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Verification & Validation / Evidence

Half Car · 4 DOF — Verification evidence

Body heave and pitch with two axles; independent state-space comparison, Quarter-Car reduction, convergence, Worker parity and harmonic frequency cross-checks.

Modelvehiclelab.half-car.linear-passive v0.1.0
Transient solvervehiclelab.rk4.fixed-step v0.1.0
Product release1.3.1
Frequency solvervehiclelab.half-car.dynamic-stiffness v0.1.0

Evidence status

Implementation & independent numerical reference
Verified — recorded regression evidence
Published literature reproduction
Not currently available
Physical test correlation
Not performed

A dedicated external published Half-Car literature reproduction has not yet been added to the current evidence set and is not currently claimed.

Recorded verification describes checks backed by the canonical regression suites and reviewed release evidence. It is distinct from the computed PASS/FAIL plots. Acceptance criteria below come from the existing registry or unchanged canonical test assertions.

Canonical model verification

HC-001exact zero equilibriumVerified
Category
Analytical invariant
Reference type
Analytical zero equilibrium
Acceptance criteria
Every dynamic channel is exactly zero on flat roads with zero initial state.
Test provenance
tests/validation/half-car.validation.test.ts
HC-002symmetric excitation and initial conditions give exact zero pitch and matching axlesVerified
Category
Symmetry
Reference type
Symmetric excitation
Acceptance criteria
Pitch angle, rate and acceleration are exactly zero; front/rear unsprung displacements are exactly equal.
Test provenance
tests/validation/half-car.validation.test.ts
HC-003symmetric half-car reduces to quarter-car with half the sprung massVerified
Category
Model reduction
Reference type
Quarter-Car correspondence
Acceptance criteria
Maximum heave and front-wheel displacement difference is < 1e-14 m.
Test provenance
tests/validation/half-car.validation.test.ts
HC-004agrees with independent energy-assembled state space, free and forcedVerified
Category
Independent reference
Reference type
Independent energy-assembled M/K/C state space
Acceptance criteria
Each free/forced state error is strictly below its ordered bound: [1e-9, 1e-8, 1e-9, 1e-8, 5e-9, 2e-7, 5e-9, 2e-7]. Position bounds use m or rad; velocity bounds use m/s or rad/s. State order interleaves position and velocity. Independent stiffness/damping matrices are symmetric.
Test provenance
tests/validation/half-car.validation.test.ts
HC-005converges at approximately fourth order for smooth free responseVerified
Category
Numerical convergence
Reference type
Independent matrix-exponential reference
Acceptance criteria
Successive time-step refinement error ratios are > 10 and < 22. Errors decrease across both refinements.
Test provenance
tests/validation/half-car.validation.test.ts
HC-006front axle rise generates a nose-up moment and an initial nose-up bump responseVerified
Category
Equation/sign check
Reference type
Hand-calculated force and moment
Acceptance criteria
Front-wheel rise gives exactly the hand-calculated pitch acceleration; the initial front-only bump has positive pitch angle and acceleration.
Test provenance
tests/validation/half-car.validation.test.ts
HC-007direct/Worker records match exactly and all 19 buffers transferVerified
Category
Worker integration
Reference type
Direct execution and transferred evidence
Acceptance criteria
Direct and Worker records are exactly equal; 19 distinct buffers transfer and detach; request identity is preserved.
Test provenance
tests/validation/half-car.validation.test.ts
HC-008model/definition isolation rejects mismatches and unsupported ids/versionsVerified
Category
Contract rejection
Reference type
Strict model/schema/solver contract
Acceptance criteria
Unsupported identities and cross-model definitions throw; the Worker returns the original request ID with SIMULATION_ERROR. No fallback model is accepted.
Test provenance
tests/validation/half-car.validation.test.ts

Frequency and workflow evidence

The Half-Car frequency suite compares an independent eight-state / sixteen-real harmonic system, checks all nine complex response channels, harmonic transient amplitude and phase, symmetry, limits and modes. Its frequency solver is vehiclelab.half-car.dynamic-stiffness v0.1.0.

Typed Worker/direct frequency parity and definition-only projects are checked separately. Study, Compare and Explore browser suites check completed evidence retention, model isolation, exports and responsive workflows.

Frequency reference and harmonic cross-check
Verified — packages/frequency-analysis/src/half-car-frequency.test.ts
Frequency Worker/project integrity
Verified — packages/frequency-analysis/src/half-car-frequency-integration.test.ts
Transient workflows
Verified — tests/e2e/half-car-study.spec.ts, half-car-compare.spec.ts and half-car-explore.spec.ts
Reference checkCanonical acceptance
Independent complex state-space responseComplex error < 1e-9 × max(1, reference magnitude); derived travel/tire components retain their separate precision assertions.
Settled transient complex responseComplex error < 2e-5 × max(1, reference magnitude)
Settled transient relative magnitude< 2e-4
Settled transient wrapped phase< 0.02 degrees

Read the Half-Car frequency formulation and interpretation.

Evidence boundary

These checks verify the documented passive linear mathematical model and software path. Generic presets have no measured production-vehicle correlation. Review model and evidence boundaries.

Read the model equations and assumptions →