The digital transformation of port systems has advanced from isolated automation toward integrated decision-support environments in which physical operations, data streams, simulation models, and predictive algorithms interact continuously. In this context, the digital twin has become more than a visualisation tool. It is increasingly viewed as a dynamic representation of port assets and processes that can support monitoring, forecasting, optimisation, and operational decision-making. The broader digital twin literature has established the value of dynamic virtual models for maintenance, lifecycle monitoring, model updating, and decision support, while also identifying persistent challenges related to data quality, system fidelity, interoperability, and uncertainty representation (Errandonea et al. 2020; Fuller et al. 2020; Gao et al. 2023a; Gao et al. 2024; Gao et al. 2023b; Jiang et al. 2021; Jones et al. 2020; Rasheed et al. 2020; Sun et al. 2025). In port systems, this concept has been extended toward smart-port architectures, automated terminal operation, berth planning, AGV scheduling, energy-aware operation, digital platform ecosystems, and port decarbonisation assessment (Belmoukari et al. 2023; Boullauazan et al. 2023; Eom et al. 2023; Gao et al. 2023a; Gao et al. 2024; Heikkilä et al. 2022; Heilig et al. 2017; Kapkaeva et al. 2021; Klar et al. 2023; Li et al. 2023; Li et al. 2021). These studies show that port digitalisation is not only a technological upgrade. It is also a shift in how port systems coordinate infrastructure, equipment, energy, data, and decision-making. Smart-port research has shown that digital maturity, operational integration, automation, sustainability, and performance management are now closely connected in modern terminal systems (Belmoukari et al. 2023; Boullauazan et al. 2023; Heikkilä et al. 2022; Heilig et al. 2017; Tijan et al. 2021). However, the degree to which these digital systems can remain reliable under degraded sensing and uncertain data conditions is still not fully resolved.

Several studies have moved closer to operational port digital twins. Digital twin models have been proposed for decarbonisation-oriented port monitoring, automated container terminal energy optimisation, AGV scheduling, and production-operation support (Eom et al. 2023; Gao et al. 2023a; Gao et al. 2024; Li et al. 2021). Port digital twin studies derived from smart-city and supply-chain twinning experience further show that port twins need to connect infrastructure, operation, data flows, and decision-support functions within a single architecture (Klar et al. 2023). These contributions provide an important foundation for the present study, but most existing port digital twins still place stronger emphasis on operational visibility and scheduling performance than on explicit uncertainty propagation, synchronisation error, and infrastructure-health coupling.

The logistics optimisation literature also provides important foundations for the operational layer of port digital twins. Berth allocation, quay-crane assignment, tug coordination, AGV scheduling, shore-power coordination, and uncertain operation time have all been studied as key determinants of port performance (Aslam et al. 2023; Li et al. 2023; Li et al. 2021; Peng et al. 2021; Wang and Zou 2024; Xiang and Liu 2021; Zhang et al. 2025). These studies confirm that port operation is inherently multi-objective and uncertainty-sensitive. Vessel delay, berth occupancy, equipment allocation, yard congestion, service time, energy demand, and environmental performance are strongly linked. However, many optimisation models focus on specific decisions under predefined inputs rather than on the continuous state estimation of a coupled physical-digital system. This distinction is important because a scheduling model may provide an efficient plan, while a digital twin must continue estimating the system state when data are noisy, delayed, missing, or temporally inconsistent.

A further limitation is that many port digital twin models are developed under assumptions of stable observability. In practice, port systems are monitored by heterogeneous data sources, including operational databases, energy meters, environmental sensors, structural monitoring devices, equipment-control systems, and terminal-management platforms (Kapkaeva et al. 2021; Klar et al. 2023; Lu et al. 2020). These data streams do not always arrive at the same frequency, with the same accuracy, or with consistent timestamps. When a digital twin combines these data without explicitly accounting for missing values, delayed measurements, sensor drift, and synchronisation mismatch, the resulting state estimate may appear precise while actually carrying hidden uncertainty. This issue becomes more serious under peak operating conditions, when decisions must be made quickly and the consequences of state-estimation error can propagate across logistics, energy, and infrastructure layers (Iris and Lam 2021; Ma et al. 2025b; Pu et al. 2025; Samaei and Riffat 2026d).

The decarbonisation of port activity has created strong interest in electrified terminal operations. Shore power, electric cargo-handling equipment, battery-supported terminal microgrids, electric terminal vehicles, renewable generation, and energy-storage systems are now central elements of low-carbon port planning (Abu Bakar et al. 2023; Iris and Lam 2019; Iris and Lam 2021; Lu et al. 2023; Mo et al. 2024; Peng et al. 2021; Samaei and Riffat 2026a; Zhang et al. 2024). These technologies can reduce emissions from berthed vessels and cargo-handling operations, but they also introduce new operational dependencies. A conventional terminal may evaluate service performance mainly through time, capacity, and productivity. An electrified terminal must also evaluate when energy is required, where it is consumed, whether local supply can meet demand, how storage should be dispatched, and how peak demand affects overall system resilience.

Port energy management has been studied through optimisation models, microgrid scheduling, shore-power planning, renewable integration, and demand-response strategies (Iris and Lam 2019; Iris and Lam 2021; Ma et al. 2025b; Ma et al. 2025a; Mo et al. 2024; Peng et al. 2021; Pu et al. 2025; Samaei and Riffat 2026a). These studies show that port electrification cannot be managed effectively by treating energy demand as a static external input. Instead, energy demand is shaped by vessel schedules, berth allocation, crane assignment, yard operations, equipment availability, renewable generation, storage limitations, and grid-import constraints. Integrated scheduling studies have shown that coordination between seaside operation, yard activity, energy demand, and port microgrid management can improve both operational service and energy efficiency (Iris and Lam 2021; Ma et al. 2025b; Mo et al. 2024; Peng et al. 2021; Pu et al. 2025). This direction is directly relevant to digital twin development because it shows that the port’s operational state and energy state should be updated together.

More recent work has expanded the port-energy literature toward integrated energy systems, robust configuration, and cross-domain uncertainty. Distributionally robust optimisation, integrated energy-logistics scheduling, multi-energy resilience configuration, and cooperative dispatching have shown that future port energy systems are not independent energy assets; they are coupled logistics-energy systems operating under uncertainty (Ma et al. 2025b; Ma et al. 2025a; Mo et al. 2024; Pu et al. 2025). Energy demand can rise because of shore-power connection, electric cargo handling, charging requirements, extended vessel service time, repeated handling, or congestion-induced inefficiency. Supply capacity may also vary because of renewable availability, battery state of charge, grid-import limits, and operational constraints. A digital twin that does not represent these interactions may underestimate energy shortfall or misinterpret the effect of electrification on resilience.

The electrification of port equipment and transport also changes the operational meaning of energy flexibility. Electric vehicles, AGVs, battery systems, and charging infrastructure are not passive energy loads. Their demand depends on scheduling, task allocation, service intensity, and operational disruption (Gao et al. 2024; Li et al. 2023; Lu et al. 2023). When vessel arrivals increase or yard processing slows, electric equipment may operate longer and charging demand may shift into peak periods. This means that electrification must be linked to dynamic equipment use, service demand, energy availability, and uncertainty. A port-scale digital twin should therefore represent energy demand as an operational state variable rather than a fixed input.

