# Data Analytics for Improving Energy Efficiency in Short Sea Shipping

Mohamed Abuella, Hadi Fanaee, M. Amine Atou, Slawomir Nowaczyk, Simon
Johansson, and Ethan Faghani Manuscript received March 1, 2024; revised March
16, 2024.This work was supported by the Sweden’s innovation agency
(Vinnova).(Corresponding author: Mohamed Abuella.)
Mohamed Abuella, Hadi Fanaee, Amine Atoui, and Slawomir Nowaczy are with
Center for Applied Intelligent Systems Research (CAISR), Halmstad University,
Kristian IV:s väg 80523, Halmstad, 30118 Sweden (e-mail: {mohamed.abuella;
hadi.fanaee; amine.atoui; Slawomir.Nowaczyk}@hh.se). Simon Johansson and Ethan
Faghani are with CetaSol AB, Gothenburg, 41251, Sweden (e-mail:
{simon.johansson and<EMAIL_ADDRESS>
###### Abstract

To meet the urgent requirements for the climate change mitigation, several
proactive measures of energy efficiency have been implemented in maritime
industry. Many of these practices depend highly on the onboard data of
vessel’s operation and environmental conditions. In this paper, a high
resolution onboard data from passenger vessels in short-sea shipping (SSS)
have been collected and preprocessed. We first investigated the available data
to deploy it effectively to model the physics of the vessel, and hence the
vessel performance. Since in SSS, the weather measurements and forecasts might
have not been in temporal and spatial resolutions that accurately representing
the actual environmental conditions. Then, We proposed a data-driven modeling
approach for vessel energy efficiency. This approach addresses the challenges
of data representation and energy modeling by combining and aggregating data
from multiple sources and seamlessly integrates explainable artificial
intelligence (XAI) to attain clear insights about the energy efficiency for a
vessel in SSS. After that, the developed model of energy efficiency has been
utilized in developing a framework for optimizing the vessel voyage to
minimize the fuel consumption and meeting the constraint of arrival time.
Moreover, we developed a spatial clustering approach for labeling the vessel
paths to detect the paths for vessels with operating routes of repeatable and
semi-repeatable paths.

###### Index Terms:

Short-sea shipping, energy efficiency, spatio-temporal aggregation, voyage
speed optimization, Time-series analysis, spatial clustering, vessel path
identification, maritime transportation,

##  I Introduction

###  I-A General Background

Short-Sea Shipping (SSS) is a commercial transportation mode that does not
involve intercontinental cross-ocean. The SSS provides a cost-efficient and
environment-friendly alternative for transportation by utilizing inland and
coastal waterways to transport the commercial freight [1].

On the other hand, the SSS produces some negative effects on the natural
habitats and polluting the air along the coasts of populated cites [2]. As a
response to this, the International Maritime Organization (IMO) have conducted
many studies and recommended standards and imposed policies for the maritime
sector to reduce the carbon dioxide (CO2) to 40% by 2030 and cut 50% of all
GHGs by 2050, based on the emissions in 2008 [3].

Figure 1: European short-sea shipping of freight versus total sea transport,
in 2021 [4].

Furthermore, COVID-19 pandemic has accelerated the digitalization of the
entire shipping industry globally, and hence attracted a profound
consideration to data collection and preparation stages [5]. The operational
and some environmental conditions can be accessed through an Automatic
Identification System (AIS) messages, which is a service developed by the
International Maritime Organization (IMO) in 2002 to record the sensor
measurements and send the vessel position information for the traffic between
other ships and neighboring shores [6].

In a broader perspective, for improving the vessel’s energy efficiency and
harnessing more fuel savings and less GHG emissions, there are mainly two
procedures. The first strategy is in the ship design stage, where the ship is
built to obtain a body and equipped machinery that work efficiently. The
second strategy is during the ship operation over the water or at the ports.
This latter procedure can be achieved by adopting energy management plans that
optimally enhance the energy efficiency and fuel consumption [7].

Maritime transportation is crucial for global trade, generating extensive
vessel trajectory data that reveals intricate spatial and temporal navigation
patterns. Understanding these patterns is vital for effective maritime traffic
surveillance and management [8].

It is crucial to distinguish between trajectory and path when studying
movement data.
The term path refers to the specific course taken by the object. While, a
trajectory refers to a sequence of consecutive geographical points, each
representing a specific location at a given timestamp [9]. Thus, the
trajectory typically denotes the movement of an object over time. In other
words, a trajectory is a path with schedule and speed information. For
instance, if a vessel travels from origin port to destination port, its
trajectory is the sequence of geographical points it passes through, while its
path is the specific course taken, such as a fairway in a small river or
through a specific canal. While the vessel trajectory is its navigation
including time and space information, such as time schedule, speed, and
location [10], [11].

Trajectories, observed in various scenarios such as pedestrian movements,
vehicular routes, and natural events like wildlife migrations or hurricanes,
involve time-evolving position data. Trajectory mining aims to uncover
significant patterns within datasets, enabling tasks like path classification,
anomaly detection for accidents or traffic congestions, surveillance for
suspicious activities, and prediction of vessel trajectories in different
landscapes [12].

Additionally, the term route is synonymous with path or trajectory as long as
it shares the same origin and destination. Conversely, any difference in
either the origin or destination represents another route. For example, when a
vessel travels from an origin port to three destination ports, we say this
vessel has three distinct routes to reach its three destinations.

Moreover, a Voyage is generally means the period between a departure from a
port to the departure from the next port. Voyage is commonly used in reference
to sea travel, much like the term ’trip’ is used in the context of air travel.

Path clustering - same as trajectory clustering, but we do not consider the
time information. Our focus is primarily on spatial information of the moving
object. Path clustering, a versatile technique, involves grouping paths into
clusters based on their similarity, demonstrating its effectiveness in a
myriad of practical applications. In the realm of navigation, path
identification empowers systems to generate clear and detailed instructions
for users seeking their way. Traffic analysis benefits from path clustering as
it facilitates the identification of diverse traffic patterns, such as the
smooth flow of traffic on highways and the congestion often encountered on
city streets. Path identification proves equally valuable in route planning,
enabling the optimization of routes for transportation systems, including
public and maritime transportation services [13].

In the scope of the maritime industry, path identification from Automatic
Identification System (AIS) data is a challenging task due to the high spatial
freedom and, especially in coastal areas, the high frequency of ship’s
navigation maneuvers. Thus, it is imperative to develop a path identification
tool that integrates with route planning systems for improving maritime safety
and optimizing vessel routing. As data-driven approaches from AIS data
continue to grow and evolve, path clustering will undoubtedly play an
increasingly important role in understanding vessel behavior and supporting
decision-making in maritime transportation [14].

This paper proposes a data-driven frameworks for modeling, optimizing, and
path identification approaches to improve energy efficiency in short-sea
shipping. In addition, a framework for vessel path identification has been
developed for route planning and management of resources in maritime industry.

###  I-B Main Outcomes

The main outcomes of this paper can be summarized as follow:

  * •

Modeling of energy efficiency: Develop a data-driven model for voyage energy
efficiency, including:
A spatiotemporal aggregation of operation and navigation data from onboard and
external sources to capture the impact of both spatial and temporal factors on
voyage energy efficiency.
Introduce an efficiency score that considers both total fuel consumption and
voyage duration to measure the voyage energy efficiency.

  * •

Data clustering: Clustering the data of voyages and sorting them based on
their efficiency scores. This clustering enables the voyage optimization
algorithm to learn more insights for better actions, either by selecting the
best voyages or by eliminating the worst voyages.

  * •

Time-series analysis models and comparative analysis: Four time-series based
models are implemented as algorithms of voyage speed optimization. Then, a
rigorous evaluation of their performance is conducted across different data
clusters and using metrics that account for voyage efficiency.

  * •

Practical implication: Demonstrate the significant effectiveness and
practicality of the proposed approach for fixed-route vessels in short sea
shipping, where the options for obtaining efficient voyages are limited. The
approach also aligns with the guidance of domain experts, adhering to safety
and traffic considerations.

  * •

The proposed clustering approach of vessel paths requires only position
information, specifically longitude and latitude.

  * •

The clustering approach has a proven added value for clustering challenging
unseen or unknown paths.

  * •

The approach is robust and interpretable by applying a similarity measure that
reduces the influence of noise or outliers and offers a clear interpretation
of path clustering.

