Trust-Aware Predictive Emissions Monitoring for Gas Turbine Fleets with Limited Labelled Data

Aiden Durrant; Georgios Leontidis; Rebecca Potts; Rick Hackney

arxiv: 2606.06156 · v1 · pith:D3FWWGMRnew · submitted 2026-06-04 · 💻 cs.LG

Trust-Aware Predictive Emissions Monitoring for Gas Turbine Fleets with Limited Labelled Data

Rebecca Potts , Aiden Durrant , Rick Hackney , Georgios Leontidis This is my paper

Pith reviewed 2026-06-28 02:01 UTC · model grok-4.3

classification 💻 cs.LG

keywords predictive emissions monitoringgas turbinesNOx predictionlimited labelled datatrust frameworkconfidence estimationuncertainty quantificationfleet deployment

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The pith

Trust scores calibrated on few labelled turbines can flag which NOx predictions to trust across an entire unlabelled fleet.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops a framework that attaches per-sample trust scores to machine learning predictions of gas turbine NOx emissions. The scores are built by combining a multi-head recurrent model with learned confidence, ensemble uncertainty, auxiliary feature predictions, distance analysis, and operating-range checks, all calibrated only on the small labelled subset. If these scores track actual error, operators can filter to high-trust cases and achieve substantially lower error on the much larger unlabelled portion of the fleet. The work shows that unlabelled and shifted samples receive lower trust, and that filtering the top 10 percent by trust drops MAE from 0.202 to 0.070. This setup aims to make predictive emissions monitoring deployable without requiring emission labels on every asset.

Core claim

A trust-aware probabilistic framework that fuses multi-head recurrent prediction with learned confidence estimation, ensemble uncertainty quantification, auxiliary feature prediction, feature-space distance analysis, and operating-range diagnostics produces interpretable per-sample trust scores; these scores are meaningfully related to prediction error on unlabelled turbines, support confidence-based filtering that reduces MAE from 0.202 to 0.070 on the highest-confidence decile, and respond appropriately to distributional shift by assigning higher uncertainty and lower confidence to unlabelled and out-of-distribution samples.

What carries the argument

The trust-aware probabilistic framework that integrates a multi-head recurrent prediction model with multiple calibrated uncertainty and confidence signals to output per-sample trust scores.

If this is right

Filtering predictions by trust score reduces mean absolute error from 0.202 on the full set to 0.070 on the top 10 percent.
Unlabelled and out-of-distribution samples receive measurably higher uncertainty and lower trust scores.
The framework supplies per-sample reliability indicators that can guide cautious use during fleet-wide deployment of predictive emissions monitoring.
Trust scores remain interpretable after calibration on the limited labelled data alone.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

The same multi-signal trust construction could be applied to other fleet monitoring tasks where labels are expensive but sensor data are abundant.
Running the calibrated trust scores on turbines from a different manufacturer or geographic region would test whether the distributional-shift response generalizes.
Embedding the trust scores into an automated alerting system could reduce false regulatory triggers by de-emphasizing low-trust forecasts.

Load-bearing premise

Trust scores calibrated exclusively on the labelled subset will correctly indicate prediction reliability for unlabelled turbines whose operating data may follow different distributions.

What would settle it

Collect actual emissions measurements on a held-out set of unlabelled turbines and test whether predictions with low trust scores show systematically higher error than those with high trust scores.

Figures

Figures reproduced from arXiv: 2606.06156 by Aiden Durrant, Georgios Leontidis, Rebecca Potts, Rick Hackney.

**Figure 2.** Figure 2: Predicted confidence compared to normalised prediction error on labelled data. [PITH_FULL_IMAGE:figures/full_fig_p009_2.png] view at source ↗

**Figure 3.** Figure 3: Prediction error (MAE and RMSE) as a function of retained high-confidence samples. Performance improves [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗

**Figure 4.** Figure 4: Relationship between Mahalanobis distance and predicted emissions confidence for [PITH_FULL_IMAGE:figures/full_fig_p010_4.png] view at source ↗

**Figure 5.** Figure 5: Relationship between Mahalanobis distance and mean feature confidence for [PITH_FULL_IMAGE:figures/full_fig_p010_5.png] view at source ↗

