Uncertainty-aware AI-enabled framework for predicting hydrogen dispersion in confined spaces to enhance operator situational awareness

1.1. Motivation and Background

• Hydrogen’s buoyancy, flammability, and difficult detectability make leaks hazardous in enclosed spaces, while early forecasts could support preventive barriers before the costly, disruptive ESD.The ESD is described as the ultimate barrier before a potentially catastrophic event.Source: §1.1 · p. 1

1.2.1. AI systems for hydrogen dispersion

• Prior hydrogen-dispersion AI studies largely target open vehicle-refueling settings, and the reviewed approaches differ from the need to forecast evolving concentrations for operator decisions.The studies include reconstruction, CFD-surrogate, physics-informed forecasting, and leak-classification approaches.Source: §1.2.1 · p. 2

1.2.2. AI systems in safety-critical systems

• The literature also lacks explicit treatment of compressed bunkering in confined spaces, system-level safety integration, and uncertainty communication to operators.Prior system-design work is described as lacking a concrete operational use case.Source: §1.2.1 · p. 2, §1.2.2 · p. 3

1.3. Research gap and problem formulation

• The paper identifies a gap in combining real-time leakage-rate estimation with probabilistic short-horizon concentration forecasting and calibrated uncertainty for confined-space bunkering.It also notes the absence of an integrated treatment that provides both a tested predictive model and guidance for incorporating it into a safety-related system.Source: §1.3 · p. 3
• The proposed contributions are a two-stage MLP-and-Gaussian-process framework and an initial ISO/IEC TR 5469-aligned design that segregates AI at usage level D from the independent emergency shutdown function.The demonstration uses an open confined-channel dataset because the authors report no open dataset for dispersion inside a ship’s tank connection space.Source: §1.3 · p. 3

• The methodology proceeds through system design, dataset acquisition and processing, and the two-stage framework’s algorithms, model selection, training, testing, and runtime inference.Source: §2 · p. 3

2.1. System Design

• The design process reviews bunkering-system literature, guidance for incorporating AI into safety-related systems, and safe-system-design research.Source: §2.1 · p. 3

2.1.1. Compressed 퐻2 Bunkering System

• The ESD is the bunkering system’s main safety system, shutting down operations through manifold, pump, and tank-filling valve actions when the considered hydrogen concentration exceeds the LFL.The study focuses on confined releases where wind effects are negligible and hydrogen disperses through ventilation.Source: §2.1.1 · p. 4

2.1.2. Incorporation of AI systems into safety-critical systems

• The AI is assigned usage level D: it enhances operator situational awareness but is not part of the safety function, which remains an independent conventional emergency shutdown system.The authors state that this usage level allows existing risk-reduction measures to be applied.Source: §2.1.2 · p. 4
• The design combines an input guard, AI monitoring, and human supervision, with continuous real-time signal-integrity checks and operator authority over AI outputs.The AI system is independent of the safety function, so faults in the guard or monitoring may trigger unnecessary action but do not compromise overall system safety.Source: Figure 2 · p. 4, §2.1.2 · p. 5

2.1.3. Safe System Design

• The authors frame their safety discussion as a perspective on extending functional-safety principles to AI, not as a complete solution.Direct adoption of proven-in-use to AI remains an open question.Source: §2.1.2 · p. 5

2.2.1. Experimental setup

• The open dataset contains 22 experimental and 10 CFD tests of downward hydrogen releases in a confined open-ended channel, with CFD tests partly duplicating experiments.The channel is a simplified geometry rather than a ship’s tank connection space, but represents a confined, poorly ventilated volume with buoyant hydrogen release.Source: §2.2 · p. 5, §2.2.1 · p. 6

2.2.2. Data processing for training

• Trimming the leakage intervals leaves about 182,000 samples; readings below 0.009 are treated as background noise, with the threshold set slightly below sensor accuracy to capture first leak indications.Log-transforming the exposed-only subset produces an approximately Gaussian distribution, while the processing figure notes information loss from this transformation.Source: §2.2.2 · p. 6, Figure 4 · p. 6
• The first-stage MLP ensemble uses 15 features from the 10 seconds after leakage onset, combining sensor exposure, concentration and spatial snapshots with temporal derivatives.Leakage onset is the first instant any sensor exceeds the 0.009 threshold.Source: §2.2.2 · p. 6

