A machine learning method for the prediction of ship motion trajectories in real operational conditions

Mingyang Zhang, Pentti Kujala, Mashrura Musharraf, Jinfen Zhang, Spyros Hirdaris

Research output: Contribution to journalArticleScientificpeer-review

43 Citations (Scopus)
137 Downloads (Pure)


This paper presents a big data analytics method for the proactive mitigation of grounding risk. The model encompasses the dynamics of ship motion trajectories while accounting for kinematic uncertainties in real operational conditions. The approach combines K-means and DB-SCAN (Density-Based Spatial Clustering of Applications with Noise) big data clustering methods with Principal Component Analysis (PCA) to group environmental factors. A Multiple-Output Gaussian Process Regression (MOGPR) method is consequently used to predict selected ship motion dynamics. Ship sway is defined as the deviation between a ship and her motion trajectory centreline. Surge accelerations are used to idealise the time-varying manoeuvring of ships in various routes. Operational conditions are simulated by Automatic Identification System (AIS), General Bathymetric Chart of the Oceans (GEBCO), and nowcast hydro-meteorological data records. A Dynamic Time Warping (DTW) method is adopted to identify ship centre-line trajectories along selected paths. The machine learning algorithm is applied for ship motion predictions of Ro-Pax ships operating between two ports in the Gulf of Finland. Ship motion dynamics are visualised along the ship’s route using a Gaussian Progress Regression (GPR) flow method. Results indicate that the present methodology may assist with predicting the probabilistic distribution of ship dynamics (speed, sway distance, drift angle, and surge accelerations) and grounding risk along selected ship routes.
Original languageEnglish
Article number114905
Number of pages24
JournalOcean Engineering
Publication statusPublished - 1 Sept 2023
MoE publication typeA1 Journal article-refereed


  • Ship dynamics
  • Motions
  • Machine learning
  • Ship grounding
  • Safety in operations


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