**Figure 6.** Figure 6: Sequential predictions for unlabelled data with low-trust regions highlighted. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

read the original abstract

Machine learning-based predictive emissions monitoring systems offer a practical alternative to direct emissions measurement, but their deployment across gas turbine fleets is challenging when emissions labels are available for only a small subset of assets. In this work, a trust-aware probabilistic framework is proposed for fleet-level gas turbine NOx prediction under limited labelled supervision. The framework combines a multi-head recurrent prediction model with learned confidence estimation, ensemble-based uncertainty quantification, auxiliary feature prediction, feature-space distance analysis, and operating-range diagnostics. These signals are calibrated on labelled data to produce interpretable per-sample trust scores, providing indicators of prediction reliability on unlabelled turbines, supporting the identification of predictions that should be treated with greater caution during fleet-level deployment. Confidence-based filtering reduces MAE from 0.202 at full coverage to 0.070 for the highest-confidence 10\% of predictions, demonstrating that confidence estimates are meaningfully related to prediction error. Unlabelled and out-of-distribution samples exhibit increased uncertainty and reduced confidence, indicating that the framework responds appropriately to distributional shift. The results show that the proposed trust framework provides actionable reliability information for emissions prediction on unlabelled turbines, supporting more transparent and trustworthy deployment of PEMS across industrial fleets.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The trust scores reduce reported MAE under filtering but are calibrated only on labelled data, leaving their reliability on unlabelled turbines untested.

read the letter

The central point is that this framework produces trust scores by fitting signals to the small labelled set, then claims those scores flag reliable predictions on the much larger unlabelled fleet. The abstract shows MAE dropping from 0.202 to 0.070 when keeping only the top 10% confidence, and lower scores on OOD points, but both observations come from data where labels exist.

What is new is the specific bundle of multi-head RNN, learned confidence, ensemble uncertainty, auxiliary prediction, distance analysis, and range diagnostics, all turned into a single calibrated trust score for this emissions task. The paper does a clean job of showing the filtering effect and the expected OOD response on the data they can measure.

The soft spot is exactly the one the stress test flags. Without ground-truth emissions on unlabelled turbines, there is no direct check that high trust scores actually correspond to low error once the distribution shifts. The MAE gain is real on the labelled subset, but it partly reflects how well the calibration fits that subset. If the unlabelled turbines differ in operating conditions, the mapping may not transfer.

This is a domain paper for engineers building or deploying PEMS on gas turbine fleets. It gives a workable recipe for handling limited labels and produces numbers that practitioners can examine. It is not a foundational ML result.

The work shows clear thinking on the industrial constraint and deserves peer review. Reviewers will likely press on the generalization step, but the concrete filtering result and the signal combination are worth a full read.

Referee Report

2 major / 1 minor

Summary. The paper proposes a trust-aware probabilistic framework for NOx emissions prediction in gas turbine fleets under limited labelled supervision. It integrates a multi-head recurrent model with learned confidence estimation, ensemble uncertainty, auxiliary feature prediction, feature-space distance, and operating-range diagnostics. These signals are calibrated on the labelled subset to yield per-sample trust scores intended to indicate reliability for unlabelled turbines. The abstract reports that confidence filtering reduces MAE from 0.202 (full coverage) to 0.070 (top 10% confidence) and that unlabelled/OOD samples receive lower confidence.

Significance. If the trust scores were shown to correlate with actual prediction error on unlabelled turbines under distributional shift, the work would offer a practical mechanism for selective, risk-aware deployment of PEMS models across industrial fleets. The current evidence, however, leaves the generalization of the calibration untested.

major comments (2)

[Abstract] Abstract: the central claim that trust scores supply actionable reliability indicators for unlabelled turbines rests on calibration performed exclusively against the labelled subset; the reported MAE reduction is measured on labelled data, and no ground-truth emissions exist for the unlabelled fleet, so the mapping from trust score to actual error under shift remains unverified.
[Abstract] Abstract: the observation that unlabelled/OOD samples exhibit increased uncertainty and reduced confidence is consistent with evaluation on labelled data only and does not constitute a direct test of whether high-trust predictions on shifted data have low error.

minor comments (1)

The manuscript provides no details on model architecture, training procedure, calibration method, or statistical significance testing, which limits assessment of reproducibility.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which correctly identify that our evidence for trust-score reliability is derived from labelled-data calibration. We agree that the abstract claims require clarification to avoid overstating what has been directly verified. We will revise the abstract and add discussion of this limitation.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that trust scores supply actionable reliability indicators for unlabelled turbines rests on calibration performed exclusively against the labelled subset; the reported MAE reduction is measured on labelled data, and no ground-truth emissions exist for the unlabelled fleet, so the mapping from trust score to actual error under shift remains unverified.

