Early-stage design assessment of loads such as vertical bending moments can be a critical quantity of interest for design exploration. Traditionally, classification societies’ rules are used to calculate such loads. However, relying solely on these rules for designing new vessels may be insufficient, and conducting direct analyses of a large number of designs to support design exploration is computationally infeasible. Currently, key factors such as wave-induced loads are typically evaluated only in later design stages, where a limited number of promising designs are under consideration. This research explores the potential of harnessing multi-fidelity models for early-stage predictions of wave-induced loads, with a specific focus on wave-induced vertical bending moments. As an initial step in this direction, the vertical bending moment analysis was simplified to consider responses in a regular sea state, where the wavelength matches the vessel’s length. The assessed multi-fidelity models include the application of both linear and nonlinear Gaussian processes and compositional kernels to improve predictions of wave-induced loads, specifically focusing on wave-induced vertical bending moments. The case study focuses on the early-stage exploration of the AXE frigates. Multi-fidelity models were constructed using both frequency- and time-domain methods to evaluate the vertical bending moments experienced by the hull. Finally, a critical reflection is provided on how traditional early-stage design processes can be enhanced by integrating multi-fidelity models.

Submarine power cables (SPCs) experience complex multi-physical effects in practical engineering scenarios, particularly involving mechanical, thermal, and electrical interactions. When electrical current passes through inner conductors, temperature rises induce thermal expansion, leading to deformation and influencing the bending behavior through alterations in the stick–slip mechanism. Although experimental studies have highlighted temperature’s significant impact on the bending performance of SPCs, detailed insights into the underlying multi-physical interactions remain scarce. This paper introduces a novel repetitive unit cell (RUC) numerical model to investigate the bending behavior of SPCs comprehensively under coupled electrical, thermal, and mechanical fields. An innovative thermal expansion method is proposed to effectively simulate initial residual stresses present at component interfaces post-manufacturing. Furthermore, a temperature-dependent constitutive model based on the Ramberg–Osgood framework is developed and validated against experimental data obtained at varying temperatures. The simulation distinctly identifies the competing effects of material softening and contact stress variations induced by temperature changes, providing critical insights into their contributions to overall cable bending behavior. The outcomes offer valuable guidelines for engineers in the practical design and optimization of submarine power cables. All relevant computational codes developed in this study are publicly accessible athttps://pan-fang.github.io/Codes/.

Submarine power cables (SPCs) are subjected to complex mechanical loadings during service, including tension, bending, torsion, and their combinations. However, systematic studies on the behavior of SPCs – particularly multi-core configurations – under such combined environmental loadings remain limited. This lack of comprehensive analysis hampers a full understanding of their mechanical responses and consequently restricts the design and development of these critical structures. Building upon our previously validated Representative Unit Cell (RUC) model for local mechanical analysis under pure tension and pure bending, this paper extends the investigation to a three-core SPC under a range of combined load cases. In addition, full-scale models are developed to study the torsional response in greater detail. The findings of this study provide valuable guidance for cable engineers, offering new insights into the internal interactions within SPCs and supporting more robust cable design.

As the wind industry expands into remoter and deeper areas of the open sea with abundant wind energy, environmental loadings become harsher. This increases the requirements for submarine power cables (SPCs), which serve as the ‘lifeline’ for transporting electricity. Consequently, a more advanced design based on a thorough understanding of this structure is needed. However, the complex configuration and intensive contact issues within SPCs limit our understanding and make them black boxes for cable engineers. To gain more insights, methods for performing local mechanical analysis of SPCs are necessary. Despite this need, a comprehensive review of existing methods for local mechanical analysis of SPC is still lacking. Therefore, it is essential to review the available methods and provide guidelines for utilizing and developing these methods.

The complex interplay of numerous helical components within submarine power cables (SPCs), especially those with significant contact issues due to initial residual stress, complicates their modelling and limits our understanding of these structures. In this paper we proposed an effective modelling method designed for the local mechanical analysis of SPCs under bending. The method was developed based on three key aspects: (1) constructing appropriate finite elements to reduce the number of elements required; (2) employing contact damping to address the effects of initial residual stress at contact interfaces; and (3) applying periodic boundary conditions on a repeated unit cell (RUC) to reduce the model size. The accuracy of this method was validated through extensive testing on both single-core and three-core SPC samples, and its efficiency was confirmed by comparing these results with those obtained from traditional full-scale models. Following validation, the model was employed to illustrate the local mechanical behaviours of SPCs under bending, both at the overall level and at the component level. This model serves as a powerful tool for cable engineers, offering deeper insights into the internal interplays of SPCs. All relevant codes developed in this paper are freely available at https://pan-fang.github.io/Codes/.

