metadata/LHS_DESIGN.md

Constrained-LHS design

Design coordinates

Each constrained Latin hypercube design uses seven normalized coordinates:

[x, y, impact_speed, mass_ratio, theta_deg, phi_deg, material_index].

The continuous domains are:

Parameter	Domain	Unit
impact speed	[1732.05, 5196.15]	mm/s
mass ratio	[0.75, 1.25]	dimensionless
theta	[0, 15]	degree
phi	[0, 360]	degree

Theta is measured from global +Z. Phi is measured in global XY from +X toward +Y. Speed and angles are converted to the Cartesian velocity vector as

v = speed * [sin(theta) cos(phi), sin(theta) sin(phi), cos(theta)].

Material is a three-level categorical coordinate with balanced counts. It selects one of the rigid-impactor E/nu pairs listed in SIMULATION_PROTOCOL.md; it is not a continuously interpolated material.

Geometry-constrained position sampling

Impact positions are panel-shell centroids, not arbitrary points in a rectangular three-dimensional box. The topological outer boundary is computed from shell edges occurring in only one element. Candidate centroids must be at least 80 mm from all outer-boundary nodes in XY.

The first two LHS coordinates are projected to the nearest available candidate centroid in normalized XY, without reusing a centroid. Consequently:

• X and Y are space-filling design coordinates constrained by the mesh;
• Z is inherited from the selected shell centroid;
• the geometry JSON ranges are observed coordinate extrema, not continuous LHS box bounds.

Maximin selection and seeds

For a requested batch, 128 candidate seven-dimensional LHS designs are generated. Material coordinates are mapped to category-bin centers for scoring, and the design maximizing the normalized minimum pairwise distance is retained.

Geometry	Construction	Seed
floorfrontR	independent single batch	20260728
trunkfloor	independent single batch	20260723
floorfrontdriver, cases 001--100	initial batch	20260721
floorfrontdriver, cases 101--200	complementary nested extension	20260722
floorfrontdriver, cases 201--500	independent augmentation	20260722

Thus, the final set for each geometry contains 500 constrained-LHS cases, but the floorfrontdriver set is not one monolithic 500-point Latin hypercube. The three geometries share design bounds but use different eligible position sets and are not case-wise paired.