Thermo-mathematical modeling and multi-objective optimization of marine propulsion using artificial neural network and a novel physics-based metaheuristic optimization algorithm: Thermo-economic-environmental analysis

This study presents a robust thermoeconomic framework for marine nuclear propulsion, utilizing the Nuclear Ship Savannah as a case study. To overcome data limitations, creative solutions are applied, including the application of artificial neural network approach to solve nonlinear coupled exergoeconomic equations and determine the thermodynamic properties of the flow within the Savannah's Nuclear Propulsion (SNP). Upon validating the proposed model, the study introduces innovative design modifications to enhance the thermal efficiencies of the SNP. Furthermore, single-objective optimization (SOO) and multi-objective optimization (MOO) are incorporated into the improved SNP (ISNP) to optimize system performance criteria, such as exergy efficiency ( η II ), total capital cost rate ( C ˙ tot I & O & M ), and total product exergy cost rate ( C ˙ P ). Afterwards, the ISNP optimization is executed using Henry Gas Solubility Optimization (HGSO) to determine the optimal non-dominated solutions, allowing for the evaluation of trade-offs in system performance. The final optimal design of the optimized ISNP (OISNP) is then selected through a multi-criteria decision-making process. Subsequently, a comprehensive comparative analysis is conducted on the SNP, ISNP, and OISNP models, considering energy, exergy, exergoeconomic, and environmental economics (4-E) viewpoints. The 4-E analysis reveals that the SNP exhibits an energy efficiency of 26.18 % and an exergy efficiency of 51.8 %, whereas the ISNP demonstrates enhanced performance with an energy efficiency of 28.42 % and an exergy efficiency of 55.50 %. The improvement lead to a 1.31 MW boost in propulsion power compared to the SNP, bringing it to 16.4 MW. This comparative evaluation underscores the significant improvements achieved through the modifications implemented in the SNP. Also, the OISNP demonstrates further advancements, achieving an exergy efficiency of 55.01 %, representing a 3.2 % improvement over the SNP, while its energy efficiency is recorded at 28.4 %, a 2.22 % increase compared to the SNP. Additionally, the propulsion power reaches 16 MW, marking a 1 MW increase over the SNP. Notably, the C ˙ tot , OISNP I & O & M and C ˙ P , OISNP are reduced to $282.3/hour and $4290/hour, respectively, indicating substantial cost savings relative to both the ISNP and SNP models. Besides, the environmental analysis indicates that transitioning from a fossil fuel-powered MSP to an OISNP annually cuts fossil fuel consumption by 61,320 tons, generating $30.66 million in potential export revenue. This change reduces emissions by 193 kilotons (kt) of CO 2 , 4.3 kt of NO x , 3 kt of SO 2 , and 0.92 kt of PM, while decreasing external costs by $6.132 million and potentially avoiding $9.65 million in annual carbon tax liabilities for the shipping industry. Furthermore, to evaluate the comparative statistical performance of the competing algorithms, a Wilcoxon rank sum test is conducted. The comparative results show that the HGSO algorithm outperforms the others, delivering both competitive and superior outcomes in solving complex optimization problems.