  * •

The approach has a customizable parameter to determine the number of path
clusters, thereby enhancing the flexibility and adaptability of the framework
and allowing users to tailor it to their specific needs.

  * •

The approach also includes a method to study and analyze the patterns within
specific segments of a path.

  * •

It is a data-driven solution that can be used as a valuable asset for informed
decision-making in route planning and optimization, traffic management, and
resource allocation.

##  II Related Work

As digitalization and automation become increasingly prevalent in the maritime
sector, the research addressing new challenges has been growing rapidly,
particularly with regard to developing frameworks for energy efficiency and
Maritime Situational Awareness (MSA) in cross-ocean shipping. On the other
hand, the research progress has not kept pace for vessels operating in coastal
areas. Thus, this literature review will focus on our primary area of
interest, which is research that is related to short-sea shipping.

###  II-A Vessel Energy Efficiency Modeling

Recent research studies [15, 16] have explored energy-efficient routing for an
electric ferry in Western Norway. They rely on operational data from onboard
measurements and environmental conditions from the Norwegian Meteorological
Institute, interpolated to the nearest temporal and spatial resolutions of the
vessel’s onboard data. Similarly, the researchers from Napa Ltd. in Finland
conducted several studies on voyage optimization, including two cases [17, 18]
where environmental conditions were collected from the weather forecasts.
Other studies in the literature have also processed environmental data from
different weather providers to match the vessel’s operational onboard data, as
reviewed in [19]. However, such approaches do not account for weather factors
that influence both fuel consumption and the Estimated Time of Arrival (ETA),
which is a crucial constraint when optimizing the vessel’s voyage, especially
in SSS.

The maritime industry increasingly adopts digitization and Machine Learning
(ML) techniques; however, their black-box nature remains a significant
challenge. While ML can provide valuable insights, the reasoning behind the
predictions made by such models is often difficult to comprehend due to their
lack of explainability. To address this issue, Shapley additive explanations
(SHAP) [20] were developed, providing a way to determine the contribution of
each input feature toward the model’s output. SHAP is commonly used as a
solution to the explainability issue in ML. A recent study [21] analyzed
feature importance for the power consumption of a chemical tanker. The results
indicate that the ship’s speed through the water is the most influential
feature, while ship heading and other weather features have relatively minor
influences. Kim et al. [22] utilized SHAP in combination with an anomaly
detection algorithm to detect and interpret anomalies in onboard data from a
cargo vessel. It allowed the identification of the specific sensor variable
responsible for an anomaly, and SHAP-based clustering was used to interpret
and group common anomaly patterns. A validation study for explainability in
the maritime time-series data [23] compared two common model-agnostic XAI
approaches, SHAP for a global method and LIME as a local method. A literature
review on XAI [24] discusses the importance of XAI as a key component in
modern AI techniques. The authors present a taxonomy of existing contributions
related to the explainability of different machine learning models. Overall,
the use and development of ML techniques in the maritime industry requires a
careful balance between performance gain and explainability.

###  II-B Vessel Voyage Optimization

Various techniques can be applied for the voyage optimization problem, as
demonstrated in prior studies such as [25, 26, 27, 28]. Some of these
approaches have been implemented specifically for short-sea shipping, as
indicated in the domain of [19] and [29].

Different modeling and optimization algorithms for ship weather routing have
been investigated thoroughly in [30]. It was found that the effectiveness of
these algorithms strongly depends on specific requirements concerning the
objectives, control variables and constraints as well as the implementation.
The majority of these voyage optimization approaches are applied to ocean-
crossing ships by controlling mainly the vessel speed and its route. Whereas,
in the SSS, especially for fixed-route vessels like ours, there are fewer
options available for voyage optimization. Therefore, the scope of this paper
is mainly focused on short-sea shipping and the pertinent research literature.

In the third IMO GHG study 2014 [31], it was assumed that weather effects
alone would be responsible for 15% of additional power margin on top of the
theoretical propulsion requirements of ocean-going ships, and a 10% additional
power requirement for coastal ships.
In a recent adaption of the Ship Traffic Emission Assessment Model (STEAM),
propelling power is determined by wave height and directions, accounting for
the environmental conditions in a highly detailed manner [6].

Recent research studies [15, 16] have explored energy-efficient routing for an
electric ferry in Western Norway. They rely on operational data from onboard
measurements and environmental conditions from the Norwegian Meteorological
Institute, and proposed a hybrid physics-guided machine learning model for
optimizing the ship route. Based on their findings, the hybrid model was
showing an energy reduction of 3.7% compared to the actual consumption, simply
by applying minor route and speed profile alterations as guided by the
provided weather forecasts.

Researchers from Napa Ltd. in Finland conducted several studies on voyage
optimization. In two of their studies [17] and [18]. These experts stated that
their products of voyage optimization can achieve a fuel cost reduction of
more than 10% with 2% to 4% savings from trim optimization and 6% to 8% from
speed and route optimization. [32].

In the study conducted by Huotari et al. [33], where they used a combined
model with both dynamic programming and convex optimisation to obtain optimal
speed profiles. The fuel savings were around 1.1% and for voyages with
substantial variance in environmental conditions, the fuel savings reached as
high as 3.5%.

In the review paper by Wang et al. [34] numerous studies are explored,
including coastal and inland shipping, also revealing a diverse range of fuel
savings outcomes.
Meanwhile, regarding weather routing, specifically through speed and route
optimization, it has been demonstrated in [35] that the potential savings of
carbon dioxide emissions and fuel costs are in range of 5% to 10%.

###  II-C Vessel Path Identification

Path clustering can be done using a variety of different methods [36]. We will
explore the related works of these various methods.

Clustering is gaining popularity for route extraction. Machine learning (ML)
has recently been applied extensively for vessel path identification by
learning patterns from historical data. Lee et al., in [12] introduced
TRACLUS, a trajectory clustering algorithm employing a partition-and-group
framework to discover common sub-trajectories. Demonstrating efficacy through
formal trajectory partitioning and density-based clustering and efficiently
identifies shared patterns in real trajectory data. The study presented in
[37] introduced a framework, Traffic Route Extraction and Anomaly Detection
(TREAD), which utilizes unsupervised learning for maritime route extraction.
The primary emphasis is on anomaly detection and route prediction,
highlighting the crucial role of AIS data in enhancing maritime situational
awareness. The work specifically addresses challenges related to intermittency
and persistence in AIS data. Another method of route extraction was proposed
in [38], transforming ship trajectories into ship trip semantic objects (STSO)
and utilizing graph theory for route extraction. The method proves robustness
in extracting traffic routes for merchant ships but may have limitations for
vessels with frequent navigation behavior changes, such as fishing vessels.
The approach in [39], on the other hand, adopts a dynamic time warping (DTW)
distance as a similarity measure and considers vessel course changes to
analyze its trajectories. Experiments demonstrated its high accuracy in
distinguishing and detecting similar vessel trajectories, outperforming
existing methods in accuracy and cluster degree evaluation. Moreover, [40]
presents a machine learning framework for maritime vessel trajectory analysis,
incorporating clustering, classification, and outlier detection. It employs
piecewise linear segmentation for compression and alignment kernels to
integrate geographical domain knowledge, enhancing task performance. Results
show reduced computation time without compromising accuracy.

Capobianco et al.[41] proposed a deep learning approach using recurrent neural
networks, employing a Bidirectional Long Short-Term Memory (BiLSTM) layer as
an encoder and a Unidirectional Long Short-Term Memory (LSTM) layer as a
decoder, for vessel trajectory prediction. Their model outperforms baseline
approaches, showcasing the effectiveness of sequence-to-sequence neural
networks. In their study, Li et al. [42] present an AIS data-based machine
learning method for feature extraction and unsupervised route planning for
Maritime Autonomous Surface Ships (MASS). The method uses Automatic and
Adaptive Dynamic Time Warping (AADTW), Spectral Clustering with Affinity
Feature (SCAF), and a route optimization algorithm based on dynamic
programming to extract features, obtain movement patterns, and plan routes.
The proposed method outperforms existing methods by considering the impact of
hidden factors and providing different routes for different types of MASS. The
work in [43] systematically analyzes the performance of twelve ship trajectory
prediction methods, including classical machine learning and emerging deep
learning techniques. It compares twelve methods across three AIS datasets,
representing different maritime traffic scenarios, and evaluates their
effectiveness based on six indexes. The study concludes that traditional
machine learning-based trajectory prediction methods struggle to meet the
rising demands for accuracy and real-time performance, leading to increased
interest in and promising results from deep learning-based approaches.
EnvClus*, introduced in [44], it is an innovative unsupervised data-driven
framework for vessel trajectory forecasting, achieving a 33% improvement over
state-of-the-art methods. EnvClus* excels in accurately predicting vessel
routes, particularly in long trips, showcasing its effectiveness in mobility
analytics and trajectory prediction.

