MCM/A题/数值分析检验/Response/论文结构2.md

Below is an updated paper blueprint that cleanly integrates the three gap patches without breaking your frozen MODEL_SPEC logic (except the explicit, minimal power-mapping extension for GPS). I’ll show (i) where each patch lands, (ii) what each section must now contain, and (iii) what new data/evidence is required so the added content is rigorous (not “text-only fluff”).

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Updated Paper Blueprint (with GPS + Monte Carlo UQ + Multi-cycle aging)

Summary Sheet (1 page)

Logical progression (updated)

1. Model: continuous-time ODE + CPL closure + extended power mapping including GPS.

2. Core outputs: SOC(t), V_term(t), Δ(t), TTE.

3. Key findings:

   • Baseline TTE
   • Navigation/GPS drain impact
   • Uncertainty band (MC distribution + survival curve)
   • TTE degradation across cycles (aging trajectory)

4. Recommendations: user + OS + lifecycle-aware battery management.

Must include (new evidence)

• A one-line quantification of GPS impact on TTE (ΔTTE from turning GPS “on” vs “off” in a navigation segment).
• UQ: mean/CI and at least one survival milestone (e.g., 90% survival time).
• Aging: a mini table/plot of TTE vs cycle index (e.g., cycles 0, 50, 100, 200).

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1) Introduction and framing

Logical progression (updated)

• “Unpredictability” arises from time-varying usage and environment; navigation/location services are a common drain source.

• We address both short-horizon discharge and long-horizon degradation.

• Outline three analyses:

  1. Mechanistic model with GPS term
  2. Monte Carlo UQ for stochastic usage
  3. Multi-cycle aging forecast for TTE decline

Must include

• Motivation sentence tying GPS to the real-world “navigation drains phone quickly” phenomenon.
• A roadmap paragraph mapping to sections: baseline → scenario drivers (including GPS) → global sensitivity → UQ → aging forecast → recommendations.

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2) Model overview: states/inputs/outputs/assumptions (minor extension)

What changes

• Add one new input: GPS duty variable (G(t)\in[0,1]). (This is the minimal extension implied by your patch: add (P_{\text{gps}}(G)) to (P_{\text{tot}}).)

Must include (new items)

• Table updates

  • Inputs now include (G(t)) (unitless, [0,1], “GPS duty / navigation intensity”)
  • Parameters now include (P_{\text{gps},0}), (k_{\text{gps}})

• Assumption: (G(t)) is an externally specified scenario signal (like (L,C,N,\Psi,T_a)), not a new state.

Evidence required

• A short justification for treating GPS drain as linear in duty cycle (first-order approximation).
• A stated range for (P_{\text{gps},0}), (k_{\text{gps}}) (even if “calibrated / assumed”; must be declared).

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3) Governing equations (PATCH P10 + P11)

3.1 Power mapping (UPDATED)

Logical progression

1. Screen + CPU + Network + background (existing)
2. GPS term added additively
3. Total power drives CPL current through quadratic closure

Must include (specific equations)

• Replace total power line exactly as patch indicates: [ P_{\mathrm{tot}}(t)=P_{\mathrm{bg}}+P_{\mathrm{scr}}(L)+P_{\mathrm{cpu}}(C)+P_{\mathrm{net}}(N,\Psi,w)+P_{\mathrm{gps}}(G). ]
• GPS submodel (BLOCK_A): [ P_{\mathrm{gps}}(G) = P_{\mathrm{gps},0}+k_{\mathrm{gps}},G(t). ]

Evidence/data required to make this rigorous

• Provide either:

  • (Preferred) a citation/value range from a source (your placeholder [REF-GPS-POWER]) or
  • (If no citation) a calibration protocol: “Set (P_{\text{gps},0},k_{\text{gps}}) so that navigation scenario reproduces observed drain factor X,” and report the chosen values.

3.2–3.5 Constitutive + CPL + ODEs (unchanged)

• No new dynamics are needed; GPS affects (P_{\text{tot}}) only.

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4) Time-to-Empty (TTE) and event logic (unchanged structure, stronger interpretation)

Logical progression (unchanged)

• Event functions (g_V,g_z,g_\Delta)
• earliest crossing via interpolation
• termination reason recorded

New content to add (one paragraph)

• Explain how GPS affects TTE indirectly:

  • (G(t)\uparrow \Rightarrow P_{\text{tot}}\uparrow \Rightarrow I\uparrow) via CPL, accelerating SOC decay and potentially increasing the risk of Δ collapse / voltage cutoff earlier.

Evidence required

• A navigation/GPS scenario result showing:

  • higher avg (P_{\text{tot}}), higher max (I), and reduced TTE relative to baseline.

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5) Parameterization and data support (must now include GPS + aging-law parameters)

Logical progression (expanded)

1. Parameter groups: power mapping, battery ECM, thermal, radio tail
2. GPS parameters included in power mapping
3. Aging parameters (from Section 3.5 SOH law) clearly listed and sourced/assumed
4. Plausibility checks (energy, bounds, monotonicity)

Must include (new items)

• GPS parameter table entries: (P_{\text{gps},0},k_{\text{gps}})

• Aging-law parameter table entries (whatever Section 3.5 uses; must be explicit)

• Clear labeling:

  • “Measured / literature”
  • “Calibrated”
  • “Assumed for demonstration”

Evidence required

• For aging: at least one reference point like “capacity drops to 80% after N cycles” OR cite your [REF-LIION-AGING].
• If no empirical anchor, you must add a limitation note: aging trajectory is qualitative.

