Digital Vitality, Finite Energy: A Continuous-Time Framework for Battery Discharge Behavior
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Keywords
CTBD model, bayesian inference, L-BFGS-B, laplace approximation, random process simulation
Abstract
With the widespread adoption of smartphones, battery endurance has become a critical factor affecting user experience. To systematically characterize battery discharge behavior under real-world usage conditions, this study proposes a Continuous-Time Battery Discharge (CTBD) model. The model is grounded in fundamental physical principles and is progressively extended to incorporate multiple influencing factors, including screen display, processor workload, network connectivity, GPS operation, and background activities. Furthermore, a State of Health (SOH) correction factor is introduced to capture the effects of environmental temperature and battery aging on the effective capacity. Distinct modeling strategies are employed for high- and low-temperature operating conditions. To improve parameter estimation accuracy, a Bayesian inference framework is adopted, combined with the Limited-memory Broyden–Fletcher–Goldfarb–Shanno algorithm with bound constraints (L-BFGS-B) and Laplace approximation. Experimental results on the test dataset show that the proposed model achieves a mean absolute percentage error (MAPE) of 5.54%, demonstrating strong predictive performance. To simulate stochastic signals in practical electronic systems, a random process simulation method based on time discretization, Gaussian sequence generation, and rectangular approximation is developed. Based on this approach, three representative usage scenarios—daily use, office applications, and gaming—are constructed. Under fully charged conditions, the predicted battery lifetimes are approximately 7.8 hours, 5.3 hours, and 4.5 hours, respectively, showing good consistency. Finally, sensitivity analysis is conducted to identify the key factors contributing to battery consumption. The results indicate that screen power consumption dominates (approximately 40%–60%), followed by CPU usage. Based on these findings, the model is further extended to other portable electronic devices, and practical recommendations are proposed from both user behavior and operating system optimization perspectives.
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