Authors: We agree. The MAE reduction (0.202 to 0.070) and trust-score calibration are demonstrated exclusively on the labelled subset. No ground truth exists for the unlabelled fleet, so direct verification of the trust-to-error mapping under shift is not possible. We will revise the abstract to state that trust scores are calibrated on labelled data to produce reliability indicators intended for unlabelled turbines, and that lower confidence on unlabelled/OOD samples indicates the framework responds to shift, without claiming verified error reduction on unlabelled data. We will also add a limitations paragraph discussing this point. revision: yes
Referee: [Abstract] Abstract: the observation that unlabelled/OOD samples exhibit increased uncertainty and reduced confidence is consistent with evaluation on labelled data only and does not constitute a direct test of whether high-trust predictions on shifted data have low error.

Authors: This observation is accurate. The increased uncertainty and reduced confidence on unlabelled/OOD samples are measured via the model's internal signals after calibration on labelled data; they do not constitute a direct test of prediction error on shifted data. We will revise the abstract wording to describe this as evidence that the framework appropriately down-weights predictions under shift, rather than as a direct test of error on unlabelled turbines. revision: yes

Circularity Check

1 steps flagged

Trust calibration fitted on labelled data; MAE reduction on high-confidence subset is evaluation on calibration data

specific steps

fitted input called prediction [Abstract]
"These signals are calibrated on labelled data to produce interpretable per-sample trust scores, providing indicators of prediction reliability on unlabelled turbines... Confidence-based filtering reduces MAE from 0.202 at full coverage to 0.070 for the highest-confidence 10% of predictions, demonstrating that confidence estimates are meaningfully related to prediction error. Unlabelled and out-of-distribution samples exhibit increased uncertainty and reduced confidence, indicating that the framework responds appropriately to distributional shift."

Calibration occurs solely on labelled data; the MAE reduction is then shown for high-confidence predictions. Since error can only be measured where labels exist, the filtering result is computed on the labelled set, making the 'demonstration' a statement about how well the fitted trust model matches its own training distribution rather than an independent test of reliability on unlabelled turbines.

full rationale

The framework calibrates multiple signals exclusively on the labelled subset to produce trust scores, then reports that confidence filtering reduces MAE from 0.202 to 0.070 on the top 10% as evidence that the scores indicate reliability for unlabelled turbines. Because ground-truth emissions labels exist only for the labelled turbines, the MAE-vs-confidence curve is necessarily computed on the same labelled distribution used for calibration; the reported improvement therefore demonstrates in-sample fit rather than out-of-distribution error correlation on the unlabelled fleet. No additional external validation or ground-truth comparison on unlabelled samples is described, so the central claim that the scores supply actionable reliability information for unlabelled turbines reduces to the calibration step itself.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on the assumption that the listed signals (uncertainty, distance, auxiliary error, range) can be linearly or simply combined into a trust score whose calibration on labelled data transfers to unlabelled turbines; no independent evidence for this transfer is supplied beyond the reported filtering result.

free parameters (1)

trust-score calibration mapping
Parameters that map the raw signals to interpretable trust scores are fitted on the labelled subset.

axioms (1)

domain assumption The ensemble uncertainty, feature-space distance, auxiliary prediction error, and operating-range diagnostics are valid proxies for prediction error on unseen turbines.
Invoked when these signals are combined and calibrated to produce trust scores.

pith-pipeline@v0.9.1-grok · 5746 in / 1425 out tokens · 32672 ms · 2026-06-28T02:01:41.195660+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

14 extracted references · 4 canonical work pages · 2 internal anchors

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Aslan, E. (2024). Prediction and comparative analysis of emissions from gas turbines using random search optimization and different machine learning-based algorithms.Bulletin of the Polish Academy of Sciences. Technical Sciences72

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Blatz, J., Fitzgerald, E., Foster, G., Gandrabur, S., Goutte, C., Kulesza, A., et al. (2004). Confidence estimation for machine translation. InColing 2004: Proceedings of the 20th international conference on computational linguistics. 315–321 [Dataset] Corbière, C., Thome, N., Bar-Hen, A., Cord, M., and Pérez, P. (2019). Addressing failure prediction by l...

