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2.1 Problem Restatement and Deliverables
Question 2 asks us to predict the Time-to-Empty (TTE) of a smartphone battery under (i) varying initial charge and (ii) multiple usage/environment scenarios, including conditions that can produce rapid drain, while remaining consistent with the “unpredictable” but bounded behavior implied by the prompt. Our deliverables for Q2 are: Table A (TTE vs initial SOC), Table B (scenario comparison vs baseline), Table C (driver attribution / ranking for rapid drain), an Uncertainty Quantification (UQ) summary table, and the required Fig2- set* (listed with captions and plotting specs in Section 2.9).
Issues in “Paper Structure 2” (reference-only): (i) it proposes adding a GPS power term and related patches without providing Q2-traceable numerical outputs for a GPS scenario, risking untraceable claims if included ; (ii) it introduces multi-cycle aging / long-horizon forecasting content that is outside the single-discharge scope used to generate the Q2 numerical outputs, which would again break Q2 traceability . The current structure fixes this by (a) constraining all Q2 statements to explicit output tables (Tables A–C + UQ), (b) linking every comparison to scenario-deliverable figures (Fig2-1…Fig2-7), and (c) separating deterministic scenario comparisons (Sections 2.4–2.6) from UQ consistency checks (Section 2.7).
2.2 TTE Definition, Termination Criteria, and Calculation Method
We define TTE as the elapsed time from the start of discharge (t_0) to the earliest termination event time (t^*): TTE = (t^ - t_0)*. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MODEL_SPEC → tte_definition]
Termination criteria (earliest-event): the simulation terminates at the first time (t^*) where any of the following event functions reaches zero:
- (g_V(t)=V_{\text{term}}(t)-V_{\text{cut}}) (voltage cutoff)
- (g_z(t)=z(t)) (SOC reaches zero)
- (g_\Delta(t)=\Delta(t)) (CPL feasibility discriminant reaches zero) with termination logic “Terminate at (t^*) where (\min(g_V,g_z,g_\Delta)=0).” [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MODEL_SPEC → events]
Event time interpolation: when a crossing is detected between steps, the event time is linearly interpolated within the step using the provided formula (t^* = t_{n-1} + (t_n-t_{n-1})\frac{-g(t_{n-1})}{g(t_n)-g(t_{n-1})}). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MODEL_SPEC → tte_definition]
CPL coupling and feasibility: the model enforces constant-power discharge through the algebraic closure (\Delta = (V_{oc}-v_p)^2 - 4R_0P_{tot}), (I = \frac{V_{oc}-v_p-\sqrt{\Delta}}{2R_0}), and (V_{term}=V_{oc}-v_p-IR_0). If (\Delta<0) occurs, feasibility fails and the model triggers a (\Delta)-based termination. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MODEL_SPEC → cpl_closure + validation feasibility_check]
2.3 Scenarios, Initial Conditions, and Simulation Settings
Baseline scenario (S0): the numerical output defines a six-segment “standard usage” schedule (standby → streaming → gaming → navigation-poor-signal → streaming → standby) with piecewise-smooth windowing; the segment boundaries and levels are explicitly listed in the baseline configuration. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: BASELINE_CONFIG_v1 → scenario.segments]
Initial conditions and SOC sweep: the output evaluates (z_0) over ({1.0, 0.75, 0.5, 0.25}) with (v_{p0}=0), (w_0=0), (S_0=1), and (T_{b0}=298.15\text{ K}). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: BASELINE_CONFIG_v1 → initial_conditions]
Numerics: the simulation uses RK4 nested with the CPL solver and fixed step (dt=1.0) with (t_{\max}=86400) and seed (20260201). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: BASELINE_CONFIG_v1 → numerics]
Scenario set for Q2 comparisons: the scenario comparison table includes (S0) baseline and seven variants: brightness reduced, CPU reduced, network reduced, poor signal, cold ambient, hot ambient, and background cut. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]
2.4 Result Table A: TTE Variation with Initial Charge
Table A (TTE vs initial SOC (z_0)) — all values are directly reported by the numerical output; see Fig2-1 for the corresponding trend plot.
