135 lines
30 KiB
Markdown
135 lines
30 KiB
Markdown
## 2.1 Problem Restatement & Deliverables
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This part of the problem asks for **time-to-empty (TTE)** predictions from our continuous-time battery model under **multiple initial charge levels** and **multiple usage/environment scenarios**, together with (i) an explanation of why outcomes differ, (ii) identification of the **drivers of rapid drain**, (iii) identification of conditions that **change TTE little**, and (iv) **uncertainty quantification** (UQ) and consistency checks against plausible behavior.
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**Deliverables provided in Sections 2.4–2.7**: (i) a TTE-versus-initial-SOC table (Table A), (ii) a cross-scenario comparison table with ΔTTE relative to baseline (Table B), (iii) a quantified driver-impact ranking table grounded in scenario deltas/mechanistic signatures/sensitivity indices (Table C), and (iv) a UQ table including distributional summaries and survival-curve checkpoints.
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**Critical note on “Paper Structure 2” (negative reference):** The blueprint in Structure 2 expands the narrative toward GPS/aging/recommendations and introduces broad re-scoping that is not targeted to the TTE-prediction sub-question, which risks burying the required Q2 comparisons. It also does not enforce a strict, audit-friendly pipeline that binds every conclusion to a traceable numerical output (e.g., scenario-by-scenario ΔTTE and a dedicated TTE-vs-initial-SOC table), making it easy to state mechanisms without numeric support. Finally, it treats uncertainty and validation mainly as “must include” bullets rather than a tightly reported results object with explicit distributional numbers and survival checkpoints. In contrast, we adopt a Q2-only structure: we (i) define TTE and termination logic up front (2.2), (ii) specify only the scenarios and settings needed to interpret Q2 outputs (2.3), (iii) report TTE by initial SOC and by scenario with explicit ΔTTE tables (2.4–2.5), (iv) provide quantified driver ranking from the actual comparative/sensitivity outputs (2.6), and (v) report UQ numerically with survival-curve evidence (2.7), culminating in a single-sentence numeric answer (2.8).
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---
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## 2.2 TTE Definition, Termination Criteria & Calculation Method
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We define **time-to-empty (TTE)** as the elapsed time from simulation start until the **earliest termination event** occurs. Termination is event-based and uses the model’s physically motivated stop conditions tied to:
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* **Voltage cutoff:** terminal voltage (V_{\mathrm{term}}) reaches the cutoff (V_{\mathrm{cut}}).
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* **SOC depletion:** state of charge (z) reaches zero.
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* **CPL feasibility loss:** the CPL discriminant (\Delta) reaches zero (no real current solution), signaling infeasible constant-power operation.
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At each discrete time step, we evaluate the event signals corresponding to (g_V = V_{\mathrm{term}}-V_{\mathrm{cut}}), (g_z=z), and (g_\Delta=\Delta). An event is detected when its signal crosses from positive to non-positive between consecutive samples. The event time (t^*) is computed by **linear interpolation** between the last bracketing samples of the triggering event signal, and **TTE = (t^* - t_0)**. If multiple events cross within the same step, we select the smallest interpolated event time; if tied (within the implementation tolerance), the termination reason priority is **DELTA_ZERO > V_CUTOFF > SOC_ZERO** (per the frozen TTE specification in the outputs).
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---
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## 2.3 Scenarios, Initial Conditions & Simulation Settings (Write only what is relevant to Q2)
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**Initial SOC sweep (Table A):** We evaluate TTE under the baseline usage schedule for all initial SOC values reported in the numerical output table (Table A). These values are treated as the only required initial-condition variation for Q2’s “initial charge levels” deliverable.
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**Scenario sweep (Table B & Table C):** For scenario comparison and driver attribution, we use the scenario matrix already simulated and reported in the numerical outputs (baseline plus controlled “one-factor” modifications). These scenarios isolate the impact of screen brightness (L(t)), CPU load (C(t)), network activity (N(t)), signal quality (\Psi(t)), ambient temperature (T_a(t)), and background power (P_{\mathrm{bg}}) on the total power (P_{\mathrm{tot}}), and hence on CPL current (I), SOC depletion, and termination mode.
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**Core simulation logic used for all Q2 results:** A coupled electro-thermal equivalent-circuit model with a **constant-power-load (CPL)** algebraic closure is integrated forward in time; at each step, (P_{\mathrm{tot}}) determines (I) through (\Delta), which then updates SOC and other states, and termination is detected by the event logic defined in Section 2.2.
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---
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## 2.4 Results Table A: TTE vs. Initial Battery State (SOC/z0)
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**Table A — TTE vs. Initial Charge (baseline schedule).** Values are reported verbatim from **TTE_TABLE_v1**.
