Nonlinear energy modeling for UAVs in critical missions using multiplicative calculus

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.