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A parallel high-order discontinuous Galerkin shallow water model

Claes Eskilsson, Yaakoub El-Khamra, David Rideout, Gabrielle Allen, Q. Jim Chen & Mayank Tyagi

The depth-integrated shallow water equations are frequently used for simulating geophysical flows, such as storm-surges, tsunamis and river flooding. In this paper a parallel shallow water solver using an unstructured high-order discontinuous Galerkin method is presented. The spatial discretization of the model is based on the Nektar++ spectral/hp library and the model is numerically shown to exhibit the expected exponential convergence. The parallelism of the model has been achieved within the Cactus Framework. The model has so far been executed successfully on up to 128 cores and it is shown that both weak and strong scaling are largely independent of the spatial order of the scheme. Results are also presented for the wave flume interaction with five upright cylinders.

Computational Science / 2009
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paper

A practical AIS-based route library for voyage planning at the pre-fixture stage

Jie Cai*, Gang Chen, Marie Lützen, Niels Gorm Maly Rytter

In tramp shipping, a preliminary route is required for voyage planning at the pre-fixture stage (before a chartering contract is agreed). Such routes are conventionally designated by using pilot charts or software considering long-term statistical weather. However, it has been experienced by tramp operators that such route solutions often poorly estimated sailing distances for long journeys and thereby cause inappropriate cost estimation and bad voyage plan. To fill this gap, a data-driven methodology is proposed in this paper to establish a practical route library with the consideration of ship sizes, load conditions and seasonality. In this method, it first requires a dividing of ship trajectories into local sea passage and open sea passage. The voyage trajectories made of AIS points are then simplified to pattern nodes based on a speed-weighted geolocation method. Afterwards, the KMeans algorithm is deployed to properly classify these pattern nodes, identifying the most representative nodes (routes) in open sea passages. Simultaneously, the connection points are identified by DBSCAN algorithm, representing local sea passages. Combining the representative routes in open sea passages and the connection points in local sea passages, the most navigated routes between two ports are obtained. Finally, case studies are conducted for the Pacific Ocean and the Atlantic Ocean respectively using global AIS data from tanker vessels to demonstrate the feasibility and effectiveness of this methodology. The proposed route library is capable of providing reliable route references to support the decision-making at the pre-fixture stage.

Ocean Engineering / 2021
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paper

A practical data quality assessment method for raw data in vessel operations

Gang Chen, Jie Cai*, Niels Rytter, Marie Lützen

With the current revolution in Shipping 4.0, a tremendous amount of data is accumulated during vessel operations.
Data quality (DQ) is becoming more and more important for the further digitalization and effective decision-making
in shipping industry. In this study, a practical DQ assessment method for raw data in vessel operations is proposed.
In this method, specific data categories and data dimensions are developed based on engineering practice and existing
literature. Concrete validation rules are then formed, which can be used to properly divide raw datasets. Afterwards,
a scoring method is used for the assessment of the data quality. Three levels, namely good, warning and alarm,
are adopted to reflect the final data quality. The root causes of bad data quality could be revealed once the internal
dependency among rules has been built, which will facilitate the further improvement of DQ in practice. A case study
based on the datasets from a Danish shipping company is conducted, where the DQ variation is monitored, assessed
and compared. The results indicate that the proposed method is effective to help shipping industry improve the quality
of raw data in practice. This innovation research can facilitate shipping industry to set a solid foundation at the early
stage of their digitalization journeys.

