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P. Dao

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Open access Aug 2026

Energy distance approach for the condition monitoring of multi turbines using distributional studies.

This study presents the energy distance non-parametric approach for condition monitoring of multiple wind turbines within the same wind farm. The main objective of this work is to monitor the performance of wind turbines by comparing them against each other within the same farm. Traditional methods often rely on parametric assumptions, including normality, which are rarely satisfied in real-world applications. In contrast, the energy distance approach is fully non-parametric, does not assume normality, and is effective for distributions of any shape or location. It enables comparison at the distributional level without requiring explicit assumptions. To validate the proposed approach, SCADA data from a wind farm in Portugal was analyzed. Four wind turbines, including the unit operating in a fault condition, were comparatively analyzed using multiple parameters through the application of the Energy Distance method. The results demonstrate that this method provides a robust means of detecting faults earlier than traditional approaches, as faulty turbines show clear deviations from healthy turbine states. The analysis considered multiple parameters, including generated power, wind speed, hydraulic oil temperature, gearbox oil temperature, generator bearing temperature 2, gearbox bearing temperature, and others. Overall, the results of the study clearly indicate that when comparing the four wind turbines using the energy distance method, the turbine with a fault exhibits a significantly larger energy distance relative to all other turbines. This distinct difference effectively distinguishes the faulty turbine from the healthy ones. These findings confirm that the energy distance approach, based on distributional comparisons, is a robust, efficient, and easily interpretable method for the condition monitoring of wind turbines.

D. Teklemariyem, Syed Nasir Hussain Razvi, Abual Hassan et al. · 0 citations
Open access Aug 2026

Hybrid Energy Distance and Permutation Testing for Vibration-Based Wind Turbine Blade Fault Diagnosis

Wind turbine blade failure diagnosis is of critical importance, as the inability to reliably detect such faults can result in substantial financial losses, prolonged downtime, extensive repair activities, as well as increased operation and maintenance costs. This paper introduces a new application of energy distance and permutation testing for wind turbine blade fault diagnosis based on vibration data analysis. The proposed approach combines a non-parametric energy distance and permutation testing for the identification and characterization of blade faults in wind turbines. Unlike conventional approaches, this method does not require the assumption of a normal data distribution, which is particularly important when analysing vibration signals, as such data often deviates from normality. The approach is also robust against the presence of outliers. The energy distance metric is employed to classify the blade condition of the wind turbine and to investigate subtle changes in blade behaviour by comparing healthy and corresponding faulty states while considering the entire data distribution rather than conventional summary statistics. In the second stage, a permutation test is applied to statistically validate the energy distance results via p-values. The proposed method is validated using experimental vibration datasets representing healthy and faulty blade conditions, including cracked, eroded, twisted, and imbalanced faults. These datasets are analysed under varying wind speed conditions to assess the robustness of the proposed method under different operating conditions. In the second stage, the permutation test confirms the statistical significance of the detected distributional differences, providing additional confidence in the diagnostic results. The findings indicate that the combined use of energy distance and permutation testing effectively identifies and detects the faults from the healthy blade behaviour across two different wind speed conditions. The findings of this study indicate the potential of the proposed approach as a simple, robust, and interpretable solution for wind turbine blade fault diagnosis based on vibration data analysis.

D. Teklemariyem, N. Syed, W. Staszewski et al. · 0 citations

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