Early-stage design of complex systems is considered by many to be one of the most critical design phases because that is where many of the major decisions are made. The design process typically starts with low-fidelity tools, such as simplified models and reference data, but these prove insufficient for novel designs, necessitating the introduction of high-fidelity tools. This challenge can be tackled through the incorporation of multifidelity models. The application of multifidelity (MF) models in the context of design optimization problems represents a developing area of research. This study proposes incorporating compositional kernels into the autoregressive scheme (AR1) of multifidelity Gaussian processes, aiming to enhance the predictive accuracy and reduce uncertainty in design space estimation. The effectiveness of this method is assessed by applying it to five benchmark problems and a simplified design scenario of a cantilever beam. The results demonstrate significant improvement in the prediction accuracy and a reduction in the prediction uncertainty. Additionally, the article offers a critical reflection on scaling up the method and its applicability in early-stage design of complex engineering systems, providing insights into its practical implementation and potential benefits.

Solid oxide fuel cell systems are considered for the power plant of ships, because of their high efficiency, low pollutant emissions, and fuel flexibility. This research compares the volume, mass, fuel consumption, and emissions of different hybrid power plants for cruise ships using solid oxide fuel cells, fuelled with marine gas oil and liquefied natural gas. A component sizing model allocates the installed power over the selected power plant components and determines their size and weight. The components and energy management strategy are simulated with a cruise ship for five years of operation. A simple method is implemented to estimate the degradation and its effect on component operation. The combined component sizing and time-domain model highlights the importance of dynamic simulation for battery sizing. The results show that using solid oxide fuel cells for the auxiliary consumers can reduce greenhouse gas emissions by 21% and pollutants by 38% to 46% with only 17.5% installed power, which has limited consequences for the cost and size of the power plant. With 31% installed power, the ship can operate in low-emission zones while reducing greenhouse gas emissions by 33% and pollutants by 60% to 70%. Performing all cruise operations requires 51% installed fuel cell power and reduces greenhouse gas emissions by 49% and pollutants by 94% to 96%. In conclusion, the study affirms that solid oxide fuel cell systems, with proper sizing and energy management, can be used to reduce shipping emissions and reach IMO's 30% GHG emission reduction target for 2030.

The complex structure and material property of a cable, particularly the stick-slip issue among its components pose the challenge for the bending analysis of submarine power cables. The calculation time and convergence problem of a full model makes the simulation unpractical during the design phase. This paper takes advantage of the peculiar structural property of helical components inside a cable, proposing a computational homogenization approach for analyzing the cable behavior under bending from global and local perspectives. This method assumes a macro model that is based on the theory of periodic beamlike structure, and a short-size micro model that is solved through a detailed finite element study. Results demonstrate the efficiency and capability of the proposed model that considers the structure nonlinearity and contact condition of a multi-layer cable with helical wires.

Early-stage design exploration is crucial since most of the major design decision are locked-in and only small design modifications are possible at later stages. To assess the performance of the various design candidates while performing design exploration, there are available methods and tools of various fidelities. These methods can be combined to form a multi-fidelity (MF) framework that guarantees accuracy through the high-fidelity model and achieves faster computational speeds through low-fidelity models. The present study proposes the adoption of information-theoretic entropy to improve a MF design framework based on Gaussian Processes (GPs). Entropy quantifies the uncertainty associated with the prediction of the design space. We propose using this uncertainty metric both as a criterion to determine whether further designs should be sampled to construct a reliable approximation of the design space and as a criterion to establish in which optimization step the optimization of the covariance matrix for the MF-GPs should be performed. The approach was tested to benchmark analytical functions and to a ship design problem of an AXEfrigate. The approach holds potential in practical applications, as it aids in the determination of whether additional resources should be allocated for high-fidelity analysis to support early-stage exploration.

The structural complexity of submarine power cables (SPCs) presents significant challenges in their local mechanical analysis. This paper introduces an advanced modeling method developed for analyzing the mechanical behavior of SPCs under tension, emphasizing both accuracy and efficiency. The method’s accuracy is validated through a comparison of simulation results with tension tests conducted on a three-core SPC sample. Efficiency is demonstrated by the superior calculation speed of our model relative to traditional full-scale models. This improved performance is achieved by adopting periodic boundary conditions derived from the homogenization method applied to slender beam-like structures, and by employing a specialized combination of elements to model the helical metal components within the SPCs. The resulting model provides robust capabilities for the mechanical analysis of SPCs under tension and demonstrates significant possibility in accommodating various other loadings.

