Relying on a traffic simulator is often necessary when multiple traffic conditions need to be replicated, either to predict specific quantities of particular interest or to assess more general network properties, such as efficiency or resilience, under different scenarios. While potentially delivering a high level of fidelity, producing such a simulation may come at a prohibitive computational cost when it is applied in a real context, making this approach unsuitable for real-time applications in most cases. In this regard, the goal of the present work is twofold. Firstly, we aim to surrogate a traffic simulator with a data-driven approach in order to produce real-time traffic predictions that are also sufficiently accurate and effective. Secondly, we want to determine the minimum amount of data, i.e., the smallest number of sensors deployed on the network, that still allow to obtain predictions within a predefined bound. The effectiveness of the approach is evaluated on the full-scale urban network of Rapallo, Italy, in which we employ the AIMSUN NEXT simulator targeting the morning peak hours, i.e. between 7:00 a.m. and 9:00 a.m. In the paper, multiple state-of-the art ML algorithms are tested to assess their effectiveness as surrogate models under the considered problem.

Renewably produced methanol is a promising fuel for internal combustion engines in long-range transportation thanks to its scalability, liquid storage, and favorable combustion properties. However, the distinction between different injection and ignition strategies for methanol engines and the resulting combustion mechanisms has not been consistently defined. Moreover, diffusion combustion strategies are favored over premixed strategies in large engines because of higher methanol energy fractions, disregarding the advantages of premixed approaches, such as reduced nitrogen oxide emissions and retrofitting opportunities. To address ambiguity in terminology, this paper proposes a classification framework for injection and ignition strategies and applies it to methanol-fueled internal combustion engines. Subsequently, this review focuses on experimental studies of methanol-fueled heavy-duty engines, which are crucial for transitioning to renewable and sustainable energy in long-range transportation. This research summarizes the impact of the reviewed injection and ignition strategies on combustion characteristics, engine performance and emissions to identify key trends. Furthermore, this review highlights how specific design and operating parameters influence premixed dual-fuel combustion, offering insights into optimizing performance and emissions. While mono-fuel and premixed dual-fuel strategies with methanol can significantly promote methanol use in heavy-duty engines and reduce harmful emissions like nitrogen oxides, a rise in unburned hydrocarbon emissions may also be expected, necessitating further research in this area. Additionally, methanol injection location in premixed dual-fuel schemes affects its cooling effect, influencing volumetric and thermal efficiency. Overall, this study deepens our understanding of methanol's impact on heavy-duty engine performance, highlighting critical challenges to be addressed for advancing sustainable transportation.

The push to attain commercialization of the floating offshore wind industry and subsequently achieving net-zero carbon emission by the year 2050 requires the utilization of cutting-edge design and analyses techniques. Geometric design parameterization and optimization is an effective technique that can be employed in modelling and optimizing a Floating Offshore Wind Turbine (FOWT) substructure. It is an essential framework with the capability of innovative concept generation of platform types in the FEED design phase. This study addresses the conceptual design shape generation, multidisciplinary design analysis and optimization (MDAO) of spar variants FOWT substructure developed from the standard NREL OC3 spar. The methodology involves the use of non-uniform rational basis spline (NURBS) parameterization technique to generate design variants with the flexibility of varying the control points to facilitate varying geometric shapes due to the local propagation property of the NURBS curve. Design variables passed through the NURBS curves control points generates a robust and rich design space and the potential flow hydrodynamic analysis tool in the DNV SESAM suite is used to estimate the hydrodynamic response. The design and analysis phases are explored and exploited for optimal design solution based on specified objectives and constraints with the use of state-of-the-art derivative-free optimizers. The optimal designs were evaluated for three sets of FOWT static pitch angle constraints (5, 7 and 10) degrees, a positive ballast constraint for stability and a constraint on nacelle acceleration root mean square (RMS) value below 30 % of the gravitational acceleration. The single objective function considered in the study is to ensure a minimum mass of the steel material utilized in the design, which invariably leads to a reduction in cost of the substructure material used in fabrication. Achieving this single objective results in an altered geometric shape variants from the baseline OC3 spar substructure for all the three cases evaluated. Verification of the nacelle acceleration response in time domain was further evaluated for the three optimal design cases selected and compared with recommended standards which is below 0.3 g. Although, the nacelle acceleration for the optimal variants is more conservative in time domain assessment than the frequency domain assessment, the values are still below the recommended 0.3 g from standards. Also, the masses of selected optimal design for each constraint were compared to the standard OC3 case study. An observation made in this study is that as the static pitch angle of the FOWT system gets larger, the lower the mass of the optimal substructure and inherently the capital expenditure of the substructure. Finally, the selected optimized platforms were analysed with a non-linear, time domain approach to confirm the level of accuracy of the key response parameters obtained with the frequency-based approach.

