11-EFT.WP.Core.DrawingKinetics v1.0 | Chapter 12 Benchmark Cases and Calibration

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Chapter 12 Benchmark Cases and Calibration

I. Scope and Objectives

• Establish a reproducible family of drawing/stretching benchmarks to verify the end-to-end consistency of geometry & kinematics (Chapter 2), conservation (Chapter 3), constitutive behavior & tension evolution (Chapter 4), and concurrent execution & metrology workflows (Chapters 8 and 10).
• Define three core operating scenarios — constant-speed draw, step draw, and ramp draw — with input gauges, target outputs, and score synthesis rules, forming a unified Mx-14 benchmark-report.
• Provide parameter identification and calibration workflows so that K_el, K_vis, theta and related constitutive parameters are estimable, reviewable, and traceable under aligned ts and guaranteed hb.

II. Terminology and Symbols

1. Benchmarks and scoring
   • bench.id (benchmark identifier), bench.type ∈ { const-speed , step-draw , ramp-draw }.
   • score.total (overall score), score.correctness, score.stability, score.SLO (timing & concurrency SLO), score.throughput, with weights w_c, w_s, w_o, w_t.
2. Calibration targets and parameters
   • Constitutive parameter vector theta = { K_el , K_vis , theta_aux[*] }; tension model T_fil( lambda , s ; theta) (Chapter 4).
   • Observation set y_obs = { T_fil(t) , v(t) , lambda(t) , s(t) , A(t) }, simulation/prediction set y_pred(.;theta).
3. Inputs and windows
   • bc.* (boundary conditions, Chapter 5), window.id (time window), gamma(ell) (path), d ell (measure).
   • Time base and causality: tau_mono, ts = alpha + beta * tau_mono, TS.hb.
4. Nondimensional coverage
   We, De, Re (coverage binning and report fields), coverage[X] (coverage score of X, 0..1).

III. Postulates and Minimal Equations

1. P11-30 (benchmark reproducibility)
   Each bench.id must be uniquely defined by explicit bc.*, window.id, gamma(ell), ts, and the version fingerprints of Mx-11 sensor calibrations.
2. P11-31 (monotone, bounded scoring)
   On identical data, adding physical constraints or improving metrology must not reduce score.correctness. Every sub-score is upper-bounded by 1.
3. P11-32 (identifiability region)
   Identification of theta is valid only when the excitation coverage satisfies coverage[s] >= c_min; otherwise report flag.unidentifiable = true.
4. S12-40 (parameter identification objective)
   • J_theta = ( ∑_{t ∈ window.id} w_T * ( T_pred(t;theta) - T_obs(t) )^2 + w_v * ( v_pred(t;theta) - v_obs(t) )^2 ) + R(theta).
   • Here R(theta) is a regularizer (e.g., L2 or physics priors); the calibration solution is theta_hat = argmin_theta J_theta.
5. S12-41 (score synthesis)
   • score.total = w_c * score.correctness + w_s * score.stability + w_o * score.SLO + w_t * score.throughput, with w_c + w_s + w_o + w_t = 1.
   • Default weights: w_c=0.45 , w_s=0.25 , w_o=0.20 , w_t=0.10.
6. S12-42 (correctness sub-score)
   score.correctness = 1 - min( 1 , rmse_T / gate_T_ref ), rmse_T = sqrt( mean_t ( T_pred - T_obs )^2 ), where gate_T_ref is the reference tension threshold.
7. S12-43 (stability sub-score, spectral gauge)
   Define tension jitter sigma_T and spectral leakage ratio leak_ratio (Chapter 7):
   score.stability = 1 - min( 1 , ( sigma_T / T_ref ) * k_sigma + leak_ratio * k_leak ), with coefficients k_sigma, k_leak declared in bench.card.
8. S12-44 (SLO sub-score, threads & time-base gauge)
   • Using Chapter 10 TS.* metrics:
     score.SLO = 1 - min( 1 , ( TS.latency.p95 / L_ref ) * k_L + TS.hb.violations * k_hb + TS.backlog.max / B_ref ).
   • If TS.hb.violations > 0 then score.SLO = 0.
9. S12-45 (throughput sub-score)
   score.throughput = min( 1 , R_eff / R_target ), where R_eff is the effective sample processing rate and R_target is the target throughput.
10. S12-46 (pre-gates for conservation and normalization)
    If gate.mass or gate.norm fails (Chapter 11 S12-31, S12-32), the corresponding window.id is invalid and score.total is not computed.

IV. Data and Manifest Gauges

1. bench.card (input operating card, required fields)
   • bench.id, bench.type, bc.inlet.{ v_in , lambda_in , T_in }, bc.outlet.{ v_out , lambda_out , T_out }, ramp.{ slope , duration } or step.{ amplitude , hold }.
   • env.{ temperature , humidity }, parameterization and support of gamma(ell), geometric gauge for A(x,t) (sensor–model mapping).
2. bench.metrics (outputs and scoring fields)
   • rmse.T_fil, sigma_T, leak_ratio, TS.latency.p95, TS.backlog.max, R_eff, coverage[s], coverage[lambda], We, De, Re.
   • score.* and w_*, gate pass markers gates.*, flag.unidentifiable.
3. Traceability and versions
   timebase.alpha, beta, TS.hb.digest, method.id and version hashes for Mx-11/12/13, model.theta_hat with CI_p (Chapter 11).