Submarine power cables in offshore wind farm operate within a complex multiphysics environment. Despite being designed to be both flexible and robust though, their mechanical characteristics are susceptible to variations of thermal field. Bending studies of submarine power cables present challenges rooted in geometry complexity, component contact, and material non-linearity, compounded by the intricate stick–slip mechanism. The difficulty is further intensified when incorporating the thermal impact on material and contact properties. This paper presents a three-dimensional Representative Volume Element (RVE) model for predicting the nonlinear bending stiffness of three-core submarine power cables. The RVE model, developed with constant curvature and periodic boundary conditions, incorporates dashpots to address the stick–slip challenges associated with cable bending. This modeling approach minimizes the required cable length for bending analysis, significantly reducing computational costs. Validation against the bending test of a three-core cable at room temperature, alongside comparison with a 3D full-scale finite element (FE) model, demonstrates the efficiency and accuracy of the proposed RVE approach. Furthermore, the study explores the thermal effect on cable bending, highlighting the capabilities of the proposed RVE model in facilitating thermal–mechanical coupled flexural analysis of submarine power cables. This research contributes to advancing understanding and optimization of submarine power cable design for offshore applications.

Helical wires are a type of structure winding around on an underneath layer in flexible structures. They constitute a structure layer that provides mechanical protection and sufficient flexibility. The cross section of a helical wire could differ from round to rectangular. The curvature increments of a helical wire on a bent flexible structure can be influenced by the cross section shape due to the contact restriction from the neighbouring layer. The shape effect causes a different mechanical behaviour of the wire itself. However, this effect is not fully understood up till now. This paper mainly investigates the curvature increments of helical wires with rectangular and round cross section by using numerical method. This model takes advantage of the properties belonging to solid elements and beam elements by embedding the latter into the former. The solid element is able to retain the geometry detail of the cross section as much as possible in order to get deep insight of the shape effect. The beam element based on Timoshenko beam theory with well defined Frenet-Serret frames can accurately output the curvature increments in three local directions. Then widly-used analytical models are presented and deployed to verify the numerical results. The research results show the application condition of the analytical expressions and benefit the cable/umbilical/flexible pipe designers.

Design rationale is a promising way of capturing design decisions and considerations for later retrieval and traceability to improve collaborative design decision-making. To achieve these perceived benefits for early-stage complex ship design, this paper first elaborates on the development of a proof-of-concept design rationale method. The method aims to aid ship designers in the continuous capturing and reuse of design rationale during the collaborative concept design process. Second, the setup and results of an experiment conducted with marine design students and with experts are discussed. This experiment shows how the developed design rationale method benefits collaborative design decision-making such that it leads to improved insight into design issues across the design team during a single design session.

This paper introduces a novel analytical approach aimed at predicting the growth of surface cracks in metallic pipes reinforced with Fibre-Reinforced Polymers (FRPs) subjected to cyclic bending and/or tension loads. The primary objective of this study is to develop a comprehensive analytical model that accounts for multiple factors influencing crack growth, namely stress reduction, crack-bridging effect, stiffness degradation, and fatigue damage of the FRP-to-metal interface simultaneously. By considering these simultaneous effects, our proposed approach enables accurate evaluations of the stress intensity factors (SIFs) at both the surface point and the deepest point of a surface crack. To facilitate practical implementation, we have developed an in-house program that automates crack growth rate and residual fatigue life predictions. The proposed analytical method has been validated through a series of comparisons with experimental data and finite element results, demonstrating its accuracy in estimating fatigue lives. The key novelties of this research lie in the holistic consideration of multiple dominating and influencing factors, the achievement of precise SIF evaluations, and the development of an automated prediction tool for practical applications. Overall, our findings confirm the suitability of the proposed analytical approach for predicting crack growth and provide valuable insights for guiding the design of FRP reinforcement in surface-cracked metallic pipes. This work contributes to advancing the understanding of crack growth behaviour in FRP-reinforced metallic pipes and opens new possibilities for the safe and efficient design of such structures.

Marine actors are showing an increased interest in the application of Solid Oxide Fuel Cells (SOFCs) for deep sea shipping, because of their high conversion efficiency, low pollutant emissions, and fuel flexibility. However, it is unknown how the operation of SOFC systems is affected by large inclinations and motions, which can be present in ships for instance by seawaves. The goal of this research is to evaluate the influence of static and dynamic inclinations on the operation and safety of SOFC systems. Ship motions are emulated using a one-axial oscillation platform up to 30 degrees of inclination. The SOFC system was successfully operated on the platform and demonstrated stable power production under a variety of test conditions without any noticeable safety hazards. The results of the experiments are used to propose design improvements for marine SOFC systems, ultimately contributing to reduce the emissions of the shipping industry.

