Verification & Validation

Evidence version0.4.0

Modelvehiclelab.quarter-car.linear-passive v0.2.0

Solvervehiclelab.rk4.fixed-step v0.1.0

Verification versus validation

Verification

Are the stated equations and numerical methods implemented correctly?

Verification uses invariants, independent calculations, convergence, repeatability, and integration assertions.

Validation

Does the model reproduce an appropriate independent, published, or physical reference for its intended use?

Reference type and intended-use boundary must be explicit; software tests alone are not production-vehicle validation.

Current evidence status

Evidence layer	Current status
Equation and invariant checks	Verified
Deterministic solver behavior	Verified
Numerical convergence	Verified
Browser Worker parity	Verified
Baseline-versus-variant workflow	Verified
Deterministic parameter-sweep workflow	Verified — eight canonical sweep cases
Display-only motion playback	Verified
Independent transient reference	Verified — featured damped response
Published-literature reproduction	Published numerical benchmark — one passive quarter-car case reproduced
Physical test correlation	Not performed

Computed from the canonical pipeline

Featured visual evidence

Error metrics and PASS/FAIL statuses are generated from full-resolution arrays. The browser plot payload is deterministically downsampled only after acceptance is evaluated.

VL-LIT-001

literature reproduction

Published passive bump response

PASS

Reference type: published literature result
Study: Zhao et al. Case 2 passive quarter car; 0.05 m raised-cosine-equivalent bump; 0.5 s duration; zero state; VehicleLab step 0.001 s.

Published source

Feng Zhao, Mingming Dong, Yechen Qin, Liang Gu, and Jifu Guan, “Adaptive Neural-Sliding Mode Control of Active Suspension System for Camera Stabilization,” Shock and Vibration, 2015, Article ID 542364.

DOI: 10.1155/2015/542364

Published passive response against VehicleLab reproduction

The published Figure 9 vector path and both numerical implementations are aligned once to bump-relative time. Metrics use all 5,003 source points before browser plot downsampling.

Digitized published Passive curve (dotted)
VehicleLab production RK4 (solid)
Independent fine-step reference (dashed)

Computed metric	Value	Acceptance tolerance
Maximum absolute error	1.905e-4 m	≤ 0.0007 m
Normalized RMS error (published range)	3.639e-4	≤ 0.01
Peak-amplitude relative error	3.808e-4	≤ 0.01
Event-relative peak-time error	0.0020969 s	≤ 0.02 s

Interpretation

Reproduced within digitization-aware tolerance. The production result stays within the predeclared digitization-aware amplitude, timing, RMS, and maximum-error limits.

Limitation

The comparison is a published numerical reproduction extracted from a plotted vector path, not raw author data or measured physical correlation.

VL-QC-003

independent reference

Damped free response

PASS

Reference type: independent state-space reference
Study: Flat road; z_s(0) = 0.03 m; zero initial velocities; 8 s; VehicleLab step 0.001 s.

\mathbf{x}(t)=e^{\mathbf{A}t}\mathbf{x}(0)

e_{\max}=\max_i\left|y_i-y_{\mathrm{ref},i}\right|

Sprung displacement against independent state-space reference

The complete damped transient is compared on the same time samples.

VehicleLab RK4 (solid)
Independent state-space reference (dashed)

Computed metric	Value	Acceptance tolerance
Maximum absolute displacement deviation	5.286e-11 m	≤ 1e-6 m
RMS displacement deviation	4.380e-12 m	Reported, not a pass/fail criterion

Interpretation

The independently propagated linear state-space response overlays the production fixed-step RK4 response across the complete decay. The error is evaluated before plot downsampling.

Limitation

This is an independent numerical reference for the documented linear model, not measured-vehicle correlation.

VL-QC-004

analytical invariant

Permanent road-height equilibrium

PASS

Reference type: analytical reference
Study: 0.03 m permanent cubic smooth step; starts 0.25 s; rises over 0.1 s; 12 s at 0.001 s.

z_s=z_u=z_r

Permanent road-height response and analytical equilibrium target

The horizontal analytical line is the final target, not the expected transient response.

Prescribed road (dashed)
VehicleLab sprung (solid)
VehicleLab unsprung (solid)
Analytical final equilibrium (dashed)

Computed metric	Value	Acceptance tolerance
Final sprung displacement error	5.037e-13 m	≤ 2e-4 m
Final unsprung displacement error	4.795e-14 m	≤ 2e-4 m
Final absolute suspension travel	4.557e-13 m	≤ 2e-4 m
Final absolute dynamic tire deflection	4.795e-14 m	≤ 2e-4 m

Interpretation

After the smooth road transition excites the two modes, both masses settle toward the prescribed road height while suspension travel and dynamic tire deflection return toward zero.

Limitation

The analytical line describes only the final static equilibrium of the continuous-contact linear model.

VL-QC-005

numerical convergence

Time-step convergence

PASS

Reference type: fine-step numerical reference
Study: Generic half-sine study; standard step 0.001 s; fine-step numerical reference 0.0005 s.

e_{\mathrm{RMS}}=\sqrt{\frac{1}{N}\sum_{i=1}^{N}(y_i-y_{\mathrm{ref},i})^2}

Sprung acceleration around the road event

Fine-step values are sampled at matching standard-step times for visual comparison.

VehicleLab standard step (solid)
Fine-step numerical reference (dashed)

Computed metric	Value	Acceptance tolerance
Peak acceleration relative difference	3.873e-4	< 5e-4
RMS acceleration difference	4.142e-5 m/s²	Reported, not a pass/fail criterion
Maximum matching-sample acceleration deviation	1.059e-6 m/s²	Reported, not a pass/fail criterion

Interpretation

Halving the requested RK4 step produces a closely aligned acceleration transient and a peak difference below the declared convergence tolerance.

Limitation

This demonstrates numerical convergence for one canonical study. It is not an experimental or production-vehicle validation.

One typed canonical registry

Canonical V&V matrix

VL-QC-001Zero equilibriumverified

Category: analytical invariant
Purpose: Confirm that flat road and a zero initial state remain exactly at equilibrium.
Reference type: analytical reference
Acceptance criterion: Every dynamic channel and derived metric remains within 1e-12 of zero.
Why it matters: Detects sign errors, unintended forcing, and state drift.

VL-QC-002Deterministic repeatabilityverified

Category: software integration
Purpose: Execute the generic half-sine study twice with identical inputs.
Reference type: exact repeatability
Acceptance criterion: All channels and metrics are exactly equal.
Why it matters: Protects repeatability and excludes wall-clock or random inputs.

VL-QC-003Damped free responseverified

Category: independent reference
Purpose: Compare a damped flat-road response with an independent state-space transition.
Reference type: independent state-space reference
Acceptance criterion: Maximum sprung-displacement deviation is at most 1e-6 m; energy and settling checks remain satisfied.
Why it matters: Checks damping direction, bounded motion, and the full transient against an independent method.

VL-QC-004Permanent road-height equilibriumverified

Category: analytical invariant
Purpose: Confirm both masses settle to a permanent 0.03 m smooth-step road height.
Reference type: analytical reference
Acceptance criterion: Final position errors and relative deflections are at most 2e-4 m.
Why it matters: Checks road sign, static response, and relative-displacement definitions.

VL-QC-005Time-step convergenceverified

Category: numerical convergence
Purpose: Compare the generic study at 0.001 s and 0.0005 s fixed steps.
Reference type: fine-step numerical reference
Acceptance criterion: Peak sprung-acceleration relative difference is below 5e-4.
Why it matters: Detects integration-order and time-base regressions without claiming physical validation.

VL-QC-006Invalid-input rejectionverified

Category: software integration
Purpose: Submit unsafe physical values, road timing, and workloads.
Reference type: software integration assertion
Acceptance criterion: The authoritative schema rejects every unsafe input.
Why it matters: Prevents undefined or unsafe integration requests.

VL-QC-007Worker/direct parityverified

Category: software integration
Purpose: Run one typed study through both the core and Worker adapter.
Reference type: software integration assertion
Acceptance criterion: All channels and metrics are exactly equal.
Why it matters: Confirms serialization and transferable buffers do not alter results.