A maritime traffic route extraction approach based on multi-dimensional
density-based spatial clustering of applications with noise (MD-DBSCAN) was
developed in [45]. The approach incorporates trajectory compression,
similarity measures, and extraction of ship trajectory clusters. The approach
demonstrates effectiveness in noise reduction and route extraction. The
authors in [46] proposed a trajectory clustering method based on Hierarchical
Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) and
Hausdorff distance to generate a similarity matrix. The method adapts to shape
characteristics and exhibits good clustering scalability and improved
clustering results compared to DBSCAN, k-means, and spectral clustering
algorithms.

Eljabu et al. proposed spatial clustering methods (SPTCLUST and SPTCLUST-II)
in [47] and [48] respectively, for maritime traffic routes extraction from AIS
data. The approach consists of data preprocessing, pathfinding, and route
extraction without using traditional clustering algorithms. It achieved high
F1-scores, 97% and 99%, for tankers and cargo maritime traffic routes.

The study in [49] enhanced the DBSCAN method by integrating the Mahalanobis
distance metric for vessel behavior modeling. The proposed methodology
includes clustering historical AIS data and detecting anomalies. The study
showcases applicability to diverse water regions, contributing to situational
awareness, collision prevention, and route planning.

Farahnakian et al. [50] conducted a comprehensive examination of clustering-
based techniques, including k-means, DBSCAN, Affinity Propagation (AP), and
the Gaussian Mixtures Model (GMM), for detecting abnormal vessel behaviors
from AIS data. Results indicate that k-means is particularly effective in
detecting dark ships and spiral vessel movements, which is crucial for
enhancing maritime safety. Furthermore, the study [51] proposed two methods
for trajectory outlier detection, with the first utilizing DBSCAN clustering
and Hausdorff distance, and the second employing Support Vector Machine (SVM)
classifier and the Generalized Sequence Pattern algorithm. Both models
outperform the baselines, with the SVM approach demonstrating superior
performance in the identification of traffic patterns and outliers. The study
[10] developed MUITAS, a novel trajectory similarity measure addressing
limitations in existing approaches for multiple-aspect trajectories enriched
with heterogeneous semantic dimensions. Through evaluation on real datasets,
MUITAS demonstrates robustness and outperforms current methods in precision at
recall and clustering techniques for diverse mobility data. Moreover, the
authors in [52] presented a methodology for extracting navigation network
information from vessel trajectories, utilizing AIS data. The proposed model
identifies key areas, speed, and course patterns, forming a network
abstraction for optimizing ship routing and scheduling in the maritime
industry, demonstrated through analysis in the eastern Mediterranean sea. This
model is also useful in an outlier behavior detection.

The research paper [53] offers a detailed survey of visual analytics for
vessel trajectory data. The authors discuss a variety of methods, including
map-based visualization, timeline-based visualization, and interactive
visualization.

The survey [11] delves into the growing focus on semantically rich
trajectories in movement data analysis, covering concepts, management issues,
and techniques for constructing, enriching, and mining trajectories, with
attention to emerging privacy challenges.

The paper [54] comprehensively reviews various approaches for vessel
trajectory predicting, including clustering algorithms and machine learning
algorithms. It also discusses the challenges and future research directions,
such as the uncertainty in the data, the dynamic environment, and the
computational complexity.

Among the identified challenges, which are subjects of ongoing research and
require additional attention, three are worthy of specific mention: navigating
dynamic maritime environments poses a substantial challenge in accurately
identifying vessel paths (I); ensuring stability, explainability, and managing
the computational cost of the model add further complexity (II); finally,
addressing the need for flexibility, scalability, and practical applicability
is crucial for a comprehensive solution in the field of vessel path
identification (III). Motivated by these challenges, we aim to develop a
framework that focuses on vessel path identification and potentially tackling
such challenges faced in maritime transportation.

##  III Data Collection and Preparation

###  III-A Data Collection

The ship’s onboard data have been received from our industry partner CetaSol
AB in Gothenburg [55]. The data has been gathered over a period of 15 months,
between January 2020 and March 2021. It has a 3Hz frequency and records about
the ship’s position, course direction, and speed. It is also including some of
operational and meteorological data, such as fuel rate, engine speed, torque,
acceleration, wind speed and direction.

Some information about the ship and its voyage can be found on Marine Traffic
website [56].
Other weather variables such as wave height and sea current speed and
direction have been collected from external sources, Copernicus Marine Service
[57] and Stormglass [58] APIs.

TABLE I: The navigational variables and their data sources. Variable | Source | Variable | Source
---|---|---|---
Latitude | Onboard | WindSpeed_cps | Copernicus
Longitude | Onboard | WindDirection_cps | Copernicus
SpeedOverGround | Onboard | WaveHeight | Copernicus
HeadingMagnetic | Onboard | WaveDirection | Copernicus
Pitch | Onboard | WindSpeed_sg | Stormglass
Roll | Onboard | WindDirection_sg | Stormglass
WindSpeed_onb | Onboard | CurrentSpeed | Stormglass
WindDirection_onb | Onboard | CurrentDirection | Stormglass

###  III-B Data Preparation and Validation

The external weather data are past forecasts (hindcasts), which have
reanalysed to become hourly in temporal resolution and with 0.25 to 0.5 degree
as a spatial resolution. Trilinear interpolation in time and space dimensions
has been applied on external weather data to be more suitable for time and
position frames of the given vessel routing. Therefore, the weather and
onboard data are used in this analysis with a temporal resolution of 1-minute
in average.

The data validation is conducted through the cruising-speeds mode is to reduce
the other vessel effects on the fuel consumption, and thus, producing graphs
that can be then compared with the general ship’s standard performance. The
operational and weather data validation is carried out visually, as shown in
Figure 2.

(a) General data analytics for ship’s standard performance [59].

(b) Vessel Buro’s standard performance

Figure 2: Vessel’s data analytics and standard performance graph for the case
study

##  IV Methodology

Energy efficiency modeling and data clustering is a vital component of our
framework. The primary objective is to identify and sort the voyages based on
their efficiency scores. Then, train the models with the sorted data clusters
iteratively, to distill insights from the voyages with different behaviours.
Thus, the trained models will gain valuable insights into the performance and
operational patterns of the vessel.

###  IV-A Energy Efficiency Modeling

This part presents a mathematical and visual overview of the fundamental
theoretical background that forms the basis for modeling vessel energy
efficiency—an indispensable element within our comprehensive framework.

To estimate the vessel’s energy efficiency in this framework of voyage
optimization, we employed a previously developed model equipped with
artificial intelligence (XAI) and machine learning techniques. More details
about this energy efficiency modeling approach can be found in [60].

The efficiency score ($\mathrm{Eff_{score}}$) is calculated from the
normalized total fuel and time for every voyage, as following:

$\mathrm{Eff_{Score}}=1-\frac{2\times[Fuel_{Tl_{Nm}}\times
Time_{Tl_{Nm}}]}{[Fuel_{Tl_{Nm}}+Time_{Tl_{Nm}}]}$ (1)

The efficiency score considers the proportional reduction in both fuel
consumption and time, assessing the vessel’s efficient use of resources during
the voyage.

Figure 3 facilitates to visualize the process of aggregation for the vessel’s
voyages. First by illustrating the voyages in terms of space (i.e., latitude
and longitude) as shown in Figure 3(a), and second by representing the
aggregated voyages as points in new dimensions of Efficiency Score versus
total fuel and total time. The aggregated data and its new dimensions are
projected as in Figure 3(b).

(a) Vessel’s route.

(b) Data are projected by Efficiency Score vs. fuel and time.

Figure 3: The vessel voyages and the aggregated data projected by the
Efficiency Score.