However, most energy-focused port studies still give limited attention to infrastructure health and degraded sensing. Energy-management models often assume that operational and electrical measurements are available with sufficient accuracy for real-time control (Iris and Lam 2019; Iris and Lam 2021; Ma et al. 2025b; Ma et al. 2025a; Mo et al. 2024; Pu et al. 2025). Similarly, many port electrification studies focus on load scheduling, cost reduction, emissions mitigation, or microgrid reliability without modelling how uncertainty in sensor data affects state estimation and decision support (Abu Bakar et al. 2023; Lu et al. 2023; Peng et al. 2021; Samaei and Riffat 2026a; Zhang et al. 2025). This creates a gap between optimisation under assumed data quality and digital twin operation under degraded information. In a realistic electrified port, energy demand may be estimated from incomplete equipment-use records, delayed shore-power measurements, uncertain vessel service times, or noisy renewable-generation forecasts. If this uncertainty is not represented, the digital twin may underestimate energy shortfall or overstate the resilience of the electrified terminal.

Low-carbon ports also require a wider interpretation of resilience. A system may reduce emissions under normal operation but become fragile under compound stress if energy capacity, storage limits, yard saturation, and sensor degradation are not considered together (Iris and Lam 2019; Iris and Lam 2021; Ma et al. 2025b; Ma et al. 2025a; Mo et al. 2024; Samaei and Riffat 2026a; Zhang et al. 2024). High electrification levels can be beneficial during stable operation but may amplify operational stress when vessel arrivals increase, renewable availability decreases, or grid-import capacity becomes constrained. Under such conditions, resilience depends not only on energy efficiency but also on the ability of the digital twin to recognise uncertainty, anticipate overload, and coordinate corrective actions before service degradation becomes severe.

Port infrastructure includes berths, quay walls, piles, decks, pavements, cranes, fenders, mooring systems, yard surfaces, utility corridors, and energy-related assets. Many of these components are exposed to repeated operational loading, marine environmental effects, corrosion, fatigue, settlement, vibration, and long service periods. Structural health monitoring has therefore become increasingly important for maintaining the serviceability and reliability of marine and port infrastructure (Gürdür Broo et al. 2022; Callcut et al. 2021; Gao et al. 2023b; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Riffat et al. 2025a; Riffat et al. 2025c; Shim et al. 2019; Song et al. 2025). Conventional inspection-based maintenance can identify visible deterioration, but it may not provide continuous information on hidden damage, progressive degradation, or the dynamic interaction between infrastructure condition and operational demand.

Sensor-based monitoring can partly address this limitation by collecting strain, acceleration, displacement, temperature, corrosion, and environmental data from critical assets (Gao et al. 2023b; Lu et al. 2020; Nasim et al. 2026; Riffat et al. 2025a; Riffat et al. 2025c; Shim et al. 2019; Song et al. 2025). Digital twin-based structural health monitoring extends conventional monitoring by linking sensor measurements with computational models, diagnostic algorithms, anomaly detection, and predictive maintenance logic (Gürdür Broo et al. 2022; Callcut et al. 2021; Gao et al. 2023b; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Rasheed et al. 2020; Riffat et al. 2025a; Riffat et al. 2025c; Shim et al. 2019; Song et al. 2025; Sun et al. 2025; Tao et al. 2019). In civil infrastructure, digital twins can support monitoring, anomaly detection, asset maintenance, condition assessment, lifecycle management, and diagnosis-informed intervention planning (Gürdür Broo et al. 2022; Callcut et al. 2021; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Shim et al. 2019; Song et al. 2025). These developments are important for port systems because infrastructure condition directly affects operational capacity. A degraded berth, restricted quay segment, reduced crane availability, deteriorated yard zone, or weakened equipment-support area can change service capacity, increase delay, and alter the reliability of operational decisions. Therefore, infrastructure health should not be treated as a separate maintenance variable outside the port digital twin. It should be represented as a dynamic state variable that affects the resilience of the terminal.

The relevance of structural health monitoring becomes stronger in marine and offshore infrastructure because monitoring data are often uncertain, noisy, and affected by environmental exposure. Recent work on digital twin-enabled monitoring, offshore structural diagnosis, jack-up platforms, wharves, offshore wind-related systems, and adaptive marine infrastructure monitoring indicates that structural condition should not be treated as a static background assumption when operational loads and environmental effects evolve (Riffat et al. 2025a; Riffat et al. 2025b; Riffat et al. 2026; Riffat et al. 2025c; Samaei and Riffat 2025; Samaei and Riffat 2026b). In the context of ports, this means that berth, quay, pile, deck, and equipment-support conditions can influence service capacity, maintenance priority, and operational confidence.

Infrastructure health data are themselves uncertain. Sensor measurements may contain noise, drift, missing values, calibration error, environmental variability, and partial observability (Gao et al. 2023b; Lu et al. 2020; Nasim et al. 2026; Riffat et al. 2025a; Riffat et al. 2025c; Shim et al. 2019; Song et al. 2025). These issues may be amplified by harsh exposure conditions, access limitations, sensor ageing, and heterogeneous monitoring layouts. A digital twin that uses health-monitoring data without representing this uncertainty may overestimate the accuracy of the infrastructure-health state. This is especially problematic when infrastructure condition is used to support operational decisions, such as berth assignment, equipment deployment, load restrictions, or maintenance prioritisation. In these cases, uncertainty in health estimation can propagate into logistics performance and energy demand.

The present study addresses this issue by representing infrastructure health through a normalised health index and an associated risk measure within the port digital twin. The health index does not replace detailed structural analysis of individual assets. Instead, it provides a system-level representation of monitored infrastructure condition that can interact with operational and energy states. This modelling choice is consistent with broader digital twin research in civil infrastructure and health-aware systems, where asset condition is increasingly represented as a dynamic state variable linked to monitoring, diagnosis, and decision support (Gürdür Broo et al. 2022; Callcut et al. 2021; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Rasheed et al. 2020; Riffat et al. 2025a; Shim et al. 2019; Song et al. 2025; Sun et al. 2025; Tao et al. 2019). More detailed asset-level models can be integrated in future work, but the present framework focuses on the coupled behaviour of the port system.

Uncertainty is a defining feature of practical digital twin operation. In port systems, uncertainty arises from stochastic vessel arrivals, variable cargo exchange, changing crane productivity, fluctuating yard conditions, renewable-generation variability, uncertain shore-power demand, equipment availability, and infrastructure-condition estimation (Iris and Lam 2021; Li et al. 2023; Ma et al. 2025b; Mo et al. 2024; Pu et al. 2025; Samaei and Riffat 2026d). In addition to these physical and operational uncertainties, the digital twin must also handle data-quality uncertainty. Sensor loss, measurement noise, timestamp mismatch, delayed reporting, and synchronisation error can distort the estimated state of the system (Errandonea et al. 2020; Fuller et al. 2020; Gao et al. 2023a; Gao et al. 2024; Gao et al. 2023b; Jiang et al. 2021; Jones et al. 2020; Lu et al. 2020; Rasheed et al. 2020). These effects are not minor technical details. They influence how the digital twin interprets congestion, energy shortfall, asset health, and recovery behaviour.

