333 lines
11 KiB
Markdown
333 lines
11 KiB
Markdown
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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---
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# Updated Paper Blueprint (with GPS + Monte Carlo UQ + Multi-cycle aging)
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## Summary Sheet (1 page)
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### Logical progression (updated)
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1. Model: continuous-time ODE + CPL closure + **extended power mapping including GPS**.
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2. Core outputs: SOC(t), V_term(t), Δ(t), TTE.
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3. Key findings:
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* Baseline TTE
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* **Navigation/GPS drain impact**
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* **Uncertainty band** (MC distribution + survival curve)
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* **TTE degradation across cycles** (aging trajectory)
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4. Recommendations: user + OS + lifecycle-aware battery management.
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### Must include (new evidence)
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* A **one-line quantification** of GPS impact on TTE (ΔTTE from turning GPS “on” vs “off” in a navigation segment).
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* UQ: mean/CI and at least one survival milestone (e.g., 90% survival time).
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* Aging: a mini table/plot of TTE vs cycle index (e.g., cycles 0, 50, 100, 200).
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---
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## 1) Introduction and framing
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### Logical progression (updated)
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* “Unpredictability” arises from time-varying usage and environment; **navigation/location services** are a common drain source.
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* We address both **short-horizon discharge** and **long-horizon degradation**.
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* Outline three analyses:
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1. Mechanistic model with GPS term
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2. Monte Carlo UQ for stochastic usage
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3. Multi-cycle aging forecast for TTE decline
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### Must include
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* Motivation sentence tying GPS to the real-world “navigation drains phone quickly” phenomenon.
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* A roadmap paragraph mapping to sections: baseline → scenario drivers (including GPS) → global sensitivity → UQ → aging forecast → recommendations.
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---
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## 2) Model overview: states/inputs/outputs/assumptions (minor extension)
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### What changes
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* Add **one new input**: GPS duty variable (G(t)\in[0,1]).
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(This is the minimal extension implied by your patch: add (P_{\text{gps}}(G)) to (P_{\text{tot}}).)
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### Must include (new items)
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* **Table updates**
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* Inputs now include (G(t)) (unitless, [0,1], “GPS duty / navigation intensity”)
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* Parameters now include (P_{\text{gps},0}), (k_{\text{gps}})
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* Assumption: (G(t)) is an externally specified scenario signal (like (L,C,N,\Psi,T_a)), not a new state.
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### Evidence required
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* A short justification for treating GPS drain as linear in duty cycle (first-order approximation).
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* A stated range for (P_{\text{gps},0}), (k_{\text{gps}}) (even if “calibrated / assumed”; must be declared).
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---
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## 3) Governing equations (PATCH P10 + P11)
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### 3.1 Power mapping (UPDATED)
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#### Logical progression
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1. Screen + CPU + Network + background (existing)
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2. **GPS term** added additively
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3. Total power drives CPL current through quadratic closure
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#### Must include (specific equations)
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* Replace total power line exactly as patch indicates:
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[
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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).
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]
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* GPS submodel (BLOCK_A):
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[
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P_{\mathrm{gps}}(G) = P_{\mathrm{gps},0}+k_{\mathrm{gps}},G(t).
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]
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#### Evidence/data required to make this rigorous
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* Provide either:
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* (Preferred) a citation/value range from a source (your placeholder [REF-GPS-POWER]) **or**
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* (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.
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### 3.2–3.5 Constitutive + CPL + ODEs (unchanged)
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* No new dynamics are needed; GPS affects (P_{\text{tot}}) only.
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---
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## 4) Time-to-Empty (TTE) and event logic (unchanged structure, stronger interpretation)
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### Logical progression (unchanged)
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* Event functions (g_V,g_z,g_\Delta)
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* earliest crossing via interpolation
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* termination reason recorded
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### New content to add (one paragraph)
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* Explain how GPS affects TTE *indirectly*:
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* (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.
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### Evidence required
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* A navigation/GPS scenario result showing:
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* higher avg (P_{\text{tot}}), higher max (I), and reduced TTE relative to baseline.
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---
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## 5) Parameterization and data support (must now include GPS + aging-law parameters)
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### Logical progression (expanded)
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1. Parameter groups: power mapping, battery ECM, thermal, radio tail
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2. **GPS parameters** included in power mapping
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3. **Aging parameters** (from Section 3.5 SOH law) clearly listed and sourced/assumed
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4. Plausibility checks (energy, bounds, monotonicity)
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### Must include (new items)
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* GPS parameter table entries: (P_{\text{gps},0},k_{\text{gps}})
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* Aging-law parameter table entries (whatever Section 3.5 uses; must be explicit)
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* Clear labeling:
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* “Measured / literature”
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* “Calibrated”
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* “Assumed for demonstration”
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### Evidence required
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* For aging: at least one **reference point** like “capacity drops to 80% after N cycles” OR cite your [REF-LIION-AGING].
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* If no empirical anchor, you must add a limitation note: aging trajectory is qualitative.
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---
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## 6) Numerical method and reproducibility (minor add)
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### Logical progression
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* RK4 nested CPL unchanged.
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* Add that (G(t)) is treated identically to other inputs in scenario function.
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### Must include
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* Updated trajectory column list to include:
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* (G(t)) and (P_{\text{gps}}(t)) (optional but recommended for clarity)
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* Reproducibility: seed fixed for MC; dt fixed; step-halving.
