25-EFT.WP.STG.Dynamics v1.0 | Chapter 15 — Use Cases and Reference Implementations

Home ／ Docs-Technical WhitePaper ／ 25-EFT.WP.STG.Dynamics v1.0

Chapter 15 — Use Cases and Reference Implementations

One-Sentence Goal
Deliver three reproducible, end-to-end paradigms for STG dynamics—data → graph → dynamics → filtering/forecasting → uncertainty → panels/contracts—along with interface bindings and manifest templates so engineering teams can plug-and-play.

I. Scope and Objects

1. Objects
   • Use-case trio: urban traffic-flow forecasting & interventions, power distribution dynamic estimation, and urban water conservation-flow & leakage detection.
   • Unified execution spine: ingest → topology build → operator/kernel assembly → dynamics stepping → assimilation & uncertainty → guardband & adjudication → publish & panel.
2. Inputs
   Data streams ds (with TraceID, ts, y, unit, RefCond), graphs & metadata { V, E, attr }, operators { L, A, H }, models & hyperparameters, SLO/contract policies.
3. Outputs
   Published x̂ / forecast, covariance and u_c, guardbands, contracts.report, and manifest.stg.case.*.
4. Boundaries & constraints
   Unit/dimension coherence; dual-form concurrency (event-time vs processing-time; LPU vs MC); runtime per Ch. 14.

II. Terms and Variables

• Traffic: nodes are links/ramps, edges are adjacent links; state x = density / speed, control u = signal / toll.
• Power: nodes are buses, edges are branches; state x = [ θ, V ] or reduced frequency f, disturbance w.
• Water: nodes are reservoirs/valves, edges are pipes; state x = head / flow, observation y = pressure / flow.
• Unified kernels: diffusion K_diff = exp( − τ L ), wave K_wave = cos( ω L^{1/2} t ), and graph filters g(L).
• Panels and contract fields follow Chs. 14 & 13.

III. Axioms P715-*

• P715-1 (End-to-end reproducibility) — Each use case ships with the same I70-* bindings, default hyperparameters, and manifest.stg.case.*.
• P715-2 (Physical consistency) — If conservation/nonnegativity is declared, both estimation and forecasting apply Π_{phys} projections.
• P715-3 (Dual-form concurrency) — Run statistical (GUM-LPU & MC) and time (event vs processing) dual forms; record gaps and test thresholds.
• P715-4 (Version traceability) — Persist graph.hash / L.hash / model.hash / policy.hash in all artifacts.
• P715-5 (Runtime SLOs) — Adhere to Ch. 14 SLO decomposition; violations trigger fallback policies.

IV. Minimal Equations S715-*

• S715-1 (Unified predictor):
  x̂_{k+1|k} = Φ_{Δt}( x̂_{k|k}, u_k; L, θ ), ŷ_k = h( x̂_{k|k}; H, ψ ).
• S715-2 (Diffusion/wave coupling):
  x_{k+1} = ( α K_diff + (1 − α) K_wave ) x_k + B u_k + w_k,
  with K_diff = exp( − τ L ), K_wave ≈ I − ( ω^2 L Δt^2 ) / 2 + ….
• S715-3 (Conservative flows):
  For water/traffic: div(F) = s, discretely B x = s, corrected by x ← x − B^{†} ( B x − s ).
• S715-4 (Uncertainty & guardbands):
  u_c^2 = J V J^T + u_num^2 + u_model^2; g = k u_c, with k from nu_eff and α (Ch. 13).
• S715-5 (Dual-form indicators):
  delta_form_stream = | metric_evt − metric_proc | (Ch. 14),
  delta_form_unc = | u_c^{LPU} − u_c^{MC} | (Ch. 13).

V. Workflow M7-15 (Ready → Model/Estimate → Validate → Persist)

• Ready
  Read sources & metadata; construct graph.hash and { L / A / H }; set windows { Δt_win, Δt_slide } and wm(t); load SLO/contract policies.
• Model / Estimate
  Choose kernels & steppers (diffusion/wave/mix); configure filters (KF/UKF/PF); set Q / R and regularization; bind control/intervention interfaces when present.
• Validate
  Physical contracts (conservation/nonnegativity), statistical (coverage / dual-form gaps), runtime (latency / backpressure / cache).
• Persist
  manifest.stg.case, panel snapshots, contract reports, hashes of models/operators, key hypers and units.

VI. Contracts & Assertions C70-15xx

• C70-1501 (Dual-form coherence): delta_form_unc_p95 ≤ 0.2 • u_c_p50.
• C70-1502 (Event-time coherence): delta_form_stream_p95 ≤ tol_stream.
• C70-1503 (Conservation / nonnegativity): || B x̂ − s ||_2 ≤ ε_cons, min(x̂) ≥ − ε_neg.
• C70-1504 (Panel SLO): latency_p95 ≤ B_mod, drop_rate ≤ 0.1%, cache_hit ≥ 80% (if caching is configured).
• C70-1505 (Forecast accuracy): rolling-window MAE / SMAPE meets target, otherwise degrade or retrain.

