University of Oulu

Antti Solonen, Ramona Maraia, Sebastian Springer, Heikki Haario, Marko Laine, Olle Räty, Jukka-Pekka Jalkanen, Matti Antola, Hierarchical Bayesian propulsion power models — A simplified example with cruise ships, Ocean Engineering, Volume 285, Part 1, 2023, 115226, ISSN 0029-8018,

Hierarchical Bayesian propulsion power models : a simplified example with cruise ships

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Author: Solonen, Antti1; Maraia, Ramona1; Springer, Sebastian2;
Organizations: 1School of Engineering Science, Computational and Process Engineering, LUT University, Lappeenranta, 53850, Finland
2Research unit of Mathematical Sciences, University of Oulu, Oulu, 90570, Finland
3Meteorological Research, Finnish Meteorological Institute, Helsinki, 00101, Finland
4Atmospheric Composition Research, Finnish Meteorological Institute, Helsinki, 00101, Finland
5Eniram, a Wärtsilä Company, Helsinki, 00210, Finland
Format: article
Version: published version
Access: open
Online Access: PDF Full Text (PDF, 2.7 MB)
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Language: English
Published: Elsevier, 2023
Publish Date: 2023-10-31


Mathematical models for ships’ consumption are in a central role in assessing the CO₂ emissions of marine traffic. Moreover, such models are needed when optimizing the ways the vessels are operated (e.g. routing). Nowadays, many ships are equipped with data collection systems, enabling data-based calibration of the models. Typically this calibration is done independently for each ship. In this paper, we demonstrate a hierarchical Bayesian approach, where we fit a single model over many vessels, with the assumption that the parameters of vessels of similar characteristics are likely close to each other. The benefits of such an approach are two-fold; (1) we can borrow information about parameters that are not well informed by the vessel-specific data using data from similar ships, and (2) we can use the hierarchical model to predict the behavior of a vessel from which we have no data, based only on its characteristics. In this paper, we discuss the basic concept and present a simple version of the model using cruise vessels. We apply the Stan modeling tool for the fitting and use real data from 64 ships collected via the commercial Eniram platform. The prediction accuracy of the model is compared to an existing data-free method. We demonstrate that the accuracy of such an approach can improve upon the classical resistance calculation-based methods.

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Series: Ocean engineering
ISSN: 0029-8018
ISSN-E: 1873-5258
ISSN-L: 0029-8018
Volume: 285
Article number: 115226
DOI: 10.1016/j.oceaneng.2023.115226
Type of Publication: A1 Journal article – refereed
Field of Science: 111 Mathematics
214 Mechanical engineering
Funding: This work was supported by the Academy of Finland, decision number 313827, “Industrial Internet and Data Analysis in Marine Industries”, decision number 321890, “Advanced data fusion methods for environmental modeling ADAFUME”, and by the Centre of Excellence of Inverse Modelling and Imaging (CoE), Academy of Finland, decision number 312122. This work has been supported by the European Regional Development Fund (Interreg Baltic Sea Region) project C006 CSHIPP.
Copyright information: © 2023 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (