211 CFC 1000 filter applied), and confirm that every response was extracted at the same simulation end time and with the same filter class. Mixed filter classes across runs will show up later as bimodal histograms and are a data-pipeline defect, not a physical finding.

Histograms: distribution shape and coverage

Histograms answer whether a response is well-sampled across its range and whether its shape is consistent with the physics. For HIC15 in a frontal DOE, a roughly unimodal distribution centered near 600–700 with a spread of ±150 is plausible; a strongly bimodal histogram usually indicates two distinct design regimes (for example, runs with the airbag firing versus runs where it was suppressed) or a categorical factor that was not recorded. A truncated distribution with a hard edge at a regulatory threshold suggests the DOE was filtered or that failed runs were silently dropped. Bin counts should be chosen so that each bin holds at least five runs; with 80 runs, 10–12 bins is a reasonable starting point. Record the count of runs per bin alongside the plot so that sparse tails are not over-interpreted.

Boxplots: comparing groups and spotting spread

Boxplots are most useful when responses are compared across a categorical split — occupant position (driver/passenger), impact mode (full frontal, offset, oblique), or restraint configuration. Plotting HIC15 by impact mode on a common axis immediately reveals whether the oblique cases sit systematically higher and whether their interquartile range is wider, which matters because a regression pooled across modes may be fitting two different populations. The boxplot also exposes the 1.5×IQR fence, which is the conventional flag for candidate outliers. In occupant data, a run beyond the upper fence is not automatically wrong: a high-HIC run may be a legitimate worst-case design point. The boxplot's role is to prioritize which runs to inspect, not to delete them.

Scatterplot matrices: pairwise structure

A scatterplot matrix places every response against every other response (and against key DOE factors) in a grid, with the diagonal showing each variable's own distribution. This is where physically expected couplings should be confirmed: chest deflection versus belt force, Nij versus head-to-neck relative velocity, femur force versus knee bolster stiffness. Two patterns deserve attention. First, a strong but curved relationship (for example, HIC rising steeply only above a belt force threshold) warns that a linear correlation coefficient will understate the association and that a transformed or nonlinear term may be needed. Second, a scatter that looks like two parallel bands indicates a lurking categorical variable — often occupant size or a restraint variant — and the matrix should be re-faceted by that variable. With more than about eight responses, split the matrix into blocks (injury metrics, kinematics, restraint loads) to keep panels legible.

Outlier screening: flag, diagnose, decide

Outlier screening in occupant CAE is a diagnostic procedure, not a deletion step. Three complementary flags are practical. The univariate 1.5×IQR fence from the boxplot catches single-response extremes. The standardized score |z| > 3 catches the same thing when responses are approximately normal, but is unreliable for skewed metrics such as HIC. The Mahalanobis distance catches multivariate outliers — runs that are unremarkable on each response individually but inconsistent in combination, for example a run with moderate HIC and moderate chest deflection but an implausibly low belt force. Compute it on the standardized response vector with the pooled covariance, and compare against a chi-square threshold at the desired confidence level.

Once a run is flagged, diagnose before deciding. The most common causes in occupant CAE are: a different filter class or sampling rate on one channel; a simulation that terminated early, so the response was extracted over a truncated window; a unit or sign error in post-processing (chest deflection entered as negative); a mislabeled DOE row; and a genuinely non-physical result from a failed contact or an unstable element. Only the first four are data defects. A run that is physically extreme but numerically sound — a worst-case design point that genuinely produces high Nij — must be retained, because removing it would bias the regression toward optimistic restraint performance. Every exclusion should be logged with the run ID, the flag that triggered it, the diagnosis, and the action taken, so the modeling chapter can state exactly how the analysis dataset was derived.

A compact EDA checklist for the analysis dataset

The output of this stage is a documented, cleaned analysis dataset plus a short EDA log. That log becomes the provenance record for every correlation and regression result that follows: it states which runs were excluded, why, and what the remaining response distributions look like. With that foundation in place, the next analytical steps — correlation screening and regression model form selection — can be defended on the basis of the data actually used.