4. Feature engineering from simulation results

Raw CAE output is not a feature set. A completed crash or NVH solve may produce gigabytes of nodal displacement, element stress, and contact force history, yet a downstream decision-support model cannot consume that volume directly. Feature engineering is the deliberate reduction of simulation results into compact, physically meaningful, and reproducible descriptors that preserve the decision-relevant signal while discarding numerical noise and mesh-dependent detail. This chapter covers the four principal feature families used in automotive CAE decision support: field data, scalar KPIs, time series, and geometry-aware descriptors.

Why Feature Engineering Determines Model Quality

Two failure modes dominate when features are extracted carelessly. The first is mesh dependence: a peak stress value read from a single element changes when the mesh is refined, so a model trained on that value learns the mesh, not the design. The second is information collapse: reducing an entire deformation field to one maximum value discards spatial patterns that distinguish a good design from a marginal one. Good feature engineering addresses both by choosing descriptors that are stable under discretization change and rich enough to separate design intent.

A practical rule: a feature is acceptable if two analysts, given the same result database and the same documented extraction recipe, obtain the same number to within a stated tolerance. If the recipe depends on "the element near the weld," it is not yet a feature.

Field Data: Structured Access to Contour Results

Field data is the full spatial distribution of a result quantity — displacement magnitude, von Mises stress, plastic strain, temperature — sampled on the mesh. It is the richest representation but the least directly usable. The standard approach is to resample fields onto a fixed reference grid or a set of named regions so that the feature vector has constant length across designs.

For a body-in-white (BIW) frontal impact study, a common recipe resamples the plastic strain field onto the vehicle's global coordinate system at a fixed voxel pitch, for example 20 mm. Each voxel stores the maximum plastic strain within it. The result is a fixed-size tensor independent of the underlying mesh. Coordinate convention must be fixed and documented: here +X points rearward along the vehicle centerline, +Y points to the driver's left, +Z points upward, with the origin at the front bumper center at ground level. Any change to this convention invalidates comparison across runs.

# Example: voxelized plastic strain field extraction (illustrative)
# Input : d3plot / result database, part set = BIW
# Output: strain_field.npy  shape (NX, NY, NZ)

voxel_pitch = 20.0          # mm
origin      = (0.0, 0.0, 0.0)  # front bumper center, ground level
quantity    = "plastic_strain"
reduction   = "max"         # max within voxel

# For each element centroid (x, y, z) with value v:
#   ix = floor((x - origin_x) / voxel_pitch)
#   iy = floor((y - origin_y) / voxel_pitch)
#   iz = floor((z - origin_z) / voxel_pitch)
#   field[ix, iy, iz] = max(field[ix, iy, iz], v)

Field features are typically consumed by convolutional or graph neural networks rather than tabular models. Their advantage is that they retain spatial structure; their cost is storage and sensitivity to the resampling grid. Always record the pitch, origin, and reduction rule alongside the tensor.

Scalar KPIs: The Workhorse Features

Scalar KPIs are single numbers summarizing a physical response. They are the most interpretable and the easiest to validate against physical test. Typical automotive CAE KPIs include:

• Intrusion: maximum displacement of a named node set along a defined axis, e.g. toe pan intrusion in mm along +X.
• Peak acceleration: maximum resultant acceleration at a sensor location, filtered per SAE J211 channel frequency class.
• Energy absorption: integral of force over displacement for a specified component, in kJ.
• Mass: total or per-part mass, used as a constraint feature.
• Section force: resultant axial force through a defined cross-section at a given time.

Each KPI must specify its extraction region, its filtering, and its time window. A peak acceleration reported without a channel frequency class is not reproducible. The following table shows a compact KPI definition sheet suitable for a decision-support pipeline.

Time Series: Capturing the Response Path

Many decisions depend not on a single peak but on how a response evolves. A force–displacement curve, an acceleration pulse, or a strain history at a critical location carries information about crash mode, timing, and energy management that no scalar can express. Time series features fall into three groups:

1. Raw resampled histories: the signal sampled at a fixed rate, e.g. 10 kHz, over a fixed window. Suitable for sequence models but high-dimensional.
2. Parametric summaries: peak value, time of peak, pulse duration above a threshold, rise time, decay slope, number of oscillations. Compact and interpretable.
3. Transform features: coefficients from a Fourier or wavelet transform, or principal component scores from a training set of histories. Useful when the shape matters more than the amplitude.

For a frontal rail force history, a practical parametric set is: peak force, time to peak, mean force over 0–60 ms, and the ratio of mean to peak (a crush-efficiency indicator). These four numbers often separate stable axial crush from bending collapse, which is exactly the design distinction the decision-support model must learn.

Geometry-Aware Descriptors

Geometry-aware descriptors encode the relationship between the response and the shape that produced it. They are what allow a model to generalize across design variants rather than memorize specific meshes. Common forms include:

• Distance-to-feature fields: for each node, the distance to the nearest weld, bead, or hole. Combined with a stress field, this reveals whether peaks sit at geometric discontinuities.
• Section properties: cross-sectional area, second moment of inertia, and gauge along a defined path, sampled at fixed stations.
• Curvature and thickness gradients: local shape descriptors that correlate with buckling and springback behavior.
• Topological descriptors: number of connected components, genus, or adjacency counts in a part graph.

These descriptors are computed from the geometry, not the result, but they are joined to result-derived features by node or region identifier. The join key must be stable across design iterations — node IDs are not, because remeshing changes them. Use named sets, part IDs, or spatial coordinates instead.

Putting the Families Together

The four families are complementary, not competing. A typical decision-support feature vector for a frontal impact variant study might combine: 12 scalar KPIs, 4 parametric time-series summaries per sensor (3 sensors), a 64-component PCA reduction of the rail force history, and 8 geometry-aware descriptors per critical section. The field data is retained separately for a CNN branch when spatial pattern recognition is required.

The diagram below shows how the four feature families are extracted from a single result database and joined into a unified feature vector, with the join key and coordinate convention applied consistently across all branches.

Validation and Failure Symptoms

Feature extraction pipelines fail in characteristic ways. If a scalar KPI changes by more than a few percent when the mesh is refined but the design is unchanged, the extraction region is too small or tied to a single element. If a time-series feature shows a phase shift between two runs of the same design, the resampling time base is inconsistent. If a geometry-aware descriptor has a different length across variants, the section path or station spacing is not fixed. Each of these is detectable by running the extractor on a known-unchanged design and comparing outputs; this regression check should be part of the pipeline, not an afterthought.

The output of this stage is a documented, versioned feature table plus the extraction scripts that produced it. Every column should trace back to a named region, a stated filter, and a fixed coordinate convention. With that discipline in place, the feature set becomes a reliable interface between CAE simulation and the decision-support models developed in later chapters.