Home / Current Issue / Paper 1724290
Stochastic Operator Residual Learning with Conformal Calibration for Risk-Aware Wind Turbine Maintenance
Subject area: Science,Engineering and Technology · Area of research: Wind Turbine
Abstract
Wind turbine maintenance decisions are frequently made under uncertainty, yet conventional degradation models often provide deterministic predictions that ignore the tail risks associated with unexpected component failure. We propose a stochastic operator residual learning framework with conformal calibration for risk-aware wind turbine maintenance. The proposed method learns a distribution over the residual field of governing fatigue and wear equations, rather than enforcing fixed physical laws through penalty terms, so that complex loading spectra and material heterogeneities can be captured without relying on potentially inaccurate constants. An ensemble of neural operators is then trained to separate epistemic from aleatoric uncertainty, and conformal prediction is applied to calibrate the resulting confidence intervals, yielding a remaining useful life distribution with guaranteed coverage. These calibrated distributions are subsequently passed to a risk-sensitive deep reinforcement learning agent whose objective combines power production gains, maintenance costs, and a conditional value-at-risk penalty on the remaining useful life. Furthermore, gradients from the policy update flow back through the calibration layer and the stochastic operator, which allows the uncertainty representation to be shaped by the risk profile required by the controller. The main contribution is a differentiable integration of stochastic residual learning, calibrated uncertainty quantification, and risk-constrained control within a single digital twin architecture. Simulation-based evaluation on representative turbine degradation scenarios will assess whether the framework reduces unexpected failures while preserving energy yield, and the results are expected to inform safer maintenance scheduling under uncertain operating conditions.
Keywords
wind turbine; predictive maintenance; neural operators; conformal prediction; risk-sensitive reinforcement learning; remaining useful life
References
[1] Dao C, Kazemtabrizi B, et al. Modelling the effects of reliability and maintenance on levelised cost of wind energy. In: Proceedings of the ASME Turbo Expo 2019, Volume 9: Oil and Gas Applications; Supercritical CO2 Power Cycles; Wind Energy. ASME; 2019.
[2] Wang X, Hou J, Guo H, Wang Y, Sun Y, Teng B. A Miner’s rule based fatigue life prediction model for combined high and low cycle fatigue considering loading interaction effect. Fatigue Fract Eng Mater Struct. 2023;46(12):4525–40.
[3] McKittrick L, Cairns D, Mandell J, Combs D, et al. Analysis of a composite blade design for the AOC 15/50 wind turbine using a finite element model. OSTI; 2001.
[4] Yuan C, Cai Y, Zhang Z. Application of SHAP-based explainable machine learning in remaining useful life prediction for aircraft engine systems. Int J Mach Learn Cybern. 2026.
[5] Chandran S, Makki M, Raissi M, Grenier A, et al. NewPINNs: physics-informing neural networks using conventional solvers for partial differential equations. arXiv:2601.17207 [Preprint]. 2026.
[6] Lu Z, Qu J, Liu H, He C, Zhang B, Chen Q. Surrogate modeling for physical fields of heat transfer processes based on physics-informed neural network. CIESC J. 2021.
[7] Zhou G, Zeng Z, Luo Y, Xie Q, et al. Tucker-FNO: tensor Tucker-Fourier neural operator and its universal approximation theory. In: International Conference on Learning Representations. 2026.
[8] Kossaifi J, Kovachki N, Li Z, Pitt D, et al. A library for learning neural operators. J Mach Learn Res. 2026.
[9] Wilson A, Izmailov P. Bayesian deep learning and a probabilistic perspective of generalization. In: Advances in Neural Information Processing Systems. 2020.
[10] Gal Y, Ghahramani Z. Dropout as a Bayesian approximation: representing model uncertainty in deep learning. In: Proceedings of the 33rd International Conference on Machine Learning (PMLR 48). 2016. p. 1050–9.
[11] Lakshminarayanan B, Pritzel A, Blundell C. Simple and scalable predictive uncertainty estimation using deep ensembles. In: Advances in Neural Information Processing Systems. 2017.
[12] Xue L, Wang T, Cheung Y, Zhao X, et al. A unified framework for reliable deep learning: conformal prediction meets out-of-distribution detection. IEEE Trans Reliab. 2026.
[13] Dong M, He D. Hidden semi-Markov model-based methodology for multi-sensor equipment health diagnosis and prognosis. Eur J Oper Res. 2007.