Digital twin research has increasingly emphasised the need to represent uncertainty, model fidelity, data quality, and decision confidence (Errandonea et al. 2020; Fuller et al. 2020; Gao et al. 2023a; Gao et al. 2024; Gao et al. 2023b; Jones et al. 2020; Rasheed et al. 2020; Sun et al. 2025). The broader digital twin literature identifies data integration, model updating, interoperability, and trustworthiness as central challenges for digital twin development. In infrastructure applications, digital twins must connect monitoring data with reliable models and interpretable maintenance decisions (Gürdür Broo et al. 2022; Callcut et al. 2021; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Shim et al. 2019; Song et al. 2025). These points are particularly relevant to port systems because operational, energy, and monitoring data are often produced by different platforms with different sampling rates and reliability levels (Kapkaeva et al. 2021; Klar et al. 2023).

Uncertainty also appears in port optimisation and scheduling studies. Uncertain operation time, stochastic AGV tasks, renewable variability, port-integrated energy scheduling, berth allocation under uncertainty, and cross-domain dispatch uncertainty all show that ports cannot be represented as deterministic systems (Iris and Lam 2021; Li et al. 2023; Ma et al. 2025b; Mo et al. 2024; Pu et al. 2025; Samaei and Riffat 2026d). However, much of this work focuses on mathematical scheduling or energy dispatch rather than degraded sensing and state-estimation confidence inside a digital twin. This distinction matters because a digital twin must continue to estimate the system state even when observations are incomplete, delayed, noisy, or temporally inconsistent.

Synchronisation error is particularly relevant in multi-layer port digital twins. Operational events, energy measurements, and structural monitoring data may not be recorded at identical time intervals. A crane productivity record may represent a completed service period, while an energy meter may provide near-continuous measurements and a structural sensor may report at another sampling rate. If these streams are fused without temporal correction, the digital twin may combine variables that do not correspond to the same physical state (Errandonea et al. 2020; Fuller et al. 2020; Gao et al. 2023a; Gao et al. 2024; Gao et al. 2023b; Jiang et al. 2021; Jones et al. 2020; Lu et al. 2020). This can create artificial correlations or hide real stress propagation. For example, an apparent reduction in energy demand may simply reflect delayed reporting rather than actual load reduction. Similarly, a health-risk estimate may be associated with the wrong operational condition if timestamps are not aligned. For this reason, synchronisation correction is treated in this study as a necessary part of the uncertainty-aware digital twin rather than as a minor preprocessing step.

Degraded sensing also affects resilience assessment. If a portion of the monitoring network is unavailable, the digital twin may still operate, but with lower confidence. A robust framework should not fail immediately when data become incomplete. It should adjust the uncertainty level, rely on available measurements, use model-based estimation where appropriate, and report the increased uncertainty in the state estimate (Gao et al. 2023b; Lu et al. 2020; Nasim et al. 2026; Rasheed et al. 2020; Shim et al. 2019; Song et al. 2025). This capability is essential for ports because sensing networks are distributed, exposed, and often maintained under operational constraints. A practical port digital twin must therefore support decision-making under partial observability rather than assume perfect data availability.

The reviewed literature shows that port digital twins, electrified port energy systems, structural health monitoring, and uncertainty-aware infrastructure models have each developed rapidly. Yet the intersection of these areas remains insufficiently integrated. Port digital twin studies often emphasise logistics coordination, automated terminal operation, port digitalisation, and operational efficiency (Belmoukari et al. 2023; Boullauazan et al. 2023; Eom et al. 2023; Gao et al. 2023a; Gao et al. 2024; Heikkilä et al. 2022; Heilig et al. 2017; Kapkaeva et al. 2021; Klar et al. 2023; Li et al. 2021). Port electrification studies often focus on microgrid scheduling, shore-power demand, renewable integration, energy efficiency, or emissions reduction (Abu Bakar et al. 2023; Iris and Lam 2019; Iris and Lam 2021; Lu et al. 2023; Ma et al. 2025b; Ma et al. 2025a; Mo et al. 2024; Peng et al. 2021; Pu et al. 2025; Samaei and Riffat 2026a; Zhang et al. 2024; Zhang et al. 2025). Structural health monitoring studies often focus on asset-level damage detection, condition assessment, anomaly detection, or predictive maintenance (Gürdür Broo et al. 2022; Callcut et al. 2021; Gao et al. 2023b; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Riffat et al. 2025a; Riffat et al. 2025c; Shim et al. 2019; Song et al. 2025). Uncertainty-aware optimisation studies often address berth allocation, energy dispatch, AGV scheduling, and operational planning, but not the coupled digital twin environment in which logistics, electrification, sensing quality, synchronisation, and infrastructure health evolve together (Aslam et al. 2023; Iris and Lam 2021; Li et al. 2023; Ma et al. 2025b; Mo et al. 2024; Pu et al. 2025; Riffat et al. 2026; Samaei and Riffat 2026c; Samaei and Riffat 2026d).

This separation leaves several unresolved issues. First, many port digital twin models do not explicitly quantify how degraded sensing affects operational state estimation (Eom et al. 2023; Gao et al. 2023a; Gao et al. 2024; Klar et al. 2023; Li et al. 2021). Second, electrification is often modelled as an energy-management problem without sufficient linkage to infrastructure condition and data uncertainty (Abu Bakar et al. 2023; Iris and Lam 2019; Iris and Lam 2021; Lu et al. 2023; Ma et al. 2025b; Ma et al. 2025a; Mo et al. 2024; Peng et al. 2021; Pu et al. 2025; Samaei and Riffat 2026a). Third, structural health monitoring is rarely integrated as a dynamic operational layer within port digital twins (Gürdür Broo et al. 2022; Callcut et al. 2021; Gao et al. 2023b; Jiang et al. 2021; Lu et al. 2020; Nasim et al. 2026; Riffat et al. 2025a; Riffat et al. 2025c; Shim et al. 2019; Song et al. 2025). Fourth, synchronisation error between operational, energy, and monitoring data streams is often overlooked, even though it can affect decision reliability (Errandonea et al. 2020; Fuller et al. 2020; Gao et al. 2023a; Gao et al. 2024; Gao et al. 2023b; Jiang et al. 2021; Jones et al. 2020; Rasheed et al. 2020). Fifth, benchmark comparisons and ablation studies are not consistently used to isolate the contribution of uncertainty propagation, energy modelling, infrastructure-health tracking, and synchronisation correction in port-scale low-carbon digital twins (Klar et al. 2023; Li et al. 2021; Ma et al. 2025b; Mo et al. 2024; Pu et al. 2025).

The present study is positioned to address these gaps through an integrated uncertainty-aware digital twin framework for resilient low-carbon port infrastructure. The framework connects operational flow, electrification demand, infrastructure health, and uncertainty propagation within a single simulation-based decision-support structure. It does not assume perfect sensing. Instead, it evaluates port performance under sensor loss, measurement noise, synchronisation delay, operational variability, energy stress, and compound degraded-data conditions. The framework is tested using a controlled synthetic stochastic simulation environment so that the model configuration, scenario assumptions, performance indicators, and benchmark comparisons can be stated transparently. This positioning builds on prior advances in port digitalisation, energy-aware terminal operation, infrastructure digital twins, and uncertainty-aware optimisation while addressing their limited integration (Samaei and Riffat 2026a; Shim et al. 2019; Song et al. 2025; Sun et al. 2025; Tao et al. 2019; Tijan et al. 2021; Wang and Zou 2024; Xiang and Liu 2021; Zhang et al. 2024; Zhang et al. 2025).

