Noninvasive Radar Sensing Augmented with Machine Learning for Reliable Detection of Motor Imbalance

1  Introduction

Rotating electrical machines play a pivotal role in industrial processes, transportation systems, and energy applications, where their reliability and operational efficiency are critical for productivity and safety. Among the various mechanical faults affecting rotating machinery, imbalance remains one of the most prevalent and detrimental, often manifesting as excessive vibrations, accelerated component wear, reduced efficiency, and in severe cases, catastrophic failures. Early detection of imbalance is therefore essential to prevent unplanned downtime, reduce maintenance costs, and ensure safe operation.

Traditional fault detection techniques primarily rely on vibration sensors, current signature analysis, and displacement measurements [1–5]. Although effective, these approaches present inherent limitations, including invasive installation requirements, susceptibility to environmental noise, and high deployment costs, particularly when scaling to large industrial systems. To address these challenges, recent studies have explored advanced diagnostic techniques such as electrostatic sensing [6–9], machine learning-based vibration analysis [10–12], and signal decomposition methods [13–17]. While these approaches demonstrate promise, their effectiveness can be constrained under non-stationary operating conditions, and the reliance on direct mechanical or electrical contact reduces flexibility for wide-scale industrial integration.

Emerging noncontact sensing modalities, such as antenna- and radar-based measurements, have shown potential for reliable and cost-efficient machine health monitoring. Recent works utilizing antenna-based reflection coefficients have demonstrated accurate fault detection capabilities [14,18,19], while vibration-sensor-driven deep learning (DL) frameworks have achieved high accuracies for imbalance classification [20–23]. However, these methods often require complex signal acquisition hardware or large-scale datasets, and their performance can degrade when applied to dynamic industrial environments with varying load conditions. Moreover, limited efforts have been directed toward exploiting radar sensing for imbalance detection, despite its inherent advantages of robustness, noninvasiveness, and adaptability to non-stationary loads.

To address these research gaps, this study proposes a radar-based framework for imbalance detection that combines noncontact sensing with machine learning techniques. The approach leverages advanced signal processing to extract informative features from radar measurements and applies systematic feature selection to enhance discriminative capability while reducing redundancy. Multiple state-of-the-art classifiers are evaluated to determine the most effective model for reliable fault identification. Experimental validation confirms that the proposed method achieves higher accuracy and efficiency compared to conventional techniques, offering a practical pathway toward robust and real-time industrial fault monitoring.

The contributions of this study are:

2  Contributions

This work makes several key contributions to motor fault diagnosis and radar-based condition monitoring:

•   Development of a standoff radar system for motor imbalance detection, eliminating mechanical coupling effects and installation complexity of traditional sensors.

•   Extraction of 65 features from time, frequency, complex, and envelope domains to comprehensively capture imbalance signatures.

•   Integration of Kruskal-Wallis testing with recursive feature elimination, yielding an optimal 20-feature subset with 69% dimensionality reduction and 98.52% accuracy.

•   Comparative analysis of six machine learning algorithms with hyperparameter optimization, identifying Extra Trees Classifier (ETC) as the optimal model.

This work establishes a novel pathway for scalable, noninvasive, and computationally efficient imbalance diagnosis, contributing to the advancement of intelligent predictive maintenance strategies in modern industrial systems.

3  Literature Review

Induction motor fault diagnosis has long been a critical research area due to its importance in ensuring reliable and efficient industrial operations. Traditional approaches have predominantly relied on vibration signal analysis combined with machine learning (ML) and deep learning (DL) models to detect and classify motor faults under varying operating conditions. For example, a study by [24] developed a defective induction motor model to collect vibration signals under five operating states and different load conditions. Using convolutional neural networks (CNNs), they achieved high accuracy (95%–96%) with balanced datasets; however, performance declined significantly under imbalanced data conditions. To mitigate this, deep convolutional generative adversarial networks (DCGANs) were employed for data augmentation, which generated realistic samples with 80% similarity and improved accuracy to 90%. The pro-balanced method further enhanced cross-load testing performance to 85%. Similarly, reference [25] combined residual networks (ResNet) with CNNs to detect shaft unbalance using accelerometer data. By training on vibration signatures transformed using short-time Fourier transform (STFT), they achieved accuracies of 99.23% for binary classification (balanced vs. unbalanced) and 95.15% for multiclass classification (five unbalance levels).