Methanol is a promising alternative fuel, which can assist in reducing emissions in heavy-duty (HD) dual-fuel (DF) compression ignition (CI) engines. In medium and large bore marine engines, DF operation is achieved through either direct injection (DI) or port fuel injection (PFI) of methanol with diesel acting as a DI pilot fuel for ignition. However, the injection of methanol presents a significant challenge due to its high latent heat of vaporization and decreased lower heating value (LHV) compared to diesel. Therefore, for the same energy content operation, methanol requires around eight times the amount of heat to evaporate completely in comparison to diesel, which results in lower in-cylinder temperatures. This charge cooling effect leads to a strong negative temperature gradient influencing ignition and flame propagation. This paper aims to quantify the cooling effect of methanol in a heavy-duty dual-fuel direct injection compression ignition (DICI) engine environment. The presented methodology uses computational fluid dynamics (CFD) simulations to model methanol sprays with validation originating from the engine combustion network (ECN) Spray D experimental data. The CFD models operate within the Lagrangian–Eulerian framework in CONVERGE-CFD using the Reynolds Averaged Navier Stokes (RANS) turbulence modeling. Compared to diesel, injecting methanol with the same energy content exhibited up to 100 K more decreased temperature within the mixture. Consequently, this cooled mixture may pose challenges to combustion stability due to the intense temperature gradients. Nonetheless, lower mixture temperature decreases NOx emissions, which can prove beneficial for high methanol energy fractions in dual-fuel DICI engines.

In contemporary industrial applications, predictive models have been pivotal in bolstering production efficiency, product quality, scalability, and cost-effectiveness while promoting sustainability. These predictive models can be constructed solely based on domain-specific knowledge, exclusively on observational data, or by amalgamating both approaches. They are commonly referred to as Full-, Zero-, or Partial-knowledge-based predictive models, respectively. Full-knowledge based models are highly explainable, point-wise accurate, data efficient, computationally demanding in the prediction phase to achieve high accuracy. Zero-knowledge based models are poorly explainable, data hungry, highly accurate on average, computationally demanding in the construction phase but inexpensive the prediction phase. Partial-knowledge based models focus on taking the best of the two worlds. To maintain a focused scope and avoid redundancy with existing literature, our review will primarily delve into the key industrial applications within a narrow context, encompassing sectors such as extraction, chemical processes, manufacturing, transportation, energy, and construction. Our approach entails several steps. Initially, we conducted a meta-review to pinpoint gaps in previously published surveys on Full-, Zero-, and Partial-knowledge-based predictive models for industrial applications. Subsequently, we present a formal analysis of the subject matter, supplemented with illustrative examples to offer valuable insights. The core of our work comprises a review of existing research categorized by specific industrial applications. Finally, we outline the unresolved challenges and future prospects in this burgeoning field of research. We contend that our work serves as a valuable resource, catering to the needs of both young researchers seeking a solid foundation for their studies, industrial practitioners aiming to grasp core concepts and applications, and senior researchers seeking potential real-world applications for their findings.

In the scope of the energy transition, the maritime industry, still heavily relying on fossil fuels, is facing expectations to reduce its carbon output. Electrified shipboard power systems (SPSs) equipped with hydrogen fuel cells (FCs) and energy storage systems (ESSs) are a promising solution for the shift to zero-emission shipping. A remaining challenge is the efficient coordination of multiple parallel power generation and storage modules. This article proposes a modular approach to the power system control to offer a plug-and-play capability for multiple FCs and ESSs, facilitating a topology reconfiguration. Virtual impedance-based droop is implemented to achieve power sharing and load frequency decoupling in a decentralised architecture. An additional low-bandwidth communication is leveraged to enable parameter adaptation after a topology reconfiguration. The methodology is tested numerically with a short-sea cargo vessel serving as a case study. The local controllers are tuned to achieve load frequency decoupling between FCs and batteries matching the specified time constant. For a maneuvering power profile, the average FC power gradient could be decreased by 36%, limiting their degradation caused by dynamic operation, while increasing the depth-of-discharge of the batteries. The simulations further show that an adaptation of control parameters after a component fault can be used to maintain the system’s voltage dynamics. The voltage drop caused by a load step in a reconfigured system that disconnected one of two ESS could be reduced by 37.5% by control parameter adaptation.