2.3. Framework architecture

• The two-stage framework estimates leakage rate from features in the first 10 seconds after onset, then predicts the concentration field using that estimate.The first stage uses an MLP ensemble; the second is a regressor.Source: §2.3 · p. 7

2.3.1. Gaussian processes

• Gaussian processes provide non-parametric function priors, and their kernels determine the structures they can capture while naturally estimating prediction uncertainty.Exact inference scales as O(N^3), and computational cost remains limiting for datasets exceeding one million points despite approximate methods.Source: §2.3.1 · p. 7

2.3.2. Training data

• The trimmed dataset retains leakage-interval samples, while the exposed-only dataset keeps exposed samples and uses hydrogen concentration as the regression target.Splitting by scenario keeps each experiment or CFD test entirely within one split, with validation data used for tuning and early stopping.Source: §2.3.2 · p. 7

2.3.3. Model architectures

• Stage 1 maps sensor measurements across three consecutive time steps and a 15-dimensional feature vector to leakage rate; Stage 2 maps time, leakage rate, and sensor coordinates to concentration.Stage 1 aggregates independently initialized MLP predictions and uses their variance as a heuristic uncertainty; Stage 2 uses a GP posterior mean and covariance for concentration and uncertainty. Its additive kernel combines five input-dimension kernels, initially considering 31 products and retaining 12 important combinations.Source: §2.3.3 · pp. 7–8

2.3.4. Training

• The MLP ensemble uses leave-one-experiment-out cross-validation, while GP training compares VNNGP and SVGP approximations and Gaussian and Beta likelihoods.For GP models, neighbor counts or inducing-point counts trade approximation accuracy against computational cost.Source: §2.3.3 · p. 8, §2.3.4 · pp. 8–9

2.3.5. Real-time inference

• After a 10-second observation window, the leakage-rate estimate is frozen and used for short-horizon GP forecasts at future times and arbitrary compartment coordinates.The posterior mean gives the concentration field and covariance is displayed as a confidence map; latency is seconds for a sparse sensor network and forecast horizon H≤20.Source: §2.3.5 · p. 9

2.3.6. Evaluation metrics

• The study reports RMSE and MAE for leakage-rate and concentration predictions, with MAE expressing average concentration error in hydrogen volume-fraction units.Leakage-rate estimation error propagates directly into the GP forecast, and ensemble variance is monitored as a heuristic indicator of disagreement.Source: §2.3.6 · pp. 9–10

3.1. System design

• The AI system advises operators through a two-stage forecast, while a separate non-AI ESD remains the independent automatic safety layer.Input guards and AI monitoring check data integrity and flag out-of-distribution inputs or unreliable internal behavior; the proven-in-use discussion notes that runtime updating is outside this work’s scope and that sparse data above 1.0 g/s warrant manual supervision.Source: §3.1 · p. 10

3.2. Leakage rate estimation

• 0.052 g/s MAE: the Stage-1 MLP ensemble estimated leakage rate from early sensor observations.The ensemble used seven independently initialized networks, and its standard deviation served as an epistemic uncertainty estimate.Source: §3.2 · p. 11, Figure 6 · p. 11

3.3.1. Full kernel screening with VNNGP

• Screening found 18 near-zero-scale kernels and motivated a 12-term light kernel; light-kernel VNNGP and SVGP models improved speed and prediction performance.The best reported light-kernel SVGP point-estimation configuration achieved validation MAE 0.0116 and RMSE 0.0156.Source: §3.3.1 · p. 11, §3.3.2 · p. 11

3.3.3. Likelihood selection: Gaussian vs. Beta

• Under VNNGP, the Beta likelihood performed poorly, whereas Beta-likelihood SVGP models performed well and were better calibrated than Gaussian-likelihood models.The Gaussian model’s 95% bands were overconfident; the Beta model traded a marginal increase in MAE for better calibration.Source: §3.3.3 · pp. 11–12

3.3.4. Final model and test-set evaluation

• 0.0176 MAE on the held-out test set: the selected Beta-likelihood SVGP outperformed the other tested models and approached the sensor precision limit.It also achieved RMSE 0.0226 and NLL −1.5340.Source: §3.3.4 · p. 12, Table 2 · p. 12