The representation of voyages in terms of fuel and time is done by adopting
the concept of the Efficiency Score (Eff-Score). The efficiency scores for all
vessel’s voyages are presented in Figure 3(b). It is evident that the voyage
with lower fuel and shorter time have higher efficiency scores, and vice
versa.

Data: Voyages data of the vessel

Result: Clusters of Voyages

Load the operational and navigational data, including speed, course, fuel,
position, distance, and weather;

Tag the datapoints to its corresponding voyage, $V_{id}$;

foreach  _voyage $V_{i}$ in voyages data_ do

Calculate total fuel consumption and time for $V_{i}$;

Normalize total fuel and time for $V_{i}$ based on their maximum values of all
voyages;

Calculate the Eff-Score as described in Eq. (1), and assign it to all
datapoints of this voyage $V_{i}$;

Initialize four empty lists for each cluster: $Top75Pr$, $Top50Pr$, $Top25Pr$,
$Top10Pr$ (Percentiles of Eff-Scores);

foreach  _data point in all data_ do

Extract the Eff-Score of the data point;

if  _Eff-Score is in the top 75%_ then

Append the data point to $Top75Pr$;

else if  _Eff-Score is in the top 50%_ then

Append the data point to $Top50Pr$;

else if  _Eff-Score is in the top 25%_ then

Append the data point to $Top25Pr$;

else if  _Eff-Score is in the top 10%_ then

Append the data point to $Top10Pr$;

Algorithm 1 Modeling of Energy Efficiency and Clustering of Voyages Data Based
on Their Energy Efficiency

There are four voyage data clusters, namely $Top75Pr$, $Top50Pr$, $Top25Pr$,
and $Top10Pr$, as shown in Figure 4, These clusters are categorized on their
respective Eff-Score percentiles, enabling a structured analysis of voyage
efficiency across various percentile groups.

Figure 4: Four clusters of voyages based on their efficiency.

We introduced a data-driven approach for modeling of vessel energy efficiency,
by integrating data from various sources and employing explainable artificial
intelligence (XAI) and artificial neural network (ANN) to gain clear insights
into a vessel’s energy efficiency in SSS. For more details, refer to our
publication [60].
The workflow for modeling of vessel energy efficiency is shown in Figure 5.

Figure 5: Workflow of modeling and analysis of energy efficiency in short-sea
shipping

###  IV-B Framework of Voyage Optimization

One of the main objective of this paper is to improve the vessel voyage by
optimizing its speed to enhance the vessel’s energy efficiency. In other
words, reducing the vessel’s fuel consumption within constrained arrival time.
More details about the voyage optimization approach can be found in [61].
The framework of the developed approach for improving the vessel voyages is
depicted in Figure 6.

Figure 6: Framework of vessel voyage optimization.

For the purpose of vessel voyage optimization, we need a model to optimize the
vessel’s speed profile for improving the vessel’s energy efficiency. This
ideal model should mainly be able to:

  * •

Model the temporal dependencies in vessel speed profiles.

  * •

Incorporate external variables, such as weather conditions, into the modeling
process.

  * •

Adapt to changing conditions to provide real-time optimized speed profiles.

In order to meet these requirements, we adopt several time-series analysis
models, specifically they are: Long Short-Term Memory (LSTM), k-Nearest
Neighbors (kNN), 1-Nearest Neighbor with Dynamic Time Warping (1NN-DTW), and
Hidden Markov Model (HMM). These models are described with some details as
follow.

####  IV-B1 Long Short-Term Memory (LSTM)

It is a type of recurrent neural network (RNN) architecture designed for
sequential data analysis. It is particularly useful for modeling and
predicting time-series data, making it a valuable tool for improving energy
efficiency in vessel operations [62].
LSTM networks are well-suited for tasks involving time-series sequences of
varying lengths, capturing long-term dependencies, and handling irregular
temporal patterns. The LSTM architecture deals specifically to address the
problem of vanishing gradients that often occurs in other RNN structures [63].

The LSTM’s capability to learn the hidden insights from selected data,
particularly in terms of vessel’s efficiency scores, comes with a trade-off.
The data clustering may result in a smaller dataset, which potentially
limiting the LSTM’s deep learning capabilities. Additionally, data clustering
increases the susceptibility of LSTM to overfitting.
LSTM can be employed to model and predict the vessel’s speed to improve its
fuel efficiency, taking into account various factors such as weather
conditions and operational parameters

####  IV-B2 k-Nearest Neighbors (kNN)

The kNN algorithm is a non-parametric model that makes no assumptions and
operates on the principle of determining an unknown observation’s class by
measuring distances to nearby observations, attributing the observation to the
majority class of its nearest neighbors. The parameter k represents the number
of neighboring observations considered when classifying a given observation,
and its value is determined through a search for the optimal choice that
maximizes accuracy in the training set.

The paper by Cover and Hart [64] is a foundational work in pattern recognition
and machine learning, introduced the KNN algorithm for pattern classification
by utilizing the nearest neighbors to classify data points based on majority
vote.

KNN can be employed to analyze and predict energy consumption patterns based
on similar historical data. By considering the nearest neighbors of a given
operational scenario, KNN provides a straightforward approach to making
energy-efficient decisions. The choice of the parameter ’k,’ representing the
number of neighbors, plays a crucial role in the accuracy of KNN-based models.

####  IV-B3 1-Nearest Neighbor with Dynamic Time Warping (1NN-DTW)

This model is a distinctive variant of kNN with (k=1) and with a distance-wise
measure that utilizes Dynamic Time Warping (DTW) algorithm for a comparison of
two time-series sequences that may have different lengths, time shifts, and
speed variations [65, 66, 67, 68, 69]. The 1NN-DTW algorithm can be utilized
to measure the similarity between the given speed profile and other measured
vessel speed profiles with higher efficiency scores. 1NN-DTW is capable to
capture the temporal dependency of speed profiles, even in short-sea shipping
where the options of control the ship to improve its energy efficiency are
limited.

Thus, the 1NN-DTW identifies the efficient observed speed profile that most
similar to the given speed profile to be chosen as suggested an optimized
speed profile for the current journey of the vessel that can lead to improved
energy efficiency.

####  IV-B4 Hidden Markov Model (HMM)

This model is based on probabilistic modeling and use a variety of techniques
from the statistical modeling, and they are widely used in time-series
analysis and pattern recognition.
The work by Rabiner in 1989 [70] is an essential reference in the application
of HMM. This tutorial delved into the formulation of a statistical method for
representing speech, showcasing a successful HMM system implementation with a
focus on discrete or continuous density parameter distributions.

In the context of improving energy efficiency in constrained environments,
HMMs can be applied to model the underlying patterns and transitions in ship
operational data, allowing for more informed decisions on optimizing energy
consumption.
The HMM estimates three main weather states and dynamically adjusts the
SpeedOverGround (SOG) predictions. During calm weather, it selects the maximum
observed speed in the historical data at that condition. In moderate
conditions, it uses the average speed, while in rough weather, it relies on
the minimum speed profiles. For instance, Eq. 2 indicates that the predicted
speed (SOG${}_{\text{Pred}_{i}}$) by HMM is the minimum value of measured
speed profiles in rough weather state, and likewise for other weather states.

$SOG_{\text{Pred.}_{i}}=\min(SOG_{\text{Meas.}}\,|\,\text{Rough weather})$ (2)

This adaptability to changing weather conditions enhances voyage optimization,
making it a crucial component of the overall framework.

###  IV-C Framework of Path Identification

The theoretical background and description of the underling methodology of our
proposed framework are covered within this section. Additional details about
the framework of path identification can be found in [71].
The framework of vessel path identification is depicted in Figure 7.

(a)

(b)

Figure 7: Framework of vessel path identification. (a) Flowchart of distance-
based method. (b) Flowchart of segmented Gaussian likelihood method.

####  IV-C1 Problem Formulation

The equations (3-5) serve as a mathematical representation to describe the
clustering of vessel paths.
It is worth mentioning that the clustering process is conducted sequentially,
point by point, while the labeling of path clusters is performed for the
entire voyage. Therefore, each voyage has a single label of path cluster.

