CNN-assisted automated order selection for SARIMAX in online ship roll prediction

Autonomous ships require reliable response-prediction units to enhance safety and decision-making, with roll forecasting central to stability control and propulsion efficiency. In this study, we develop a SARIMAX-based roll predictor that treats ship speed as an exogenous input and employs a lightweight CNN to determine the orders directly from ACF/PACF images, thereby eliminating iterative AIC/BIC sweeps. The pipeline is designed for online/edge deployment, offering low-latency training and inference suitable for modest onboard hardware. Granger-causality analyses across varied operating scenarios confirm that speed materially improves roll predictability. Under matched 200-s windows, the approach reduces order-selection time by ∼92 % (sub-second versus >14 s) and delivers better forecast accuracy than classical SARIMA and deep-learning baselines (LSTM, GRU, TCN, Transformer). CPU-only timing is reported for fairness, with GPU used solely for CNN training. Experiments spanning 36 simulator runs (routes/speeds/sea states) and open-source model-test cases (KCS, KVLCC) demonstrate scalability and robustness of the proposed framework. The method operates on short sliding windows and does not rely on long historical logs, enabling cold-start deployment in intermittently connected settings. • Proposes an engineering-oriented SARIMAX-CNN framework for real-time prediction of ship roll motion. • Presents a scalable order identification method using ACF/PACF image classification with over 87,000 pre-trained patterns. • Enables computationally efficient forecasting with 92 % runtime reduction, supporting Industry 4.0 in smart ship systems.