The maritime sector aims to achieve short and medium-term sustainability targets through the conversion of Internal Combustion Engines to methanol operation. For small to medium sized engines, Port Fuel Injection (PFI) is the most viable injection method to achieve this conversion. However, the knowledge of the behaviour of methanol in combustion engines, particularly its spray characteristics under PFI conditions, is limited. To better understand liquid methanol sprays, this paper studies the injection of methanol in marine PFI conditions through Computational Fluid Dynamics (CFD) modelling. The CFD models use the Lagrangian-Eulerian (LE) coupling method within the Reynolds Averaged Navier Stokes (RANS) turbulence framework. Numerical results were validated using dedicated methanol experiments from the literature for both high and low injection pressures. Subsequently, this predictive CFD framework was used in a number of different injection pressures with scaled injection quantities that represent marine applications. Moreover, we demonstrated that high injection pressure improves atomisation and, thus, evaporation prior to wall impingement. This work strongly contributes to our understanding of marine PFI methanol engines by modelling fuel quantities relevant for ship applications. Our approach can be implemented in full engine simulations to solve evaporation challenges often found in small-bore methanol marine engines.

Floating Offshore Wind Turbines (FOWT) can harness the abundant wind resource in deep-water offshore conditions. However, they face challenges in harsh, unsheltered marine environments. The mean hydro- and aerodynamic loads coupled with fluctuating stochastic wind and wave loads contribute to varied failure mechanisms. Therefore, the serviceability, ultimate, and fatigue limit states are vital in ensuring the safety and reliability of FOWT. This paper investigates how specific loads and states drive the design of a spar-type support structure, utilising a computationally efficient frequency-domain model. This approach combines quasi-static aerodynamic and mooring models with a potential-theory-based radiation-diffraction solver. The serviceability criteria concern the platform and tower top displacements and accelerations. The ultimate and fatigue limit states are assessed for the tower base, the waterline section, and the mooring lines, including the effects of yielding under the bending moment and compressive axial load, column buckling, and tension-tension effects in the mooring lines. The full factorial design of experiments is employed to investigate the non-trivial relationships between the limit states and the various features of the support structure. The results demonstrate that the design of the spar platform above the waterline is mainly driven by fatigue, which results from significant dynamic tilt and increased stress concentration at the platform-tower intersection. On the other hand, the catenary mooring lines' design is mainly driven by the requirements of maximum offset (serviceability limit state) and fatigue.

Meta-heuristic optimisation algorithms are high-level procedures designed to discover near-optimal solutions to optimisation problems. These strategies can efficiently explore the design space of the problems; therefore, they perform well even when incomplete and scarce information is available. Such characteristics make them the ideal approach for solving nonlinear parameter identification problems from experimental data. Nonetheless, selecting the meta-heuristic optimisation algorithm remains a challenging task that can dramatically affect the required time, accuracy, and computational burden to solve such identification problems. To this end, we propose investigating how different meta-heuristic optimisation algorithms can influence the identification process of nonlinear parameters in mechanical systems. Two mature meta-heuristic optimisation methods, i.e. particle swarm optimisation (PSO) method and genetic algorithm (GA), are used to identify the nonlinear parameters of an experimental two-degrees-of-freedom system with cubic stiffness. These naturally inspired algorithms are based on the definition of an initial population: this advantageously increases the chances of identifying the global minimum of the optimisation problem as the design space is searched simultaneously in multiple locations. The results show that the PSO method drastically increases the accuracy and robustness of the solution, but it requires a quite expensive computational burden. On the contrary, the GA requires similar computational effort but does not provide accurate solutions.

