Skip to content

Realistic test conditions — the "realism foundation"

To judge whether a state estimator is good enough for the project goal (state estimation on a real agricultural biogas plant, ultimately to support operating recommendations), the twin experiment must run under conditions close to a real plant. This page defines those conditions and — crucially — how they are chosen.

Guiding principle: plant-agnostic and literature-based, not fitted

The sensor suite of the real test plant is not final (sensors are still being added), and the goal is a method that works for biogas plants in general, not one dataset. Therefore the noise and model-error settings are not fitted to the current plant data. Two consequences:

  • Measurement noise is attached to sensor types as generic
    instrument-accuracy specs, so adding or removing a sensor does not change the others, and the conditions transfer across plants.
  • Model error — the gap between ADM1 and reality — cannot be identified
    from operating data     (it is confounded with input and measurement error). It is therefore set from the kinetic-parameter uncertainty reported in the ADM1 literature, applied as a multiplicative perturbation.

The values live in estimation/realism.py and are applied by the twin's --realistic preset.

Model error: kinetic-parameter uncertainty

The model error is a multiplicative lognormal perturbation of the filter's biological kinetics, while the truth keeps the "real" values:

\[ k_\text{filter} = k_\text{nominal}\cdot e^{\mathcal N(0,\sigma)},\qquad \sigma = 0.25 \]

applied to the rate/affinity prefixes k_dis, k_hyd, k_m_, k_dec, K_S. Physical equilibrium constants (K_a, K_w, K_H) and stoichiometry (Y_*, f_*) are left untouched.

Why this form and magnitude:

Evidence Value
ADM1 local/global sensitivity studies perturb kinetic/stoichiometric parameters ~10 %
The gas-relevant sensitive parameters are exactly decay / disintegration / hydrolysis / k_m / K_S —
UKF-for-AD studies inject a deliberate plant-model mismatch on the rate constants ~28–30 %
Monte-Carlo uncertainty studies treat kinetic parameters as lognormal; hydrolysis is the most uncertain, yet biogas flow stays comparatively robust lognormal, CoV up to ~50 %

σ = 0.25 (CoV ≈ 25 %) sits between the sensitivity range (10 %) and the plant-model-mismatch end (30 %). It is the transferable stand-in for "the model is not 100 % reality": the observed quantities (gas) stay trackable, while un-corrected states drift — the realistic behaviour the estimator must cope with.

Measurement noise (1-σ, per sensor type)

Generic instrument-accuracy specs, relative unless noted absolute:

Sensor Noise (1-σ) Basis
Biogas flow q_gas 3 % rel. biogas-volume metrology, ~3 % expanded uncertainty, drift < 0.15 %/24 h
Methane flow q_ch4 4 % rel. q_gas × NDIR CH₄ (≈ 0.7–1 % abs.) combined
CO₂ flow q_co2 4 % rel. q_gas × NDIR CO₂
pH 0.05 (absolute, pH units) glass-electrode probe accuracy
VFA / FOS 8 % rel. FOS/TAC titration
TS / VS 3 % rel. gravimetric
Substrate dose 3 % rel. dosing scale

Some UKF-for-AD studies inflate R by ~1.5× for robustness; that factor is exposed as R_INFLATION (default 1.0).

Sampling (real-plant cadence)

  • Online (hourly in the twin, seconds on the plant): q_gas, pH, substrate
    doses, levels, CHP, temperatures.
  • Daily: gas composition CH₄ / CO₂ (NDIR). O₂ and H₂S are also measured
    daily in practice but are not ADM1da states → monitoring only, not assimilated.
  • Lab cadence: TS, VFA (gated, e.g. every 12 h for VFA).

Deliberately not included (and why)

  • Plant-specific gas-derivation chain. On the real plant, Q_gas is not a
    flow meter reading but is reconstructed from gas-dome level changes (ΔV, differentiated → noise-amplified) + CHP consumption + flare. That error structure is plant-specific; the foundation uses the generic flow-meter spec instead so the conditions stay transferable. (A plant-specific noise model can be layered on top when evaluating that plant.)
  • O₂ / H₂S. Not ADM1da states — cannot inform the UKF.
  • Fitting σ or R to the current dataset — would bias toward the incomplete
    sensor suite.

Usage

# Realism preset (model error + per-sensor noise + daily gas analytics):
python examples/run_twin_experiment.py --realistic --warmup-days 30 --duration-days 14
# Reduced state vector under realistic conditions:
python examples/run_twin_experiment.py --realistic --state-blocks methanogenesis charge_balance

Individual flags (--model-error-std, --gas-noise-std) still override the preset for sensitivity sweeps.

Evaluation harness & provenance

The estimator is evaluated by a paired Monte-Carlo ensemble (monte_carlo_eval.py): each seed draws an independent model-error realisation (this foundation) plus noise and prior perturbation, and all candidates see the same world (open-loop model, raw-sensor floor, UKF full-41, UKF A+D core, and A+D core with known input adcore_ki — the substrate feed is fed forward from the measured dosing instead of estimated, so the filter is not "surprised" by feed changes; this collapses the feed-change NIS from ~10³ to the consistency band). Metric: decision-weighted per-block NRMSE (block median, converged second half to discount the UKF's initial transient; charge_balance reported separately because its near-zero ions are ill-conditioned), plus calibration (mean NIS, 2σ coverage) and paired win-rates.

Which estimator/version was tested is recorded per run in output/mc_eval_meta.txt — keep it with any archived result, since output/ is git-ignored. It captures the timestamp, the PyADM1ODE_estimate and pyadm1 git commits (with a +dirty flag if the working tree had uncommitted changes), the pyadm1 version, the filter class + parameters, the model-error σ and the sensor schedule. The estimator under test is the Square-Root UKF estimation.filters.sr_ukf.UnscentedKalmanFilter (α = 1.0, β = 2.0, κ = 0.0, γ = canonical √(n+λ)); the reduced "A+D core" is the same filter restricted to --state-blocks methanogenesis charge_balance (18 of 41 ADM1 states).

Sources