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Learning Confidence for Out-of-Distribution Detection in Neural Networks

DeVries, T. and Taylor, G. W. (2018). Learning confidence for out-of-distribution detection in neural networks.arXiv preprint arXiv:1802.04865 Dos Santos Coelho, L., Hultmann Ayala, H. V ., and Cocco Mariani, V . (2024). Co and nox emissions prediction in gas turbine using a novel modeling pipeline based on the combination of deep forest regressor and fea...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.fuel.2023.129366 2018
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Hackney, R., Sadasivuni, S., Rogerson, J., and Bulat, G. (2016). Predictive emissions monitoring system for small siemens dry low emissions combustors: validation and application. InTurbo Expo: Power for Land, Sea, and Air (American Society of Mechanical Engineers), vol. 49767, V04BT04A032

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E., Hossain, T., Haque, A

Hoque, K. E., Hossain, T., Haque, A. M., Miah, M. A. K., and Haque, M. A. (2024). Nox emission predictions in gas turbines through integrated data-driven machine learning approaches.Journal of Energy Resources Technology146, 071201. doi:10.1115/1.4065200 Hüllermeier, E. and Waegeman, W. (2021). Aleatoric and epistemic uncertainty in machine learning: An i...

work page doi:10.1115/1.4065200 2024
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Kaya, H., Tüfekci, P., and Uzun, E. (2019). Predicting co and nox emissions from gas turbines: novel data and a benchmark pems.Turkish Journal of Electrical Engineering and Computer Sciences27, 4783–4796

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Lakshminarayanan, B., Pritzel, A., and Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles.Advances in neural information processing systems30

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Lee, K., Lee, H., Lee, K., and Shin, J. (2017). Training confidence-calibrated classifiers for detecting out-of-distribution samples.arXiv preprint arXiv:1711.09325

work page internal anchor Pith review Pith/arXiv arXiv 2017
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Lee, K., Lee, K., Lee, H., and Shin, J. (2018). A simple unified framework for detecting out-of-distribution samples and adversarial attacks. InAdvances in Neural Information Processing Systems, eds. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett (Curran Associates, Inc.), vol. 31

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and Karimi, I

Liu, Z. and Karimi, I. A. (2020). Gas turbine performance prediction via machine learning.Energy192, 116627. doi:https://doi.org/10.1016/j.energy.2019.116627

work page doi:10.1016/j.energy.2019.116627 2020
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Mo, D., Lin, Y ., Liu, Y ., Wang, Y ., Qin, Z., and Han, X. (2025). A review of recent advances in the application of machine learning algorithms for gas turbine combustion.Propulsion and Energy1, 20 [Dataset] Moon, J., Kim, J., Shin, Y ., and Hwang, S. (2020). Confidence-aware learning for deep neural networks

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Potts, R., Hackney, R., and Leontidis, G. (2023). Tabular machine learning methods for predicting gas turbine emissions. Machine Learning and Knowledge Extraction5, 1055–1075

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Wang, K., Ma, Q., Shen, C., and Lu, J. (2025). Application of uncertainty to out-of-distribution detection for autonomous driving perception safety.IEEE Transactions on Intelligent Transportation Systems

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Zhao, Z., Alzubaidi, L., Zhang, J., Duan, Y ., and Gu, Y . (2024). A comparison review of transfer learning and self-supervised learning: Definitions, applications, advantages and limitations.Expert Systems with Applications242, 122807 14

2024

[1] [1]

Aslan, E. (2024). Prediction and comparative analysis of emissions from gas turbines using random search optimization and different machine learning-based algorithms.Bulletin of the Polish Academy of Sciences. Technical Sciences72

2024

[2] [2]

Blatz, J., Fitzgerald, E., Foster, G., Gandrabur, S., Goutte, C., Kulesza, A., et al. (2004). Confidence estimation for machine translation. InColing 2004: Proceedings of the 20th international conference on computational linguistics. 315–321 [Dataset] Corbière, C., Thome, N., Bar-Hen, A., Cord, M., and Pérez, P. (2019). Addressing failure prediction by l...