Journal of Marine Science and Application / 2023
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paper

A practical data quality assessment method for raw data in vessel operations

Gang Chen, Jie Cai*, Niels Rytter, Marie Lützen

With the current revolution in Shipping 4.0, a tremendous amount of data is accumulated during vessel operations.
Data quality (DQ) is becoming more and more important for the further digitalization and effective decision-making
in shipping industry. In this study, a practical DQ assessment method for raw data in vessel operations is proposed.
In this method, specific data categories and data dimensions are developed based on engineering practice and existing
literature. Concrete validation rules are then formed, which can be used to properly divide raw datasets. Afterwards,
a scoring method is used for the assessment of the data quality. Three levels, namely good, warning and alarm,
are adopted to reflect the final data quality. The root causes of bad data quality could be revealed once the internal
dependency among rules has been built, which will facilitate the further improvement of DQ in practice. A case study
based on the datasets from a Danish shipping company is conducted, where the DQ variation is monitored, assessed
and compared. The results indicate that the proposed method is effective to help shipping industry improve the quality
of raw data in practice. This innovation research can facilitate shipping industry to set a solid foundation at the early
stage of their digitalization journeys.

Journal of Marine Science and Application / 2022
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paper

A Quantitative Parametric Study on Output Time Delays for Autonomous Underwater Cleaning Operations

Fredrik Fogh Sørensen*, Malte von Benzon, Jesper Liniger, Simon Pedersen

Offshore pipelines and structures require regular marine growth removal and inspection to ensure structural integrity. These operations are typically carried out by Remotely Operated Vehicles (ROVs) and demand reliable and accurate feedback signals for operating the ROVs efficiently under harsh offshore conditions. This study investigates and quantifies how sensor delays impact the expected control performance without the need for defining the control parameters. Input-output (IO) controllability analysis of the open-loop system is applied to find the lower bound of the H-infinity peaks of the unspecified optimal closed-loop systems. The performance analyses have shown that near-structure operations, such as pipeline inspection or cleaning, in which small error tolerances are required, have a small threshold for the time delays. The IO controllability analysis indicates that off-structure navigation allow substantial larger time delays. Especially heading is vulnerable to time delay; however, fast-responding sensors usually measure this motion. Lastly, a sensor comparison is presented where available sensors are evaluated for each ROV motion’s respective sensor-induced time delays. It is concluded that even though off-structure navigation have larger time delay tolerance the corresponding sensors also introduce substantially larger time delays.

Journal of Marine Science and Engineering / 2022
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paper

A representative model and benchmark suite for the container stowage planning problem

Agnieszka Sivertsen, Line Reinhardt & Rune Møller Jensen

Due to limited access to domain knowledge and domain-relevant benchmark data, the Container Stowage Planning Problem (CSPP) is notably under-researched. In particular, previous models of the CSPP have lacked two key aspects of the problem: lashing forces and paired block stowage. The former may reduce vessel capacity by up to 10%, and the latter is NP-hard. The Representative CSPP (RCSPP), which captures all critical aspects of the problem is formulated. The presented RCSPP incorporates overlooked constraints such as paired block stowage and lashing, along with an innovative method for estimating lashing forces, all while maintaining simplicity. A heuristic method, STOW, has been developed to identify solutions for the RCSPP using a specially designed benchmark suite based on real-world scenarios. STOW algorithm is an advanced search heuristic employing a diverse range of solution modification strategies, each tailored to address specific aspects of stowage optimization. Feasible solutions were successfully identified for all instances within the benchmark suite. Our initial findings emphasize the importance of accurately modeling lashing forces and employing paired block stowage. Results show that removing the lashing constraint can increase the number of containers stowed by over 7% on average, while disabling paired block stowage can result in nearly a 5% increase.

Transportation Research Part E: Logistics and Transportation Review / 2025
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paper

A representative model and benchmark suite for the container stowage planning problem

Agnieszka Sivertsen, Line Reinhardt & Rune Møller Jensen

Due to limited access to domain knowledge and domain-relevant benchmark data, the Container Stowage Planning Problem (CSPP) is notably under-researched. In particular, previous models of the CSPP have lacked two key aspects of the problem: lashing forces and paired block stowage. The former may reduce vessel capacity by up to 10%, and the latter is NP-hard. The Representative CSPP (RCSPP), which captures all critical aspects of the problem is formulated. The presented RCSPP incorporates overlooked constraints such as paired block stowage and lashing, along with an innovative method for estimating lashing forces, all while maintaining simplicity. A heuristic method, STOW, has been developed to identify solutions for the RCSPP using a specially designed benchmark suite based on real-world scenarios. STOW algorithm is an advanced search heuristic employing a diverse range of solution modification strategies, each tailored to address specific aspects of stowage optimization. Feasible solutions were successfully identified for all instances within the benchmark suite. Our initial findings emphasize the importance of accurately modeling lashing forces and employing paired block stowage. Results show that removing the lashing constraint can increase the number of containers stowed by over 7% on average, while disabling paired block stowage can result in nearly a 5% increase.

