Version 1
: Received: 20 October 2024 / Approved: 20 October 2024 / Online: 21 October 2024 (11:38:20 CEST)
Version 2
: Received: 21 October 2024 / Approved: 22 October 2024 / Online: 22 October 2024 (11:13:51 CEST)
How to cite:
Lu, J.; Zhang, Z.; Xiao, K.; Pang, Y. Mathematical Modeling for Submersible Safety: Location Prediction and Emergency Procedures. Preprints2024, 2024101557. https://doi.org/10.20944/preprints202410.1557.v1
Lu, J.; Zhang, Z.; Xiao, K.; Pang, Y. Mathematical Modeling for Submersible Safety: Location Prediction and Emergency Procedures. Preprints 2024, 2024101557. https://doi.org/10.20944/preprints202410.1557.v1
Lu, J.; Zhang, Z.; Xiao, K.; Pang, Y. Mathematical Modeling for Submersible Safety: Location Prediction and Emergency Procedures. Preprints2024, 2024101557. https://doi.org/10.20944/preprints202410.1557.v1
APA Style
Lu, J., Zhang, Z., Xiao, K., & Pang, Y. (2024). Mathematical Modeling for Submersible Safety: Location Prediction and Emergency Procedures. Preprints. https://doi.org/10.20944/preprints202410.1557.v1
Chicago/Turabian Style
Lu, J., Kangqi Xiao and Yuxiang Pang. 2024 "Mathematical Modeling for Submersible Safety: Location Prediction and Emergency Procedures" Preprints. https://doi.org/10.20944/preprints202410.1557.v1
Abstract
This paper presents a comprehensive approach to enhancing submersible safety through mathematical modeling and decision-making frameworks. We develop models for submersible location prediction, emergency preparedness, and scenario extrapolation, including a Seawater Density Model, Submersible Mechanical Model, Bayesian Searching Model, and Extended Kalman Filter. Sensitivity analysis confirms the robustness of these models under varying conditions, making them adaptable for different marine environments.In the first section, we focus on accurately locating a submersible after communication loss. The Seawater Density Model employs a hyperbolic tangent function to model depth-dependent density in the Ionian Sea, while the Submersible Mechanical Model simulates underwater dynamics using the 4th order Runge-Kutta method. Uncertainties are addressed using an Extended Kalman Filter, enhancing accuracy, as shown by trajectory and Mean Squared Error (MSE) comparisons.In the second section, we develop a Bayesian Searching Model to efficiently locate a missing submersible. This model iteratively updates location probabilities using a bimodal Gaussian distribution. The search zone is discretized into grids, and simulations demonstrate the model's ability to effectively narrow down the search area and improve detection success.In the third section, we adapt the models to different environments, such as the Caribbean Sea. A warning and obstacle avoidance system is introduced to manage multiple submersibles in close proximity, dynamically adjusting their paths to avoid collisions.Reliability analysis demonstrates the robustness of the models against changes in density and sudden environmental shifts, showing minimal deviation from neutral buoyancy. These results confirm the reliability and adaptability of the models for enhancing submersible safety across various marine settings.
Computer Science and Mathematics, Applied Mathematics
Copyright:
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