V. Algorithms and Implementation Bindings

1. I10-11 run_benchmark_case( bench_card:dict , params_init:dict ) -> dict
   • Function: run the specified benchmark’s simulation and side-by-side experiment, emitting y_pred, y_obs, theta_hat, and intermediate audits.
   • Contract: if TS.hb.violations > 0, return E_THREADS_CASUALITY; if gate.mass fails, return E_CONSERVATION_FAIL.
2. I10-12 score_benchmark( y_obs:any , y_pred:any , ts:SLO , gates:dict , refs:dict ) -> dict
   • Function: compute score.* and score.total, and produce bench.metrics.
   • Contract: idempotent; on unit inconsistency return E_DIMENSION_MISMATCH.
3. I10-13 fit_constitutive_params( y_obs:any , model:any , priors:dict ) -> dict
   • Function: minimize S12-40 to obtain theta_hat and uncertainty (via linearization or numerical approximation).
   • Contract: when coverage[s] < c_min, return flag.unidentifiable = true with feasible-set guidance.
4. Pseudocode (core flow)

I10-11 run_benchmark_case(card, params_init):

attach_timebase(card)

ensure_units_and_geometry(card)

y_obs <- acquire_or_load(card)

theta_hat <- I10-13.fit_constitutive_params(y_obs, model, priors)

y_pred <- simulate(model, card.bc, theta_hat)

gates <- I10-9.check_conservation( rho_L:J:trace_from(y_obs), card.window, card.path )

scores <- I10-12.score_benchmark(y_obs, y_pred, TS, gates, refs)

return {theta_hat:theta_hat, y_pred:y_pred, y_obs:y_obs, scores:scores, gates:gates}

VI. Metrology Workflow and Run Graph

1. Mx-14 benchmark-report
   • bootstrap: load bench.card, audit ts & hb, lock env.* and gamma(ell).
   • pre-check: enforce Chapter 11 gates gate.mass and gate.norm.
   • identify: call I10-13 to obtain theta_hat with CI_p.
   • simulate: generate y_pred under identical bc.* and align to ts.
   • score: call I10-12 to compute score.* and score.total.
   • report: write bench.report.json with qc.*, score.*, theta_hat, method.id, refs.
   • publish: if score.total >= score.min and all mandatory gates pass, mark publishable; otherwise enter rollback & recalibration branches.
2. Fallback strategies
   • flag.unidentifiable = true: apply stronger excitation (increase step.amplitude or ramp.slope) or extend hold.
   • gate.spectrum.leak exceeded: adjust window.id or U_w, ENBW and recompute.

VII. Verification and Test Matrix

1. Benchmark catalog and inputs
   • Constant-speed const-speed: v(t) = v0, lambda(t) = lambda0 constant; examine steady conservation and jitter.
   • Step-draw step-draw: v(t) = v0 + Delta_v * H(t - t0) or step in lambda(t); examine transient response and parameter identifiability.
   • Ramp-draw ramp-draw: v(t) = v0 + r * ( t - t0 ); examine rate coupling and drift robustness.
2. Metric families and pass lines
   • Correctness: rmse.T_fil <= gate_T_ref.
   • Stability: sigma_T / T_ref <= k_sigma^{-1} and leak_ratio <= gate.spectrum.leak.
   • SLO: TS.latency.p95 <= L_ref and TS.hb.violations == 0.
   • Throughput: R_eff >= R_target.
3. Coverage and binning
   Bin We, De, Re in multiple segments; require at least two bins per benchmark type. Report coverage[*] and compute the coverage penalty
   penalty.coverage = max( 0 , coverage_min - coverage[*] ), folded into score.correctness.

VIII. Cross-References and Dependencies

• Chapter 2: definitions and measures of lambda, s, v, A for constructing bc.* and excitation coverage.
• Chapter 3: continuity of rho_L, J for pre-check conservation gates.
• Chapter 4: constitutive families of T_fil and the identification objective for theta.
• Chapter 5: inlet/outlet, clamping, and slip modeling fed into bench.card and simulation boundaries.
• Chapter 7: spectral gauges S_xx(f), U_w, ENBW supporting leak_ratio and stability scoring.
• Chapter 8: Mx-11/12/13 time-base, calibration, and conservation audits as prerequisites for Mx-14.
• Chapter 10: TS.* metrics and hb constraints feeding score.SLO.
• Chapter 11: error budgets and CI_p co-published with bench.report.json.

IX. Risks, Limits, and Open Questions

• Strong nonlinearity and thermal drift may induce path dependence in theta; include env.* in the report and provide re-calibration advice.
• When measurement error in A(x,t) coincides with slip, T_fil identification may be multi-modal; use multi-scenario joint fitting with priors.
• Heavy-tailed noise can skew rmse.T_fil and spectral stability consistency; enable robust losses or quantile gauges and document them.
• If cross-node ts alignment is under-modeled, SLO and correctness can trade off; record source and confidence under qc.timebase.*.

X. Deliverables and Version Management

1. Deliverables
   • bench.report.json (containing bench.card, theta_hat, CI_p, score.*, gates.*, coverage[*], We, De, Re).
   • bench.methods.yaml (method.id, objective, windows & spectral gauges, regularization & hyper-parameters).
   • bench.replay.manifest (data slices, ts mapping, hb evidence, random seeds).
   • bench.changelog.md (weight, threshold, and scenario changes).
2. Version policy
   • Weight or threshold updates are MOD; constitutive-model changes that affect scoring are ADD. Any change that breaks score comparability must ship a migration script and a parallel dual-run period.
   • Publication requires passing Chapter 11 quality gates and score.total >= score.min.