The global shipping industry is at a crucial juncture, facing an urgent need to reduce greenhouse gas emissions in the short to medium term to mitigate climate change. A shift towards alternative fuels is imminent, necessitated by the limitations in current fuel cell and battery technology in terms of power density. Addressing this, navies worldwide are not only exploring the use of alternative fuels to diminish environmental impact but also seeking solutions to reduce emissions signatures and decrease reliance on fossil fuels. In this paper, we investigate the use of hybrid turbocharging to improve the dynamic performance of alternatively fueled combustion engines. We extended an existing and validated Mean Value First Principle (MVFP) engine model of a spark-ignited (SI) throttle-controlled Caterpillar 3508A gas engine with a hybrid turbocharger. The study investigates the impact of electrical power Power-Take-In/Off from the turbocharger shaft on the engine’s air path dynamics for different use cases, considering transient and steady state phases. We demonstrate that a generator set can benefit from hybrid turbocharger by significantly reducing the engine speed drop and settling time after a load step. While accelerating from 0 to cruise speed, propulsion engines benefit less from hybrid turbocharger, due to risk of compressor surge during low engine speeds. The overall results show that simply adding electric power to the turbocharger shaft during transient phases does not unlock the full potential of hybrid turbocharging for alternatively fueled combustion engines. The implementation of hybrid turbocharging requires careful integration, reconsideration of sizing and matching of turbine and compressor, and the combination with blow-off, blow-by, and waste gate valves to prevent compressor surge. However, the capability for electrical power take-off/in within a larger propulsion and electrical power generation plant context suggests a reduction in spinning reserves and an increase in overall system efficiency during steady state. Thus, implementing hybrid turbocharging can play an important role in the transition to alternative fuels and the reduction of greenhouse gas emissions.

The maritime industry is under increasing pressure to reduce its carbon footprint by adopting new energy generation and storage technologies in shipboard power systems (SPS). Fuel cells (FCs) show great potential as primary power sources when hybridized with energy storage systems (ESS). Integrating different technologies in future SPS requires the coordination of power generation and storage modules, which can be facilitated by DC technology with power electronics interfaces. However, studies on FC integration have primarily focused on small-scale applications with centralized control architectures. There has been little research on the modular control of multiple FC and battery modules in SPS. This study proposes a decentralized droop-based power sharing approach with load frequency decoupling to efficiently utilize power system modules based on their dynamic capabilities. The proposed strategy further incorporates decentralized voltage regulation and state-of-charge (SoC) management functions. The methodology was applied to a short-sea cargo vessel with an FC-battery DC power system. The results indicate that the mission load profile can be satisfied while limiting fluctuations in the FC output power. Moreover, the proposed strategy achieves the same voltage regulation performance as a centralized proportional-integral (PI) controller and can be easily tuned to achieve load frequency decoupling with the desired time constant. Finally, a comparative analysis shows how the trade-off between the dynamic operation of the FC and the discharge depth of the ESS is affected by the choice of time constant.

Due to increasing environmental concerns and global energy demand, the development of Floating Offshore Wind Turbines (FOWTs) is on the rise. FOWTs offer a promising solution to expand wind farm deployment into deeper waters with abundant wind resources. However, their harsh operating conditions and lower maturity level compared to fixed structures pose significant engineering challenges, notably in the design phase. A critical challenge is the time-consuming hydromechanics analysis traditionally done using computationally intensive Computational Fluid Dynamics (CFD) models. In this study, we introduce Artificial Intelligence-based surrogate models using state-of-the-art Machine Learning algorithms. These surrogate models achieve CFD-level accuracy (within 3% difference) while dramatically reducing computational requirements from minutes to milliseconds. Specifically, we build a surrogate model for characterizing the hydrodynamic response of a floating spar-type offshore wind turbine (including added mass, radiation damping matrices, and hydrodynamic excitation) using computationally efficient shallow Machine Learning models, optimizing the trade-off between computational efficiency and accuracy, based on data generated by a cutting-edge potential-flow code.