Other works have explored alternative sensing approaches. For instance, reference [26] proposed a noninvasive, low-cost method for induction motor fault detection using an antenna to measure time-varying reflection coefficient (S11). Distinct fault signatures were validated via fast Fourier transform (FFT) analysis, and a DL model classified faults with up to 98.2% accuracy using both magnitude and phase information. Similarly, reference [27] introduced a generative adversarial network (GAN)-based data generation method to address imbalance in harmonic drive fault diagnosis. After transforming vibration signals using FFT and filtering synthetic spectra through a data selection module (DSM), they combined real and generated data into a balanced dataset. Classification using a multiscale convolutional neural network (MSCNN) achieved 98.49% accuracy.

For incipient stator faults, reference [28] developed a wavelet-based denoising technique using stationary wavelet transform (SWT) to extract weak features from noisy current signals. Statistical norms of error signals were used as discriminative indicators, and an ensemble AdaBoost decision tree (EADT) was adopted for classification, achieving 98.48% accuracy even with imbalanced datasets. In another study, reference [29] addressed rotor unbalance in a two-mass permanent magnet synchronous motor (PMSM) drive system using the reference current signal from the field-oriented control (FOC) speed controller. Features were extracted using STFT and classified using a multilayer perceptron (MLP) neural network, yielding over 95% detection accuracy and 93% unbalance level estimation.

A vibration dataset for unbalance detection was also introduced by [30], where different unbalance levels were induced on a rotating shaft and recorded across speeds from 630–2330 RPM using three vibration sensors at 4096 Hz. Multiple algorithms—including fully connected neural networks (FCNNs), CNNs, hidden Markov models (HMMs), and random forests—were tested, with the FCNN using FFT-transformed data achieving the highest accuracy of 98.6%. Similarly, reference [31] addressed electric vehicle (EV) motor unbalance under non-stationary load conditions using local iterative filter decomposition. Their method improved classification of load-varying signals and successfully detected even low-speed unbalances, achieving over 80% accuracy. A novel noncontact approach was proposed by [32], which introduced an electrostatic sensing system for continuous displacement measurement of rotary shafts under imbalance faults. Both simulations and experimental tests validated the system’s effectiveness, yielding a relative error within ±0.6%.

Despite the significant progress achieved in fault diagnosis of induction motors and rotating machinery, several limitations persist in the existing body of work. Most studies rely heavily on vibration or current sensors, which, although effective, require physical contact or close proximity to the machine, thereby increasing system complexity, installation cost, and limiting applicability in sealed or harsh industrial environments. Furthermore, many of these approaches are sensitive to variations in operating conditions such as fluctuating loads, speed variations, and external noise, which can reduce diagnostic accuracy, particularly in non-stationary or low-speed regimes. Another challenge lies in the availability and quality of fault data, where class imbalance often necessitates the use of data augmentation techniques, yet the synthetic data generated may not fully capture the variability of real-world conditions. Finally, existing feature extraction and classification methods, while achieving high reported accuracies, often demonstrate limited robustness and generalizability when applied across different operating environments or fault severities.

To address these limitations, this study proposes a radar-based framework for detecting motor imbalance faults, providing a noncontact, robust, and cost-effective alternative to conventional sensing approaches. The framework is designed around a structured multi-phase process that includes signal preprocessing, comprehensive feature extraction across multiple domains, feature selection to retain the most informative indicators, and supervised machine learning for fault classification. By combining radar sensing with advanced data-driven analysis, the proposed approach enhances the reliability of imbalance detection while reducing dependency on traditional vibration or current sensors. This integration enables accurate, generalizable, and efficient diagnosis of motor imbalance under diverse operating conditions, offering a practical pathway for improving the robustness of fault detection in real-world applications.

4  Methodology

The proposed framework as shown in Fig. 1 for radar-based motor imbalance detection consists of a structured multi-phase process, including signal preprocessing, multi-domain feature extraction, feature selection, and supervised classification. Raw in-phase (I) and quadrature (Q) radar signals are initially preprocessed to ensure uniform length and signal integrity. Complex representation of the signals is constructed to extract amplitude and phase characteristics, which are subsequently decomposed into time-domain, spectral, and envelope-based features.