[14] Gibbs M. Bayesian Gaussian processes for regression and classification [dissertation]. Cambridge: University of Cambridge; 1998.
[15] Zheng H, Lin G. Multi-fidelity prediction and uncertainty quantification with Laplace neural operators for parametric partial differential equations. SSRN 5142239 [Preprint]. 2025.
[16] Schulman J, Wolski F, Dhariwal P, Radford A, Klimov O. Proximal policy optimization algorithms. arXiv:1707.06347 [Preprint]. 2017.
[17] Zhou S, et al. Variance-adaptive distributional soft actor-critic with expected-value targets and dual-priority replay. Neurocomputing. 2026.
[18] Ameur H, Ftiti Z, Louhichi W, Yousfi M. Do green investments improve portfolio diversification? Evidence from mean conditional value-at-risk optimization. Int Rev Financ Anal. 2024.
[19] Zhang H. Risk-aware budget-constrained auto-bidding under first-price RTB: a distributional constrained deep reinforcement learning framework. J Adv Comput Syst. 2024.
[20] Ringeval M, Sosso F, Cousineau M, et al. Advancing health care with digital twins: meta-review of applications and implementation challenges. J Med Internet Res. 2025.
[21] Ghahfarokhi M, Riffat J, et al. Physics-informed multimodal sensing and machine learning framework with real-time digital twin for intelligent structural health monitoring of marine wharves. J Clim Change. 2026.
[22] León RR. Desarrollo de un entorno amigable para la realización de simulaciones numéricas de sistemas eólicos con OpenFAST [thesis]. Cartagena: Universidad Politécnica de Cartagena; 2025.
[23] Zhang J. Machine learning based modelling and control of wind turbine structures and wind farm wakes [dissertation]. 2021.
[24] Gillis H, Trappenberg T. Uncertainty quantification for trustworthy deep learning: methods and measures. Neural Netw. 2026.
[25] Jatavallabhula K, Macklin M, Fox D, et al. Bayesian object models for robotic interaction with differentiable probabilistic programming. In: Conference on Robot Learning. 2023.
[26] Varetti E, Torzoni M, Tezzele M, et al. Adaptive digital twins for predictive decision-making: online Bayesian learning of transition dynamics. Data-Centric Eng. 2026.
[27] Varetti E. Probabilistic digital twin for structural safety assurance and optimal decision making via reinforcement learning [thesis]. Milan: Politecnico di Milano; 2023.
How to cite this paper
@article{1724290,
author = {Pankaj Sharma},
title = {Stochastic Operator Residual Learning with Conformal Calibration for Risk-Aware Wind Turbine Maintenance},
journal = {Iconic Research And Engineering Journals},
year = {2026},
volume = {10},
number = {4},
pages = {4226-4242},
issn = {2456-8880},
url = {https://www.irejournals.com/formatedpaper/1724290.pdf},
abstract = {Wind turbine maintenance decisions are frequently made under uncertainty, yet conventional degradation models often provide deterministic predictions that ignore the tail risks associated with unexpected component failure. We propose a stochastic operator residual learning framework with conformal calibration for risk-aware wind turbine maintenance. The proposed method learns a distribution over the residual field of governing fatigue and wear equations, rather than enforcing fixed physical laws through penalty terms, so that complex loading spectra and material heterogeneities can be captured without relying on potentially inaccurate constants. An ensemble of neural operators is then trained to separate epistemic from aleatoric uncertainty, and conformal prediction is applied to calibrate the resulting confidence intervals, yielding a remaining useful life distribution with guaranteed coverage. These calibrated distributions are subsequently passed to a risk-sensitive deep reinforcement learning agent whose objective combines power production gains, maintenance costs, and a conditional value-at-risk penalty on the remaining useful life. Furthermore, gradients from the policy update flow back through the calibration layer and the stochastic operator, which allows the uncertainty representation to be shaped by the risk profile required by the controller. The main contribution is a differentiable integration of stochastic residual learning, calibrated uncertainty quantification, and risk-constrained control within a single digital twin architecture. Simulation-based evaluation on representative turbine degradation scenarios will assess whether the framework reduces unexpected failures while preserving energy yield, and the results are expected to inform safer maintenance scheduling under uncertain operating conditions.},
keywords = {wind turbine; predictive maintenance; neural operators; conformal prediction; risk-sensitive reinforcement learning; remaining useful life},
month = {October},
}