2004

[3] [3]

Learning Confidence for Out-of-Distribution Detection in Neural Networks

DeVries, T. and Taylor, G. W. (2018). Learning confidence for out-of-distribution detection in neural networks.arXiv preprint arXiv:1802.04865 Dos Santos Coelho, L., Hultmann Ayala, H. V ., and Cocco Mariani, V . (2024). Co and nox emissions prediction in gas turbine using a novel modeling pipeline based on the combination of deep forest regressor and fea...

work page internal anchor Pith review Pith/arXiv arXiv doi:10.1016/j.fuel.2023.129366 2018

[4] [4]

Hackney, R., Sadasivuni, S., Rogerson, J., and Bulat, G. (2016). Predictive emissions monitoring system for small siemens dry low emissions combustors: validation and application. InTurbo Expo: Power for Land, Sea, and Air (American Society of Mechanical Engineers), vol. 49767, V04BT04A032

2016

[5] [5]

E., Hossain, T., Haque, A

Hoque, K. E., Hossain, T., Haque, A. M., Miah, M. A. K., and Haque, M. A. (2024). Nox emission predictions in gas turbines through integrated data-driven machine learning approaches.Journal of Energy Resources Technology146, 071201. doi:10.1115/1.4065200 Hüllermeier, E. and Waegeman, W. (2021). Aleatoric and epistemic uncertainty in machine learning: An i...

work page doi:10.1115/1.4065200 2024

[6] [6]

Kaya, H., Tüfekci, P., and Uzun, E. (2019). Predicting co and nox emissions from gas turbines: novel data and a benchmark pems.Turkish Journal of Electrical Engineering and Computer Sciences27, 4783–4796

2019

[7] [7]

Lakshminarayanan, B., Pritzel, A., and Blundell, C. (2017). Simple and scalable predictive uncertainty estimation using deep ensembles.Advances in neural information processing systems30

2017

[8] [8]

Lee, K., Lee, H., Lee, K., and Shin, J. (2017). Training confidence-calibrated classifiers for detecting out-of-distribution samples.arXiv preprint arXiv:1711.09325

work page internal anchor Pith review Pith/arXiv arXiv 2017

[9] [9]

Lee, K., Lee, K., Lee, H., and Shin, J. (2018). A simple unified framework for detecting out-of-distribution samples and adversarial attacks. InAdvances in Neural Information Processing Systems, eds. S. Bengio, H. Wallach, H. Larochelle, K. Grauman, N. Cesa-Bianchi, and R. Garnett (Curran Associates, Inc.), vol. 31

2018

[10] [10]

and Karimi, I

Liu, Z. and Karimi, I. A. (2020). Gas turbine performance prediction via machine learning.Energy192, 116627. doi:https://doi.org/10.1016/j.energy.2019.116627

work page doi:10.1016/j.energy.2019.116627 2020

[11] [11]

Mo, D., Lin, Y ., Liu, Y ., Wang, Y ., Qin, Z., and Han, X. (2025). A review of recent advances in the application of machine learning algorithms for gas turbine combustion.Propulsion and Energy1, 20 [Dataset] Moon, J., Kim, J., Shin, Y ., and Hwang, S. (2020). Confidence-aware learning for deep neural networks

2025

[12] [12]

Potts, R., Hackney, R., and Leontidis, G. (2023). Tabular machine learning methods for predicting gas turbine emissions. Machine Learning and Knowledge Extraction5, 1055–1075

2023

[13] [13]

Wang, K., Ma, Q., Shen, C., and Lu, J. (2025). Application of uncertainty to out-of-distribution detection for autonomous driving perception safety.IEEE Transactions on Intelligent Transportation Systems

2025

[14] [14]

Zhao, Z., Alzubaidi, L., Zhang, J., Duan, Y ., and Gu, Y . (2024). A comparison review of transfer learning and self-supervised learning: Definitions, applications, advantages and limitations.Expert Systems with Applications242, 122807 14

2024