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6) Numerical method and reproducibility (minor add)

Logical progression

• RK4 nested CPL unchanged.
• Add that (G(t)) is treated identically to other inputs in scenario function.

Must include

• Updated trajectory column list to include:

  • (G(t)) and (P_{\text{gps}}(t)) (optional but recommended for clarity)

• Reproducibility: seed fixed for MC; dt fixed; step-halving.

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7) Baseline results (update: add one GPS/navigation stress baseline)

Logical progression (updated)

1. Baseline scenario plots and TTE table (existing)
2. Navigation with GPS “high duty” as an extended baseline variant
3. Compare TTE and identify mechanism (P_tot, I, Δ)

Must include (new evidence)

• A small 2-row comparison:

  • Baseline (G=0 or low)
  • Navigation/GPS-active (G high during navigation segment)

• Plot overlay or table:

  • ΔTTE, avg (P_{\text{tot}}), avg (P_{\text{gps}})

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8) Scenario analysis: drivers of rapid drain (expand the matrix to include GPS)

Logical progression (updated)

• The scenario matrix should now include a GPS-focused scenario explicitly.

Must include

• Add scenario like:

  • S8: “Navigation + GPS high duty” (or fold into your existing navigation_poor_signal segment by setting G(t)=1 there)

• Keep the ranking output but ensure GPS is represented in driver comparisons.

Evidence required

• Quantified ΔTTE for GPS scenario.
• Mechanistic signature entries include avg (P_{\text{gps}}) and show how it shifts current draw.

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9) Sensitivity analysis (optional: include GPS parameters)

Logical progression

• Your current Sobol set is fine; but the blueprint should specify a choice:

  • Either keep the 6-parameter set unchanged or
  • Replace the weakest contributor with (k_{\text{gps}}) to test GPS importance.

Must include (if you include GPS)

• Ranges for (k_{\text{gps}}) and/or (P_{\text{gps},0}) (±20% around baseline).
• Updated ranking interpretation: whether GPS is a primary driver in navigation-dominant regimes.

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10) Uncertainty Quantification (PATCH P12: MC is now required, not optional)

Logical progression (updated)

10.1 Define uncertainty source (usage variability) 10.2 Deterministic solver stability/step-halving (existing) 10.3 Monte Carlo UQ (BLOCK_B) 10.4 Survival curve and uncertainty reporting

Must include (new “hard” components)

• MC method statement:

  • number of paths (M=300)
  • perturbation model (OU on L,C,N; optionally also N/Ψ/G if you want)
  • fixed seed

• Outputs:

  • mean TTE, CI, p10/p50/p90, survival curve (P(\text{TTE}>t))

Evidence required

• UQ summary table + survival curve plot/table.
• A brief comparison: deterministic baseline TTE vs MC mean vs percentile spread (to interpret “unpredictable”).

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11) Multi-cycle aging and lifespan TTE forecasting (PATCH P13)

Logical progression

1. Explain time-scale separation: discharge seconds vs aging days.
2. Define outer-loop over cycles (j).
3. At each cycle: run discharge simulation → compute throughput → update SOH → update (R_0,Q_{\text{eff}}) → next cycle.
4. Produce TTE degradation trajectory.

Must include (new evidence)

• A formal algorithm box for the outer loop (BLOCK_C).

• Define (Q_{\text{thr},j}=\int |I(t)|,dt) and how it drives your SOH update (must reference Section 3.5 law).

• A plot/table:

  • cycle index (j) vs (S_j) and TTE(_j)

• Interpretation:

  • explain why TTE declines (capacity loss + resistance increase).

Evidence required

• Explicit SOH update equation (from your Section 3.5).
• At least one aging reference anchor (or clearly marked as “illustrative”).

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12) Recommendations (updated: add GPS + lifecycle-aware policy)

Logical progression

• Convert scenario rankings + Sobol + UQ + aging forecast into actions.

Must include (new recommendation types)

• GPS/location service policy:

  • adaptive duty-cycling, batching location updates, “navigation mode” warnings
  • quantify expected gain using your GPS scenario ΔTTE

• Lifecycle-aware recommendations:

  • as S declines, OS should lower peak power demands to avoid V_cut/Δ collapse earlier
  • user guidance: avoid high-drain use in cold/poor signal when battery aged

Evidence required

• Each recommendation must cite a model result:

  • “This action targets parameter/driver X and yields ΔTTE ≈ Y in scenario tests.”

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13) Validation, limitations, and extensions (expanded)

Must include (new limitation + validation points)

• GPS model limitation: linear duty approximation; could refine with acquisition bursts.
• Aging limitation: if no calibrated dataset, trajectory is qualitative.
• UQ limitation: OU is a stylized model; could use empirical traces.

Validation evidence (additions)

• Show GPS inclusion doesn’t break:

  • unit checks, Δ feasibility checks, step-halving convergence.

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What you should update in your appendix/tables (minimum edits)

1. Variable table: add (G(t)).

2. Parameter table: add (P_{\text{gps},0},k_{\text{gps}}) + aging-law parameters.

3. Scenario matrix: add one GPS-heavy scenario (navigation).

4. Results:

   • Baseline + GPS variant TTE comparison
   • MC summary + survival curve
   • Multi-cycle TTE vs cycle plot/table

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If you paste your current section headings (or your LaTeX/Word outline), I can produce a “diff-style” outline: exact headings to add/renumber, and exactly which existing paragraphs need one new sentence vs a full new subsection.