An ensemble multi-step forecasting model for ship roll motion under different external conditions: A case study on the South China Sea

•Propose a novel DBN ensemble model for ship roll multi-step forecasting under different external conditions.•Reduce the error accumulation of multi-step prediction by the DBN model under the MIMO strategy.•Obtain the optimal hyperparameters of the DBN model by the MOJS algorithm.•Reduce nonlinear and nonstationary of ship roll data by the adaptive secondary decomposition method.•Correct the initial prediction error by the adaptive error correction method. The external environment is the main factor affecting the stability of ship roll motion. Accurate forecasting of ship roll motion under different external conditions can help assure navigational safety and increase ship operating efficiency. In this study, an ensemble multi-step forecasting model for ship roll motion under different environmental conditions is proposed, which consists of adaptive secondary decomposition (ASD), deep belief network (DBN) under multi-input multi-output (MIMO) strategy, multi-objective optimization, and adaptive error correction (AEC). To evaluate the performance of the proposed ensemble model, five experiments are set up to make the 5-step, 7-step, and 9-step ahead prediction for the ship roll series, respectively. Four different external environment ship roll datasets from the South China Sea in 2020 were employed to validate the robustness of the ensemble multi-step forecasting model. The experimental results demonstrate that the proposed model based on adaptive secondary decomposition, multi-objective optimization, and adaptive error correction can accurately and effectively predict ship roll motion under different external conditions.