4. Response variables and performance metrics

In a DOE for restraint system design, the design variables (airbag vent size, inflator mass flow, seat belt anchor height, pretensioner force, etc.) are only half of the experiment definition. The other half — and the half that most often determines whether the study produces actionable conclusions — is the set of response variables. A response variable is any scalar quantity extracted from the LS-DYNA simulation that you intend to model, compare, or optimize. Choosing the right responses, extracting them consistently, and understanding their sensitivity and noise characteristics is what separates a DOE that guides design from one that merely generates a large pile of d3plot files.

From Time Histories to Scalar Responses

LS-DYNA produces time histories: accelerations at the seat track, belt forces at the retractor and buckle, head and chest accelerations from the Hybrid III or THOR dummy, contact forces, and so on. DOE methods, however, require one number per run per response. The conversion from history to scalar is itself a modeling decision that must be fixed before the matrix is generated, because inconsistent extraction invalidates the statistical model.

For injury criteria, the standard conversions are well defined. HIC36 and HIC15 are computed from the resultant head acceleration a(t) in g over a 36 ms or 15 ms window:

HIC = max over t1,t2 of [ (t2 - t1) * ( (1/(t2-t1)) * ∫ a(t) dt )^2.5 ]
      subject to t2 - t1 ≤ 36 ms (or 15 ms)

In practice you extract the resultant head acceleration from the dummy's head CG accelerometer, filter it per SAE J211 channel frequency class 1000 (CFC 1000), and evaluate the double integral over sliding windows. Chest deflection criteria (e.g., 63 mm limit for the 50th percentile Hybrid III), Nij for the neck, and femur force limits follow analogous fixed procedures. The key DOE discipline is to script these extractions identically for every run — typically with a Python or LS-DYNA MPP post-processing script reading the nodout, rcforc, or secforc files — and to log the extraction version alongside the run ID.

Occupant kinematics responses are less standardized and require more judgment. Typical scalars include maximum forward head excursion (X displacement of the head CG relative to the vehicle buck), head rotation angle at peak excursion, torso pitch, knee excursion, and the time of peak values. These are often more informative than injury criteria during early design exploration because they reveal why a criterion changed: a larger vent may reduce chest deflection but increase head excursion, and only the kinematic response shows the trade-off.

Restraint Performance Measures

Beyond dummy injury metrics, restraint-specific measures describe how the system itself behaves. Useful examples include: peak belt force at the retractor and buckle, belt payout (spool-out length), airbag internal pressure peak and time-to-peak, airbag vent mass flow integral, and the timing of belt force onset relative to airbag contact. These are directly tied to design variables and are often more sensitive to small parameter changes than injury criteria, which saturate or plateau. Including them gives the DOE surrogate model more information and helps diagnose non-physical runs.

The figure below shows how a single run's time histories map to the scalar response set used in the DOE, and how those responses partition into the three families discussed here.

Selecting and Screening Responses for the Matrix

Not every available output belongs in the DOE. A practical screening rule is to keep a response if it is (a) physically meaningful for the design question, (b) sensitive to at least one design variable over the planned range, and (c) numerically stable across runs. Sensitivity can be checked cheaply with a small pilot: run the baseline plus two extreme corner points and compare response spreads. If a response barely moves across the corners, it will contribute noise to the surrogate model and should be dropped or replaced.

Numerical stability deserves explicit attention. Injury criteria computed from accelerometer data are sensitive to filtering and to contact instabilities; a run with hourglassing in the dummy's chest or a spurious belt slip can produce a HIC value that is physically implausible. Build a screening step into the workflow: flag runs where peak head acceleration exceeds, say, 250 g, where belt force drops to zero before 40 ms, or where the dummy penetrates the airbag module. These runs should be inspected and, if non-physical, either corrected and re-run or excluded with a documented reason — never silently averaged into the response table.

Response Table and Acceptance Bands

The deliverable of this stage is a response definition table that travels with the DOE matrix. Each row defines one response: its name, the source channel, the extraction method, the filter class, the sign convention, and the acceptance band used to judge whether a design point is feasible. A compact example for a driver frontal restraint study:

The acceptance bands are illustrative and must be set from the applicable regulation or internal target for the specific program. Their role in DOE planning is to convert the response table into a feasibility filter: after the surrogate model is fitted, you can map the design space and identify regions where all bands are satisfied simultaneously. Responses marked "report only" still enter the model but do not constrain the feasible region.

Practical Checklist Before Generating the Matrix

• Every response has a written definition, source channel, filter class, and sign convention.
• Extraction is scripted and versioned; the script is archived with the matrix.
• A pilot of baseline plus corner points confirms each response is sensitive and stable.
• Acceptance bands are documented, with "report only" responses explicitly labeled.
• Non-physical run criteria are defined in advance, with a documented exclusion procedure.

With the response set fixed and validated, the DOE matrix can be generated with confidence that each run will yield a complete, comparable row of data — which is the precondition for any meaningful surrogate model, sensitivity analysis, or optimization that follows.