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| z0/SOC | TTE (h) | Termination Reason | avg_P (W) | max_I (A) | Remarks |
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| ----------------------------------------------------------------------------- | ----------------------------------------------------------------------------: | ------------------------ | ----------------------------------------------------------------------------: | ----------------------------------------------------------------------------: | ------------------------------------------------------------------------------------------------------------------------------------------------------------------ |
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| 1.00 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 4.60 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | SOC_ZERO (SOC depletion) | 3.22 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 1.96 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | With more initial energy, the trajectory experiences more of the high-demand segments; termination is still governed by (z \to 0) rather than voltage/feasibility. |
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| 0.75 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 3.65 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | SOC_ZERO (SOC depletion) | 3.04 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 1.96 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | Reduced initial SOC shortens exposure to later (and potentially more expensive) segments; termination remains SOC depletion. |
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| 0.50 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 3.10 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | SOC_ZERO (SOC depletion) | 2.39 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 1.96 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | Lower initial SOC reduces total time under sustained CPL demand; termination remains SOC depletion rather than a constraint on (V_{\mathrm{term}}) or (\Delta). |
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| 0.25 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 2.19 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | SOC_ZERO (SOC depletion) | 1.69 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | 1.07 [Source: Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] | The shortest run ends before the most energy-intensive periods dominate; termination remains SOC depletion in the baseline schedule. |
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---
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## 2.5 Results Table B: Comparison of Different Usage Scenarios (inc. ΔTTE & Termination Reasons)
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**Baseline definition (explicit):** We take **“Baseline”** as the baseline scenario because it is the unmodified reference case in the scenario matrix used to compute all reported (\Delta\mathrm{TTE}) values (and is the scenario with (\Delta\mathrm{TTE}=0) by construction in the outputs).
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**Table B — Scenario comparison (full-charge scenario matrix).** Values are reported verbatim from **SCENARIO_TTE_TABLE_v1**.
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| Scenario Name | Key Parameters/Activity Description | TTE (h) | ΔTTE vs Baseline (h) | Termination Reason | Brief Mechanism Explanation (model-based; one sentence) |
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| ------------------------------------------------------------------------------------------------------------ | ------------------------------------------------------------------------------------------------------------ | -------------------------------------------------------------------------------------: | --------------------------------------------------------------------------------------: | ------------------ | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- |
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| Baseline | Baseline | 4.60 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 0.00 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Baseline power mapping yields (P_{\mathrm{tot}}) that determines (I) via CPL, driving (dz/dt<0) until (z\to 0). |
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| Brightness Reduced (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | Brightness Reduced (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 5.82 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 1.22 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Lower (L(t)) reduces the screen term in (P_{\mathrm{tot}}), lowering CPL current (I) and slowing SOC depletion. |
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| CPU Reduced (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | CPU Reduced (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 5.45 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 0.85 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Lower (C(t)) reduces the CPU term in (P_{\mathrm{tot}}), which reduces (I) through CPL and delays (z\to 0). |
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| Network Reduced (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | Network Reduced (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 4.92 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 0.32 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Lower (N(t)) reduces (P_{\mathrm{net}}\subset P_{\mathrm{tot}}), reducing CPL current (I) and slowing SOC depletion. |
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| Poor Signal (Constant 0.2) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | Poor Signal (Constant 0.2) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 2.78 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | -1.82 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Lower (\Psi(t)) increases the signal-penalized (P_{\mathrm{net}}), raising (P_{\mathrm{tot}}) and forcing higher (I) (and faster (z) decay) under CPL. |
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| Cold Ambient (0°C) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | Cold Ambient (0°C) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 3.15 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | -1.45 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | V_CUTOFF | Lower (T_a(t)) drives higher (R_0(T_b,S)) and lower (Q_{\mathrm{eff}}(T_b,S)), reducing (V_{\mathrm{term}}) under CPL so voltage cutoff can occur before (z\to 0). |
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| Hot Ambient (40°C) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | Hot Ambient (40°C) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 4.98 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 0.38 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Higher (T_a(t)) reduces resistive/thermal penalties in (R_0) and supports higher effective capacity (Q_{\mathrm{eff}}), slowing SOC depletion under the same (P_{\mathrm{tot}}) schedule. |
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| Background Cut (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | Background Cut (0.5x) [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 4.74 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | 0.14 [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] | SOC_ZERO | Lower (P_{\mathrm{bg}}) reduces (P_{\mathrm{tot}}) additively, slightly reducing (I) and delaying SOC depletion. |
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---
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## 2.6 Attribution of "Rapid Drain" Drivers & Impact Ranking (Must Quantify)
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We attribute “rapid drain” to factors that increase the **total requested power** (P_{\mathrm{tot}} = P_{\mathrm{bg}}+P_{\mathrm{scr}}(L)+P_{\mathrm{cpu}}(C)+P_{\mathrm{net}}(N,\Psi,w)), which (under CPL closure) increases the discharge current (I) and accelerates SOC depletion. In addition, temperature-driven changes in (R_0(T_b,S)) and (Q_{\mathrm{eff}}(T_b,S)) can shift termination mode from SOC depletion to voltage cutoff by depressing (V_{\mathrm{term}} = V_{\mathrm{oc}}(z)-v_p-I R_0).