3.3.5. Calibration of final model

• The final GP’s predictive intervals met or exceeded nominal coverage, with conservative intervals and PIT values centered near 0.508.The calibration curve lies above the diagonal over most of the range.Source: §3.3.5 · p. 12, Figure 8 · p. 12, Table 3 · p. 12

3.3.6. Sensor threshold sensitivity

• Changing the exposure threshold to 0.0085 or 0.0095 produced no significant deviations from the default model’s reported performance metrics.The passage reports MAE, RMSE, and predictive log-likelihood values for both alternatives.Source: §3.3.6 · p. 12

3.4. End-to-end framework evaluation

• Using the MLP-estimated leakage rate increased Stage-2 MAE from 0.0176 to 0.0249 compared with supplying ground-truth mass flow.The comparison evaluates how Stage-1 errors propagate through the sequential framework.Source: §3.4 · p. 13, Table 5 · p. 13

4.1. System design and compliance with policies

• The design is an initial baseline under ISO/IEC TR 5469, with independent ESD, input guarding, and AI monitoring; translating proven-in-use to AI still needs deeper evaluation.Operators also need preparation to interpret AI and monitoring outputs without compromising the independent ESD system.Source: §4.1 · p. 13

4.2. Uncertainty-aware AI systems and human operators

• Uncertainty estimates help operators judge forecasts only when correctly interpreted, so the paper recommends operator involvement or training and conservative action in high-uncertainty regions.A further layer could flag point estimates in high-uncertainty regions as potentially unreliable.Source: §4.2 · p. 13

4.3. Tank connection space geometry

• The open-ended channel captures localized leaks and natural ventilation, but active ventilation and obstructions in ship spaces prevent direct transfer; the framework is intended for retraining on new geometries.The authors call for validation on different geometries and model extensions for active safety barriers as runtime inputs.Source: §4.3 · pp. 13–14

4.4. Dataset size, distribution skew, and scalability trade-offs

• The 32-scenario dataset is small and leakage-rate coverage is skewed, degrading extreme-rate estimates and widening uncertainty where data are scarce; larger datasets also raise GP scalability trade-offs.The paper identifies targeted CFD or active learning for underrepresented rates and notes computational limits for very large GP datasets.Source: §4.4 · p. 14

4.5. Model selection

• The model choices favor compactness and uncertainty: GPs suit limited data, while the final 12-term additive kernel is interpretable offline but may be complex for runtime use.Time matters mainly during the initial ramp-up; after about 50 s its effect largely vanishes, while position and mass flow dominate.Source: §4.5 · pp. 14–15

4.6. MLP ensemble for leakage estimation

• Leakage-rate accuracy depends on data coverage: estimates remain reliable for m < 0.7 g/s, but high-flow cases above 1.0 g/s are severely under-predicted.The authors identify sparse training coverage, rather than model architecture, as the main performance bottleneck.Source: §4.6 · p. 15

4.7. GP regression for hydrogen dispersion

• VNNGP screened kernel hyperparameters but plateaued or degraded as neighborhood size increased; SVGP ultimately performed better because global inducing points suited the small spatial domain.The proposed explanation is data sparsity in the five-dimensional input space for larger VNNGP neighborhoods.Source: §4.7 · p. 15
• MAE 0.0176 for the final SVGP with Beta likelihood approaches sensor accuracy 0.01, while its intervals provide calibrated uncertainty that widens in extrapolation regimes.The likelihood comparison found Gaussian models had orders-of-magnitude-worse NLL despite good point estimates.Source: §4.7 · p. 15

4.8. Calibration

• The model’s prediction intervals over-cover nominal targets mildly, a conservative bias the authors consider acceptable because intervals remain informative and avoid systematic under-coverage.The proposed sources are inflated learned observation noise and variational GP approximations that may overestimate posterior variance.Source: §4.8 · pp. 15–16

4.9. Two-stage framework and its hazard underestimation

• Stage 1 under-prediction at high leak rates biases Stage 2 toward lower concentrations, increasing test-set MAE by about 1% of hydrogen concentration.Input guards, AI monitoring, ensemble variance flags, and the independent ESD mitigate the risk; the AI remains advisory only.Source: §4.9 · p. 16

