The research team, led by Kuineng Chen of the Hunan Engineering Research Center of Special Robot Control Technology and Equipment in Complex Environment, together with Huan Liu of State Grid Changle Power Supply Company and Fenglu Li of State Grid Shouguang Power Supply Company, tackled a problem that has frustrated condition-monitoring engineers for years. Infrared thermography is widely used to inspect electrical equipment without contact, but a measured surface temperature is not determined by contact degradation alone. Load current, ambient temperature, enclosure airflow, conductor geometry, and heat-transfer conditions all jointly shape the observed thermal field. A sound joint under a heavy load may look hotter than a severely degraded joint under a light load, which limits the usefulness of any single temperature reading as a fault indicator.

To disentangle these coupled influences, the researchers first constructed a three-dimensional electro-thermal finite-element model of a real bolted busbar joint: two overlapping copper bars, each 300 millimeters long, 50 millimeters wide, and 8 millimeters thick, connected over an 80-millimeter lap joint by two steel bolts spaced 40 millimeters apart. Rather than representing the degraded interface as a uniformly high-resistance block, the model divided the 0.5-millimeter contact layer between the bars into an effective conducting region and a degraded near-insulating region. This representation reproduces the physical mechanism by which deterioration contracts the conducting area and intensifies current constriction, forcing current through annular conducting patches centered on the bolt axes. As the effective contact ratio decreases, the conducting annuli shrink and localized Joule heating concentrates accordingly.

A crucial methodological decision was to assign distinct physical roles to the two contact parameters. The prescribed joint contact resistance specifies the target lumped resistance of the effective current path, while the effective contact ratio determines the spatial extent of that path and hence the degree of current constriction. When the contact ratio changes, the equivalent resistivity of the contact layer is recalculated so that the prescribed lumped resistance is retained, avoiding the double counting of conducting-area reduction through both geometry and resistance. The degraded region was assigned a resistivity contrast of one thousand relative to the effective region, which a parallel-path analysis showed limits bypass current to approximately 0.023 percent of the total, below the baseline power-consistency deviation of 0.056 percent.

Before any machine learning began, the team verified the numerical integrity of the simulation itself. Four mesh refinement levels were evaluated, from 21,958 to 368,625 tetrahedral elements, and a locally refined production mesh of 190,271 degrees of freedom was retained because it resolved the steep current-density and temperature gradients around the contact regions, bolt holes, and washers. More strikingly, the integrated Joule-heating power generated within the effective contact region was checked against the theoretical lumped relation P = I²Rc across all 400 parametric simulations. The maximum relative deviation was just 0.173 percent, with a mean of 0.059 percent, confirming that the distributed contact-heating implementation remained internally consistent throughout the entire dataset. Such explicit consistency checks between simulated contact heating and the theoretical relation are rarely reported in existing electro-thermal studies.

The parametric dataset was generated using Latin hypercube sampling across five physically defined inputs: load current from 400 to 1,200 amperes, contact resistance from 50 to 300 microohms, effective contact ratio from 0.10 to 0.50, ambient temperature from 293.15 to 313.15 kelvin, and convective heat-transfer coefficient from 5 to 20 watts per square meter per kelvin. Eighteen cases with effective-contact temperature rises exceeding 106.9 kelvin were excluded as high-temperature boundary-risk cases outside the intended applicability domain of the constant-property, sequentially coupled model, leaving 382 retained cases with temperature rises up to 106.9 kelvin. The team also introduced load-normalized thermal descriptors, dividing temperature responses by the squared load current, which reduced the direct correlation with current and provided a more comparable basis for evaluating contact-related thermal effects under different operating levels.

Four candidate model families were then compared for two complementary learning tasks: continuous prediction of the effective-contact temperature rise and four-class simulation-oriented thermal-risk classification using thresholds of 5, 15, and 30 kelvin. Evaluation used repeated five-fold cross-validation with 10 repeats, giving 50 train-validation iterations, with strict target-leakage controls ensuring that only the five original physical inputs served as predictors. The XGBoost regressor achieved a coefficient of determination of 0.990 ± 0.005, a root-mean-square error of 1.877 ± 0.542 kelvin, and a mean absolute error of 1.042 ± 0.198 kelvin, with performance comparable to random forest. For classification, XGBoost reached an accuracy of 0.938 ± 0.026 and a macro F1-score of 0.941 ± 0.033, with a more balanced macro recall than random forest. Across three threshold schemes, all out-of-fold classification errors occurred between adjacent classes, meaning the classifier never confused a Normal case with a Critical one.

Interpretability came through SHapley Additive exPlanations analysis, which decomposed each prediction into additive feature contributions. The results identified load current and prescribed contact resistance as the dominant contributors, with mean absolute SHAP values of 8.899 kelvin and 5.558 kelvin respectively for regression, while convection, ambient temperature, and effective contact ratio produced smaller, condition-dependent effects. The comparatively low global importance of the effective contact ratio reflects the area-averaged nature of the temperature-rise target rather than any claim that current constriction is physically unimportant. Once current and resistance establish the overall electrical power scale, variation in the contact ratio primarily redistributes current transfer within the contact region and produces a smaller average contribution to the area-averaged response. The non-monotonic dependence of the contact ratio further demonstrated that its contribution varies with the accompanying operating and contact conditions.

The authors are explicit about what the framework is and is not. Physics enters through finite-element generation of the training data, physically defined input variables, and post hoc consistency checks, rather than through constraints embedded in the learning algorithm, distinguishing the approach from physics-informed neural networks. The model is a forward surrogate that predicts internal effective-contact temperature rise from prescribed inputs; it does not inversely estimate contact degradation from infrared images, and relating the predicted internal quantity to surface measurements requires further validation. The framework is geometry-specific, built on one busbar configuration, and has not been experimentally validated, so its reported performance quantifies reproduction of finite-element outputs within the simulated design space rather than agreement with operating switchgear.

Future validation should proceed in controlled stages, the authors suggest: laboratory bolted-joint specimens with documented geometry and independently measured contact resistance, tested over multiple current levels and cooling conditions, followed by repeated heating cycles, bolt relaxation, and controlled surface degradation to determine whether prescribed contact scenarios adequately represent evolving joints. Until such work is completed, the framework stands as an interpretable tool for simulation-based scenario assessment and sensitivity analysis, capable of evaluating dense combinations of load, contact state, and thermal boundary conditions essentially instantaneously instead of the roughly 8.4 seconds of solver time each finite-element case requires. For an industry where a single overlooked hotspot can cascade into insulation failure and equipment outage, an explainable model that shows exactly how loading and contact condition jointly shape thermal risk represents a meaningful step toward smarter, load-aware inspection of the joints that hold the power grid together.

Subject of Research: Interpretable surrogate modeling for load-aware thermal risk assessment of bolted switchgear busbar joints using electro-thermal finite-element simulation and XGBoost with SHAP analysis

Article Title: Interpretable surrogate modeling for load-aware thermal risk assessment of bolted switchgear busbar joints using electro-thermal simulation

Article References: Chen, K., Liu, H., & Li, F. (2026). Interpretable surrogate modeling for load-aware thermal risk assessment of bolted switchgear busbar joints using electro-thermal simulation. Frontiers in Mechanical Engineering, 12, Article 1904437. https://doi.org/10.3389/fmech.2026.1904437

Image Credits: AI Generated

DOI: 10.3389/fmech.2026.1904437

Keywords: surrogate modeling, electro-thermal simulation, busbar joints, XGBoost, SHAP, thermal risk, switchgear, finite element analysis, Interpretable, surrogate, modeling, load-aware