| z0 | TTE_hours | termination_reason | t_star_sec | avg_P_W | max_I_A | max_Tb_C | Source |
|---|---|---|---|---|---|---|---|
| 1.00 | 4.60 | SOC_ZERO | 16571 | 3.22 | 1.96 | 29.0 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] |
| 0.75 | 3.65 | SOC_ZERO | 13144 | 3.04 | 1.96 | 29.0 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] |
| 0.50 | 3.10 | SOC_ZERO | 11147 | 2.39 | 1.96 | 27.6 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] |
| 0.25 | 2.19 | SOC_ZERO | 7871 | 1.69 | 1.07 | 26.1 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] |
Interpretation: TTE decreases monotonically as (z_0) decreases, and for all four initial SOC values the termination mode is SOC_ZERO (not voltage cutoff or (\Delta)-collapse), consistent with the event definition in Section 2.2. The plot in Fig2-1 is used to visually confirm the monotone dependence of TTE on initial charge level.
2.5 Result Table B: Comparison of Different Usage Scenarios
Table B (Scenario comparison vs baseline) — reported scenario-level TTE and (\Delta)TTE; see Fig2-2 for the corresponding scenario comparison plot.
| scenario_id | description | TTE_hours | ΔTTE_hours | termination_reason | avg_P_W | max_I_A | max_Tb_C | Source |
|---|---|---|---|---|---|---|---|---|
| S0 | Baseline | 4.60 | 0.00 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S1 | Brightness Reduced (0.5x) | 5.82 | 1.22 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S2 | CPU Reduced (0.5x) | 5.45 | 0.85 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S3 | Network Reduced (0.5x) | 4.92 | 0.32 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S4 | Poor Signal (Constant 0.2) | 2.78 | -1.82 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S5 | Cold Ambient (0°C) | 3.15 | -1.45 | V_CUTOFF | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S6 | Hot Ambient (40°C) | 4.98 | 0.38 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
| S7 | Background Cut (0.5x) | 4.74 | 0.14 | SOC_ZERO | Not provided in output | Not provided in output | Not provided in output | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] |
Key outcomes: energy-saving actions (brightness reduced, CPU reduced, network reduced, background cut) increase TTE relative to baseline, while poor signal and extreme cold reduce TTE. A notable qualitative change is that the cold ambient scenario ends via V_CUTOFF rather than SOC depletion, indicating a mechanism shift (voltage-limited termination). This difference is highlighted in the narrative for Fig2-2 and used in Section 2.6 for driver attribution.
2.6 "Rapid Drain" Driver Attribution and Impact Ranking
To attribute “rapid drain,” we rank scenarios by their reported (\Delta)TTE relative to baseline and then interpret the mechanistic signatures reported by the numerical output. Table C provides the ranking, and Fig2-3–Fig2-6 are the intended mechanism plots (SOC, current/power, temperature, discriminant).
Table C (Driver / impact ranking by (\Delta)TTE)
| Rank order (as reported) | scenario_id | delta_tte_hours | Source |
|---|---|---|---|
| 1 | S4 | -1.82 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 2 | S5 | -1.45 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 3 | S0 | 0.00 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 4 | S7 | 0.14 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 5 | S3 | 0.32 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 6 | S6 | 0.38 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 7 | S2 | 0.85 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
| 8 | S1 | 1.22 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: DRIVER_RANKING_v1] |
Mechanism interpretation (rapid drain scenarios):
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S4 (Poor Signal) is the largest rapid-drain driver. The output explicitly identifies the non-linear signal-quality penalty (P_{net}\propto(\Psi+\epsilon)^{-\kappa}) as dominant and reports that TTE drops from baseline 4.60h to 2.78h (≈40% reduction). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: FINAL_SUMMARY_v1 → TECHNICAL_HIGHLIGHTS_v1] Mechanistic signatures quantify the power/current increase: (avg_P=5.32), (max_I=2.45), and (min_\Delta=3.82) for S4. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1] This is what Fig2-4 (current & power) and Fig2-6 (discriminant) are intended to display: higher (P_{tot}) forces higher CPL current (I), accelerating SOC depletion.
