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<p>The thermal management of high-voltage (HV) buried power cables is a key focus for grid reliability and ampacity rating, but the surrounding soils impose uncertain boundary conditions: Thermal resistivity varies with moisture and seasonal drying, and ambient surface temperature and loading from adjacent cables vary continuously. The IEC 60287 family of deterministic finite-element (FE) solvers can provide precise conductor temperatures only when the values of these boundary parameters are known with high precision, and Monte Carlo error propagation over FE is too costly to be used in real-time digital-twin applications. The work suggests a Bayesian-optimized ensemble machine learning (BO-EML) model where the aleatoric boundary uncertainty is modelled by triangular and trapezoidal fuzzy number inputs, and the epistemic model uncertainty is modelled by a heterogeneous ensemble with members—gradient-boosted trees, random forest, support-vector regression and a multilayer perceptron—being independently optimized by Bayesian techniques on Gaussian-process surrogate of the validation root-mean-square error. A fuzzy α-cut sampling plan propagates the input membership functions across all base learners to yield possibility-weighted prediction intervals for the conductor’s temperature. The framework runs on a synthetic data set of 5 000 thermal states created by an IEC-60287-inspired analytical–numerical model of a 132&#xa0;kV XLPE single-core cable in flat formation, corrupted by Gaussian measurement noise. The BO-EML achieves RMSE = 0.55&#xa0;°C, MAE = 0.42&#xa0;°C and R<sup>2</sup> = 0.999 on 750 unknown test samples, 7% better than the best Bayesian-optimized single model (BO-SVR) and 83% better than the weakest BO-tuned baseline (BO-RF), and 36% better than a manually-tuned deep ensemble. Calibrated uncertainty: Fuzzy α-cut intervals at an <i>α</i> = 0.05 possibility level enumerate 100% of reference temperatures against a nominal 95% objective and confirm the calibrated uncertainty in the face of vague soil parameters. Permutation-based feature attribution identifies names as the most important drivers of ambient temperature, load current, and soil resistivity, in agreement with IEC 60287 sensitivity relations. The framework bridges an existing documented gap in research (the explicit combination of fuzzy boundary modelling with Bayesian-optimized ensembles to analyse cable thermal behaviour) and is directly applicable to deployments in digital twins.</p>

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Bayesian-optimized ensemble machine learning with fuzzy boundary conditions for robust subsurface temperature forecasting around high-voltage buried cables

  • 期刊论文

  • 发表日期：

    2026年8月3日

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  • M. Sudha,
  • R. Thamizhamuthu,
  • M. Aparna,
  • V. Daya Sagar Ketaraju,
  • G. Manikandan,
  • Harsh Khatter

摘要

The thermal management of high-voltage (HV) buried power cables is a key focus for grid reliability and ampacity rating, but the surrounding soils impose uncertain boundary conditions: Thermal resistivity varies with moisture and seasonal drying, and ambient surface temperature and loading from adjacent cables vary continuously. The IEC 60287 family of deterministic finite-element (FE) solvers can provide precise conductor temperatures only when the values of these boundary parameters are known with high precision, and Monte Carlo error propagation over FE is too costly to be used in real-time digital-twin applications. The work suggests a Bayesian-optimized ensemble machine learning (BO-EML) model where the aleatoric boundary uncertainty is modelled by triangular and trapezoidal fuzzy number inputs, and the epistemic model uncertainty is modelled by a heterogeneous ensemble with members—gradient-boosted trees, random forest, support-vector regression and a multilayer perceptron—being independently optimized by Bayesian techniques on Gaussian-process surrogate of the validation root-mean-square error. A fuzzy α-cut sampling plan propagates the input membership functions across all base learners to yield possibility-weighted prediction intervals for the conductor’s temperature. The framework runs on a synthetic data set of 5 000 thermal states created by an IEC-60287-inspired analytical–numerical model of a 132 kV XLPE single-core cable in flat formation, corrupted by Gaussian measurement noise. The BO-EML achieves RMSE = 0.55 °C, MAE = 0.42 °C and R2 = 0.999 on 750 unknown test samples, 7% better than the best Bayesian-optimized single model (BO-SVR) and 83% better than the weakest BO-tuned baseline (BO-RF), and 36% better than a manually-tuned deep ensemble. Calibrated uncertainty: Fuzzy α-cut intervals at an α = 0.05 possibility level enumerate 100% of reference temperatures against a nominal 95% objective and confirm the calibrated uncertainty in the face of vague soil parameters. Permutation-based feature attribution identifies names as the most important drivers of ambient temperature, load current, and soil resistivity, in agreement with IEC 60287 sensitivity relations. The framework bridges an existing documented gap in research (the explicit combination of fuzzy boundary modelling with Bayesian-optimized ensembles to analyse cable thermal behaviour) and is directly applicable to deployments in digital twins.