4. Data acquisition and preprocessing for crash PINNs

A physics-informed neural network for crash response prediction is only as trustworthy as the data that constrains it. Unlike a purely data-driven surrogate, a PINN consumes two distinct information streams: observational data that anchors the solution to reality, and physical residuals (governing equations, boundary and initial conditions, contact and constitutive constraints) that regularize the solution where data are sparse. Crash problems make both streams difficult. Full-field measurements arrive as noisy, spatially irregular displacement or strain fields from high-speed stereo-DIC; physical sensors are few and often placed where packaging allows rather than where the physics is most informative; and finite element (FE) simulations provide dense but model-dependent fields whose sampling strategy directly shapes the training distribution. This chapter treats data acquisition and preprocessing as a single pipeline whose output is a normalized, physically consistent dataset ready for collocation-point sampling and loss assembly.

Full-field DIC measurements: from cameras to displacement fields

Stereo digital image correlation recovers three-dimensional surface motion by triangulating corresponding speckle patterns across a synchronized camera pair. For crash events, the acquisition chain typically runs at 5,000–20,000 frames per second with exposure times of a few microseconds, and the speckle pattern must survive large local deformation without decorrelating. The practical outputs are a mesh of subset centers, each carrying a 3D displacement vector u = (u_x, u_y, u_z) and a correlation confidence metric. Two properties matter for PINNs. First, the measurement is surface-only: interior fields are unobserved, so the network must rely on physics to extrapolate inward. Second, the spatial support is irregular and the temporal sampling is discrete, which means the raw DIC output cannot be fed directly as collocation points without resampling and confidence filtering.

A defensible preprocessing sequence for a typical component (for example, a hat-section bumper beam struck by a rigid impactor) is:

1. Confidence masking. Discard subsets whose correlation coefficient falls below a threshold (commonly 0.85–0.95) or whose stereo reprojection error exceeds a calibrated bound (e.g., 0.05 px). Decorrelated subsets cluster near cracks, edges, and specular highlights; retaining them injects structured, non-Gaussian noise that the PINN will happily fit.
2. Outlier rejection. Apply a robust local fit (e.g., a moving median or a thin-plate spline residual test) and flag displacements deviating by more than three scaled median absolute deviations from their spatial neighborhood.
3. Temporal smoothing. Use a low-order Savitzky–Golay filter along each subset trajectory to suppress frame-to-frame jitter while preserving the sharp acceleration transients that characterize impact. Over-smoothing here is a common failure: it removes the very high-frequency content the PINN needs to learn.
4. Resampling to a canonical grid. Interpolate the scattered displacement field onto a structured surface grid (or a surface mesh shared with the FE model) so that measurement points and simulation points live in one coordinate system.

Sensor placement: choosing where sparse data earns its keep

Physical sensors—strain gauges, accelerometers, and displacement transducers—provide the low-noise, high-rate anchors that DIC cannot: they survive beyond the field of view, they capture boundary reactions, and they are not limited by surface visibility. Their placement should be driven by sensitivity rather than convenience. A practical criterion is to place sensors where the gradient of the quantity of interest with respect to the response is large and where the PINN's physics residual alone is least constraining—typically near strain concentrations, plastic hinges, and boundary conditions. A simple, reproducible heuristic is to run a coarse FE model, compute the field of the target quantity, and select locations that maximize a coverage objective such as the determinant of the sensor sensitivity matrix (a D-optimality criterion) subject to packaging constraints.

For the bumper-beam example, a reasonable layout might combine four strain gauges on the flanges at the predicted plastic hinge lines, two accelerometers at the support brackets, and one displacement transducer at the impactor face. These seven channels are then time-synchronized with the DIC system using a common trigger; a residual time offset of even one frame at 10 kHz corresponds to 0.1 ms and can bias the inferred strain rate substantially.

FE simulation sampling: building the training distribution

FE simulations supply the dense interior fields and the parametric variation that measurements cannot. The sampling strategy has two axes: parameter space (impact velocity, impactor mass, angle, material properties) and spatiotemporal collocation (where and when residuals are evaluated). For parameter space, a Latin hypercube or Sobol sequence over the design ranges gives better coverage than a grid, and the ranges should be chosen to bracket the measured event rather than to be uniformly wide. For collocation, uniform random sampling over the space–time domain is the default, but crash fields concentrate gradients in thin shear bands and contact zones; a hybrid scheme that mixes uniform samples with samples drawn near high-residual regions (adaptive resampling every few thousand iterations) markedly improves convergence.

# Example: hybrid collocation sampling (illustrative parameters)
domain = {"x": (0.0, 1.2), "y": (-0.15, 0.15), "t": (0.0, 0.012)}  # m, m, s
n_uniform = 20000
n_adaptive = 5000   # resampled near top-residual points each 2000 iters
velocity_range = (4.0, 8.0)   # m/s, Sobol-sampled
mass_range = (8.0, 14.0)      # kg

FE outputs must also be checked for mesh convergence before they are trusted as training targets; a simulation whose peak strain changes by more than a few percent between refinement levels will teach the PINN a mesh artifact rather than physics.

Normalization for heterogeneous crash data

Crash datasets are heterogeneous in units, magnitude, and noise level: displacements in millimeters, strains of order 10^-2, accelerations in thousands of g, and time spans of milliseconds. Feeding these raw into a network produces ill-conditioned gradients and lets large-magnitude channels dominate the loss. Normalize each field to a dimensionless form using physically meaningful scales—impact velocity V₀ for velocity, a characteristic length L for displacement, L/V₀ for time, and the yield strain for strain—so that the governing equations remain dimensionally consistent after non-dimensionalization. A second, data-driven standardization (subtract mean, divide by standard deviation computed on the training split only) is appropriate for sensor channels. Critically, the same normalization constants must be applied to measurement data, FE data, and the physics residual, and they must be stored with the model so that predictions can be de-normalized at inference.

Assembling the dataset and verifying it

The pipeline converges on a single dataset object containing: normalized DIC displacement fields on the canonical grid with per-point confidence weights; synchronized sensor time series with their normalization constants; FE fields sampled over the parameter space; and the collocation-point set for residual evaluation. Before training, verify three things. First, check that the measurement and simulation fields agree in the overlap region to within the expected model-form error—a systematic offset usually indicates a frame or time-sync error, not physics. Second, confirm that the normalized fields have comparable magnitudes across channels; if one channel's standard deviation is orders of magnitude larger, the loss weighting is wrong. Third, inspect the collocation-point distribution against the high-gradient regions; if adaptive resampling has collapsed all points into a single shear band, the residual loss will be under-constrained elsewhere. A dataset that passes these checks gives the PINN a fair chance to learn the physics rather than the artifacts of its inputs.