Zhao et al. 2015 passive quarter-car benchmark

Evidence summary

A computed reproduction with explicit provenance

Benchmark ID: vehiclelab.literature.zhao-2015.case-2.passive
Reference type: Digitized published numerical result
Compared channel: passive published body displacement vs VehicleLab sprung displacement
Product: VehicleLab 0.6.0
Model: vehiclelab.quarter-car.linear-passive v0.2.0
Solver: vehiclelab.rk4.fixed-step v0.1.0
Evidence release: 0.4.0
Licence: Creative Commons Attribution License; version not stated in the PDF

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, Volume 2015, Article ID 542364, 8 pages, 2015.

DOI: 10.1155/2015/542364

What is reproduced

Passive Case 2 subsystem

Passive, uncontrolled two-degree-of-freedom quarter-car subsystem
Isolated road-bump case and published parameter set
Published road profile after an exact phase transformation
Passive sprung-mass/body displacement
Zero initial displacement and velocity, supported by the plotted pre-event baseline

What is not reproduced

Active and physical claims

Hydraulic actuator, neural network, sliding-mode controller, or LQR
Random-road and sinusoidal-road cases
Camera imaging dynamics
Physical experiment, production vehicle, certification, or safety correlation

Parameter mapping

Published quantities map directly into the passive model

Published symbol	Meaning	Published value	VehicleLab field	VehicleLab value	Mapping note
m_b	Sprung mass	290 kg	sprungMass	290 kg	Direct
m_w	Unsprung mass	59 kg	unsprungMass	59 kg	Direct
k_s	Suspension stiffness	16,812 N/m	suspensionStiffness	16,812 N/m	Direct
c_p	Suspension damping	1,000 N/m/s	suspensionDamping	1,000 N·s/m	Dimensionally equivalent unit notation
k_t	Tire stiffness	190,000 N/m	tireStiffness	190,000 N/m	Direct
—	Tire damping	Absent	Not represented	0 N·s/m	Equation (1) models the tire as a spring only
x(0)	Initial state	Printed value conflicts with Figure 9	initialState	[0, 0, 0, 0]	Explicit audited assumption; see limitations

Road mapping

The bounded source sine is the same raised cosine in event time

Source Equation (28):

x_{r2}(t)=\begin{cases}\frac{h}{2}\left[1+\sin\left(\frac{2\pi v}{L}t\right)\right],&t_l\le t\le t_h\\0,&\text{otherwise}\end{cases}

The source values are h = 0.05 m, L = 2.5 m, and v = 18 km/h = 5 m/s, giving T_b = L/v = 0.5 s. Figure 4 and the phase identify the source onset as 0.375 s:

\tau=t-0.375\ \mathrm{s},\qquad \sin\!\left(4\pi(\tau+0.375)\right)=-\cos(4\pi\tau)

VehicleLab evaluates the equivalent event-relative form:

z_r(\tau)=\begin{cases}\frac{h}{2}\left[1-\cos\left(\frac{2\pi\tau}{T_b}\right)\right],&0\le\tau\le T_b\\0,&\text{otherwise}\end{cases}

VehicleLab event start: 0.5 s
Alignment: τ = time − bump onset
Sign: Identity; upward-positive displacement
Units: Seconds and metres

Main evidence plot

Published path, production RK4, and independent reference

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)

Acceptance uses all 5,003 independently extracted source points. The browser chart contains a deterministic reduced payload only after metrics are calculated.

Quantitative results

Amplitude, timing, and shape are evaluated separately

Metric	Computed value	Acceptance
Maximum absolute error	1.905e-4 m	≤ 7.000e-4 m
RMS error	3.401e-5 m	Reported
Normalized RMS error	3.639e-4	≤ 0.01
Published peak amplitude	0.060782 m	Reference
VehicleLab peak amplitude	0.060806 m	Compared
Peak-amplitude absolute error	2.315e-5 m	Reported
Peak-amplitude relative error	3.808e-4	≤ 0.01
Peak-time error	0.0020969 s	≤ 0.02 s
Correlation coefficient	0.9999979	Supplemental only
Estimated vertical digitization uncertainty	±0.00035 m	Declared before evaluation
Independent-reference maximum difference	2.866e-9 m	≤ 5.000e-6 m
Computed status	Reproduced within digitization-aware tolerance

Reproduction procedure

From publication to computed evidence

Transcribe the source parameters and distinguish passive from active quantities.
Map Equation (28) to the mathematically equivalent event-relative raised cosine.
Extract the Figure 9 Passive PDF vector path independently of VehicleLab.
Execute the real VehicleLab production fixed-step RK4 path.
Align both responses once relative to bump onset.
Interpolate the full-resolution VehicleLab response at the published path times.
Calculate maximum, RMS, normalized RMS, peak-amplitude, peak-time, and shape metrics.
Evaluate every predeclared acceptance criterion to compute the public status.
Generate a fine-step explicit-midpoint reference from independently constructed state-space matrices.

Limitations

This is one published numerical reproduction, not physical correlation.

Raw author data were unavailable; the published vector curve was digitized.
Plot line thickness and source reporting limit achievable precision.
The paper prints an initial state that conflicts with Figure 9's zero pre-bump baseline; the zero-state assumption and evidence are documented in the source audit.
One benchmark does not validate all vehicles, road inputs, parameters, or intended applications.
The source itself may contain modelling or reporting limitations.
No measured physical data, production-vehicle correlation, or safety claim is made.

Reproduce locally

Open the exact benchmark in the editable Studio

290 kg sprung mass; 59 kg unsprung mass; 16,812 N/m suspension stiffness; 1,000 N·s/m damping; 190,000 N/m tire stiffness; 0.05 m by 0.5 s raised-cosine bump; zero state; 5.125 s at a 0.001 s RK4 step.

VehicleLab places the bump at 0.5 s. Published and simulated responses are compared in event-relative time, so absolute clock placement is not treated as a physical model parameter.

Open this benchmark in Studio Back to all V&V evidence

Model vehiclelab.quarter-car.linear-passive v0.2.0 · Solver vehiclelab.rk4.fixed-step v0.1.0