Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Uncertainty and sensitivity analysis for the performance evaluation of ship dynamical model
Chunlin Wang, Tongtong Wang, Torodd Skjerve Nord, Houxiang Zhang, Guoyuan Li
Department of Ocean Operations and Civil Engineering, Norwegian University of Science and Technology, Ålesund, Norway

Ottar Osen
Department of ICT and Natural Sciences, Norwegian University of Science and Technology, Ålesund, Norway

ABSTRACTmodel improvement and accurate ship motion prediction.

Model uncertainty is pervasive and inherent in the engineering field. It
could bring potential risks in real applications, especially for ship behaviour prediction under environmental disturbances. The evaluationand quantification of model uncertainty are of importance for accurate
ship motion prediction. This study applies model uncertainty analysis
and sensitivity analysis methods to evaluate the ship motion model’slevel of uncertainty against environmental disturbances and ship manoeuvres. Firstly, three models are created based on the a dynamicalmodel (Mariner) in Marine Systems Simulator. After that, models aretested on various predefined scenarios. The similarity of predicted trajectories and the reference is evaluated by Euclidean distance and used
to quantify the uncertainty of models. Next, statistical analysis is used
to analyze the uncertainty of models. Sensitivity analysis (SA) method
called ‘PAWN’ and ‘UnivariateSpline’ interpolation technology are combined to identify which factors contribute the most to model’s performance. The results suggest that the uncertainty caused by external factors varies from different models under different manoeuvres. SA cantell us which factors (wind angle, wind velocity, and surge speed) havea large influence to the model uncertainty given a ship maneuver. Suchanalyses, on the one hand, contribute operators to choosing the optimum
model according to the current conditions for better ship motion prediction. On the other hand, they can pick up the most important factors forfast uncertainty modelling.

Model uncertainty comes from two sources: model discrepancies andinput parameters [Smith, 2013]. Model discrepancies are caused by animprecise representation of real physics. Input uncertainty refers to uncertain model parameters. These two factors are inherent in ship motion
models. In addition, the collected sensor data probably worsens this caseas it is mixed with noise from the environment and measured errors. Researchers proposed a large variety of models for future ship position prediction. For example, the extended Kalman filter was used to estimate
ship motion states and predict the trajectory of a vessel by means of akinematic model [Perera et al., 2012; Sutulo et al., 2002; Perera, 2017].
Li et al. leveraged the Support Vector Machine to predict the heave
motion under the impact of waves [Li et al., 2016]. Skulstad et al. offer ship position predictions based on an integration of a supervised
Machine Learning model of the ship into the ship dynamic model[Skulstad et al., 2020]. Although these models could achieve a good performance in terms of ship motion prediction, their robustness can not beguaranteed due to the lack of model uncertainty evaluation and quantification, which would bring risks in real applications. This problem
highlights the necessity of uncertainty analysis (UA) of ship models.
The uncertainty mainly contains two types: aleatoric uncertainty andepistemic uncertainty [Smith, 2013]. Aleatoric uncertainty is also called
data uncertainty which is caused by errors in the dataset. Epistemic uncertainty refers to model uncertainty that comes from model structure andmodel parameters. That means different methods applied to the same setof data often obtain different conclusions [Young and Holsteen, 2017].
That would bring a huge risk for decision making in the engineering
field, especially for accurate motion control. This problem implies thenecessity of model uncertainty evaluation. A novel data-driven (namedSDMU) was proposed to conduct hydrologic model uncertainty evaluation [Pathiraja et al., 2018]. It is critical to provide improved predictionsof system outputs. Mathevet et al. assessed the performance of two conceptual rainfall-runoff models based on Kling-Gupta Efficiency metric[Mathevet et al., 2020]. Simulations present the limitation of both models when they were applied in different watersheds. Hu et al. carriedout time-dependent reliability analysis by integrating the fast integration
method and surrogate model method [Hu et al., 2016]. This method is

KEY WORDS: Ship motion prediction; Model uncertainty analysis;
Statistical analysis; Sensitivity analysis; UnivariateSpline interpolation.

INTRODUCTION
Digital technology has become an enabler for making ship motion more
intelligent and safe. A large variety of advanced ship motion prediction
models have been developed and present a good performance. However, the model’s robustness and stability have been a huge challengethat might lead to serious accidents. This problem results from modeluncertainty. Uncertainty is ubiquitous in modelling-related engineering
fields, especially for ship motion prediction [Arendt et al., 2012]. Therefore, it is of importance to evaluate model uncertainty for the support of2309