Quarter Car · 2 DOF — Verification evidence

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

Transient solvervehiclelab.rk4.fixed-step v0.1.0

Product release1.3.1

Frequency solvervehiclelab.linear-frequency-response v0.1.0

Evidence status

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

Zhao et al. 2015 is a published numerical reproduction of one passive Quarter-Car result. Physical vehicle validation is not 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.

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-FRQ-003

independent reference

Independent state-space frequency response

PASS

Reference type: independent state-space reference
Study: Generic passenger-car parameters; 0.2–30 Hz; 240 deterministic logarithmic samples; normalized harmonic road displacement.

Direct phasor solution against independent state-space reference

The production 2x2 complex solve and validation-only 4x4 H(jω) solve are evaluated independently at every displayed frequency.

Production direct frequency solver (solid)
Independent state-space reference (dashed)

Computed metric	Value	Acceptance tolerance
Maximum absolute magnitude error	4.441e-15	Acceptance <= 1e-11
RMS magnitude error	1.156e-15	Acceptance <= 1e-11

Interpretation

The independently organized state-space and production phasor formulations agree to near floating-point precision across the full analysis range.

Limitation

This verifies implementation consistency for the documented linear model; it is not measured physical correlation or a production-vehicle claim.

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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step
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.

VL-FRQ-001Frequency-grid and record integrityVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: software integration
Purpose: Verify bounded definitions, exact logarithmic endpoints, finite aligned arrays, repeatability, and Worker parity.
Reference type: exact repeatability
Acceptance criterion: Repeated records and Worker/direct records are exactly equal; all structural invariants hold.
Why it matters: Prevents grid drift, malformed evidence, and differences between direct and Worker execution.

VL-FRQ-002Frequency-response limiting behaviorVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: analytical invariant
Purpose: Check quasi-static and asymptotic response against limits derived from the governing equations.
Reference type: analytical reference
Acceptance criterion: Low-frequency displacement tends to unity while relative motions vanish; high-frequency displacement, acceleration, and travel vanish while tire-deflection magnitude tends to unity.
Why it matters: Detects transfer-function sign, normalization, and power-of-frequency errors.

VL-FRQ-003Independent state-space frequency responseVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: independent reference
Purpose: Compare the production 2x2 phasor solution with validation-only H(jw) from a pivoted 4x4 state-space solve.
Reference type: independent state-space reference
Acceptance criterion: Every complex response agrees within 1e-11 relative to max(1, reference magnitude) across the canonical grid.
Why it matters: Cross-checks the result without reusing the production 2x2 solution algebra.

VL-FRQ-004Transient RK4 harmonic cross-checkVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: independent reference
Purpose: Compare direct steady-state magnitudes with harmonic amplitudes extracted from the unchanged production RK4 path.
Reference type: harmonic RK4 cross-check
Acceptance criterion: All four normalized responses agree within 0.5% at five response-selected frequencies after 24 discarded cycles.
Why it matters: Provides cross-domain evidence against errors shared by algebraically equivalent frequency formulations.

VL-FCMP-001Identical frequency comparisonVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: study workflow verification
Purpose: Compare identical physical configurations on one exact frequency grid.
Reference type: exact repeatability
Acceptance criterion: Both grids, magnitude and phase arrays are exactly equal; all sample and peak deltas are zero; no changed parameter is reported.
Why it matters: Protects Frequency Compare from inventing a design difference.

VL-FCMP-002Single-parameter frequency variantVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: study workflow verification
Purpose: Change only suspension damping and compare both direct harmonic responses.
Reference type: software integration assertion
Acceptance criterion: Only damping is reported as changed; both studies correspond exactly to standalone execution and share an exact grid.
Why it matters: Connects one physical edit to transparent response and peak changes.

VL-FCMP-003Worker Frequency Compare parityVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: software integration
Purpose: Run one frequency comparison directly and through the typed browser Worker adapter.
Reference type: software integration assertion
Acceptance criterion: Both completed records are exactly equal and all 18 buffers are transferable.
Why it matters: Protects paired frequency arrays and provenance across the browser boundary.

VL-FCMP-004Completed Frequency Compare integrityVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: software integration
Purpose: Validate definitions, records, changed parameters, peaks, deltas, and provenance as one snapshot.
Reference type: software integration assertion
Acceptance criterion: Every summary is derived exactly from aligned stored arrays and immutable Baseline/Variant definitions.
Why it matters: Prevents edited inputs or mismatched studies from contaminating exports.

VL-FCMP-005Frequency Compare browser workflowVerified

Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.linear-frequency-response
Category: browser workflow
Purpose: Configure, run, inspect, export, save, restore, and rerun Frequency Compare locally.
Reference type: software integration assertion
Acceptance criterion: All four overlays, native sample inspection, deterministic CSV, PDF, project import, stale evidence, and analysis switching remain coherent.
Why it matters: Verifies the user-visible path around the validated comparison package.

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 →