-
S5 (Cold Ambient) is the second rapid-drain driver and changes termination mode. The output reports TTE 3.15h with termination reason V_CUTOFF and explains the dual penalty: increased internal resistance (Arrhenius) and reduced effective capacity. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] [Source: Numerical Output File (3); Keyword/Table Name/Section Name: FINAL_SUMMARY_v1 → TECHNICAL_HIGHLIGHTS_v1] Mechanistic signatures show the resistance/capacity shift: (avg_R0=0.235) and (avg_Qeff=3.52) for S5, with a much smaller (min_\Delta=0.85), indicating proximity to CPL feasibility/voltage collapse. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1] This is what Fig2-5 (temperature) and Fig2-6 (discriminant) are intended to reveal: colder conditions push the system toward voltage-limited termination before SOC reaches zero.
-
Baseline signature for context: for S0, the mechanistic signatures report (avg_P=3.22), (max_I=1.54), and (min_\Delta=8.15). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1] These baseline levels contextualize why S4 (higher power demand) and S5 (higher resistance + lower effective capacity) create rapid drain relative to typical operation; the SOC time-path intended for Fig2-3 would show the accelerated decline in these cases.
2.7 Uncertainty Quantification and Consistency with "Observed Behavior"
Because the prompt suggests user behavior is “unpredictable,” we report a probabilistic TTE characterization using the provided Monte Carlo framework: (M=300) stochastic usage paths are generated by perturbing baseline ((L,C,N)) with Ornstein–Uhlenbeck processes, and we report mean TTE, a confidence interval, and the survival curve (P(TTE>t)). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: INSERT_TEXT_BLOCKS_v1 → BLOCK_B]
UQ Summary Table (baseline scenario stochastic wrapper)
| Metric | Value | Source |
|---|---|---|
| mean | 4.6021 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| std | 0.0542 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| p10 | 4.5314 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| p50 | 4.6018 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| p90 | 4.6725 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| CI95_low | 4.5959 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| CI95_high | 4.6083 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1] |
| M | 300 | [Source: Numerical Output File (3); Keyword/Table Name/Section Name: REPRODUCIBILITY_v1] |
Survival curve consistency (Fig2-7): the output provides survival points (S(t)=P(TTE>t)) showing (S(4.50)=0.973), (S(4.75)=0.012), and (S(5.00)=0.000). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SURVIVAL_CURVE_DATA]
The executive snippet further reports a “90% survival rate up to 4.53h,” which is consistent with the p10 value 4.5314. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: FINAL_SUMMARY_v1 → EXECUTIVE_DATA_SNIPPET + UQ_SUMMARY_v1]
Therefore, while usage varies, the predicted TTE remains tightly bounded under the baseline stochastic wrapper, and the probabilistic visualization in Fig2-7 is the correct “observed-behavior-consistent” output format for Q2.
2.8 Conclusion for Q2 ("Maximal Reduction" vs. "Minimal Impact", must be quantified)
Maximal reduction (worst-case rapid drain): among the tested scenarios, S4 (Poor Signal) produces the largest reduction, (\Delta TTE=-1.82) hours relative to baseline. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] This is explicitly restated as the “maximum observed TTE reduction of 1.82 hours.” [Source: Numerical Output File (3); Keyword/Table Name/Section Name: FINAL_SUMMARY_v1 → TECHNICAL_HIGHLIGHTS_v1]
Minimal impact (closest to baseline): the smallest absolute shift from baseline among the reported variants is S7 (Background Cut) with (\Delta TTE=+0.14) hours. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] In other words, in this output set, background power changes have comparatively small effect on TTE versus non-linear network penalties (poor signal) and temperature-driven electrochemical limits (cold), consistent with the mechanism ranking summarized in Table C.
2.9 List of Figures and Captions (Must cover all fig_id entries in JSON.figures)
Fig2-1 — TTE vs Initial SOC
Caption: This figure plots time-to-empty (TTE) as a function of the initial state-of-charge (z_0), using the four evaluated initial conditions. The reported TTE values are 4.60 h (z0=1.00), 3.65 h (z0=0.75), 3.10 h (z0=0.50), and 2.19 h (z0=0.25). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1] In all cases the termination mechanism is SOC depletion (termination_reason = SOC_ZERO), not voltage cutoff or discriminant collapse, consistent with the event logic. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1 + MODEL_SPEC → events]
Plotting Essentials: plot_type=line (or scatter+line). x-axis z0 (unitless). y-axis TTE_hours (hours). Single-panel; overlay all z0 points; show markers at each evaluated z0; optionally annotate termination_reason.
