A novel grey box model for ship fuel consumption prediction adapted to complex navigating conditions

Ship fuel consumption prediction is critical to improving energy efficiency in the shipping industry. In this paper, a grey box model is proposed, which integrates a mechanistic and data-driven method based on a strategy of classification and weighting of navigating conditions and provides accurate fuel consumption predictions for dynamic navigating conditions. First, a physical model of the ship is constructed, while using historical operational data to build three data-driven models: genetic algorithms-backpropagation neural networks, particle swarm optimisation-backpropagation neural networks, and random forest algorithms. The input navigating conditions are then divided into four groups based on the errors predicted by these models. Particle swarm optimisation-random forest method was used for classification prediction. Finally, Bayesian optimisation determines the optimal weight ratio for each category label through weighted aggregation to generate the final fuel consumption prediction. The results indicated that this model decreases RMSE, MSE, MAE, and MAPE by 1.6651, 21.9337, 1.5524, and 4.9015 %, respectively, and increases R2 by 0.0325. The standard deviation of error for upstream and downstream navigations is 5.8948 and 1.7916, which is better than the performance of a single sub-model. Through five cross-validations, the model always shows superior performance in the test data set, which further verifies its stability.