The closest prior studies clarify the specific contribution boundary. Zhou et al. (2021) developed a digital-twinning decision-support system for port resilience and predefined recovery actions. Zhu et al. (2026) integrated digital-twin concepts with resilience and sustainability assessment for a dry-bulk port facility. Homayouni et al. (2025) synthesised digital-twin sustainability applications in seaports and identified data quality, implementation and model validation as persistent barriers. More recently, Gil-Pereira et al. (2026) benchmarked digital-twin architectures across European smart-port initiatives. The present study differs by jointly modelling progressive electrification, battery dispatch, infrastructure-health uncertainty, persistent sensor loss, temporal misalignment, six-state posterior covariance and bounded uncertainty-aware response in a container-terminal setting. Recent studies further reinforce the need to distinguish information-layer degradation from physical-state change. Di Fiore et al. (2026) developed a sensing digital twin that associates corrected measurements with reliability information, while Geng et al. (2025) integrated multi-source data within a system digital twin for life-cycle infrastructure-risk assessment. These studies support the treatment of sensing reliability and infrastructure risk as explicit digital-twin functions. The present framework extends this direction to an electrified port-scale system in which operational congestion, energy demand, physical health, persistent sensor loss and bounded response are dynamically coupled.

Recent digital-twin standards and reference frameworks provide an additional basis for positioning the proposed architecture. ISO/IEC 30173:2023 establishes general digital-twin concepts, terminology, system context, functional views and lifecycle considerations, while the ISO 23247 series defines a reference architecture, digital representation and information-exchange principles for digital twins in manufacturing. Although these standards are not port-specific, their separation of physical entities, digital representations, services and information exchange is consistent with the layered structure adopted here. The Digital Twin Consortium has similarly emphasised IT/OT infrastructure, virtual representation, integration, synchronisation and application services in its Platform Stack Architectural Framework, and its more recent Digital Twin System Framework organises digital-twin systems around data, context, decision/process orchestration and actuation. The present framework is aligned with these general architectural principles but extends them for the specific problem considered here by explicitly representing persistent sensor loss, temporal misalignment, posterior state uncertainty, infrastructure-health risk, electrification stress and bounded uncertainty-aware response within one coupled port-scale simulation. It should therefore be viewed as a domain-specific analytical implementation rather than as an alternative general-purpose digital-twin standard.

The contribution of this study is therefore not the introduction of digital twins, port electrification, or structural health monitoring as separate concepts. Its contribution lies in coupling these concepts under degraded information quality. By treating information uncertainty as an explicit post-update diagnostic linked to posterior covariance, sensor availability, synchronisation delay and measurement noise, rather than as an unreported external error term, the proposed framework provides a more defensible basis for evaluating low-carbon port resilience. This positioning also supports the broader need for digital infrastructure systems that remain useful when data are incomplete, delayed, noisy, or partially inconsistent. The next section presents the proposed framework and defines the mathematical structure used to connect operational performance, energy demand, infrastructure health, and uncertainty-aware state estimation.

The port is represented as a coupled physical–digital system with operational, energy, infrastructure-health and information-quality layers. The filter estimates six physical states, while the uncertainty index is calculated after each covariance update and appended only for reporting, resilience assessment and operating-state classification.

Here, x_p contains the six physical states estimated by the normalised extended Kalman filter, x_r is the reporting vector, and q contains the discrete queue state, aggregate and cohort-specific yard stocks, battery energy, effective quay-crane allocation and flexible-load backlog required by the hybrid simulation engine (Figure 2). The operating-state class and the lagged response-action vector are stored separately from the EKF state. The uncertainty index is calculated after the covariance update and is not included in the transition function, process covariance or state-scaling matrix.

The fixed update interval is Δt = 5 min = 1/12 h. Where a flow is expressed in TEU/day, multiplication by Δt/24 converts the daily rate into the quantity processed during one simulation step.

The operational layer adopts a system-level mesoscopic representation rather than an event-level terminal microsimulation. Vessel arrivals, queue formation, berth service, crane productivity, yard stock and completed-vessel waiting delay are represented explicitly. Individual crane-dispatch sequences, crane interference, yard-block allocation, reefer clustering, plug-demand coincidence, AGV routing, truck-gate interactions and container-rehandling cycles are not represented as separate states. Their aggregate effects enter through effective quay-crane productivity, yard-service efficiency, equipment utilisation, congestion-related energy losses and scenario-specific productivity modifiers. The resulting outputs should therefore be interpreted as port-scale resilience estimates rather than dispatch-level predictions.

Vessel arrivals are represented by a non-homogeneous Poisson process. Short-term persistence is introduced through a bounded AR(1) perturbation.

The baseline intensity is λ₀ = 0.3166667 vessels h^-1, with Aλ = 0.20, ρλ = 0.75 and σε,λ = 0.08. Vessel workload is sampled once at arrival as Cship = 800 + 2,800X, where X follows a Beta(2.9464286, 7.0535714) distribution. This bounded distribution retains the 800–3,600 TEU/call range and has a mean of 1,625 TEU/call. The arrival-rate perturbation is updated every five minutes and is initialised at zero. The scenario multiplier scales the latent vessel-arrival demand intensity. To represent the finite approach-channel intake of the synthetic reference terminal, the perturbed intensity is capped at before non-homogeneous Poisson sampling. Consequently, only the admitted intensity enters the terminal event ledger, queue, berth-service process and dynamic delay-state equation. The nominal and realised arrival multipliers are reported separately in Supplementary Table S13a. The approach-channel cap is represented as an exogenous admission-intensity constraint rather than as an explicit upstream anchorage queue. Demand above the admitted intensity does not enter the terminal event ledger and is not counted as terminal waiting delay, served demand or end-of-horizon queue.

The nominal crane productivity is sampled at service commencement from a triangular distribution, μQC,j∼Triangular(30,33,36) moves h^-1 crane^-1, and remains fixed for the corresponding vessel service. The precautionary multiplier mR, defined in Equation (16a), represents the additional health-risk restriction activated by the response policy.

For each active vessel, remaining workload is reduced every five minutes by the moves completed during that step. Vessels enter a first-come-first-served queue, and free berths are assigned to the earliest waiting vessels. At berth assignment, a vessel receives three quay cranes whenever at least three cranes are idle. If only two cranes are available, service may commence with two cranes; service does not commence with fewer than two. A fourth crane is assigned only through the deterministic warning- or stressed-state response rule. Simultaneous assignments follow first-come-first-served order, with physical arrival time and fixed vessel identifier used as deterministic tie-breaks. The terminal-wide limit is twenty-two cranes. The initial state with three active berths and twelve effective cranes is a deliberate warm start with four cranes assigned to each initially active vessel and does not redefine the nominal three-crane rule. Individual completed-vessel waiting delay is calculated from event records:

At the five-minute update scale, is the dynamic port-level delay state propagated from the difference between admitted vessel-arrival intensity and effective vessel-service intensity. The notation is reserved exclusively for this five-minute digital-twin state. Event-level waiting delay is denoted by , and the replication-level completed-vessel mean is denoted by . These reporting quantities are derived from service-event records and are not substituted for the filter state. The coefficient is the delay-sensitivity parameter examined in the one-at-a-time analysis.