Data Field List:
- field_name: z0; meaning: initial state of charge; unit: dimensionless
- field_name: TTE_hours; meaning: time-to-empty; unit: h
- field_name: termination_reason; meaning: earliest termination event label; unit: null
- field_name: t_star_sec; meaning: termination time in seconds; unit: s
- field_name: avg_P_W; meaning: time-average total power; unit: W
- field_name: max_I_A; meaning: maximum discharge current; unit: A
- field_name: max_Tb_C; meaning: maximum battery temperature; unit: °C Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1]
Fig2-2 — Scenario TTE Comparison vs Baseline
Caption: This figure compares TTE across the baseline and seven scenario variants, showing both absolute TTE and the reported (\Delta)TTE relative to baseline. The baseline TTE is 4.60 h, while the worst-case reduction is 2.78 h under the poor-signal scenario (ΔTTE = -1.82 h) and 3.15 h under extreme cold (ΔTTE = -1.45 h). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] The termination mechanism is SOC_ZERO for most scenarios, but the cold scenario terminates by voltage cutoff (V_CUTOFF), indicating a mechanism shift from charge exhaustion to voltage-limited shutdown. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1 + MODEL_SPEC → events]
Plotting Essentials: plot_type=bar (recommended) or line (categorical). x-axis scenario_id (categorical). y-axis TTE_hours (hours). Optional secondary encoding (color/annotation) for ΔTTE_hours and termination_reason; include baseline reference line at 4.60 h.
Data Field List:
- field_name: scenario_id; meaning: scenario label; unit: null
- field_name: description; meaning: scenario description; unit: null
- field_name: TTE_hours; meaning: time-to-empty; unit: h
- field_name: ΔTTE_hours; meaning: difference vs baseline; unit: h
- field_name: termination_reason; meaning: earliest termination event label; unit: null Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1]
Fig2-3 — SOC Trajectory (Baseline and/or Key Scenarios) Caption: This figure is intended to show SOC (z(t)) over time, illustrating how the discharge rate changes across usage segments and accelerates near end-of-discharge under constant-power load. Output did not provide required data, so this figure cannot be generated; attempted_keywords = ["trajectory", "trajectory_columns", "t,z", "soc_v_time.png"]. The baseline run still reports SOC-based termination (SOC_ZERO) with TTE 4.60 h and a termination timestamp t_star_sec = 16571 s, which should be annotated if the trajectory were available. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: TTE_TABLE_v1 + FIGURE_SPEC_v1] The termination mechanism is SOC depletion, consistent with the event definition. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MODEL_SPEC → events] Plotting Essentials: plot_type=line. x-axis time (seconds). y-axis SOC (unitless). Multi-scenario overlay optional (baseline vs S4 vs S5) if trajectories are provided; use distinct line styles and legend. Data Field List:
- field_name: t; meaning: time; unit: s
- field_name: z; meaning: state of charge; unit: dimensionless Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: OutputSchema.trajectory_columns + FIGURE_SPEC_v1]
Fig2-4 — Current and Power vs Time (Dual-Axis) Caption: This figure is intended to display the CPL feedback between total power demand (P_{tot}(t)) and discharge current (I(t)), highlighting segments that drive rapid drain. Output did not provide required data, so this figure cannot be generated; attempted_keywords = ["trajectory", "t,I,P_tot", "current_power_v_time.png", "trajectory_columns"]. Mechanistically, the output attributes the largest rapid-drain effect to the signal-quality penalty and reports S4 has higher average power (avg_P = 5.32 W) and higher peak current (max_I = 2.45 A) than baseline (avg_P = 3.22 W, max_I = 1.54 A), which is what this plot should reveal in time-resolved form. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1] The ultimate termination cause should be annotated (SOC_ZERO for S4 and baseline). [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] Plotting Essentials: plot_type=dual_axis_line. x-axis time (seconds). left y-axis current (A). right y-axis power (W). Multi-scenario overlay optional; if overlaid, keep one scenario per panel or use transparency + clear legend. Data Field List:
- field_name: t; meaning: time; unit: s
- field_name: I; meaning: discharge current; unit: A
- field_name: P_tot; meaning: total power demand; unit: W Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: OutputSchema.trajectory_columns + FIGURE_SPEC_v1]
Fig2-5 — Battery Temperature Trajectory
Caption: This figure is intended to show battery temperature (T_b(t)) and connect environmental stress to electrochemical performance and termination mode. Output did not provide required data, so this figure cannot be generated; attempted_keywords = ["trajectory", "t,T_b", "temp_v_time.png", "trajectory_columns"]. The cold ambient case is reported to terminate by V_CUTOFF at 3.15 h (rather than SOC_ZERO), and the mechanism cited is increased resistance and reduced effective capacity under cold conditions; this figure would ideally show the resulting thermal state evolution alongside that termination. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1 + FINAL_SUMMARY_v1 → TECHNICAL_HIGHLIGHTS_v1]
Plotting Essentials: plot_type=line. x-axis time (seconds). y-axis temperature (°C or K; if plotting °C, convert consistently and label). Multi-scenario overlay optional (S5 vs S0 vs S6) if trajectories are provided.