To ensure that future autonomous surface ships sail in the most sustainable way, it is crucial to optimize the per-formance of the Energy and Power Management (EPM) system. However, marine EPM systems are complex and often coordinate various distributed energy resources, energy storage systems, and power grids to ensure reliable and safe power delivery. Traditional control methods for marine EPM systems are limited by evaluating processes using simplified component models over a short time horizon, or relying on historical insights gained from earlier journeys, and are not the optimal approach for complex hybrid marine EPM systems. Advanced control strategies, such as Model Predictive Control (MPC), offer a promising control method that considers predicted future system responses over an extended time horizon to determine the best control input, making them an effective strategy for optimizing the performance of hybrid marine EPM systems. However, to learn the onboard energy profiles based on component behavior in a hybrid system from past experiences is not a trivial task, and one of the primary barriers to implementing MPC for marine EPM control. For this reason, in this work, we address the challenge of learning energy profiles for a marine EPM system by utilizing shallow and deep machine learning for total power demand forecasting. The forecast is an essential reference for an MPC-based controller and will enable this control strategy to provide reliable and safe power delivery for hybrid marine EPM systems. The proposed approach compares state-of-the-art machine learning models to identify the best-performing algorithm, considering accuracy and computational requirements. We illustrate the potential of the proposed approach by using real world operational data from a vessel with a hybrid marine EPM system. Results indicate that shallow models, trained on engineered features handcrafted with classical signal processing techniques, allow forecasting the total power demand up to a horizon of 5min with minimal loss in accuracy and a negligible computational burden.

Fuel cell-battery electric drivetrains are attractive alternatives to reduce the shipping emissions. This research focuses on emission-free cargo vessels and provides insight on the design, lifetime operation and costs of hydrogen-hybrid systems, which require further research for increased utilization. A representative round trip is created by analysing one-year operational data, based on load ramps and power frequency. A low-pass filter controller is employed for power distribution. For the lifetime cost analysis, 14 scenarios with varying capital and operational expenses were considered. The Net Present Value of the retrofitted fuel cell-battery propulsion system can be up to $ 2.2 million lower or up to $ 18.8 million higher than the original diesel mechanical configuration, highly dependent on the costs of green hydrogen and carbon taxes. The main propulsion system weights and volumes of the two versions are comparable, but the hydrogen tank (68 tons, 193 m³) poses significant design and safety challenges.

This paper proposes a grey-box modelling approach to predict marine biofouling growth and its effects on ship performance. The approach combines empirical or experimental-based white-box models with data-driven black-box models. First, a white-box model is built to predict ship resistance considering a bare hull. This prediction is based on calm water resistance, wind, waves, and temperature differences. Subsequently, marine biofouling growth is predicted using an experimental model that estimates the level of roughness on the ship hull. Finally, a deep extreme learning machine is used as a black-box model, employing a feedforward neural network technique. To test the approach, a superyacht case study was selected as a category of vessel heavily exposed to fouling. The study used a 2-year dataset obtained through a collaboration with Feadship. Results showed that the black-box approach outperforms the white-box approach in predictive capabilities. However, when the knowledge encapsulated in the white-box model is included in the grey-box approach, the model shows the highest prediction accuracy achieved by leveraging less historical data. This study demonstrates the potential of the proposed grey-box approach to accurately predict marine biofouling growth and its effects on ship performance, which can benefit ship operators and designers in improving operational efficiency and reducing maintenance costs.

The presence of contact and backlash often leads to complex and rich dynamic responses in mechanical structures. This typically occurs in systems such as jointed structures and geared mechanisms, where the inherent complexity leads to responses which are difficult to predict. In particular, identifying models capable of performing reliable predictions is extremely challenging, both for the definition of the equations of motion and for the characterisation of their parameters. In this chapter, we present a systematic approach based on the restoring force surface method for analysing and identifying the localised piecewise nonlinear characteristics in multi-degree-of-freedom systems. Our approach builds on the knowledge of the underlying linear system and outlines a procedure to identify equivalent nonlinear characteristics via a graphic representation of the piecewise restoring forces. The approach is validated against experimental measurements of a test rig representative of a two-degree-of-freedom system with a localised nonsmooth characteristic. The reconstruction of the nonsmooth restoring force, identification of the piecewise characteristics, and the validation of the model against experimental time histories are performed following our systematic procedure, proving the flexibility of this practical approach.

The current sea margin estimate applied in early ship design, commonly assumed 15-20% extra installed engine power, is not based on calculations, but has nonetheless become an industry standard. These sea margin estimations, applied in early ship design, are insufficiently accurate. This paper evaluates if a data driven approach is suitable to more accurately predict the sea margin in early ship design. Using operational data this method considers the whole operational profile of the vessel not limited to design or calm water conditions. A case study is performed where a data driven model is trained to make power predictions, subsequently this trained model is used to make calm water predictions. This proof of concept illustrates the potential of proposed method to be utilised for sea margin estimations in early ship design.

