Behavior-Driven SOC and Time-to-Empty Prediction for Smartphone Batteries Using a Continuous-Time Electro-Thermal Model

Abstract

: Accurate smartphone time-to-empty (TTE) prediction requires a model that links user behavior, device-level power demand, and battery electro-thermal dynamics. This paper presents a continuous-time framework for predicting state of charge (SOC) and TTE under behavior-driven operating conditions. Screen brightness, CPU utilization, network activity, and background workload are represented as time-varying behavioral inputs and mapped to demand power through an interpretable additive formulation. The resulting power demand is constrained by achievable device power and coupled with a battery power-closure equation, where terminal voltage is described by an OCV-SOC relationship with temperature-dependent internal resistance. A lumped thermal balance is used to model Joule heating and heat dissipation, and the temperature state feeds back to effective capacity, internal resistance, and efficiency. The coupled differential-algebraic system is solved through fixed-step time marching to obtain SOC, voltage, temperature, and TTE trajectories. An OAT sensitivity analysis indicates that TTE is dominated by the capacity/energy scale and load-side behavior-to-power mapping, with importance values of 59.30% and 37.72%, respectively. Thermal and environmental effects account for 2.99% under the selected TTE metric, while resistance and efficiency terms exhibit weak first-order identifiability. The results suggest that reliable endurance prediction and optimization should prioritize usable-capacity estimation and load-side power reduction, with thermal control retained as a secondary but necessary mechanism for high-load robustness.