Berth occupancy and yard saturation are defined as follows:

The implemented yard update is cohort-first. Import, export and transshipment stocks are updated independently using Equation (6f), after which aggregate yard stock and saturation are calculated as accounting identities using Equation (6g). Equation (6a) is therefore retained as the equivalent aggregate conservation relationship and is not executed as a second independent stock update. The cohort capacities are TEU, TEU and TEU. Their initial stocks are 16,704, 11,136 and 6,960 TEU, respectively. The fixed yard thresholds are , and . These values are used consistently in the yard-efficiency model, congestion-loss calculation, resilience normalisation and operating-state classification.

Here, Mj,step is the number of container moves completed for active vessel j during step k, with fTEU/move = 1.25 TEU/move. The effective yard-workload shares are ωimp = 0.55, ωexp = 0.30 and ωtr = 0.15, with mean dwell times τimp = 3.0 days, τexp = 2.0 days and τtr = 1.0 day. These cohorts are system-level yard-workload classes rather than a detailed directional representation of import and export logistics. Aggregate gate-and-rail evacuation capacity is 14,000 TEU/day in S0–S2 and S4–S5 and 12,600 TEU/day in S3. When desired releases exceed available evacuation capacity, the available capacity is distributed proportionally among the three cohorts.

The base efficiency is , , and the productivity multipliers are 1.00 in S0–S3, 0.88 in S4 and 0.85 in S5.

The equipment-utilisation index is a weighted port-scale measure combining active quay-crane deployment, yard saturation and berth occupancy. The weights sum to unity and remain fixed in all scenarios and benchmark models.

A vessel’s shore-power connection status and demand are sampled at berth assignment and remain fixed until service completion. The connection indicator follows .

The auxiliary-load and wind-capacity-factor AR(1) processes are updated hourly and held constant over the twelve five-minute substeps within each hour. The auxiliary-load deviation is initialised at zero, while the wind-capacity-factor process is initialised at its calibrated mean of 0.495413.

The calibrated mean wind capacity factor is 0.495413. Together with the 16 MW photovoltaic profile, it gives 90.0 GWh/year gross renewable generation in S0–S3. Scenario multipliers reduce gross renewable energy to 67.5 GWh in S4 and 58.5 GWh in S5.

The battery begins at 36 MWh, operates between 20% and 95% SOC, has charge and discharge efficiencies of 0.95 and 0.94, and a self-discharge coefficient of 8.33 × 10^-6 h^-1. Grid charging and simultaneous charge–discharge are prohibited.

The numerical floor of 10^-6 MW is used only to prevent division by zero and has no material effect under positive terminal demand. Equation (12) is the instantaneous digital-twin state; Equation (12a) is the integrated scenario-level shortfall reported in the results. Flexible-load deferral and repayment are included through effective demand, so deferred energy cannot disappear from the power balance.

The coefficients are , and . Physical degradation is propagated independently of information quality. The perturbation is sampled from a zero-mean Gaussian distribution before application of the monotonicity projection. The projection truncates negative total increments; consequently, realised physical-damage increments are non-negative and are conservatively biased relative to the corresponding unprojected deterioration process. No physical healing is represented in the absence of an explicit repair event. The uncertainty-dependent contribution is accumulated separately in the epistemic margin and is applied only as a conservative adjustment to estimated health for decision support. The initial margin is , its cap is 0.05, and the health-process perturbation has a standard deviation of per five-minute step. The fixed physical-health thresholds are and . The same thresholds are used in the health-efficiency function, posterior infrastructure-risk calculation and scenario-level health reporting.

The health-efficiency factor ηH represents the physical effect of infrastructure condition on service efficiency. The multiplier mR is a separate precautionary restriction activated by the response policy. Each factor is applied once in Equation (3), preventing double counting.

Infrastructure risk is calculated at every update from the EKF posterior mean and variance. The variance floor 10^-12 is used only to prevent numerical division by zero and does not alter the EKF covariance. The scenario-level result is the mean of instantaneous replication-level risks, not a probability reconstructed from aggregated scenario means.

The 120 channels comprise 36 operational, 30 energy, 42 structural-health and 12 environmental channels. Their grouped mapping is reported in Table 2, while the complete observation-row weights are provided in Supplementary Table S1. For each replication, the scenario-specific unavailable-channel set is sampled once at simulation initialisation using the domain-stratified quotas in Table 3 and remains fixed throughout the 14-day warm-up and the subsequent 351-day reporting period. A statistically independent persistent set is sampled for each new replication.

All observations are normalised using the state-scaling matrix applied by the EKF. Unavailable channels and the corresponding rows in the observation vector, Ck and Rk are removed before correction. M4 performs first-order causal extrapolation from the two most recently received samples when the imposed delay does not exceed 10 min. Under the 15 min delay in S5, the state is propagated through the transition model until the next observation becomes available. M3 uses causal nearest-neighbour alignment for energy channels and zero-order hold elsewhere. M2 uses zero-order hold of the latest received sample, while M1 uses raw delayed observations. No observation acquired after tk is used in the estimate or response action calculated at tk, and model predictions are not reintroduced as pseudo-observations. The diagonal measurement-noise model assumes conditionally independent normalised channel errors with a common scenario-level noise magnitude; correlated, heteroscedastic, drifting and outlier-contaminated errors are outside the present scope.

For compactness, x(k+1|k) and x(k+1|k+1) in Equations (20)–(20d) denote the normalised predicted and corrected state estimates, respectively. The initial normalised standard deviations are [0.04,0.02,0.025,0.04,0.02,0.015], and the base process-noise standard deviations are [0.006,0.004,0.005,0.008,0.004,0.0015]. Scenario process-noise multipliers are 1.00, 1.15, 1.25, 1.45, 1.70 and 2.10 for S0–S5. The transition Jacobian is evaluated for the six normalised continuous physical states using central finite differences. The perturbation applied to state i is 10−5 max(1,|x̃i|). A one-sided difference is used when a central perturbation crosses a clipping boundary, and the derivative of an output that remains at a hard bound is set to zero. The observation Jacobian is the exact linear grouped observation matrix. Discrete queue, berth-assignment and crane-allocation variables are held fixed during differentiation and enter the transition through the auxiliary input vector. Event-driven changes are represented through the auxiliary inputs and the scenario-dependent process-noise multiplier. Jacobians are updated at every five-minute prediction step. The Joseph form in Equation (20d) preserves positive semidefiniteness under finite-precision computation and partial observability.

After measurement correction, posterior means are projected onto their physical domains: , , and , , and within . The Joseph-form covariance update is retained without artificial contraction, subject only to a diagonal numerical floor of . Measurement correction is skipped if fewer than six observation rows remain, , Cholesky factorisation of the innovation covariance fails, or . In a skipped correction, and , and no model-generated pseudo-observation is inserted.

The four components of are not interpreted as a mutually independent variance decomposition. The covariance term measures realised posterior dispersion under the adopted estimator, whereas sensor availability, delay and nominal measurement noise represent exogenous information-quality hazards. Consequently, is a conservative composite diagnostic rather than a calibrated probability of state-estimation failure. Across 5,054,400 reporting-period updates per scenario, no correction was skipped because of insufficient row count, rank deficiency, Cholesky failure or excessive innovation-covariance conditioning. The maximum condition number of the innovation covariance increased from 2.21 in S0 to 9.87 in S5 and remained far below the skip threshold. Complete observation-support and correction-availability diagnostics are reported in Supplementary Tables S11 and S11a.