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---
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## 7) Baseline results (update: add one GPS/navigation stress baseline)
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### Logical progression (updated)
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1. Baseline scenario plots and TTE table (existing)
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2. **Navigation with GPS “high duty”** as an extended baseline variant
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3. Compare TTE and identify mechanism (P_tot, I, Δ)
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### Must include (new evidence)
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* A small 2-row comparison:
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* Baseline (G=0 or low)
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* Navigation/GPS-active (G high during navigation segment)
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* Plot overlay or table:
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* ΔTTE, avg (P_{\text{tot}}), avg (P_{\text{gps}})
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---
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## 8) Scenario analysis: drivers of rapid drain (expand the matrix to include GPS)
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### Logical progression (updated)
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* The scenario matrix should now include a GPS-focused scenario explicitly.
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### Must include
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* Add scenario like:
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* **S8: “Navigation + GPS high duty”** (or fold into your existing navigation_poor_signal segment by setting G(t)=1 there)
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* Keep the ranking output but ensure GPS is represented in driver comparisons.
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### Evidence required
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* Quantified ΔTTE for GPS scenario.
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* Mechanistic signature entries include avg (P_{\text{gps}}) and show how it shifts current draw.
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---
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## 9) Sensitivity analysis (optional: include GPS parameters)
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### Logical progression
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* Your current Sobol set is fine; but the blueprint should specify a choice:
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* Either keep the 6-parameter set unchanged **or**
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* Replace the weakest contributor with (k_{\text{gps}}) to test GPS importance.
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### Must include (if you include GPS)
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* Ranges for (k_{\text{gps}}) and/or (P_{\text{gps},0}) (±20% around baseline).
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* Updated ranking interpretation: whether GPS is a primary driver *in navigation-dominant regimes*.
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---
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## 10) Uncertainty Quantification (PATCH P12: MC is now required, not optional)
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### Logical progression (updated)
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10.1 Define uncertainty source (usage variability)
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10.2 Deterministic solver stability/step-halving (existing)
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10.3 **Monte Carlo UQ** (BLOCK_B)
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10.4 Survival curve and uncertainty reporting
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### Must include (new “hard” components)
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* MC method statement:
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* number of paths (M=300)
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* perturbation model (OU on L,C,N; optionally also N/Ψ/G if you want)
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* fixed seed
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* Outputs:
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* mean TTE, CI, p10/p50/p90, survival curve (P(\text{TTE}>t))
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### Evidence required
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* UQ summary table + survival curve plot/table.
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* A brief comparison: deterministic baseline TTE vs MC mean vs percentile spread (to interpret “unpredictable”).
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---
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## 11) Multi-cycle aging and lifespan TTE forecasting (PATCH P13)
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### Logical progression
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1. Explain time-scale separation: discharge seconds vs aging days.
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2. Define outer-loop over cycles (j).
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3. At each cycle: run discharge simulation → compute throughput → update SOH → update (R_0,Q_{\text{eff}}) → next cycle.
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4. Produce TTE degradation trajectory.
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### Must include (new evidence)
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* A formal algorithm box for the outer loop (BLOCK_C).
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* Define (Q_{\text{thr},j}=\int |I(t)|,dt) and how it drives your SOH update (must reference Section 3.5 law).
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* A plot/table:
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* cycle index (j) vs (S_j) and TTE(_j)
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* Interpretation:
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* explain why TTE declines (capacity loss + resistance increase).
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### Evidence required
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* Explicit SOH update equation (from your Section 3.5).
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* At least one aging reference anchor (or clearly marked as “illustrative”).
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---
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## 12) Recommendations (updated: add GPS + lifecycle-aware policy)
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### Logical progression
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* Convert scenario rankings + Sobol + UQ + aging forecast into actions.
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### Must include (new recommendation types)
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* **GPS/location service policy**:
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* adaptive duty-cycling, batching location updates, “navigation mode” warnings
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* quantify expected gain using your GPS scenario ΔTTE
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* **Lifecycle-aware** recommendations:
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* as S declines, OS should lower peak power demands to avoid V_cut/Δ collapse earlier
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* user guidance: avoid high-drain use in cold/poor signal when battery aged
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### Evidence required
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* Each recommendation must cite a model result:
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* “This action targets parameter/driver X and yields ΔTTE ≈ Y in scenario tests.”
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---
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## 13) Validation, limitations, and extensions (expanded)
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### Must include (new limitation + validation points)
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* GPS model limitation: linear duty approximation; could refine with acquisition bursts.
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* Aging limitation: if no calibrated dataset, trajectory is qualitative.
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* UQ limitation: OU is a stylized model; could use empirical traces.
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### Validation evidence (additions)
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* Show GPS inclusion doesn’t break:
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* unit checks, Δ feasibility checks, step-halving convergence.
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---
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# What you should update in your appendix/tables (minimum edits)
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1. **Variable table**: add (G(t)).
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2. **Parameter table**: add (P_{\text{gps},0},k_{\text{gps}}) + aging-law parameters.
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3. **Scenario matrix**: add one GPS-heavy scenario (navigation).
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4. **Results**:
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* Baseline + GPS variant TTE comparison
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* MC summary + survival curve
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* Multi-cycle TTE vs cycle plot/table
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---
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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.
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