Multi-Dimensional Entropy for Vibration Measurement Data Quality Assessment and Erroneous Signal Identification in Wind Turbines

Multi-Dimensional Entropy for Vibration Data Quality Control in Wind Turbines: Properties, Deployment, and Industrial Implications

Erroneous vibration signals caused by sensor malfunction, shutdown transients, and abnormal acquisition conditions can degrade the reliability of automated industrial monitoring pipelines. This paper presents a deployment-oriented analysis of Multi-Dimensional Entropy (MDE) for vibration data quality control in wind turbines, focusing on computational efficiency, model-agnostic capability, physical interpretability, and robustness. Experiments on 57,643 labeled industrial vibration records from 12 wind farms and 14 turbine units, covering main bearings, gearboxes, and generators, together with cross-platform deployment validation and cross-turbine generalization tests on 4,152 unseen records from 3 additional wind farms, show that MDE provides a stable and discriminative feature representation across different classifiers and heterogeneous operating conditions while maintaining low computational and memory requirements. These results demonstrate that MDE can serve as a lightweight and deployment-ready feature layer for vibration data quality control, thereby improving the reliability of industrial monitoring pipelines and reducing the risk of error propagation into downstream diagnostic and prognostic tasks in wind energy applications.

On the Vibration-Based Modal Parameter Identification of Large Wind Turbine Blades

The blades directly affect the safety and power generation efficiency of the wind turbines. With the blade size increases, the reliable modal identification becomes important for vibration-based health monitoring. Although operational modal analysis (OMA) technique has been used in condition monitoring for the wind turbine blades, most existing studies focus on investigating a specific single method or under ideal excitation conditions. To overcome this limitation, this study takes the IEA-15MW large wind turbine blade as the research object and compares three OMA methods through numerical simulations, namely covariance-driven stochastic subspace identification (SSI-COV), frequency domain decomposition (FDD), and poly-reference least squares complex frequency domain (PolyMAX). The performance of the modal parameter identification methods is evaluated with respect to different sensor layouts, blade–tower coupling conditions, and environmental excitations. The results indicate that sparse sensor deployment cannot reliably identify the damage-sensitive high-order and complex modes. A nine-channel layout concentrated near second-order deformation regions significantly improves the identification of second-order flapwise frequencies and controls the average error of the first six modes within 3%. PolyMAX shows the best identification stability under different numbers and layouts of the sensors. Blade–tower coupling changes the blade modal characteristics and increases identification difficulty. Under this condition, FDD can still identify both low-order and high-order modes with good stability. Under different real wind conditions, the increasing wind speed causes the aerodynamic load to deviate from the white noise assumption, generally leading to fluctuations in the identification errors, with relatively large local errors occurring at certain medium and high wind speeds. Overall, the three OMA methods show different advantages under different identification conditions. PolyMAX shows the best stability under different sensor layouts and performs best when wind speed increases in the coupled wind turbine model, indicating that it is the most suitable for the actual complex coupling effects and environmental conditions. This research hopefully provides a basis for the subsequent engineering application of vibration-based modal identification of large offshore blades.

Multi-Sensor Fusion and Frequency-Domain Analysis for Predictive Maintenance of Industrial Induction Motors

Unplanned failures of induction motors impose serious operational and financial penalties on industrial facilities, yet the fault signatures that precede such failures are detectable well in advance through careful sensor instrumentation and data-driven analysis. This paper presents an end-to-end Internet-of-Things (IoT) predictive maintenance scheme based on two off-the-shelf sensors: a DS18B20 one-wire digital thermometer and 2 piezo vibration sensor modules, with an ESP32 edge device for running the full machine learning pipeline offline, independent from any cloud services. Four operating scenarios are considered: healthy condition, BPFO (bearing outer race fault), misaligned shaft, and rotor imbalance. Based on 1-second sampling intervals, 17 descriptors are derived, including statistics in the time domain, Fourier harmonic peaks, energy ratios between different frequency bands, and temperature gradients measured across all sensors. A dual-stage feature selection method using mutual information (MI) score and Random Forest mean decrease impurity (MDI) ranking reduces the number of features to the 10 most relevant descriptors, reducing the computational complexity by 41% at the expense of 5.6% F1-macro. On a balanced 600-sample synthetic dataset, the resulting Random Forest classifier attains 87.3% hold-out accuracy, 91.0±1.9% five-fold cross-validation accuracy, and a macro area-under-the-ROC-curve of 0.980. End-to-end inference takes just 39 ms on the ESP32, easily meeting the 200 ms requirement for real-time alerting.

CORRELATION AND REDUNDANCY ANALYSIS OF STATISTICAL FEATURES FOR PERMANENT MAGNET SYNCHRONOUS MOTOR FAULT DETECTION

Feature selection plays a critical role in designing efficient and interpretable condition monitoring frameworks for electrical drives. In this paper, a correlation analysis of statistical and spectral features is performed for Permanent Magnet Synchronous Motor (PMSM) fault detection in naval windlass systems. Using both simulated data from a MATLAB/Simulink model and real shipboard current signals acquired from five Nigerian Navy vessels over one-month monitoring periods, higher-order statistical moments (Mean, Variance, Standard Deviation, Skewness, Kurtosis) and the Fault Severity Index (FSI) were computed alongside Total Harmonic Distortion (THD). Pearson correlation coefficients were employed to quantify feature relationships under healthy and faulty operating modes, while scatter-plot clustering was used to visualize feature separability across six fault classes. The dataset comprised 2,880 observation windows per vessel (2 kHz sampling, 60-minute windows with 30-minute overlap), yielding a total analytical corpus of 14,400 windows from ship data and 12,000 high-resolution windows from simulation. Results demonstrated strong correlations between variance, standard deviation, and FSI (r ≥ 0.80–0.99), confirming their redundancy. Kurtosis and skewness exhibited weaker correlations with other first- and second-order features (r < 0.60) but showed a moderate inter-correlation of r = 0.88 with each other, indicating shared higher-order sensitivity. THD demonstrated weak correlations with all time-domain statistical moments (r < 0.65), confirming its role as an independent spectral indicator. All reported coefficients were statistically significant (p < 0.001, df = n − 2). The study highlights the potential for dimensionality reduction in PMSM diagnostic frameworks without compromising detection accuracy, with practical guidance for real-time embedded naval monitoring systems.

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.

Vibration-induced failures in industrial ventilation systems: A predictive maintenance approach