Sabuncu, Ö., & Bilgehan, B. (2025). Nonlinear energy modeling for UAVs in critical missions using multiplicative calculus. Sustainable Computing: Informatics and Systems, 101206.

In a recent article published in Sustainable Computing: Informatics and Systems, Near East University (NEU) researchers from BILTEM (Science, Technology, Engineering Application and Research Center) introduced a new, more realistic way to predict how much energy unmanned aerial vehicles (UAVs/drones) consume during mission-critical operations such as disaster relief.

Titled “Nonlinear energy modeling for UAVs in critical missions using multiplicative calculus,” the study by Assist. Prof. Dr. Özlem Sabuncu and Prof. Dr. Bülent Bilgehan focuses on the real-world factors that most strongly shape a drone’s energy use—payload weight, wind conditions, altitude, speed, and communication power. Instead of relying on simplified linear or polynomial formulas, the authors propose a nonlinear “multiplicative” framework that better reflects how these variables interact in demanding field conditions.

The results show a clear performance gain over commonly used baseline models. The proposed approach achieved approximately 85% higher prediction accuracy than the established cubic polynomial model, with substantially improved error metrics (MSE: 0.8472; RMSE: 0.9205). It also reduced MAE from 6.44 to 0.73 (an 88.66% improvement) and increased model fit from R² = 0.95 to R² = 0.99, indicating stronger agreement between predicted and observed energy consumption.

By enabling more reliable energy forecasting, this research supports more effective UAV deployment for real-time aid delivery, resource allocation, and communication support in challenging, resource-constrained environments—where accurate endurance estimates can directly influence mission success.
For collaboration and inquiries, please contact Prof. Dr. Bülent Bilgehan at [email protected].

About the researchers

Assist. Prof. Dr. Özlem Sabuncu and Prof. Dr. Bülent Bilgehan are researchers at Near East University (NEU), Northern Cyprus, affiliated with BILTEM – the Science, Technology, Engineering Application and Research Center. Their research spans communication systems, signals and systems, UAV-assisted networks, artificial intelligence, IoT, blockchain-enabled communication, and nonlinear/multiplicative modeling. They have authored numerous publications in leading international journals, with a strong focus on 5G/6G technologies, Industry 5.0, mission-critical UAV applications, and data-driven engineering solutions. By combining rigorous theoretical modeling with real-world validation, their work contributes to advancing sustainable, reliable, and intelligent communication and UAV systems. For collaboration and inquiries, they can be reached at [email protected] and [email protected].

Abstract

Energy efficiency in Unmanned Aerial Vehicles (UAVs) is crucial for operations, where effective payload delivery, stabilization, and communication are essential. This study presents a nonlinear energy consumption model tailored for UAVs, built upon exponential scaling and multiplicative calculus to reflect the interdependencies among payload weight, wind speed, altitude, velocity and communication power. Unlike conventional approaches that rely on linear or polynomial formulations, the proposed method incorporates energy demands from integrated systems, focusing on energy consumption. The proposed multiplicative model provides valuable insights into the energy trade-offs influenced by changing environmental and operational conditions. It improves the practicality of using UAVs for real-time aid delivery, resource allocation, and communication in challenging, resource-constrained environments, offering better accuracy than traditional energy consumption models. Validation using experimental datasets demonstrates that the proposed model achieves an 85 % improvement in accuracy compared to the recently established cubic polynomial model for predicting energy consumption. The effectiveness of the proposed multiplicative model was evaluated using Mean Squared Error (MSE) and Root Mean Squared Error (RMSE) as performance metrics. The basic polynomial model recorded an MSE of 57.4269, while the parametric polynomial model significantly improved this to 5.7794. In comparison, the multiplicative model demonstrated superior accuracy, achieving a markedly lower MSE of 0.8472. Consistently, the multiplicative model also outperformed the others in terms of RMSE, attaining the lowest value of 0.9205, thereby confirming its robustness and predictive reliability. The Mean Absolute Error (MAE) was reduced from 6.44 to 0.73, representing an 88.66 % improvement. Furthermore, the R² value increased from 0.95 to 0.99, indicating a stronger fit between the predicted and actual data. These results underscore the multiplicative model’s robustness, accuracy, and reliability, demonstrating its strong potential for real-world predictive applications. The findings demonstrate that the proposed model more accurately represents energy consumption, providing a robust foundation for precise analysis and design.