Predicting the bending behaviours of a submarine power cable (SPC) is always a tough task due to its complex geometry and inner layer contact, not to mention the stick–slip mechanism. A full-scale finite element model is cumbersome during the early design stage and a more efficient model for practical use is required. Therefore, in this paper, a repeated unit cell (RUC) technique-based FE model is developed, which simplifies the bending analysis of SPCs using a short-length representative cell with periodic conditions. The verification of this RUC model is conducted from cable and component levels, respectively. The cable overall response is validated by the curvature-moment relationships from our cable bending tests regarding four cable samples whose material properties are obtained through a set of material tests. As for the component level, the behaviours of particular components are studied and compared with the results from a full-scale numerical model. Discrepancy is observed between the RUC model and the test, which can be explained by the distinctions of boundary conditions between these two methods. The proposed Cable-RUC model has been found robust and computationally efficient for studying SPCs under bending.

Current EEDI (Energy Efficiency Design Index) regulations striving to reduce the installed engine power on new ships for a low EEDI may lead to underpowered ships having insufficient power when operating in adverse sea conditions. In this paper, the operational safety of a low-powered ocean-going cargo ship operating in adverse sea conditions has been investigated using an integrated ship propulsion, manoeuvring and sea state model. The ship propulsion and manoeuvring performance, especially the dynamic engine behaviour, when the ship is sailing in heavy weather and turning into head sea, have been studied. According to the results, the dynamic engine behaviour should be considered when assessing the ship operational safety, as the static engine operating envelope is inadequate for the safety assessment. The impact of PTO/PTI (power-take-off/in) operation and changing propeller pitch on the ship thrust availability in adverse sea conditions have also been investigated. To protect the engine from mechanical and thermal overloading, compressor surge and over-speeding during dynamic ship operations and/or in high sea states, the engine and propeller should be carefully controlled. The paper shows that if in (heavy) adverse weather the propeller pitch can be reduced or if the shaft generator can work as a motor (PTI), more thrust can be developed which can significantly improve the operational safety of the ship.

In order to reduce fossil fuel consumption of the Royal Netherlands Navy (RNLN) by 70% in 2050, the use of alternative fuels on the large naval surface vessels is examined. This paper examines the implications for the design and operational effectiveness of these vessels by performing two case studies of the Zeven Provinci¨en air defence and command frigate (LCF) and the Johan de Witt landing platform dock (LPD). In the case studies an operational analysis, a parametric design study, and an effectiveness assessment are performed on multiple proposed designs. Results showed that it is possible to reduce the fossil fuel consumption of the RNLN by almost 70%. This does affect the design of the vessels, however. It was also concluded that the LPD is more suitable for the application of low-energy-density fuels than the LCF, due to its missions requirements. Both the LPD and the LCF show a significant increase in displacement and fuel cost, but it is possible to reduce effects on the operational effectiveness to a minimum.

Analysis of ship propulsion system performance is often performed using detailed hydrodynamic models to assess load changes, which are subsequently compared to static engine limits, or by detailed engine models that are rarely integrated with sufficiently detailed propulsion models for load change estimation. To investigate the dynamic engine (overloading) behaviour and ship propulsion performance under various heavy operating conditions, a Mean Value First Principle Parametric (MVFPP) engine model is integrated into a ship propulsion system model in this paper. An upgraded thermodynamic-based MVFPP model for two-stroke marine diesel engines is presented, in particular a newly developed MVFPP gas exchange model. Based on the integrated propulsion system model of a benchmark ocean-going chemical tanker, the engine dynamic behaviour during ship acceleration, deceleration and crash stop has been investigated. Results show that, during dynamic processes, the engine could be thermally overloaded even if the engine power trajectory is inside the static engine operating envelope. The paper contributes to finding proper indicators for thermal overloading of modern two-stroke marine diesel engines. It is demonstrated that when matching the engine with the propeller and designing the ship propulsion control system, not only the static engine operating envelope, but also the dynamic engine behaviour should be considered.

The aim of this paper is to discuss the challenges associated with the early-stage design of novel and reliable vessels, and discuss some of the expected benefits of the application of multi-fidelity models in addressing some of their early-stage design problems. Traditionally, early-stage design tools are computationally cheap, but lack in accuracy. However, for the design of novel vessels, these tools are not sufficient. The first part of the paper discusses the challenges associated with the design of novel vessels. The second part of the paper focuses on a literature review on the application of the multi-fidelity models to the design of complex engineering systems. Finally, the most promising methods are identified and discussed.