1. Occupant safety landscape

Occupant safety engineering is fundamentally a problem of managing energy and deceleration across a very short time window. In a frontal crash at 56 km/h, a restrained occupant's torso decelerates from roughly 15.6 m/s to rest in about 80–120 ms, subjecting the body to peak accelerations on the order of 30–50 g. Every restraint component — belt, pretensioner, load limiter, airbag, seat structure, knee bolster — exists to shape that deceleration pulse so that the forces transmitted to vulnerable anatomy stay below injury thresholds. Physics-informed machine learning (PIML) enters this landscape not as a replacement for crash physics but as a way to accelerate, interpolate, and generalize across the enormous design space that physics-based simulation already describes.

Injury Mechanisms and Their Physical Basis

Injury in crashes arises from four principal loading modes: compression, tension, shear, and inertial loading of internal organs. The clinically dominant outcomes in modern vehicles are head/brain injury, cervical and thoracic spine loading, rib fracture and thoracic organ injury, abdominal injury, and lower-extremity fracture. Each maps to a measurable physical quantity that serves as a surrogate in both testing and simulation.

• Head injury is characterized by linear acceleration (translational) and angular velocity/acceleration (rotational). The Head Injury Criterion (HIC) integrates resultant translational acceleration over a 15 ms window; rotational metrics such as BrIC (Brain Injury Criterion) capture diffuse axonal injury that HIC misses.
• Neck injury is assessed through axial force, shear force, and bending moment (Nij, Nkm), reflecting the combined compression–flexion–extension loading of the cervical column.
• Thoracic injury is dominated by rib deflection and viscous response (VC), because rib fracture and underlying organ compression scale with the rate and magnitude of chest wall deformation.
• Abdominal and pelvic injury relate to belt loading path, submarining, and compression of solid organs.
• Lower extremity injury is driven by axial loading through the femur and tibia (femur force, tibia index) and by footwell intrusion.

The key engineering insight is that these injury criteria are physical functionals of the occupant's kinematic and kinetic response. A simulation that predicts occupant kinematics accurately can, in principle, predict injury criteria — provided the material models, contact definitions, and restraint deployment logic are faithful. This is precisely where PIML can be embedded: the physics constrains the model, and the data corrects for what the physics approximates.

Regulatory and Consumer-Test Protocols

Two families of protocols define the design targets. Regulatory tests (e.g., FMVSS 208 in the United States, UN R94/R95 in Europe, and equivalent national standards) establish minimum legal performance: frontal barrier impacts at specified speeds, offset deformable barrier tests, side pole and moving deformable barrier tests, and out-of-position occupant scenarios. Consumer tests (Euro NCAP, US NCAP, IIHS, C-NCAP, JNCAP) go further, using star ratings and specific crash configurations — the IIHS small overlap frontal, the Euro NCAP mobile progressive deformable barrier, and far-side occupant protection — to push manufacturers beyond compliance.

For a modeling engineer, the protocol determines the boundary conditions: impact velocity, barrier stiffness and geometry, dummy type (Hybrid III 50th percentile male, THOR, WorldSID, or the more recent THOR-AV and female dummies), seating position, and the set of injury criteria that must be reported. A model trained on one protocol does not automatically transfer to another, because the loading path and the dominant injury mode change. This is a central challenge for data-driven surrogates and a strong argument for physics-informed architectures that encode the underlying mechanics rather than memorizing protocol-specific outputs.

Where Simulation and Data-Driven Models Fit

The conventional workflow is a finite element (FE) crash simulation: a detailed occupant model (e.g., a THOR or Hybrid III FE dummy, or a human body model such as THUMS or GHBMC) is coupled to a vehicle structure model, and the solver integrates the equations of motion through the crash pulse. This is accurate but expensive — a single frontal occupant simulation can take hours, and a design-of-experiments study across dozens of parameters can take weeks. Data-driven surrogates (Gaussian processes, neural networks, polynomial response surfaces) can replace the FE solver for fast design exploration, but they extrapolate poorly and can violate physical constraints such as energy conservation or monotonicity of injury with respect to belt force.

Physics-informed machine learning addresses this by combining the two: the surrogate is trained not only on FE input–output pairs but also on physical residuals — momentum balance, restraint force–deflection relationships, or known injury-criterion definitions — so that predictions remain physically admissible even outside the training envelope. A practical example: a surrogate that predicts chest deflection from belt force, pretensioner timing, and occupant anthropometry can be regularized with the constraint that increased belt force cannot reduce chest deflection below the load-limiter threshold, preserving a physically correct monotonic relationship.

A Worked Scoping Example

Consider a team building a surrogate to support restraint tuning for a frontal offset crash. The input vector might include: impact speed (48–56 km/h), belt load-limiter force (3–5 kN), pretensioner firing time (10–30 ms), airbag vent size (30–60 mm), and occupant stature (5th–95th percentile). The output vector is the set of injury criteria (HIC15, chest deflection, Nij, femur force). A pure neural network trained on 200 FE runs may fit the training data well but produce non-physical oscillations between sample points. A physics-informed variant adds a penalty term enforcing that chest deflection increases monotonically with belt force above the load-limiter threshold and that predicted HIC remains non-negative. The practical result is a surrogate that can be evaluated in milliseconds, enabling a 10,000-point optimization sweep that would be infeasible with the FE solver, while remaining trustworthy at the edges of the design space.

The remainder of this course builds on this landscape. The next chapters formalize the occupant kinematics and restraint mechanics that underpin the injury criteria introduced here, then develop the simulation and PIML methods that let you move from a crash pulse and a restraint design to a defensible, fast, and physically consistent prediction of occupant injury.