$Voyages\in Path\ Clusters\\\ $ (3)
$Voyages=\\{ts_{1}[p_{1},\dots,p_{n}],\dots,ts_{j}[p_{1},\dots,p_{n}]\\}\\\ $
(4) $Path\ Cluster\ Set=\\{cluster_{1},\dots,cluster_{k}\\}$ (5)

where:
$Voyages$: a collection of time series, each representing a voyage of the
vessel taken following a given path, with a predicted cluster.
$ts_{j}$: a time series corresponding to voyage $j$, i.e., a sequence of $n$
data points, where each data point $p$ represents the vessel position and is
defined by a pair of coordinates, namely latitude and longitude.
$n$: the number of time steps (duration) of each voyage, which can differ from
one voyage to another.
$j$: a total number of voyages.
$Path\ Cluster\ Set$: a set of $k$ clusters into which the path of voyages are
being clustered.

Remark: In the definition of $k$ clusters, it is important to clarify that
this study is for labeling or identifying predefined fairways for vessels
navigating in confined waters rather than open sea, resulting in a
predetermined number of path clusters, $k$.

####  IV-C2 Distance-Based Method

The similarity between two paths is measured by the average nearest neighbor
distance (ANND), as shown in Eq. (6).

$ANND(i,j)=\frac{1}{n_{i}}\sum_{k=1}^{n_{i}}Distance(P_{i}^{k},NN(P_{j}^{k}))$
(6)

where:
$ANND(i,j)$: is the average nearest neighbor distance between path $i$ and
path $j$, present in the distance matrix at row $i$ and column $j$. It is a
symmetric, meaning that $ANND(i,j)$ is the same as $ANND(j,i)$
$Distance(P_{i}^{k},NN(P_{j}^{k}))$ : The distance between the $k^{th}$ point
in path $i$, denoted as $P_{i}^{k}$, and its corresponding nearest neighbor
point in path $j$, indicated as $NN(P_{j}^{k})$. $n_{i}$ is the total number
of points in path $i$.
The measure $Distance$ is an Euclidean distance. However, for longer curved
routes, Haversine or Great-circle distance would be more suitable.

The ANND, as expressed in Eq. (6), is computed by averaging the distances
between each point in one path and its nearest neighbor in the other path.
Then, the similarity value (i.e., ANND) of this pair of paths is stored as an
element in the distance matrix.
A lower ANND indicates that the paths within a cluster are more similar. The
distance matrix will have dimensions $(m\times m)$ , where $m$ is the number
of paths.
For instance, the computed distance matrix for a set of 12 paths is
illustrated in Figure 8.

After the construction of the distance matrix, the machine learning (ML)
technique is applied to cluster the paths based on their corresponding values
in this distance matrix. The ML techniques that we used are k-means, Gaussian
Mixture Model (GMM), and hierarchical clustering.

Figure 8: Heatmap of the distance matrix for 12 paths of Cinderella II vessel.

####  IV-C3 Segmented Gaussian Likelihood Method

In addition to identifying the vessel’s path, to better understand how the
vessel changes its paths, we employ Gaussian distributions on several distinct
segments of the vessel route. This technique can be summarized as follows:

  * •

Utilize a training dataset comprising vessel position information that should
adequately represent all potential paths of the vessel route.

  * •

Divide the route into different distinct segments.

  * •

Train a single GMM model for each segment to find the Gaussian distributions
of all segments of the route.

  * •

Estimate likelihoods of the segments by using the trained GMM models with
their corresponding segments of each vessel voyage in the test dataset.

  * •

Label the path clusters based on the estimated likelihood at the unique
segments of the route.

##  V Implementation of Frameworks

In this section, we present specific case studies demonstrating how the
frameworks of the paper, applied with real-world data, provide practical
insights and solutions.

###  V-A Case Study of Voyage Efficiency Modeling and Optimization

The implementation of our approach of a time-series analysis-based voyage
optimization framework for a fixed-route vessel of our case study is depicted
in Figure 6, and the step-by-step process is described by algorithms 1 and 2.
In this case study, we utilized a dataset collected from a passenger ship
named Buro, which operates in Sweden. The dataset from the vessel Cinderella
II was also available; however, it was not utilized for vessel voyage
optimization. This decision was made due to the dataset’s duration being
limited to five months, encompassing only the summer and autumn seasons. As a
result, it does not cover the full spectrum of seasonal variability in weather
impacts.
For more detailed information about setting up the models and their
specifications including various parameters, you may refer to the source
codes, which are developed in Python 3.9.7 to produce the results of this
study. These source codes are available at:
https://github.com/MohamedAbuella/TSA4EESSS.

Data: Refer to Algorithm 1 for data processing and clustering.

Add SOG${}_{\text{Meas.}}$ and Weathers to Inputs.

foreach  _$C_{k}$ in CT (sorted by Eff-Score)_ do

foreach  _model in [LSTM, kNN, 1NN-DTW, HMM]_ do

Train model with voyages in $C_{k}$;

foreach  _Voyage $v_{i}$ in test dataset $\notin C_{k}$ _ do

if  _model is LSTM_ then

Predict SOG${}_{\text{Pred.}_{i}}$ using trained LSTM;

else if  _model is kNN_ then

Predict SOG${}_{\text{Pred.}_{i}}$ using trained kNN;

else if  _model is 1NN-DTW_ then

Predict SOG${}_{\text{Pred.}_{i}}$ based on the most similar voyage in
$C_{k}$;

else if  _model is HMM_ then

Predict SOG${}_{\text{Pred.}_{i}}$ based on weather states (Calm, Moderate,
Rough);

Estimate efficiency for SOG${}_{\text{Meas.}_{i}}$ and
SOG${}_{\text{Pred.}_{i}}$;

Evaluate efficiency gains for test voyages;

Algorithm 2 Speed Optimization Models for Improving Voyage Efficiency

###  V-B Case Study of Path Identification

In this section, we describe the case study, including the data collection,
preprocessing, and analysis.

In this study, we utilized datasets collected from two passenger ships, named
Cinderella II and Buro, operating in Sweden. The vessels are shown in Figure
9, additional information about vessels Cinderella II and Buro can be found in
[72].

Cinderella II operates in Stockholm archipelago, east of Sweden. The data of
Cinderella II spans over five months (July to November 2022). It comprises
information on 124 voyages of this vessel, connecting the two main ports of
Vaxholm in the east and Sodra in the west.

While Buro works in Gothenburg, west of Sweden. It dataset has been gathered
over a period of 15 months (between January 2020 and March 2021). The data of
Buro has 1755 voyages, between two main ports, Groto in the south and Ockero
in the northwest.

(a) Cinderella II.

(b) Buro.

Figure 9: Images of two vessels that are used in the case study [72].

(a) Cinderella II route.

(b) Five clusters of path.

(c) Buro route.

(d) Three clusters of path.

Figure 10: Routes of the two vessels beside their all possible path clusters,
which will be identified by applying proposed framework.

In our approach, we emphasize the significance of data representation. As a
result, we group the path points based on their timestamps with a resolution
of one second and store these grouped path points with distinctive Voyage IDs.
The routes of Cinderella II and Buro, along their chosen paths, are depicted
in Figure 10. Path cluster distribution for both vessels are illustrated by
the histograms in Figure 11.

Afterward, these paths are ready to be processed by the path clustering
approach to determine the overall path cluster.

(a) Distribution of Cinderella II voyages across the
five path clusters.

(b) Distribution of Buro voyages across the three
path clusters.

Figure 11: Distribution of voyages if both vessels across the the path
clusters.

For further details regarding the identification framework, the reader may
refer to the source codes employed to produce the case study results. These
codes are accessible at: https://github.com/MohamedAbuella/Path_Clustering.

##  VI Results and Discussion

The vessel has a fixed-route which starts from the southern port to the
northern port or vice versa. This route can be divided into four segments,
specifically North, Middle, South, and Direct, as depicted in Figure 3(a).
Cruising speeds are more common in North, South, and Direct segments of the
vessel’s route. Meanwhile, in the Middle segment, the vessel typically
operates at maneuvering speeds, due to the presence of two ports located on
west and east sides of the canal.

###  VI-A Statistical Analysis

We have first conducted a statistical analysis on the dataset. Figure 12
illustrates some important statistic for all aggregated voyage, with regard to
the accumulated fuel, time, and distance at different route segments. These
statistics represent the routes of vessel Buro, as depicted in Figure 10.

Figure 12: Barplots for statistics of Fuel, Time, and Distance in different
route segments, for vessel Buro.

As it can be seen from Table II, the difference of fuel consumption of the and
cruising speeds is 5.47%, so that and also based on the recommendations from
domain experts in compliance with maritime regulations including safety and
traffic considerations, it might be more practical to primarily focus on
optimizing cruising speed.