5. Conclusion

• The framework estimates leakage from the first ten seconds after onset, then forecasts the spatiotemporal concentration field with calibrated uncertainty in seconds rather than CFD’s hours.Its system design includes segregation from the independent ESD, an input guard, and AI monitoring.Source: §5 · p. 16
• The MLP ensemble estimates leakage rate with MAE 0.052 g/s, and the GP predicts concentration with MAE ≈0.0176 in volume fraction against sensor precision of ±0.01.The reported calibrated NLL is −1.5340.Source: §5 · p. 16
• Validation is limited to a single idealized geometry and skewed leakage-rate distribution; transfer, safeguards, and Stage 1 reliability need further validation or implementation before deployment.The authors also call for expanded datasets and a quantitative comparison with reduced-order CFD.Source: §5 · p. 16

Generative AI disclosure statement

• Kimi (K3), Microsoft Copilot, and ChatGPT were used solely for language editing and sentence refinement.The authors state no AI tool generated original data or performed independent scientific interpretation.Source: Generative AI disclosure statement · pp. 16–17
• The authors reviewed and edited all AI-assisted outputs and take responsibility for the manuscript’s accuracy, integrity, and final content.Source: Generative AI disclosure statement · p. 17
• The authors state that AI did not replace author judgment.Source: Generative AI disclosure statement · p. 17

A. Kernel definition

• The decomposition includes weighted pairwise, higher-order, and five-dimensional kernel terms.The terms are multiplied by corresponding θ weights.Source: A. Kernel definition · p. 18
• Equation (11a) gives the final light additive kernel decomposition.The displayed expression combines kernel terms with learned weights.Source: A. Kernel definition · p. 18
• Table 6 maps lengthscales to time, leakage rate, and spatial coordinates; empty cells mark inactive dimensions.The reported hyperparameters are for SVGP with Beta likelihood and M=6000.Source: Table 6 · p. 18

B. Tables and figures

• Highlighted cells in Table 7 mark 12 dominant additive-kernel terms.The table reports kernel combinations and learned output scales for five-dimensional inputs.Source: B. Tables and figures · p. 18, Table 7 · p. 18
• The figures show a runtime-framework flowchart and training and MAE validation losses for four selected models.The loss figure covers four of the best models.Source: Figure 11 · p. 19, Figure 12 · p. 20
• The tables identify experimental-channel sensor positions, omit installed sensor 16, and describe an exposed-sensor dataset split.The split uses 80/20 stratification by mass flow for training and validation, with a held-out test set.Source: Table 8 · p. 19, Table 9 · p. 19
• Table 13 reports validation performance for VNNGP models using the full additive kernel on exposed-only data.Metrics correspond to the best checkpoint; all kernels are RBF except where noted.Source: Table 10 · p. 19
• Tables 11–12 report validation performance for VNNGP and SVGP models using the light additive kernel (11a) on exposed-only data; VNNGP metrics correspond to the best checkpoint.For SVGP, the marked model uses learning rate 0.085 and all others use 0.008.Source: Table 11 · p. 19, Table 12 · p. 19
• Table 13 reports test performance of the best models with the light additive kernel (11a), distinguishing a marked model from the others.The marked model uses a learning rate of 0.085; all others use 0.008.Source: Table 13 · p. 20
• Figure 13 maps predicted H2 volume fraction at 20 s across three leakage rates and three sensor heights.Predictions use the final SVGP model with Beta likelihood and M=6000.Source: Figure 13 · p. 20

CRediT authorship contribution statement

• Niclas Flehmig is credited with the original draft, methodology, investigation, formal analysis, and data curation.He is also credited with validation, visualization, and conceptualization.Source: CRediT authorship contribution statement · p. 20
• All three authors are credited with writing review and editing.Niclas Flehmig is additionally credited with the original draft.Source: CRediT authorship contribution statement · p. 20
• Mary Ann Lundteigen is credited with supervision, methodology, and conceptualization; Shen Yin is credited with supervision.Both are also credited with writing review and editing.Source: CRediT authorship contribution statement · p. 20