VL-QC-008Derived metricsverified

Category: metric verification
Purpose: Exercise peak and RMS definitions with an independent three-sample fixture.
Reference type: analytical reference
Acceptance criterion: Computed metrics agree to 14 floating-point digits.
Why it matters: Keeps metric verification independent from the full simulation path.

VL-QC-009Result-channel integrityverified

Category: software integration
Purpose: Simulate a duration that is not divisible by the requested step.
Reference type: software integration assertion
Acceptance criterion: Channels are finite and aligned, with exact count and endpoints.
Why it matters: Protects final-step behavior, alignment, and finite results.

VL-CMP-001Identical-study comparisonverified

Category: study workflow verification
Purpose: Compare duplicate baseline and Variant A configurations under one shared scenario.
Reference type: exact repeatability
Acceptance criterion: No parameter changes are reported; every channel is exactly equal and every metric delta is zero.
Why it matters: Protects the comparison engine from inventing differences.

VL-CMP-002Single-parameter variantverified

Category: study workflow verification
Purpose: Compare 1,500 and 2,000 N·s/m suspension damping with all other inputs shared.
Reference type: software integration assertion
Acceptance criterion: Exactly one parameter change is reported and deterministic metric deltas match direct calculations.
Why it matters: Connects one deliberate engineering edit to a complete paired response.

VL-CMP-003Shared-scenario compatibilityverified

Category: study workflow verification
Purpose: Reject paired studies with different road, initial state, duration, step, or identities.
Reference type: software integration assertion
Acceptance criterion: Every incompatible shared-scenario field prevents comparison execution.
Why it matters: Prevents misleading comparisons between different excitation or solver settings.

VL-CMP-004Relative-delta edge casesverified

Category: metric verification
Purpose: Exercise increase, decrease, unchanged, and zero-baseline delta calculations.
Reference type: analytical reference
Acceptance criterion: Signed deltas and directions are exact; a zero baseline returns no percentage and never Infinity or NaN.
Why it matters: Prevents mathematically invalid or evaluative comparison labels.

VL-CMP-005Completed comparison snapshotverified

Category: browser workflow
Purpose: Edit both configurations and the shared scenario after a completed comparison.
Reference type: software integration assertion
Acceptance criterion: Visible completed results remain unchanged until one entire replacement comparison completes.
Why it matters: Keeps every displayed comparison internally reproducible.

VL-CMP-006Worker comparison parityverified

Category: software integration
Purpose: Run one comparison directly and through the typed Worker adapter.
Reference type: software integration assertion
Acceptance criterion: The completed comparison records are exactly equal.
Why it matters: Protects progress messaging and transferable buffers from corrupting either run.

VL-SWP-001Deterministic sweep gridverified

Category: study workflow verification
Purpose: Generate damping and stiffness candidates from an inclusive linear range.
Reference type: software integration assertion
Acceptance criterion: The exact minimum and maximum are included once and all candidates remain in canonical ascending order.
Why it matters: Makes every candidate set reproducible and independently inspectable.

VL-SWP-002Sweep definition rejection and workload capverified

Category: software integration
Purpose: Submit invalid ranges, counts, bounds, shared inputs, and excessive workloads.
Reference type: software integration assertion
Acceptance criterion: The authoritative versioned schema rejects every invalid definition.
Why it matters: Bounds browser work and prevents incomparable candidate studies.

VL-SWP-003Exact sweep repeatabilityverified

Category: study workflow verification
Purpose: Execute the same versioned sweep definition twice.
Reference type: exact repeatability
Acceptance criterion: Both completed SweepRecordV1 values are exactly equal.
Why it matters: Protects design exploration from clock, random, or UI-state inputs.

VL-SWP-004Sweep shared-input invariantsverified

Category: study workflow verification
Purpose: Inspect every generated candidate physical configuration and shared scenario.
Reference type: software integration assertion
Acceptance criterion: Only the selected damping or stiffness value changes; every other physical and numerical input remains exactly Baseline.
Why it matters: Prevents confounded trade-off evidence.