Figure 1: Proposed frame work

To identify the most informative features, statistical analyses, including the Kruskal–Wallis test and Recursive Feature Elimination (RFE), are applied, reducing the dimensionality to a subset of 20 features that effectively capture imbalance-induced variations. Supervised ML models including RF, ETC, XGBoost, CatBoost, K-Nearest Neighbors (KNN), and Support Vector Machine with RBF (SVM-RBF) kernel are then trained and validated to classify the severity of motor imbalance. Hyperparameter optimization is performed using grid search to ensure optimal predictive performance while maintaining generalizability.

4.1 Dataset

The experimental investigations presented in this work utilize a comprehensive radar-based vibration monitoring dataset [33] developed by the Selcuk University Remote Sensing Laboratory. This dataset represents a systematic collection of continuous-wave (CW) radar measurements designed specifically for the characterization and detection of rotational mass imbalance in rotating machinery.

4.2 Data Acquisition Framework

The dataset comprises 1802 independent experimental trials, each conducted under controlled laboratory conditions with a standardized sensor-to-target configuration as shown in Fig. 2. The radar system operates at 24 GHz in continuous-wave mode, positioned at a fixed standoff distance of 30 cm from the target motor assembly. This non-contact sensing approach enables vibration monitoring without mechanical coupling, thereby eliminating potential measurement artifacts associated with traditional accelerometer-based methods.

Figure 2: Experimental setup configuration showing the CW radar, motor assembly, and imbalance disk with added mass

Each experimental trial captures 30 s of baseband radar returns, sampled simultaneously on in-phase (I) and quadrature (Q) channels at 10 kHz, yielding 300,000 discrete samples per channel. The extended measurement duration ensures adequate spectral resolution for frequency-domain analysis while providing sufficient temporal data for advanced signal processing techniques. The dual-channel I/Q configuration preserves both amplitude and phase information of the radar returns, enabling comprehensive characterization of the target’s vibrational dynamics.

4.3 Experimental Design and Operating Conditions

The experimental matrix encompasses a broad range of realistic operating conditions to ensure dataset representativeness as shown in Table 1. Motor rotational speeds span from 500 to 1500 rpm across 11 equally distributed levels, providing coverage of typical industrial machinery operating ranges. Applied load torque varies from 0 to 3 Nm through 6 discrete levels, representing both unloaded and loaded operational scenarios commonly encountered in practical applications.

During each measurement, both rotational speed and applied torque remain constant to ensure steady-state conditions and minimize confounding variables. This controlled approach facilitates the isolation of imbalance-induced vibration signatures from other potential sources of mechanical variation.

4.4 Fault Simulation and Classification Framework

Controlled rotational imbalance conditions were systematically introduced through the attachment of discrete masses to a coupling disk mounted on the motor shaft. This methodology enables precise control over imbalance magnitude while maintaining repeatability across experimental trials. Four distinct imbalance classifications were established based on attached mass:

•   Baseline condition: 0 g additional mass (balanced rotor)

•   Light imbalance: 10 g additional mass

•   Medium imbalance: 20 g additional mass

•   Severe imbalance: 30 g additional mass

The dataset exhibits balanced class representation with 462, 464, 413, and 463 experimental trials corresponding to baseline, light, medium, and severe imbalance conditions, respectively as shown in Fig. 3. This distribution ensures adequate statistical power for supervised learning approaches while minimizing potential class imbalance effects on classification performance.

Figure 3: Distribution of dataset samples across different imbalance severity levels (a) Bar Chart (b) Pie Chart

The complete dataset is structured as a compressed archive containing four class-specific subdirectories corresponding to each imbalance severity level. Individual experimental trials are stored in CSV format, preserving both I and Q channel data in a readily accessible tabular structure. This organization facilitates efficient data loading and preprocessing for various analytical frameworks and ML pipelines.

4.5 Dataset Characteristics

Fig. 4 presents representative frequency domain characteristics of the acquired CW radar signals across different mass imbalance conditions. The baseline condition (Fig. 4a) exhibits a dominant spectral peak at approximately 150 Hz with minimal harmonic content, indicating normal motor operation.