Data Field List:
- field_name: t; meaning: time; unit: s
- field_name: T_b; meaning: battery temperature; unit: K (or °C if converted) Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: OutputSchema.trajectory_columns + FIGURE_SPEC_v1]
Fig2-6 — Discriminant (\Delta) Trajectory
Caption: This figure is intended to plot the CPL discriminant (\Delta(t)) to diagnose proximity to power infeasibility and voltage collapse, especially under cold conditions where voltage cutoff occurs early. Output did not provide required data, so this figure cannot be generated; attempted_keywords = ["trajectory", "t,Delta", "delta_v_time.png", "trajectory_columns"]. Mechanistic signatures indicate the cold scenario has a much smaller minimum discriminant (min_Δ = 0.85 V²) than baseline (min_Δ = 8.15 V²), consistent with the reported shift to V_CUTOFF termination at 3.15 h; this figure would visualize where (\Delta) approaches its critical boundary over time. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: MECH_SIGNATURES_v1 + SCENARIO_TTE_TABLE_v1]
Plotting Essentials: plot_type=line. x-axis time (seconds). y-axis (\Delta) (V²). Add a horizontal reference at (\Delta=0) to indicate feasibility boundary. Multi-scenario overlay optional if trajectories are provided.
Data Field List:
- field_name: t; meaning: time; unit: s
- field_name: Delta; meaning: CPL discriminant; unit: V^2 Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: OutputSchema.trajectory_columns + FIGURE_SPEC_v1]
Fig2-7 — UQ Survival Curve (S(t)=P(TTE>t)) Caption: This figure plots the empirical survival curve from the Monte Carlo UQ wrapper, where (S(t)) is the probability the device remains powered past time (t). The output reports (S(4.50)=0.973), (S(4.75)=0.012), and (S(5.00)=0.000), showing a sharp drop in survival near the deterministic baseline TTE. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SURVIVAL_CURVE_DATA] The UQ distribution summary reports p10 = 4.5314 h, p50 = 4.6018 h, and p90 = 4.6725 h, and the executive snippet states a “90% survival rate up to 4.53 h,” consistent with the p10 quantile. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1 + FINAL_SUMMARY_v1 → EXECUTIVE_DATA_SNIPPET] The termination mechanism in the baseline is SOC depletion (SOC_ZERO), so the survival drop reflects SOC reaching zero under stochastic usage fluctuations rather than catastrophic feasibility loss. [Source: Numerical Output File (3); Keyword/Table Name/Section Name: SCENARIO_TTE_TABLE_v1] Plotting Essentials: plot_type=survival_curve (line). x-axis time (hours). y-axis survival probability (S(t)) (unitless, [0,1]). Single curve; optionally annotate p10/p50/p90 as vertical lines and label the 95% CI endpoints from the summary table. Data Field List:
- field_name: t_hours; meaning: time; unit: h
- field_name: S(t); meaning: survival probability (P(TTE>t)); unit: dimensionless
- field_name: p10/p50/p90, CI95_low/CI95_high (optional annotations); meaning: distribution summaries; unit: h Data Source Marker: [Source: Numerical Output File (3); Keyword/Table Name/Section Name: UQ_SUMMARY_v1 + SURVIVAL_CURVE_DATA]
Final Self-Check
- All
Fig2-*are cited at least once in the body text. - Section 2.9 covers all
fig_identries from the JSON. - All numerical values have a [Source: ...] marker and are traceable.
- Table A / Table B / Table C / UQ Table are all present.
- The "Maximal Reduction vs. Minimal Impact" question is answered (quantified).