VL-SWP-005Sweep metric correspondenceverified

Category: metric verification
Purpose: Compare every candidate metric bundle with an individual production simulation.
Reference type: software integration assertion
Acceptance criterion: All four metrics match the corresponding direct run exactly.
Why it matters: Protects the sweep layer from recalculating or relabeling numerical evidence.

VL-SWP-006Worker sweep parity and progressverified

Category: software integration
Purpose: Run one sweep directly and through the typed Worker adapter.
Reference type: software integration assertion
Acceptance criterion: Records are exactly equal and structured progress covers preparation, ordered candidates, calculation, and completion.
Why it matters: Protects the browser boundary and makes long-running work observable.

VL-SWP-007Completed sweep snapshot and stale-result safetyverified

Category: browser workflow
Purpose: Edit and rerun a completed sweep, then cancel or supersede active work.
Reference type: software integration assertion
Acceptance criterion: The completed record stays immutable until atomic replacement; cancelled or stale responses cannot replace it.
Why it matters: Prevents mixed-definition evidence and late Worker races.

VL-SWP-008Sweep browser selection, export, and promotionverified

Category: browser workflow
Purpose: Run a sweep, inspect table and plots, select a candidate, export CSV, and promote it.
Reference type: software integration assertion
Acceptance criterion: All candidates and four metrics remain accessible, the CSV is deterministic, and promotion changes only Variant A.
Why it matters: Connects numerical evidence to a deliberate, reversible comparison choice.

VL-UI-001Browser workflowverified

Category: browser workflow
Purpose: Exercise keyboard editing, road selection, run, metrics, plots, and reset.
Reference type: software integration assertion
Acceptance criterion: The study completes and generic defaults are restored.
Why it matters: Validates the product path around the numerical core.

VL-UI-002No WebGL dependencyverified

Category: browser workflow
Purpose: Run the Studio while WebGL and WebGL2 contexts are unavailable.
Reference type: software integration assertion
Acceptance criterion: The complete workflow and all plots remain usable.
Why it matters: Keeps the product accessible on browsers without WebGL.

VL-UI-003Responsive layoutverified

Category: browser workflow
Purpose: Check public routes and Studio at required desktop and mobile widths.
Reference type: software integration assertion
Acceptance criterion: No page-level horizontal overflow occurs.
Why it matters: Protects access to the complete visitor and study workflow.

VL-UI-004Quarter-car motion playbackverified

Category: browser workflow
Purpose: Exercise explicit playback visibility, controls, interpolation, shared scaling, and snapshot behavior.
Reference type: software integration assertion
Acceptance criterion: Playback never autostarts, maps upward-positive motion correctly, preserves paired scale/time, and remains keyboard/mobile usable.
Why it matters: Adds an interpretable motion view while keeping numerical evidence authoritative.

VL-LIT-001Published passive bump responseverified

Category: literature reproduction
Purpose: Compare the passive Case 2 sprung-displacement response with independently extracted Figure 9 evidence.
Reference type: published literature result
Acceptance criterion: Normalized RMS error <= 0.01, peak-amplitude relative error <= 0.01, peak-time error <= 0.02 s, maximum error <= 0.0007 m, with all transformations explained.
Why it matters: Adds traceable published numerical evidence beyond analytical and independently computed internal references.

Evidence methodology

Reference calculations are separate from the production RK4 path.
The state-space matrix is constructed directly from the documented force balances.
Acceptance is evaluated on full-resolution arrays.
Plots may use deterministic downsampling after errors and statuses are computed.
PASS/FAIL is generated from declared tolerances, never entered manually in page copy.
Every result identifies the model, solver, and evidence releases.

Evidence boundary

Correct implementation is not production-vehicle correlation.

Current evidence establishes correct and repeatable behavior for the documented mathematical model and software path. It does not establish correlation to a named production vehicle, certification, homologation, or safety suitability. The generic preset is not a production vehicle and no experimental data is claimed.

Future evidence

Additional published cases may broaden the numerical evidence boundary. Experimental correlation still requires suitable measured data, traceable test conditions, and an explicit intended-use protocol; it has not been performed and is not currently claimed.