Figure 4: Frequency spectra of CW radar signals acquired from motor vibrations under different mass imbalance conditions. (a) Baseline condition (0 g), (b) Light imbalance (10 g), (c) Medium imbalance (20 g), (d) Severe imbalance (30 g)

As imbalance severity increases, distinct spectral patterns emerge. The light imbalance condition (Fig. 4b) introduces additional frequency components while maintaining the primary operational frequency. Medium imbalance (Fig. 4c) demonstrates increased spectral complexity with emerging harmonics around 175 Hz, characteristic of mechanical irregularities. The severe imbalance condition (Fig. 4d) shows the most pronounced spectral modifications, with multiple prominent peaks and elevated harmonic content throughout the frequency range.

These spectral variations provide clear discrimination features for classification algorithms, as each imbalance level produces unique frequency signatures that correlate with the mechanical condition severity. The consistent presence of dominant peaks across all conditions ensures signal detectability, while the progressive spectral changes enable effective condition monitoring through radar-based vibration analysis.

5  Preprocessing and Feature Extraction

The acquired CW radar signals undergo systematic preprocessing to ensure data quality and consistency across all imbalance measurements. Each recorded signal comprises I and Q components sampled at fs=10 kHz for duration T=30 s, yielding N=300,000 data points per channel. Signal standardization addresses temporal variations inherent in motor vibration measurements by truncating longer signals to the first 300,000 samples and zero-padding shorter signals to achieve uniform length. The complex-valued radar return signal is constructed as:

z[n]=I[n]+jQ[n](1)

from which instantaneous amplitude and unwrapped phase are derived as:

A[n]=|z[n]|=I2[n]+Q2[n](2)

ϕunwrapped[n]=unwrap(arctan⁡(Q[n]I[n]))(3)

Phase unwrapping was applied to eliminate artificial 2π discontinuities created by the arctangent operator [34]. At 24GHz (λ≈12.5mm), a 1mm displacement produces approximately 1.0rad of phase change [35]; such small imbalance-induced displacements would be corrupted by wrap discontinuities, which appear as ±2π spikes in phase derivatives. The radar was positioned at a fixed standoff distance of 30cm along the shaft axis, ensuring that imbalance-induced radial motions projected strongly onto the radar line-of-sight and that the phase–displacement mapping remained consistent across trials. Unwrapping therefore restored the physical continuity of the displacement signal and is standard practice in Doppler radar vibration analysis [36].

A comprehensive 65-feature vector was designed to capture the multi-domain manifestations of motor imbalance in CW radar signatures, combining time-domain statistical descriptors (e.g., skewness, kurtosis of I/Q signals), frequency-domain spectral characteristics (e.g., harmonic energy, spectral centroid and spread), and advanced signal processing features such as Hilbert envelope statistics and unwrapped phase derivatives that reflect amplitude and Doppler modulations induced by rotor eccentricity. The feature extraction pipeline is shown in Fig. 5. Time-domain features provide fundamental characterization of amplitude variations induced by periodic imbalance forces, with thirteen statistical descriptors computed for each I and Q channel. The mean values μI=1N∑n=1NI[n] and μQ=1N∑n=1NQ[n] capture DC offset variations caused by mechanical misalignment, while variance estimates σI2=1N−1∑n=1N(I[n]−μI)2 and σQ2=1N−1∑n=1N(Q[n]−μQ)2 quantify amplitude fluctuation magnitude that increases systematically with imbalance severity. Higher-order statistical moments including skewness γ=E[(X−μ)3]σ3 and kurtosis β=E[(X−μ)4]σ4 characterize asymmetry and peakedness of amplitude distributions, which deviate from Gaussian behavior under mechanical imbalance conditions due to periodic forcing functions. The root-mean-square value RMS=1N∑n=1NX2[n] provides energy-based amplitude quantification that correlates strongly with vibration intensity, while robust statistics including median, quartiles (Q25, Q75), range, and mean absolute value offer outlier-resistant characterization crucial for industrial environments with measurement noise.