Floating offshore wind (FOW) is a renewable energy source that is set to play an essential role in addressing climate change and the need for sustainable development. However, due to the increasing threat of climate emergency, more wind turbines are required to be deployed in deep water locations, further offshore. This presents heightened challenges for accessing the turbines and performing maintenance, leading to increased costs. Naturally, methods to reduce operational expenditure (OpEx) are highly desirable. One method that shows potential for reducing OpEx of FOW is LIDAR-assisted pitch control. This approach uses wind velocity measurements from a nacelle-mounted LIDAR to enable feedforward control of floating offshore wind turbines (FOWTs) and can result in reductions to the variations of structural loads. Results obtained from a previous study of combined feedforward collective and individual pitch control (FFCPC + FFIPC) are translated to OpEx reductions via reduced component failure rates for future FOW developments, namely, in locations awarded in the recent ScotWind leasing round. The results indicate that LIDAR-assisted pitch control may allow for an up to 5% reduction in OpEx, increasing to up to 11% with workability constraints included. The results varied across the three ScotWind sites considered, with sites furthest from shore reaping the greatest benefit from LIDAR-assisted control. This work highlights the potential savings and reduction in the overall levelised cost of energy for future offshore wind turbine projects deliverable through the implementation of LIDAR-assisted pitch control.

Methanol has emerged as a cost-effective and scalable alternative fuel for the maritime sector. However, the use of methanol in marine engines is limited by the unknown characteristics of methanol sprays when introduced through retrofitted port fuel injection (PFI) systems. The present study investigates the characteristics of methanol sprays under relevant conditions for marine engines, such as low injection pressure PFI. The primary objective of this research is to advance knowledge into key spray characteristics, including spray penetration, droplet size, atomization quality, and evaporation. The proposed methodology evaluates the efficacy of state-of-the-art computational fluid dynamics (CFD) models in simulating PFI marine engine spray conditions. Moreover, the study compares the performance of the Kelvin-Helmholtz (KH-RT) and Taylor Analogy Breakup (TAB) droplet breakup models under low injection pressure conditions. The results demonstrated that the KH-RT model does not predict any droplet breakup occurrence suggesting that the TAB model is more suitable for the given conditions. Furthermore, the liquid penetration of the spray was observed to align with the outcomes reported in previous experimental literature on methanol sprays. Nevertheless, the droplet sizes for low pressure injectors appear relatively large, indicating poor spray atomization, which impedes rapid evaporation and increases the risk of wall wetting in the inlet manifold and combustion chamber.

Lightweight structures, once ubiquitous in specific sectors such as aeronautics and space sectors, in recent years, have increasingly attracted the attention of industries that, historically, have not been particularly concerned with structural weight. Ample examples are provided by the civil and automotive industry, in which the paradigm shift towards lower carbon footprint and sustainability prompted new trends characterised by mass reduction, the use of novel materials, and the accounting for large deformations. However, accurately modelling the dynamic behaviour of such structures requires nonlinear mathematical models, which are not widely used in common industrial practices. Reduced-Order Models (ROMs) have emerged as a popular alternative to computationally expensive Finite Element (FE) models, nonetheless, there is still a need to evaluate their effectiveness in accurately modelling strongly nonlinear behaviours. This study investigates the capacity of multiple-degree-of-freedom (MDOF) ROMs to capture and predict the nonlinear behaviour of lightweight structures subjected to large deformations. A novel identification procedure, built on existing linear and nonlinear identification methods, is used to identify an ROM from numerical and experimental data. Being based on the separation of the linear and nonlinear restoring force contributions, the proposed method can be easily embedded in the current industrial practices for the identification of mechanical systems, paving the way to an integrated usage of linear and nonlinear dynamic models. To validate the identified MDOF-ROM, a lightweight structure composed of lumped masses and nonlinear elastic connections is experimentally studied and the numerical and experimental results are compared at different excitation conditions. We demonstrated that the existence of the Nonlinear Restoring Force (NLRF) surface in a reduced subspace corresponds to the presence of local active nonlinearities in the experimental model. This information permits simplifying the nonlinear restoring force function of the ROM, improving the overall identification process. Finally, we showed that the identified ROM accurately represents the nonlinear dynamic behaviour of the experimental test rig and correctly predicts the passage from high-amplitude response to low-amplitude response (jumps) when different levels of excitation are applied to the system, demonstrating the effectiveness of the proposed procedure.