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**Quantified ranking source:** The driver ordering below is grounded in (i) the reported scenario (\Delta\mathrm{TTE}) values (scenario matrix) and (ii) the mechanistic signatures and global sensitivity indices included in the outputs.
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**Table C — Driver impact ranking (quantified).**
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| Factor | Quantified Evidence | Causal Chain (model variables) | Conclusion |
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| ----------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- | ------------------ |
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| Signal quality (\Psi) (poor signal penalty in (P_{\mathrm{net}})) | (\Delta\mathrm{TTE}=-1.82) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (TTE drops to 2.78 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]); for the same case, avg_P (=5.32) W [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1], max_I (=2.45) A [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1], and min_(\Delta) (=3.82) [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1]. | (\Psi\downarrow \Rightarrow P_{\mathrm{net}}\uparrow \Rightarrow P_{\mathrm{tot}}\uparrow \Rightarrow I\uparrow \Rightarrow dz/dt) more negative (\Rightarrow) earlier (z\to 0) (and reduced (\Delta) margin). | High impact |
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| Ambient temperature (cold (T_a)) affecting (R_0) and (Q_{\mathrm{eff}}) | (\Delta\mathrm{TTE}=-1.45) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (TTE (=3.15) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]) with termination switching to V_CUTOFF [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]; mechanistic shift: avg_R0 (=0.235) [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1] vs baseline avg_R0 (=0.108) [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1], and avg_Qeff (=3.52) [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1] vs baseline avg_Qeff (=4.00) [Source: Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1]. | (T_a\downarrow \Rightarrow T_b\downarrow \Rightarrow R_0\uparrow,\ Q_{\mathrm{eff}}\downarrow \Rightarrow V_{\mathrm{term}}=V_{\mathrm{oc}}-v_p-I R_0\downarrow \Rightarrow) voltage cutoff earlier (\Rightarrow) TTE↓. | High impact |
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| Screen brightness (L) (screen power scaling) | Brightness reduction yields (\Delta\mathrm{TTE}=1.22) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (TTE (=5.82) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]); global sensitivity: (ST_i(k_L)=0.445) [Source: Output File (3); Keyword/Table Name/Section Name: SOBOL_TABLE_v1]. | (L\downarrow \Rightarrow P_{\mathrm{scr}}(L)\downarrow \Rightarrow P_{\mathrm{tot}}\downarrow \Rightarrow I\downarrow \Rightarrow dz/dt) less negative (\Rightarrow) later termination. | Medium–High impact |
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| CPU load (C) (CPU power scaling) | CPU reduction yields (\Delta\mathrm{TTE}=0.85) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (TTE (=5.45) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]); global sensitivity: (ST_i(k_C)=0.312) [Source: Output File (3); Keyword/Table Name/Section Name: SOBOL_TABLE_v1]. | (C\downarrow \Rightarrow P_{\mathrm{cpu}}(C)\downarrow \Rightarrow P_{\mathrm{tot}}\downarrow \Rightarrow I\downarrow \Rightarrow) slower SOC depletion. | Medium impact |
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| Network activity (N) (network power scaling) | Network reduction yields (\Delta\mathrm{TTE}=0.32) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]; global sensitivity: (ST_i(k_N)=0.065) [Source: Output File (3); Keyword/Table Name/Section Name: SOBOL_TABLE_v1]. | (N\downarrow \Rightarrow P_{\mathrm{net}}(N,\Psi,w)\downarrow \Rightarrow P_{\mathrm{tot}}\downarrow \Rightarrow I\downarrow \Rightarrow) slower SOC depletion. | Low–Medium impact |
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| Background power (P_{\mathrm{bg}}) | Background cut yields (\Delta\mathrm{TTE}=0.14) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (smallest reported improvement magnitude among the one-factor reductions). | (P_{\mathrm{bg}}\downarrow \Rightarrow P_{\mathrm{tot}}\downarrow) (additively) (\Rightarrow I\downarrow) slightly (\Rightarrow) small TTE change. | Low impact |
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**Largest impact vs. little impact (Q2 requirement):** The largest TTE reductions are caused by **poor signal** ((\Psi) penalty) and **cold ambient** (via (R_0) and (Q_{\mathrm{eff}})), with (\Delta\mathrm{TTE}=-1.82) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] and (\Delta\mathrm{TTE}=-1.45) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1], respectively. In contrast, changes that alter the model surprisingly little include **background power halving** with (\Delta\mathrm{TTE}=0.14) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] and **network activity halving** with (\Delta\mathrm{TTE}=0.32) h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1].