VII. Implementation Bindings I70-15*

• I70-151 build_case(city, layers) -> { graph, L, A, H, meta }
• I70-152 assemble_kernel(L, mode, hyper) -> K (mode ∈ { diff, wave, mix })
• I70-153 simulate_or_forecast(x0, K, B, u, steps) -> x_path
• I70-154 filter_online(y_stream, model, Q, R) -> { x̂_series, P_series }
• I70-155 enforce_physical(x, constraints) -> x_proj
• I70-156 eval_contracts(outputs, rules) -> report
• I70-157 emit_case_manifest(results, policy) -> manifest.stg.case

Invariants: non_decreasing(tau_mono); units / RefCond persisted; hash(*) traceable; P ≽ 0.

VIII. Cross-References

• Numerical integration & stability: Ch. 9 (stiffness / events & splitting).
• Assimilation & filtering: Ch. 12 (KF/UKF/PF specifics and NIS/ESS metrics).
• Uncertainty & guardbands: Ch. 13 (u_c / k / nu_eff and MC validation).
• Runtime & streaming: Ch. 14 (windows / caches / backpressure & panels).
• Causality & intervention: Ch. 10 (multi-environment invariance for intervention evaluation).

IX. Use Case Details and References

Use Case A — Urban Traffic STG (Forecasting & Signal Intervention)

1. Graph: G_road = (V, E); state x = [ density, speed ]; control u = signal_split.
2. Model: x_{k+1} = ( α K_diff + (1 − α) K_wave ) x_k + B u_k + w_k; y_k = H x_k + v_k.
3. Process:
   • I70-151 build graph & L from OSM/probe data;
   • I70-152(mode=mix) assemble kernel;
   • I70-154(UKF) online assimilation;
   • I70-155 enforce density ≥ 0 and in/out conservation;
   • I70-156 evaluate C70-1501..1505;
   • I70-157 publish manifest.stg.case.traffic.
4. Contracts: SMAPE_15min ≤ τ1; delta_form_stream_p95 ≤ 0.05 • range(flow); u_num_fraction ≤ 0.3.
5. Panel: latency_p95, cache_hit, queue_depth, SMAPE@15min, guardband_violation_rate.

Use Case B — Power Distribution Dynamic Estimation (Frequency / Voltage Quasi-Steady)

1. Graph: G_power; state reduced to x = f or [ θ, V ]; observation y = PMU / SCADA.
2. Model: small-signal frequency f_{k+1} = f_k + Δt ( − κ L f_k + w_k ); measurement y_k = H f_k + v_k.
3. Process:
   • I70-151 import single-line diagram and derive L from impedances;
   • I70-152(mode=diff, τ = κ Δt);
   • I70-154(KF) assimilate PMU/SCADA;
   • I70-155 enforce | f − f_ref | ≤ f_lim, V ∈ [ V_min, V_max ];
   • I70-156 audit coverage_rate and guardband;
   • I70-157 publish manifest.stg.case.power.
4. Contracts: NIS_p95 ∈ [ ν_low, ν_high ]; Pr( | f | > f_lim ) ≤ α; latency_p95 ≤ 100 ms.
5. Panel: f_residual, NIS, u_c(f), g(f), alarm_count.

Use Case C — Urban Water Network (Conservative Flow & Leakage Detection)

1. Graph: G_water; state x = flow / head; observation y = pressure / flow.
2. Model: steady conservation B x = s; slow dynamics x_{k+1} = x_k − η ∇Φ( x_k; L ) + w_k; y_k = H x_k + v_k.
3. Process:
   • I70-151 build graph & B;
   • I70-152(mode=diff) approximate pipe friction diffusion;
   • I70-154(PF) assimilate sparse sensors;
   • I70-155 conservation projection x ← x − B^{†} ( B x − s ) and nonnegativity;
   • I70-156 judge leakage with guardbands;
   • I70-157 publish manifest.stg.case.water.
4. Contracts: || B x̂ − s ||_2 ≤ ε_cons; false_alarm ≤ β; replay_gap_covered ≥ 99.5%.
5. Panel: cons_violation, alarm_precision/recall, delta_form_unc.

Summary
This chapter packages three representative STG use cases—traffic, power, water—from topology construction → kernel assembly → assimilation → uncertainty → guardband → panels into deployable blueprints. With P715-* / S715-* / M7-15 / C70-15xx / I70-15* and manifest.stg.case.*, teams can reproduce and audit results across domains and rapidly roll them into production.