MCM/A题/数值分析检验/Response/10.md

FINAL_SUMMARY_v1

TECHNICAL_HIGHLIGHTS_v1

• Signal Quality vs. Power Consumption: The non-linear signal penalty mechanism P_{net} \propto (\Psi + \epsilon)^{-\kappa} represents the most significant driver of rapid drain. In the "Poor Signal" scenario (S_4), the TTE dropped from 4.60h to 2.78h, a reduction of approximately 40%.
• Thermal-Electrochemical Coupling: Cold ambient conditions (0^\circ\text{C}) induce a dual penalty: internal resistance R_0 increases via Arrhenius kinetics while effective capacity Q_{eff} is restricted. This shifted the termination reason from a gradual SOC_ZERO to a premature V_CUTOFF at 3.15h.
• CPL-Induced Voltage Instability: The Constant Power Load (CPL) requirement forces discharge current I to rise as terminal voltage V_{term} falls. This feedback loop accelerates depletion near the end-of-discharge and increases the risk of voltage collapse (\Delta \le 0).
• Worst-Case Impact: The transition from baseline usage to a sustained poor-signal environment (S_4) resulted in the maximum observed TTE reduction of 1.82 hours.

MODEL_STRENGTHS_v1

1. Algebraic-Differential Nesting: By nesting the quadratic CPL current solver within the RK4 integration stages, the model maintains strict physical consistency between power demand and electrochemical state at every sub-step.
2. Continuous Radio Tail Dynamics: The inclusion of the state variable w(t) with asymmetric time constants (\tau_{up} \ll \tau_{down}) allows the model to capture the "tail effect" of high-power network persistence without the numerical overhead of discrete state machines.
3. Rigorous Uncertainty Quantification: The methodology integrates Saltelli-sampled Sobol indices for parameter sensitivity and Ornstein-Uhlenbeck stochastic processes for usage variability, providing a probabilistic bound on battery life rather than a single point estimate.

EXECUTIVE_DATA_SNIPPET

Our model predicts a baseline time-to-empty (TTE) of 4.60h under standard usage at 25^\circ\text{C}. Environmental stress testing reveals a 31.5% reduction in TTE during extreme cold (0^\circ\text{C}), primarily driven by increased internal resistance and capacity contraction. Uncertainty Quantification (UQ) analysis, accounting for stochastic fluctuations in user behavior, confirms a 90% survival rate (probability that the device remains powered) up to 4.53h, demonstrating that while usage is "unpredictable," the battery behavior remains bounded by identifiable physical constraints.

FUTURE_WORK_v1

1. Dynamic SOH Aging Laws: Extend the current framework by implementing a diffusion-limited SEI-layer growth ODE to model long-term capacity fade and resistance growth over hundreds of cycles.
2. Spatial Thermal Distribution: Transition from a lumped-parameter thermal model to a multi-node spatial network to account for localized heat generation in the CPU and radio modules, enabling more accurate throttling predictions.