To address the complex nonlinear characteristics of smartphone battery power consumption, this paper constructs a continuous-time state-space framework that integrates multiple physics, aiming to achieve accurate predictions of battery state of charge and remaining runtime. The research framework consists of a nested structure comprising a fast-time-scale dynamic layer and a slow-time-scale reduced-order layer: the fast-time-scale layer utilizes an improved Thevenin equivalent circuit to capture transient current and voltage responses as well as thermal accumulation processes; the slow-time-scale layer dynamically corrects for battery capacity degradation and internal resistance changes based on the Arrhenius law and cycling history. The study conducted an in-depth analysis of power consumption mechanisms at the hardware level and established a refined power consumption model that incorporates screen pixel brightness, dynamic processor frequency scaling, network connection protocol status, and GPS signal coupling. By iteratively solving a system of nonlinear ordinary differential equations using the fourth-order Runge-Kutta algorithm, this paper conducted simulation validations across various real-world scenarios, including gaming, social media, 4K video, and voice calls. The results indicate that high-load tasks such as gaming significantly shorten battery life due to peak network and processor loads, and that low-temperature environments and health degradation have a significant negative coupling effect on battery life. Sensitivity analysis further reveals that the battery’s rated capacity and high-brightness screen loads are the core drivers affecting battery life. This study provides important theoretical support and practical recommendations for optimizing energy management systems in mobile devices.