Here, P11(k) to P66(k) denote the six diagonal entries of the posterior normalised covariance matrix. The values tr(P_max) = 0.35, τ_ref = 60 min and σ_ref = 0.20 are engineering normalisation references rather than maxima of the six scenarios. The initial value Ux(0) = 0.10 is a conservative warm start used only before the first covariance update. From the first update onward, Ux is calculated exclusively from Equation (21). All reported results exclude the 14-day warm-up period. Supplementary Table S2 reconstructs the scenario-level uncertainty indices from the four components of Equation (21).

The yard term is instantaneous; peak yard saturation is used only as a scenario-level reporting indicator. Warning-threshold exceedances are counted as nW(k) = I[D̂v(k) ≥ 8 h] + I[Ŷ(k) ≥ 0.85] + I[Êshort(k) ≥ 0.05] + I[Pgrid,pre(k) ≥ 48 MW] + I[Rinfra(k) ≥ 0.25]. Stable operation requires RI ≥ 0.75, Ux < 0.25 and nW = 0. Warning operation is assigned when 0.65 ≤ RI < 0.75, 0.25 ≤ Ux < 0.35 or nW = 1. Stressed operation is assigned when RI < 0.65, Ux ≥ 0.35 or nW ≥ 2. The thresholds are evaluated only from internally available posterior estimates and pre-dispatch grid demand; the external ground-truth evaluator is not used for classification.

A stressed episode begins after three consecutive five-minute stressed updates. Recovery is recorded after six consecutive updates with RI ≥ 0.65 and Ux < 0.35. Stress entry therefore requires 15 min persistence, recovery requires 30 min persistence, and episodes not recovered within 48 h are right-censored.

The response policy is deterministic and uses only information available at update k. In stable operation, it introduces no new crane reallocation or flexible-load deferral and repays eligible first-in-first-out backlog subject to the repayment and grid-capacity limits. In warning and stressed operation, at most two and four idle cranes, respectively, are assigned one at a time to active vessels in ascending predicted remaining-service-time order; ties are resolved by earlier service-start time and then fixed vessel identifier. Cranes are drawn only from the idle pool, so no active vessel is reduced below two cranes. The yard-evacuation limit becomes 1.05Cevac, s in warning operation and 1.10Cevac, s in stressed operation.

When connected shore-power requests cannot all be met, vessels are ranked by shortest remaining service time using the same deterministic tie-break; denied demand remains in the physical power balance and may become unmet power. Flexible-load deferral and repayment follow Equations (24–24e), oldest backlog is repaid first, and simultaneous deferral and repayment are prohibited. Renewable power is used before battery discharge and grid import. Battery discharge targets 48 MW in warning operation and 45 MW in stressed operation. Finally, the precautionary multiplier mR is applied once to the affected service-capacity contribution. Actions selected at update k affect the physical system at update k+1 and represent bounded simulation responses rather than autonomous field control.

The 10% and 20% limits are the implemented upper bounds on schedulable equipment-charging and auxiliary-traction demand contained within aggregate cargo-handling demand. No additional unreported state is used. Electrical energy directly required for productive quay-crane motion and vessel-service progress is non-deferrable. The repayment constraint uses , which is calculated before repayment, thereby avoiding circular dependence. The 45 MW repayment ceiling preserves 10 MW of headroom relative to the 55 MW physical grid-import limit.

Deferred flexible energy is stored in a first-in-first-out backlog with a 6 MWh capacity, 3 MW deferral and repayment limits, and a maximum age of 2 h. Energy not repaid within 2 h is recorded as unmet flexible energy. Any remaining backlog at the end of the reporting horizon is also added to unmet energy. Simultaneous deferral and repayment are prohibited. When neither action is selected, and the backlog is unchanged. Let denote the response selected after posterior correction at update . The physical interval uses . All physical-propagation equations use the applied quantities , , and , preventing same-step feedback. Every action applies for one five-minute physical interval and expires at the interval boundary unless explicitly reselected. Additional response cranes return to the idle pool unless reassigned at the next update.

M1 uses raw delayed and noisy observations and fixed operational thresholds. M2 updates operational and energy states using zero-order hold but has no covariance propagation or temporal correction. For M2, the common external evaluator calculates the normalised ex-post error and ; these quantities remain unavailable to the policy. M3 includes the energy model and causal nearest-neighbour alignment for energy channels. Its current normalised aligned innovation is projected into state space as , and provides an instantaneous residual-energy uncertainty proxy. This proxy is not interpreted as a propagated covariance or windowed residual variance. M4 uses the complete six-state EKF, causal temporal correction, health-risk estimation and the post-update uncertainty diagnostic. Exact thresholds, information access and evaluator roles are specified in Table 5.

The ablation analysis removes one capability at a time. A separate no-action variant retains the full estimator and diagnostics but disables all adaptive-response actions, allowing the estimation contribution to be distinguished from the response-policy contribution.

The framework is a controlled simulation-based evaluation and does not claim field deployment, autonomous terminal control, detailed electrical power-flow analysis or asset-level structural diagnosis. The operational model is mesoscopic and does not resolve crane interference, yard-block assignment, reefer clustering, vehicle routing or rehandling cycles as separate states. Their effects enter through workload, utilisation, congestion and electrical-demand parameters. The framework supports system-level resilience assessment and comparative planning; terminal-specific deployment requires measured-data calibration and lower-level operational, electrical and structural models.

The synthetic terminal represents a medium-to-large electrified container port. The implied annual throughput is 7.6 × 365 × 1,625 = 4,507,750 TEU/year, rounded to 4.5 million TEU/year.

The numerical configuration is intended to represent a technically plausible medium-to-large container-terminal system rather than to reproduce any identifiable commercial port. Parameter selection followed three principles. First, scale-defining quantities, including annual throughput, berth and quay-crane resources, yard capacity, electrical-supply capacity, renewable capacity and battery storage, were selected as mutually consistent system-level values capable of supporting the specified annual cargo flow and progressive electrification scenarios. Second, stochastic and dynamic parameters were selected to produce physically bounded and numerically stable trajectories over the annual simulation horizon while preserving meaningful operational, energy and sensing variability. Third, stress-scenario parameters were deliberately specified as controlled perturbations around the reference configuration rather than as forecasts for a particular terminal. The S0–S5 values should therefore be interpreted as an experimental stress trajectory for comparative evaluation. They are not claimed to be universal design values or empirically calibrated thresholds for operational deployment. Where deployment is intended, these quantities must be re-estimated from terminal operating-system records, electrical measurements, monitoring data and observed disruption–recovery behaviour.

The principal configuration values and their modelling roles are summarised in Table 1, while scenario-dependent perturbations are reported separately in Table 4 to distinguish baseline system scale from experimental stress assumptions.

The observation architecture comprises 120 aggregated channels: 36 operational, 30 energy, 42 structural-health and 12 environmental channels. The grouped mapping and scenario-specific persistent dropout quotas are reported in Tables 2 and 3, while the complete observation-row weights are provided in Supplementary Table S1.

Scenarios S0–S5 progressively increase information degradation and operational–energy stress (Figure 4). Sensor loss is implemented using the domain-stratified quotas in Table 3. The latent arrival-demand, renewable and productivity multipliers are applied to the baseline latent traffic intensity, renewable-generation profile and equipment-productivity process, respectively. The approach-channel cap is subsequently applied to the perturbed latent traffic intensity before admitted arrivals are sampled.