TABLE II: Statistics of the dataset for different speed modes Variable | Speeds | Difference (%)
---|---|---
All | Cruising
Fuel, total (Liter) | 1329.2 | 1256.62 | 5.47%
Time, total (Hour) | 48.04 | 22.32 | 53.57%
Distance, total (km) | 608.72 | 349.2 | 42.68%
Speed, average (m/s) | 2.67 | 1.67 | 37.5%

###  VI-B Modeling of Energy Efficiency

The first step in optimizing the model is to identify the best set of input
parameters. We consider four cases of ANN inputs, where each case consists of
different combinations of operational and weather variables. Further details
about these ANN input cases are provided in Tables III and I.

TABLE III: Description of the four input cases of ANN. Inputs Case |  Operational Variables | Weather Variables
---|---|---
|  | onboard data | external sources
I |  Vessel’s location, speed, and direction are used for all cases | wind | —
II | — | wind, wave, and current
III | wind | wave and current
IV | wind | wind, wave, and current

The Beeswarm plot in Figure 13(b) indicates that the vessel’s location has the
most significant impact on the Efficiency Score. Therefore, a spatial analysis
was conducted to identify the impact of various combinations of operational
and weather variables on the Efficiency Score concerning the vessel’s
location.

(a) Model’s output is EngineFuelRate, ($R^{2}$=0.7615)

(b) Model’s output is Efficiency Score, ($R^{2}$=0.8324)

Figure 13: Beeswarm plots of SHAP values for XGBoost regression model with
different outputs

The results are shown as heatmaps in Figure 14, revealing that the direct
route from south to north or vice versa, located on the open sea, is
particularly susceptible to the impact of weather conditions. Thus, for this
direct section of vessel routes, the estimation of Efficiency Score, as shown
in Figure 14(b), has the highest accuracy with different input combinations.

Meanwhile, in the north section, where strong either head or tail wind is more
frequent (in this area, west winds dominate) with respect to the vessel route,
the Efficiency Score estimation has the second highest accuracy, as in Figure
14(b).

In the other case, when it comes to estimating EngineFuelRate, as shown in
Figure 14(a), the results are not accurate. For instance, the direct sections
of the route are not achieving the highest accuracy, even though they are
supposed to experience more weather conditions than other sections due to
these sections being the most similar to an open sea.

(a) EngineFuelRate

(b) Efficiency Score

Figure 14: Results ($R^{2}$) for ANN regression with EngineFuelRate and
Efficiency Score as outputs across different input cases in relation to
varying vessel’s route sections.

###  VI-C Improving Voyage Efficiency

After that we have implemented the framework for improving the vessel’s energy
efficiency, as presented in Section IV-B. Then, we evaluate the results, and
for a sake of a fair comparison, we are injected both the actual measured and
optimized speed profiles into the same estimation model of energy efficiency
to predict fuel and time before and after the improving framework of energy
efficiency is being implemented. Once the fuel and time estimated, we compute
the efficiency to determine how much energy has been saved.

One of our main metrics to evaluate the model performance of voyage efficiency
optimization is the gain of efficiency scores, as represented in (7).

$Eff._{Gain}=\frac{Eff.Score_{{Pred.}}-Eff.Score_{Meas.}}{Eff.Score_{Meas.}}\times
100$ (7)

Where $Eff.Score_{{Meas.}}$ and $Eff.Score_{{Pred.}}$ represent the voyage
efficiency obtained with measured and predicted speed profiles, respectively.

TABLE IV: Average efficiency gains (Eff. Gains %, see Eq. 7) and counts of improved voyages (IV Count #) out of 162 voyages in the test dataset. Cluster | Efficiency Score | LSTM | kNN | 1NN-DTW | HMM
---|---|---|---|---|---
Top10Pr | Eff. Gains (%) | 2.61 | 2.13 | 3.20 | 6.05
IV Count (#) | 134 | 114 | 127 | 139
Top25Pr | Eff. Gains (%) | 2.38 | 1.58 | 3.23 | 1.30
IV Count (#) | 129 | 107 | 128 | 107
Top50Pr | Eff. Gains (%) | 0.97 | 0.98 | 2.58 | 7.34
IV Count (#) | 100 | 106 | 117 | 140
Top75Pr | Eff. Gains (%) | -0.84 | 0.50 | 2.28 | 9.31
IV Count (#) | 60 | 93 | 119 | 141
Average | Eff. Gains (%) | 1.28 | 1.30 | 2.82 | 6.00
IV Count (#) | 105.75 | 105.00 | 122.75 | 131.75
TABLE V: Average and deviation of gains (%) of Eff-Scores in three weather states, when models are trained with the four data clusters Model | LSTM | kNN | 1NN-DTW | HMM
---|---|---|---|---
Weather | Avg | Std | Avg | Std | Avg | Std | Avg | Std
Calm | 0.17 | 4.72 | 1.17 | 3.29 | 2.21 | 4.30 | 3.96 | 6.19
Moderate | 1.53 | 4.12 | 1.26 | 4.19 | 3.4 | 4.47 | 5.33 | 6.56
Rough | 1.94 | 3.48 | 1.42 | 3.65 | 2.84 | 4.90 | 8.17 | 9.08
Average | 1.21 | 4.11 | 1.28 | 3.71 | 2.82 | 4.56 | 5.82 | 7.28

As shown in Table IV, the HMM model achieves the highest average efficiency
gain of 6.00%, followed by the 1NN-DTW model (2.82%), the kNN model (1.30%),
and the LSTM model (1.28%). In terms of the number improved voyages out of 162
voyages in test dataset, the HMM model also improves the energy efficiency of
the most average number of improved voyages (131.75 out of 162 voyages).

The HMM model achieves its best performance when trained on the Top75Pr
cluster, which includes voyages with lower Eff-Scores and frequently
encountered adverse weather conditions. Such performance underscores the HMM
model’s capability to learn the hidden patterns between the vessel speed and
weather states, ultimately facilitates for developing more efficient speed
profiles.

(a) LSTM-based model

(b) kNN-based model

(c) 1NN-DTW-based model

(d) HMM-based model

Figure 15: Predicted speed profile for a test voyage. From four time-series
based models incorporate weather data as inputs and are trained by Top10Pr
cluster.

(a) LSTM-based model

(b) kNN-based model

(c) 1NN-DTW-based model

(d) HMM-based model

Figure 16: Sorted Eff-Scores based on their gain, for 162 test voyages. From
four time-series based models incorporate weather data as inputs and are
trained by Top10Pr cluster, $Eff._{\text{Gain}}$ as in Eq. 7.

We also present the results by plots illustrating the predicted speed profiles
for a test voyage, which are generated by four time-series based models that
incorporate weather data as inputs. These models were trained using data from
the Top10Pr cluster.

In summary, the HMM-based model is the most effective model for improving
energy efficiency for a vessel voyage in short sea. The HMM model is able to
learn the complex relationships between the input features (e.g., speed and
weather) and the output feature (Eff-Score), even in different weather
conditions.

###  VI-D Path Identification

In this section, we present the results of our spatial clustering approach for
vessel path identification and discuss the implications of these findings. The
approach involved the utilization of position information and various
clustering techniques, specifically k-means, hierarchical clustering, and
Gaussian distributions clustering to the paths of two vessels, Buro and
Cinderella II. These vessels operate in distinct locations, leading to diverse
datasets.

####  VI-D1 Evaluation Metrics for Path Clustering

The results of vessel path identification are evaluated through visual
inspection and tabulation using metrics such as confusion matrix, precision,
recall, and F1-score [73].

The hits and messes of path clustering are presented by the confusion matrix.
For our results of path clustering, the confusion matrix is a one-vs-one type
matrix. Then, the confusion matrix is converted into a one-vs-all type matrix
(binary-class confusion matrix) as shown in Eq. (8), for calculating class-
wise metrics like precision, recall, and F1-score.

$\begin{array}[]{c|cc}&\text{Pred. Pos.}&\text{Pred. Neg.}\\\
\hline\cr\text{Act. Pos.}&\text{TP }&\text{FN }\\\ \text{Act. Neg.}&\text{FP
}&\text{TN }\end{array}$ (8)

where True Positives (TP), False Positives (FP), True Negatives (TN), and
False Negatives (FN) are determined by comparing the predicted (Pred.) and
actual (Act.) path clusters.

