Load-cell measurement chain

Executed calibration, filter and uncertainty analysis using declared synthetic data. No physical calibration has been performed.

Result

A 25-sample moving average at 100 Hz reduces the modeled white-noise standard deviation to 0.403 g. A noise-free 5 kg step settles within 5 g after 0.24 s.

In the baseline budget with independent temperature terms, the combined standard uncertainty at 5 kg is 1.780 g under the stated bounds. The k = 2 expanded value is 3.560 g. This is far larger than the ideal ADC code increment of 0.00233 g.

Identical input data are used for all causal filters. Settling is assessed on a separate noise-free step; errors here include injected drift and nonlinearity.

Inputs and signal chain

10 kg bridge, 2 mV/V sensitivity, 5 V excitation; reference 24-bit ADC with 2.5 V reference and gain 128
100 Hz acquisition; 2 µV RMS independent white noise; positive 0.02 g/s drift; every trace and calibration sample is synthetic
Residual nonlinearity ±2 g, hysteresis ±1 g, temperature-zero ±1.5 g, temperature-span ±0.01% of reading over 10 °C; these are assumed uncertainty bounds

Bridge differential output → matched analog low-pass/input protection → ratiometric PGA/ADC → two-parameter calibration → causal digital filter. Excitation and reference should track; this model assumes their ideal ratio and budgets remaining span drift separately. No physical circuit is included.

item	value	unit
Rated 10 kg signal	10.0	mV
12 kg overload signal	12.0	mV
ADC positive differential full scale	19.53125	mV
Overload differential margin	7.53125	mV
Ideal code increment at nominal sensitivity	0.0023283064365386963	g
Single-reading standard uncertainty at 5 kg	1.7800266281621322	g
Expanded uncertainty, k = 2	3.5600532563242644	g

Calibration

The code fits 180 generated readings at six mass levels. The fitted sensitivity is 1.00040339 µV/g and offset is 30.02390 µV. The calibration trace contains independent white noise; the later load trace adds a separate nonlinear error and drift.

Slope and intercept covariance is propagated together through m = (V − b)/s. Treating them as independent would overstate the calibration contribution around the middle of the span.

Synthetic calibration residuals. Known reference-mass uncertainty is a separate assumed budget component.

Filter comparison

filter	single_reading_noise_std_g	step_settling_to_5g_s	final_10s_mean_error_g	causal
Raw	1.99327	0.0	3.04096	True
MA 10	0.63328	0.09	3.04068	True
MA 25	0.40305	0.24	3.03985	True
MA 50	0.28809	0.49	3.03969	True
EMA 0.1 s	0.44933	0.69	3.04055	True
EMA 0.3 s	0.26251	2.07	3.03743	True

Noise uses 100,000 separately generated samples, excluding 1,000 startup samples. Each result describes a single filtered reading; adjacent moving-average readings are correlated. The final 10 s mean error includes systematic effects and is not a repeatability estimate.

Baseline uncertainty: independent temperature terms

Standard uncertainty contributions in grams; rectangular bounds are divided by √3, rounding step by √12.

component	standard_uncertainty_g	variance_g2	distribution	basis
Filtered single-reading repeatability	0.4030533544254948	0.16245200651364353	normal	Synthetic white-noise trace; not the uncertainty of the mean
Calibration fit (slope/intercept covariance)	0.15343512982998966	0.023542339065945782	normal	OLS covariance; correlated parameters propagated together
Reference masses	0.05	0.0025000000000000005	normal	Assumed standard uncertainty, not a weight certificate
Residual nonlinearity	1.1547005383792517	1.3333333333333337	rectangular	Assumed symmetric bound
Hysteresis	0.5773502691896258	0.3333333333333334	rectangular	Assumed symmetric bound
Temperature zero shift	0.8660254037844387	0.7500000000000001	rectangular	Assumed bound over declared temperature excursion
Temperature span shift	0.2886751345948129	0.08333333333333336	rectangular	Assumed fraction of reading
60 s drift	0.6928203230275509	0.48	rectangular	Assumed symmetric bound; trace uses positive ramp as one stress case
ADC rounding	0.0006718531532528146	4.513866595357499e-07	rectangular	Quantization interval; ENOB and analog noise are separate

Verification and limits

All 18 tests pass, including exact calibration recovery, Monte Carlo covariance propagation, filter causality, analytic EMA response, moving-average noise gain, drift preservation and zero-tracker gates.

No physical bridge, ADC board or calibration masses were measured. These results validate the analysis code under stated synthetic conditions.
Differential ADC headroom is calculated; common-mode input range, excitation/reference tracking, analog anti-alias filtering, EMI, mounting and overload survival need actual component and installation checks.
The baseline budget assumes independent components except for fitted slope/intercept covariance. The separate virtual-validation report also evaluates shared temperature error; its expanded uncertainty is higher.
k = 2 is an illustrative expanded uncertainty, not a certified 95% coverage claim. The Type B bounds must be replaced by evidence before using the budget for acceptance.
Zero tracking is disabled in the reported measurements. The optional tracker requires external empty-pan confirmation; it cannot distinguish drift from a small real load if that confirmation is wrong.

Reproduction and method source

python -m pip install -r requirements.txt
python run.py
python -m unittest -v

Method: NIST TN 1297, Appendix A. It supplies the covariance propagation and rectangular-distribution treatment. The numerical bounds here are declared project assumptions. See README.md and physical_calibration.md for file details and the unexecuted hardware procedure.

Virtual validation

Executed synthetic and theoretical run-through. The report includes cases, acceptance results and model boundaries.