Figure 5: Feature extraction pipeline

Complex signal features exploit the coherent nature of CW radar returns to capture amplitude and phase modulation effects characteristic of rotating machinery imbalance. Statistical moments of instantaneous amplitude A[n] including mean, standard deviation, variance, and maximum value quantify envelope modulation depth that increases with imbalance magnitude as unbalanced masses induce periodic radial displacement. Phase derivative features computed as Δϕ[n]=ϕunwrapped[n+1]−ϕunwrapped[n] capture instantaneous frequency variations resulting from Doppler shifts caused by vibrational motion, with mean, standard deviation, and variance of phase derivatives providing sensitive indicators of frequency modulation depth that correlates with mechanical vibration amplitude.

Frequency-domain analysis reveals spectral signatures associated with rotational imbalance through Fast Fourier Transform processing X[k]=∑n=0N−1x[n]e−j2πkn/N, where peak magnitudes and corresponding dominant frequencies identify characteristic vibration components at fundamental rotation frequency and harmonics. Spectral energy calculations E=∑k=1N/2|X[k]|2 quantify total vibrational energy content, while spectral centroids fc=∑k=1N/2f[k]|X[k]|∑k=1N/2|X[k]| characterize frequency distribution shifts toward higher harmonics with increasing imbalance severity. Power spectral density (PSD) features were computed using Welch’s method (scipy.signal.welch) with a 1024-point Hann window, 50% overlap, and a sampling frequency of 10 kHz. This configuration provided a frequency resolution of approximately 9.77 Hz while maintaining low variance in the estimated spectrum. From each PSD estimate, the maximum power, total integrated power, and dominant frequency were extracted for both I and Q channels to quantify spectral energy distribution under different imbalance conditions.

Low-frequency spectral analysis specifically targets the 0–50 Hz band where motor imbalance signatures predominantly manifest, as industrial motors typically operate at rotation frequencies below 30 Hz (1800 RPM) with primary imbalance components appearing at 1× rotation frequency. Peak magnitude and energy within this critical frequency band Elow=∑f≤50|X(f)|2 provide direct quantification of imbalance-induced vibrations while rejecting higher-frequency noise and structural resonances unrelated to mass imbalance. This targeted analysis proves essential for distinguishing between different imbalance severities, as the fundamental frequency component exhibits the strongest correlation with unbalanced mass magnitude according to established rotor dynamics theory.

Envelope analysis through Hilbert transform processing xh[n]=ℋ{x[n]} enables extraction of amplitude modulation patterns characteristic of mechanical imbalance, where the analytical signal envelope Env[n]=|x[n]+jxh[n]| reveals beating phenomena caused by interaction between carrier frequency and low-frequency modulation from rotating imbalance. Statistical characterization of envelope signals including mean, standard deviation, and range quantifies modulation depth that increases monotonically with imbalance severity, providing robust features for both classification and regression applications in condition monitoring systems.

Band-specific energy analysis employs fourth-order Butterworth bandpass filtering [37] to isolate frequency components relevant to different mechanical phenomena, with energy calculated as Eband=∑n=1Nxfiltered2[n] within four distinct bands. These bands were selected based on rotor dynamics considerations: 1–10 Hz captures subharmonic components from nonlinear coupling effects; 10–50 Hz encompasses the fundamental rotation frequency range for the tested motor (500–1500 rpm ≈ 8.3–25 Hz); 50–100 Hz covers the first harmonic content, which intensifies with more severe imbalance; and 100–500 Hz represents higher-order harmonics generated by nonlinear mechanical interactions. A 4th-order Butterworth design was chosen for its maximally flat passband and moderate roll-off, which preserves amplitude-based features while providing sufficient separation between adjacent bands without introducing ripple-induced energy distortions. The filter design employed the scipy.signal.butter and filtfilt functions in Python, using normalized cutoff frequencies with respect to the Nyquist frequency (fN=5 kHz). The zero-phase filtfilt implementation ensured no phase distortion while preserving the temporal integrity of amplitude modulations. This frequency decomposition enables detailed characterization of the expected harmonic progression patterns, which theoretical rotor dynamics predicts will grow systematically in both order and energy with increasing eccentricity.