The confusion matrix transformation involves considering one class as positive
at a time, while combining all other classes as negative. This process is
repeated iteratively for each class, resulting in multiple binary-class
confusion matrices.

The following performance metrics were used:

  * •

Precision: the ratio of true positives to the total number of predicted
positives.

  * •

Recall: the ratio of true positives to the total number of actual positives in
the data.

  * •

F1-score: the harmonic mean of precision and recall.

The equations for precision, recall, and F1-score are shown in Eqs. (9), (10),
and (11).

$Precision=\frac{TP}{TP+FP}$ (9)

$Recall=\frac{TP}{TP+FN}$ (10)

$F1\text{-}score=2\times\frac{(Precision\times Recall)}{(Precision+Recall)}$
(11)

####  VI-D2 Results of Path Clustering for Cinderella II Vessel

Table VI shows the results of applying k-means or Gaussian Mixture Model (GMM)
models to identify the vessel paths from the distance matrix in the distance-
based method of the path identification approach. Notably, the paths with
clusters of North-West, South, and South-West achieved an F1-score of 1.0,
indicating that the approach correctly identified all the paths of these
clusters.

In contrast, the North-East and North-Middle paths exhibited lower F1 scores
compared to other clusters. The path cluster of North-Middle is the most
challenging path to identify since six such paths have been clustered as
North-East, as can be seen by comparing Figures 17 and 18, which are the
visualization for all the paths, color-marked based on their ground truth
clusters. Figure 19 illustrates the probability distribution of mis-clustered
paths with respect to latitude and longitude coordinates. It is obvious that
these paths have nearly identical coordinates, which makes them challenging
paths to cluster with k-means or GMM. This suggests that there is still room
for improvement by using other ML clustering methods.

Table VII presents the results of employing hierarchical clustering to the
distance matrix in the distance-based method for clustering the vessel paths.
In hierarchical clustering, there is a parameter called ”Dendrogram Cut-off
threshold,” and its value should be selected depending on the number of path
clusters. Hence, as illustrated in Figure 20, this parameter is denoted by the
Y-axis as a clustering height, and its value is set to 100 for clustering the
vessel path into five clusters.

Remarkably, all path clusters achieved an F1-score of 1, indicating that
hierarchical clustering successfully identified all paths with high accuracy
from the distance matrix using the distance-based method. This suggests that
the choice of ML clustering technique with the distance matrix can influence
the accuracy of path identification. Table VII displays the outcomes of
clustering, now by applying the segmented likelihood Gaussian method. This
method achieved perfect precision, recall, and F1-score for all path clusters.
Figures 21, 22, and 23 present visualizations for the segmented Gaussian
likelihood method.

The accuracy in results by hierarchical and segmented Gaussian likelihood
clustering for path clusters indicates the efficacy of the developed approach
of spatial clustering for vessel path identification.

Figure 17: Display of the five clusters of path for Cinderella II vessel,
(ground truth). TABLE VI: Result of implementing of both k-means and GMM
clustering of the paths of Cinderella II vessel to five clusters.

(a) Precision, Recall, and F1-score Paths | Precision | Recall | F1-score
---|---|---|---
North-East (NE) | 0.7 | 1 | 0.824
North-Middle (NM) | 1 | 0.85 | 0.919
North-West (NW) | 1 | 1 | 1
South (S) | 1 | 1 | 1
South-West (SW) | 1 | 1 | 1

(b) Confusion Matrix Actual | Predicted | Total
---|---|---
NE | NM | NW | S | SW
NE | 14 | 0 | 0 | 0 | 0 | 14
NM | 6 | 34 | 0 | 0 | 0 | 40
NW | 0 | 0 | 16 | 0 | 0 | 16
S | 0 | 0 | 0 | 52 | 0 | 52
SW | 0 | 0 | 0 | 0 | 2 | 2
Total | 20 | 34 | 16 | 52 | 2 | 124

Figure 18: Results of both k-means and GMM clustering to five path clusters
for Cinderella II. Figure 19: Probability distribution of location coordinates
for mis-clustered paths of Cinderella II by both k-means and GMM. Figure 20:
Results of hierarchical clustering the paths of Cinderella vessel to five
clusters. TABLE VII: Result of implementing both hierarchical clustering and
segmented likelihood Gaussian clustering of paths for Cinderella II vessel
into five clusters.

(a) Precision, Recall, and F1-score Paths | Precision | Recall | F1-score
---|---|---|---
North-East (NE) | 1 | 1 | 1
North-Middle (NM) | 1 | 1 | 1
North-West (NW) | 1 | 1 | 1
South (S) | 1 | 1 | 1
South-West (SW) | 1 | 1 | 1

(b) Confusion Matrix Actual | Predicted | Total
---|---|---
NE | NM | NW | S | SW
NE | 14 | 0 | 0 | 0 | 0 | 14
NM | 0 | 40 | 0 | 0 | 0 | 40
NW | 0 | 0 | 16 | 0 | 0 | 16
S | 0 | 0 | 0 | 52 | 0 | 52
SW | 0 | 0 | 0 | 0 | 2 | 2
Total | 14 | 40 | 16 | 52 | 2 | 124

Figure 21: Distribution of the route of Cinderella II into eight segments.
Figure 22: Probability distributions of location coordinates for the eight
segments of the route of Cinderella II. Figure 23: Gaussian distributions for
seven segments of Cinderella II vessel route.

####  VI-D3 Results of Path Clustering for Buro Vessel

In this part the results from applying the framework of both hierarchical
clustering and segmented likelihood Gaussian clustering of Buro vessel paths
to three clusters. Following a similar evaluation procedure as in the case of
Cinderella II vessel.

Figure 24: Results of hierarchical clustering to three path clusters of Buro
vessel. TABLE VIII: Result of Buro vessel by implementing hierarchical
clustering to three path clusters

(a) Precision, Recall, and F1-score Paths | Precision | Recall | F1-score
---|---|---|---
Direct | 1 | 1 | 1
East_Canal | 0.917 | 1 | 0.957
West_Canal | 1 | 0.993 | 0.996

(b) Confusion Matrix Actual | Predicted | Total
---|---|---
Direct | E-C | W-C
Direct | 62 | 0 | 0 | 62
E-C | 0 | 122 | 0 | 122
W-C | 0 | 11 | 1560 | 1571
Total | 62 | 133 | 1560 | 1755

Figure 25: Distribution of the route of Buro vessel into seven segments.
Figure 26: Probability distributions of location coordinates for the seven
segments of the route of Buro vessel. Figure 27: Gaussian distribution for
seven segments of the route of Buro vessel. TABLE IX: Result of Buro vessel by
implementing segmented likelihood Gaussian clustering to three path clusters

(a) Precision, Recall, and F1-score Paths | Precision | Recall | F1-score
---|---|---|---
Direct | 1 | 1 | 1
East_Canal | 1 | 1 | 1
West_Canal | 1 | 1 | 1

(b) Confusion Matrix Actual | Predicted | Total
---|---|---
Direct | E-C | W-C
Direct | 62 | 0 | 0 | 62
E-C | 0 | 122 | 0 | 122
W-C | 0 | 0 | 1571 | 1571
Total | 62 | 122 | 1571 | 1755

As it can be seen, the results of likelihood Gaussian clustering also achieved
F1-score of 1, as in Cinderella vessel. But for the hierarchical clustering in
Buro vessel case has F1-scores of 0.957 and 0.996 for clustering East_Canal
and West_Canal paths respectively. This results can be considered remarkable
when take into account that these two paths, East_Canal and West_Canal, are
challenging to be clustered, since they have several paths that are slightly
different form each other. Figure 28 shows the heatmap of the distance matrix
of 12 sample paths for Buro vessel. Notably, the East_Canal and West_Canal
paths exhibit high similarity, which make not easy clustering task.

Choosing a proper value of the agglomerative threshold for the hierarchical
clustering to get the three clusters, as shown in Figure 24, with an
agglomerative threshold = 4.7.

Figure 28: Heatmap of the distance matrix for 12 paths of Buro vessel.

##  VII Conclusion

In this section, we present briefly the key findings of this paper and provide
recommendations for future research or practical implications for the maritime
industry.