All benchmark models share identical physical equipment, grid capacity, renewable capacity, battery storage, stochastic realisations, warm-up duration, reporting horizon and maximum response-action budget. No benchmark model or scenario is tuned separately using its reported outcomes. Ground-truth states and common evaluation outputs are unavailable to all estimation and response policies.

The common external evaluator records physical outcomes for every benchmark and ablation configuration but never provides information to a policy. For M1, and externally evaluated infrastructure risk are used only to calculate a descriptive resilience outcome and remain unavailable to the response logic. For M2, the evaluator forms and , then applies Equations (15) and (21) ex post; neither quantity is available during state updating or action selection. M3 uses its instantaneous normalised residual-energy proxy internally, while infrastructure risk is evaluated ex post. M4 calculates and infrastructure risk internally. In module-removal ablations, the physical subsystem remains active, but the corresponding state, diagnostic or response capability is excluded from the estimator, classifier and action-selection logic. The benchmark comparison contrasts capability stacks with different internal information and modelling functions; it does not causally isolate the effect of each capability.

Within each replication, berth occupancy, infrastructure risk, uncertainty index and resilience index are averaged over the 351-day post-warm-up reporting period. Peak yard saturation and peak grid import are defined as the maximum five-minute values within each replication and are subsequently averaged across replications. Energy shortfall is calculated as the ratio of integrated unmet energy to integrated effective electrical demand using Equation (12a). Completed-vessel waiting delay is the event-level mean defined in Equation (4a), while vessels remaining in the queue at the horizon boundary are reported separately. Recovery time is calculated at the episode level using the persistence rules defined in Section 3.7. No M2 or M4 recovery event is censored under S4, permitting paired inference for recovery time.

Here, denotes the annualised power-flow category, including demand, renewable generation, direct renewable use, battery charging, battery discharging, grid import or unmet power. All quantities reported in GWh/year are obtained by integrating over the 351-day post-warm-up reporting period and multiplying the resulting total by . The 14-day warm-up period is excluded from the reported annual energy balances.

The simulation combines event-based vessel records with a fixed five-minute physical-system and digital-twin update. Each replication follows the same eighteen-step execution sequence (Figure 3):

The persistent dropout mask is sampled once at simulation initialisation and remains fixed through warm-up and reporting. Actions selected at update k affect the physical system at update k+1, maintaining a one-step causal lag. Ground-truth states are recorded only by the external evaluator and are inaccessible to estimators and policies. Event and stock ledgers enforce the vessel identity N_arr,report + N_carry-in = N_{served,report} + N_queue,end + N_service,end and the corresponding yard-stock balance. Boundary queues and stocks are reported explicitly rather than assigned zero delay or discarded.

The simulation contains 105,120 five-minute steps, including 4,032 warm-up steps and 101,088 reporting steps. Independent stochastic substreams are generated from NumPy SeedSequence 20260724 for vessel arrivals, vessel workload, quay-crane productivity, renewable generation, sensor degradation and health perturbations. The implementation uses Python 3.11.9, NumPy 1.26.4, SciPy 1.13.1, pandas 2.2.2, SimPy 4.1.1 and Matplotlib 3.9.0 on an Intel Core i7-12700 workstation with 32 GB RAM.

Numerical implementation safeguards include physical-domain clipping, the Joseph covariance form, prediction-only propagation under insufficient reduced observation support, prohibition of simultaneous battery charging and discharging, and explicit end-of-horizon accounting for flexible-load backlog. The annual battery-balance residual calculated from unrounded five-minute trajectories is below 10^-8 MWh in every scenario. Independent stochastic substreams and the fixed master seed make each reported replication reproducible.

Unless otherwise stated for censored recovery outcomes, reported uncertainty is the 95% confidence-interval half-width calculated from fifty replication-level means using Equation (26). Standard steady-state simulation principles guided the warm-up and replication-convergence checks (Law 2015). Because the benchmark models use common replication-specific stochastic substreams, all M2–M4 comparisons are paired by replication.

Positive paired differences denote favourable M4 performance: M2 − M4 for lower-is-better indicators and M4 − M2 for the resilience index. Two-sided paired tests, Holm family-wise adjustment (Holm 1979) and paired standardised effect sizes are applied using Equations (27a)–(27c).

State-specific 95% interval coverage is the proportion of latent ground-truth values contained within the corresponding posterior interval. Aggregate coverage is the arithmetic mean across the six normalised physical states. NIS and NEES are used as descriptive Kalman-filter consistency diagnostics (Bar-Shalom et al. 2001). NIS acceptance uses the 2.5% and 97.5% chi-square limits for the time-varying number of available observations, whereas NEES acceptance uses six degrees of freedom. These five-minute diagnostics are temporally dependent and are not interpreted as independent-sample hypothesis tests; scenario inference is based on replication-level summaries.

In Equation (29), Ŝs(t) is the Kaplan–Meier estimate of the recovery-time survival function (Kaplan and Meier 1958). For S5, recovery is reported as restricted mean recovery time up to the 48 h censoring limit. Its 95% interval uses 10,000 bias-corrected and accelerated bootstrap resamples of the fifty replication identifiers (Efron 1987). All episodes belonging to a selected replication are retained together during resampling, preserving within-replication dependence. The conventional interval for uncensored replication means is not applied to S5.

The distributions of the fifty paired differences are examined using Q–Q plots and Shapiro–Wilk tests (Shapiro and Wilk 1965). Energy-shortfall differences depart from normality at the 5% level. Bias-corrected and accelerated intervals based on 10,000 paired replication-level resamples and two-sided Wilcoxon signed-rank sensitivity tests are therefore used as robustness checks. These checks lead to the same inferential conclusions as the paired t-tests; the corresponding values are reported in Supplementary Table S6.

Rolling means of queue length, yard saturation, battery state of charge and uncertainty stabilise by Day 14 under both S4 and S5. The corresponding physical-health slopes also become approximately constant by the end of the warm-up period. Increasing the replication count from 40 to 50 changes every primary S4 and S5 mean by less than 0.8%, supporting the selected warm-up duration and replication count. For S4, completed-vessel waiting delay changes from 10.49 to 10.50 h, energy shortfall from 5.68% to 5.70%, infrastructure risk from 0.272 to 0.270, uncertainty index remains 0.310, recovery time changes from 14.58 to 14.60 h and resilience index changes from 0.641 to 0.640. For S5, completed-vessel waiting delay changes from 13.58 to 13.60 h, energy shortfall from 8.88% to 8.90%, infrastructure risk from 0.359 to 0.360, uncertainty index from 0.429 to 0.430, recovery time from 23.36 to 23.40 h and resilience index from 0.521 to 0.520. The complete warm-up and replication-convergence values are reported in Supplementary Tables S4 and S5.

The S5 recovery result is the 48-h restricted mean recovery time with its 95% BCa confidence interval. All other intervals are reported as 95% confidence-interval half-widths.

The end-of-horizon queue is reported separately to prevent vessels still waiting at the reporting boundary from being assigned zero delay or being implicitly represented as completed observations.