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---
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## 2.7 Uncertainty Quantification & Consistency with "Observed Behavior"
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### Uncertainty source (as implemented in the outputs)
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Uncertainty is introduced by **stochastic usage-path variability**: the baseline inputs ((L,C,N)) are perturbed by Ornstein–Uhlenbeck processes across Monte Carlo runs, with outputs aggregated into a TTE distribution and an empirical survival curve (S(t)=\Pr(\mathrm{TTE}>t)). The UQ run count is (M=300) [Source: Output File (3); Keyword/Table Name/Section Name: REPRODUCIBILITY_v1], and the OU parameters reported are (\theta=0.0016666666666666668) [Source: Output File (3); Keyword/Table Name/Section Name: REPRODUCIBILITY_v1] and (\sigma=0.02) [Source: Output File (3); Keyword/Table Name/Section Name: REPRODUCIBILITY_v1].
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### UQ results (numbers)
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**Table D — UQ summary and survival checkpoints (baseline with stochastic usage paths).**
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| Quantity | Value |
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| ----------------------------- | -------------------------------------------------------------------------------: |
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| Mean TTE (h) | 4.6021 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| Std. dev. (h) | 0.0542 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| p10 (h) | 4.5314 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| p50 (h) | 4.6018 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| p90 (h) | 4.6725 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| CI_low (h) | 4.5959 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| CI_high (h) | 4.6083 [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
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| Survival (S(t)) at (t=4.50) h | 0.973 [Source: Output File (3); Keyword/Table Name/Section Name: t_hours,S(t)] |
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| Survival (S(t)) at (t=4.75) h | 0.012 [Source: Output File (3); Keyword/Table Name/Section Name: t_hours,S(t)] |
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| Survival (S(t)) at (t=5.00) h | 0.000 [Source: Output File (3); Keyword/Table Name/Section Name: t_hours,S(t)] |
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### Consistency with observed/plausible behavior and internal validation signals
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1. **Consistency of stochastic vs. deterministic baseline:** The deterministic baseline TTE is 4.60 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1], while the Monte Carlo mean is 4.6021 h [Source: Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1], indicating that stochastic usage perturbations broaden outcomes without shifting the central estimate away from the baseline prediction.
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2. **Survival interpretation:** The survival curve remains near unity through mid-horizon times and then collapses sharply near the upper tail, with (S(4.50)=0.973) [Source: Output File (3); Keyword/Table Name/Section Name: t_hours,S(t)] and (S(4.75)=0.012) [Source: Output File (3); Keyword/Table Name/Section Name: t_hours,S(t)], showing that most realizations cluster tightly but a small fraction terminate shortly after the central window.
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3. **Energy plausibility check (baseline):** The integrated energy check for the full-charge baseline is 14.8 Wh [Source: Output File (3); Keyword/Table Name/Section Name: VALIDATION_REPORT_v1], matching the reported nominal baseline energy 14.8 Wh [Source: Output File (3); Keyword/Table Name/Section Name: VALIDATION_REPORT_v1], supporting internal consistency between power demand and total discharged energy for the baseline case.
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4. **Numerical consistency:** The reported validation flags indicate monotonic SOC behavior (monotonicity_pass=true) and no infeasible (\Delta) prior to termination (any_negative_delta_before_event=false) [Source: Output File (3); Keyword/Table Name/Section Name: VALIDATION_REPORT_v1], supporting that Q2 outcomes are not artifacts of numerical instability or invalid CPL evaluation.
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---
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## 2.8 Conclusion for Q2 (Answer the specific question with a single sentence + numerical evidence)
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The greatest battery-life reductions occur under **Poor Signal (Constant 0.2)** with TTE 2.78 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (ΔTTE -1.82 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]) and **Cold Ambient (0°C)** with TTE 3.15 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] (ΔTTE -1.45 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]), while changes that alter the model surprisingly little include **Background Cut (0.5x)** with ΔTTE 0.14 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] and **Network Reduced (0.5x)** with ΔTTE 0.32 h [Source: Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1].
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---
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### Self-Check List
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* [ ] Table A includes all z0/SOC values.
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* [ ] Table B includes all scenarios and identifies the Baseline.
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* [ ] At least one type of UQ number (CI/Quantile/Mean-Variance) included.
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* [ ] Every key number has a `[Source: ...]` marker.
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* [ ] "Largest impact vs. Little impact" question answered.
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* [ ] At least 2 issues in Structure 2 pointed out and fixed.
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