###  VII-A Modeling and Improving Voyage Energy Efficiency

  * •

The modeling approach by using the Efficiency Score, instead of directly
working with the EngineFuelRate onboard signal, is more effective in
facilitating decision-making.

  * •

The resulting model is based on a more comprehensive understanding of the
critical factors that impact fuel consumption, both temporally and spatially,
resulting in more dependable counterfactual predictions.

  * •

The quantitative evaluation indicates that estimating the Efficiency Score
produces more precise and less biased outcomes than estimating the measured
EngineFuelRate.

  * •

The study employs four distinct models: LSTM, kNN, 1NN-DTW, and HMM, to
optimize vessel speed profiles with the objective of enhancing energy
efficiency in short sea voyages. The key observation is that model performance
varies significantly across these algorithms. However, the performance of the
models varies depending on the data cluster used to train the model and the
weather conditions.

  * •

We developed a data-driven framework for optimizing vessel speed profiles to
improve energy efficiency in SSS. The framework integrates a data-driven
modeling approach to energy efficiency with the 1NN-DTW algorithm. We
evaluated the added value of the framework using a real-world dataset and
found that it can effectively improve vessel energy efficiency, especially
with limited options, which are common in short-sea shipping.

  * •

1NN-DTW exhibits the ability to capture temporal dependencies within speed
profiles, especially within the constraints of short-sea shipping where
opportunities for actively controlling the vessel to enhance its energy
efficiency are restricted

  * •

Although the kNN can handle multivariate data and incorporating additional
features like weather conditions, in this case study, the 1NN-DTW performs
better due to its specialized handling of time-dependent data and inherent
patterns.

  * •

The result findings emphasize that in terms of searching the best behavior of
vessel from the observed data, the 1NN-DTW exhibits superior performance
compared to LSTM and kNN, since the 1NN-DTW selects the best measured speed
profiles. On the other hand, the HMM is the most effective approach in our
study. where the HMM optimizes these measured speed profiles further by
offering strategies to them informed by their weather states.

  * •

The study also reveals that the HMM model exhibits notable adaptability to
different weather states (Calm, Moderate, and Rough). In each weather state,
the HMM consistently delivers efficiency gains, indicating its ability to
adapt speed profiles according to varying environmental conditions. This
adaptability is crucial for real-world maritime applications, where weather
can change rapidly.

###  VII-B Vessel Path Identification

  * •

The approach is able to identify the vessel paths with partially defined or
unknown paths.

  * •

In the distance-based method, the hierarchical clustering used in the approach
outperforms k-means and GMM clustering techniques.

  * •

The approach of hierarchical clustering includes a user-customized, a cut-off
threshold, which allows desired control for the number of path clusters,
enhancing the flexibility and adaptability of the proposed approach.

  * •

In the distance-based method, adopting ANND as a measure of similarity makes
path clustering less affected by noise or outliers and provides a more
intuitive interpretation of path similarity, ultimately enhancing the
robustness and interpretability of our approach.

  * •

The segmented Gaussian likelihood method is particularly useful for
identifying and analyzing the vessel path alterations at different segments of
the vessel route.

  * •

The proposed approach is computationally efficient and has the potential to be
a valuable tool for planning vessel paths. Accurate path identification can
contribute to safer and more efficient maritime transportation practices,
aiding in route planning, collision avoidance, and navigation optimization.

  * •

Nevertheless, the framework has some potential limitations, such as the
segmented Gaussian likelihood method exhibiting sensitivity to segment
definition which could affect its salable performance, particularly in complex
maritime scenarios. Moreover, while the study case demonstrates that the
framework is computationally efficient, it is essential to discuss any
potential scalability issues, especially when dealing with large datasets,
since the computational efficiency may vary depending on the dataset size and
the nature of paths.

###  VII-C Future work and Recommendations

Future work could include the following:

  * •

For modeling of vessel energy efficiency, considering spatial dimension, such
as distance variable, might be worth of investigation.

  * •

Including the use of heuristic algorithms such as genetic programming, for
optimizing voyage efficiency.

  * •

Exploring the scalability and real-world applicability of the proposed path
clustering approach, as well as its integration with related systems of
maritime transportation.

  * •

Applying incremental map-matching algorithms for real-time vessel path
identification.

  * •

Future research in path detection may involve the study of graph theory and
the application of evolutionary algorithms, including ant colony optimization.

## Acknowledgment

This research work has been funded and supported by Vinnova. We would like to
thank CetaSol AB for their support and for providing the resources necessary
to conduct this research.
We also wish to thank the diverse group at the Center for Applied Intelligent
Systems Research (CAISR), Halmstad University, for helpful discussions.

## Supplementary Materials

The source codes that are implemented on Python 3.9.7 to produce the results
are available at: https://github.com/MohamedAbuella/TSA4EESSS and
https://github.com/MohamedAbuella/Path_Clustering.

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|  Mohamed Abuella received his M.S. and PhD degrees in Electrical and
Computer Engineering from Southern Illinois University at Carbondale and
University of North Carolina at Charlotte, in 2012 and 2018 respectively. He
is a postdoctoral researcher at Halmstad University since 2022. His research
interests include energy analytics and AI for sustainability.
---|---
|  Hadi Fanaee-T is an Associate Professor at Halmstad University, Sweden. He
completed his PhD (with distinction) in Computer Science, under supervision of
Professor Joao Gama at the Faculty of Science of University of Porto, Portugal
in November 2015. He was the finalist in ERCIM Cor Baayen Young Researcher
Award 2017. Prior to this position he was a postdoctoral fellow at the
department of biostatistics, University of Oslo, Norway, and also worked as a
postdoctoral researcher in European FP7 Project ”MAESTRA” at INESC TEC
research institute, Portugal. His main research interests are
interdisciplinary applications of tensor decompositions, data fusion,
anomaly/event detection and spatiotemporal data mining. He is the first-author
of several journal and conference papers. He has served as a PC member to over
20 prestigious conferences (e.g. IJCAI, AAAI, ECML-PKDD, ISMIS, ACM SAC, IEEE
DSAA, etc.) and also reviewer to several high-impact journals (e.g. TDKE,
TKDD, DAMI, ML, KAIS, KBS, CSUR.
---|---
|  M. AMINE ATOUI obtained his Ph.D. degree from LARIS, Polytech’ Angers,
France, in 2015. Currently, he is affiliated with the Center for Applied
Intelligent Systems Research at Halmstad University, Sweden. His research
interests encompass probabilistic and explainable Machine Learning, causal and
Bayesian Inference, transmission/communication, and automatic control.
---|---
|  Slawomir Nowaczyk is a Professor in Machine Learning at the Center for
Applied Intelligent Systems Research, Halmstad University, Sweden. He received
his MSc degree from Poznan University of Technology in 2002 and his PhD from
the Lund University of Technology in 2008. During the last decades, his
research has focused on machine learning, knowledge representation, and self-
organising systems. The majority of his work concerns industrial data streams,
often with predictive maintenance as the goal. Given that accurate and
relevant labels are usually impossible to obtain in such settings, Slawomir’s
contributions primarily take advantage of proxy labels, such as transfer
learning and multi-task learning, or concern semi-supervised and unsupervised
modelling. He is a board member of the Swedish AI Society and a research
leader for the School of Information Technology at Halmstad University.
Slawomir has led multiple research projects on applying Artificial
Intelligence and Machine Learning in different domains, such as transport and
automotive, energy, smart cities, and healthcare. In most cases, this research
was done in collaboration with industry and public administration
organisations – inspired by practical challenges and leading to tangible
results and deployed solutions.
---|---
|  Simon Johansson is a MSc graduate of Chalmers University of Technology’s
program in Engineering Mathematics and Computational Science in 2020,
currently works in Cetasol, a marine company specialising in CO2 reduction and
energy optimisation for vessels. His practical application of computational
methods and dedication to environmental sustainability align with his role,
contributing to global efforts to mitigate climate change. Simon’s commitment
to advancing eco-friendly solutions in the marine industry reflects a seamless
integration of academic excellence and real-world impact.
---|---

|  Ethan Faghani is the CEO and founder of Cetasol. Before Cetasol, Ethan was
Chief Engineer of Automation and AI at Volvo Penta. Ethan has experience
working with cutting-edge technologies in other transportation segments in
both big enterprises and his own founded startup. Ethan obtained his Ph.D. in
mechatronics from UBC and Innovation and Entrepreneurship from Stanford
Business School.
---|---