S0 establishes stable operation, with a mean completed-vessel waiting delay of 3.4 h, an energy shortfall of 0.6% and a resilience index of 0.91 (Tables 6a, 6b and 6c). S1 combines moderate electrification with sensor degradation; consequently, its performance changes cannot be attributed to sensing degradation alone. S2 raises the electrification share to 75% and increases energy shortfall to 3.8%, while the resilience index remains above the warning threshold at 0.76. S3 combines a 25% increase in vessel-arrival intensity with lower operational productivity and reduced yard-evacuation capacity, producing warning-state operation. Under S4 compound stress, the simulated terminal remains operational but is classified as stressed by the prespecified decision rules. S5 reaches the fixed 55 MW grid-import capacity and produces the lowest resilience index, 0.52, together with a mean end-of-horizon queue of 28.7 vessels.

Table 7 summarises scenario-level calibration, while state-specific NRMSE, NMAE, normalised bias and coverage values are provided in Supplementary Table S3.

Interval coverage remains close to the nominal 95% level under S0 and S1 but progressively falls below the nominal level as sensor loss, measurement noise and synchronisation delay intensify. Aggregate coverage decreases to 90.8% under S4 and 86.5% under S5. The estimator therefore remains informative but becomes increasingly overconfident under severe compound degradation. The simultaneous increase in the NIS and NEES ratios above unity and the decline in their chi-square acceptance rates support the same interpretation.

The mean and fifth-percentile health values refer to the latent physical-health trajectory (Table 8). The posterior standard deviation and infrastructure-risk probability refer to the EKF posterior estimate and are calculated at the five-minute update scale. Posterior health uncertainty increases monotonically from S0 to S5. The scenario-level infrastructure-risk values are time averages of instantaneous posterior probabilities and are not reconstructed from the reported mean physical health and mean posterior standard deviation.

Realised action-use statistics in Supplementary Table S20 confirm that the bounded response mechanisms are materially active. Warning-plus-stressed operation increases from 13.2% of reporting time in S0 to 85.2% in S5, while yard-enhancement duration increases from 1,112 to 7,177 h over the 351-day reporting period. The time share under the strongest precautionary multiplier, , increases from 0.4% to 25.9%. Deferred, repaid, overdue and terminal-backlog energy are reported separately, and the flexible-load ledger closes to the displayed precision in every scenario.

Battery discharge is counted as renewable contribution because grid charging is prohibited and the battery is charged only from renewable surplus (Tables 9a and 9b). Annual power-flow quantities are reported in GWh/year, except final stored battery energy and annual self-discharge loss, which are reported in MWh. The battery-balance residual calculated from unrounded five-minute trajectories is below 10^-8 MWh in every scenario; rounded values in Table 12 are not expected to reproduce this residual exactly. Gross renewable generation is 90.0 GWh/year in S0–S3, 67.5 GWh/year in S4 and 58.5 GWh/year in S5.

A fixed scenario emission factor of 0.45 t CO₂/MWh is used solely to translate grid-electricity consumption into operational electricity-related emissions (Table 10). It is not attributed to a specific national grid, the reported values scale linearly with the selected factor, and carbon is not included in the resilience-index calculation.

The carbon boundary covers operational electricity only. It excludes marine fuel, fuel consumed by non-electrified cargo-handling equipment, embodied carbon and other Scope 3 sources. Avoided emissions are calculated relative to supplying the same served electrical demand entirely from the grid and are not estimates of the total port carbon footprint.

The five-minute duration diagnostics in Supplementary Table S19 and Figure S1 distinguish isolated maxima from sustained constrained operation. S4 records grid import of at least 48 MW for 630 h and at least 52 MW for 32 h. S5 records at least 48 MW for 1,850 h, at least 52 MW for 690 h and operation at the 55 MW grid limit for 64 h during the 351-day reporting period.

Relative to M2, M4 reduces mean completed-vessel waiting delay from 12.8 to 10.5 h, corresponding to an 18.0% reduction (Tables 11a and 11b, and Figure 5). Energy shortfall decreases from 8.4% to 5.7%, a 32.1% reduction, while the uncertainty index decreases from 0.44 to 0.31, a 29.5% reduction. Recovery time decreases from 19.8 to 14.6 h, corresponding to a 26.3% reduction. The resilience index increases from 0.53 to 0.64. Because the benchmark models share common replication-specific random-number streams, statistical inference is based on paired replication outputs.

Favourable differences are reported in hours for completed-vessel waiting delay and recovery time, percentage points for yard saturation and energy shortfall, and dimensionless units for infrastructure risk, uncertainty index and resilience index.

All seven outcomes remain statistically significant after Holm family-wise adjustment. The largest paired standardised effects occur for energy shortfall, resilience index, recovery time and uncertainty index. Peak yard saturation produces the smallest effect, although its paired difference remains statistically significant. The Shapiro–Wilk, BCa-bootstrap and Wilcoxon robustness results are reported in Supplementary Table S6.

No recovery episode is censored under S0–S4 (Table 13). Twelve of the 314 S5 episodes are right-censored at the 48-h limit, corresponding to 3.8% of its recovery episodes. S5 recovery is therefore reported as a 48-h restricted mean recovery time of 23.4 h, with a 95% replication-level BCa confidence interval of [21.6, 25.3] h. The S4 benchmark comparison contains no censored recovery event and is analysed using paired replication-level statistics.

A one-module-at-a-time ablation analysis was conducted under S4 to characterise the direction and magnitude of outcome changes associated with removal of uncertainty propagation, energy-state representation, infrastructure-health estimation, temporal synchronisation and adaptive-response actions (Tables 14a and 14b). In each module-removal variant, the corresponding physical subsystem remained active in the simulated terminal. Removal therefore refers to exclusion of the relevant state, diagnostic or capability from the digital-twin estimator, operating-state classifier and action-selection logic rather than removal of the underlying physical process. The common external evaluator continued to record all physical outcomes but remained inaccessible to every estimator and response policy. The analysis provides a controlled descriptive decomposition and does not constitute separate confirmatory hypothesis testing for every module-removal variant.

Removing uncertainty propagation degrades every reported outcome despite retaining the physical energy, health, synchronisation and response layers (Figure 6). Completed-vessel waiting delay increases from 10.5 to 11.7 h, energy shortfall from 5.7% to 7.2%, recovery time from 14.6 to 17.6 h and uncertainty index from 0.31 to 0.42. The no-energy variant produces the largest energy shortfall, 9.6%, indicating that explicit energy-state representation is important for coordinating flexible demand, battery dispatch and grid-constrained operation. The no-health variant produces the highest infrastructure risk, 0.41, because health information is excluded from classification and precautionary response logic.

Removing synchronisation correction increases uncertainty to 0.39 and recovery time to 18.9 h, demonstrating the importance of causal temporal alignment under delayed and heterogeneous observations. The no-action variant produces a resilience index of 0.51 even though its externally evaluated uncertainty index remains 0.31. This result indicates that improved estimation alone does not account for the complete simulated performance difference; the estimated information must also be incorporated into bounded response actions. The ablation results are interpreted as paired descriptive comparisons against the full framework rather than as separate hypothesis tests for every module-removal variant.

A one-at-a-time sensitivity analysis was performed under S4 by varying each selected parameter by ±20% while holding all other model inputs and stochastic realisations at their base values (Table 15). This is a local sensitivity analysis around the adopted configuration, not a global uncertainty analysis or interaction study.