Transportation Research Part E: Logistics and Transportation / 2025
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paper

A review of reformed methanol-high temperature proton exchange membrane fuel cell systems

Na Li*, Xiaoti Cui, Jimin Zhu, Mengfan Zhou, Vincenzo Liso, Giovanni Cinti, Simon Lennart Sahlin, Samuel Simon Araya

The paper presents a comprehensive review of the current status of integrated high temperature proton exchange membrane fuel cell (HT-PEMFC) and methanol steam reformer (MSR) systems. It highlights the advantages and limitations of the technology and outlines key areas for future improvement. A thorough discussion of novel reformer designs and optimizations aimed at improving the performance of the reformer, as well as different integrated MSR-HT-PEMFC system configurations are provided. The control strategies of the system operation and system diagnosis are also addressed, offering a complete picture of the integrated system design. The review revealed that several processes and components of the system should be improved to facilitate large-scale implementation of the MSR-HT-PEMFC systems. The lengthy system startup is one area that requires improvements. A structural design that is more compact without sacrificing performance is also required, which could possibly be achieved by recovering water from the fuel cell to fulfill MSR's water needs and consequently shrink the fuel tank. Reformer design should account for both heat transfer optimizations and reduced pressure drop to enhance the system's performance. Finally, research must concentrate on membrane materials for HT-PEMFC that can operate in the 200–300 °C temperature range and catalyst materials for more efficient MSR process at lower temperature should be investigated to improve the heat integration and overall system efficiency.

Renewable and Sustainable Energy Reviews / 2023
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paper

A rich model for the tramp ship routing and scheduling problem—Solved through column generation

Alberto Tamburini, Nina Lange & David Pisinger

We consider the Tramp Ship Routing and Scheduling Problem (TSRSP) in which we plan routes for a fleet of tramp shipping vessels operating on a combined contract and spot market. Earlier research has been fragmented due to variations in the side constraints studied. Hence we present the first unified model that can handle speed optimization, chartering costs, bunker planning, and hull cleaning. The model is solved by column generation, where the columns represent the possible routes of a vessel, while the master problem keeps track of the binding constraints. The pricing problem is solved efficiently using a time–space graph and several dominance rules. Real-life instances with up to 40 vessels, 35 geographic regions, and four months planning horizon can be solved to optimality in less than half an hour. The optimized routes increase earnings by 7% compared to historical schedules. Furthermore, policy-makers can use the model as a simulation of a rational agent behavior.

Transportation Research Part E: Logistics and Transportation Review / 2025
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paper

A rich model for the tramp ship routing and scheduling problem—Solved through column generation

Alberto Tamburini, Nina Lange & David Pisinger

We consider the Tramp Ship Routing and Scheduling Problem (TSRSP) in which we plan routes for a fleet of tramp shipping vessels operating on a combined contract and spot market. Earlier research has been fragmented due to variations in the side constraints studied. Hence we present the first unified model that can handle speed optimization, chartering costs, bunker planning, and hull cleaning. The model is solved by column generation, where the columns represent the possible routes of a vessel, while the master problem keeps track of the binding constraints. The pricing problem is solved efficiently using a time–space graph and several dominance rules. Real-life instances with up to 40 vessels, 35 geographic regions, and four months planning horizon can be solved to optimality in less than half an hour. The optimized routes increase earnings by 7% compared to historical schedules. Furthermore, policy-makers can use the model as a simulation of a rational agent behavior.

Transportation Research Part E: Logistics and Transportation / 2025
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