All computations were performed in Python 3.10 using the NumPy, SciPy, and scikit-learn libraries. Statistical descriptors (mean, variance, skewness, kurtosis) were computed via numpy and scipy.stats, while FFT and Hilbert transforms utilized scipy.fft and scipy.signal.hilbert, respectively. The complete feature extraction process was implemented as a reproducible class-based pipeline and validated on CW radar datasets sampled at 10 kHz for 30 s per trial. The comprehensive 65-dimensional feature set systematically captures amplitude, frequency, and modulation characteristics that vary predictably with motor imbalance conditions, forming the foundation for robust ML based classification between normal operation (0 g), mild imbalance (10 g), moderate imbalance (20 g), and severe imbalance (30 g) conditions through exploitation of both linear amplitude relationships and nonlinear harmonic generation mechanisms inherent in rotating machinery dynamics.

6  Statistical Analysis

To assess the statistical suitability of the extracted features for subsequent modeling, a series of normality tests was performed across all 65 non-categorical features. Specifically, the Shapiro–Wilk [38,39], Jarque–Bera [40,41], and Anderson–Darling [42–44] tests were employed to evaluate deviations from Gaussianity. The results consistently indicated that none of the features adhered to the null hypothesis of normality at either the 5% or 1% significance levels. Complementary distributional analysis further revealed that 12.3% of the features (8 out of 65) exhibited substantial skewness (absolute skewness >2), while 15.4% (10 out of 65) displayed pronounced kurtosis (absolute kurtosis >2). These findings demonstrate a systematic departure from Gaussian assumptions across the feature space, thereby motivating the application of appropriate transformation techniques or the use of non-parametric and distribution-robust learning algorithms in downstream classification tasks.

In light of the observed deviations from normality, non-parametric approaches were deemed appropriate for assessing the discriminative capacity of individual features across the four imbalance classes. Accordingly, the Kruskal–Wallis H-test [45–47] was applied to all 66 features, complemented by the computation of ϵ2 effect sizes to quantify the magnitude of between-group differences. The results, summarized in Table 2, reveal that a substantial subset of features exhibit statistically significant variation across operating conditions, even under stringent multiple-comparison corrections (Bonferroni and FDR).

The most discriminative features, including current-domain descriptors such as Iskew, Imedian, and Qskew, achieved p-values on the order of 10−18 to 10−52 and effect sizes in the range of 0.06 to 0.13, indicating moderate practical significance. Spectral-domain attributes (e.g., Ispectral\_std, Ispectral\_energy, Qspectral\_centroid) also ranked prominently, underscoring the combined contribution of both time- and frequency-domain features in characterizing imbalance severity. By contrast, features with lower effect sizes (e.g., certain spectral roll-off statistics) demonstrated negligible discriminatory power, suggesting limited utility for downstream classification.

These findings corroborate the hypothesis that imbalance manifests in both linear amplitude shifts and nonlinear spectral signatures. The ranked feature importance derived from the Kruskal–Wallis analysis provides a principled basis for feature selection and dimensionality reduction, while also motivating the integration of robust machine learning classifiers capable of exploiting the identified discriminative patterns.

The post-hoc pairwise comparisons summarized in Table 3 reveal significant differences in features across the experimental groups (10gr, 20gr, 30gr, and normal). Only comparisons with FDR-adjusted p-values less than 0.05 are considered, highlighting the features most sensitive to group differences.

Time-domain features such as I_mean, I_std, I_var, I_range, I_rms, I_skew, I_kurt, I_mav, I_median, I_max, and I_min exhibit significant differences across most group pairs. Notably, comparisons involving the 10gr and 30gr groups, as well as between the normal and experimental groups, show highly significant changes, indicating that both the central tendency and variability of the signals are strongly affected by the experimental conditions. Shape-related features such as I_skew and I_kurt demonstrate extremely low p-values, reflecting alterations in signal asymmetry and peakedness under higher loads.

Quadrature-domain features (Q_mean, Q_range, Q_skew, Q_kurt, Q_mav, Q_median, Q_max, and Q_min) show a pattern similar to the in-phase features, with strong differences particularly in comparisons involving the 30gr group. These results indicate that both amplitude and distribution changes occur in the quadrature component under experimental manipulation.

Spectral features, including I_spectral_energy, I_spectral_sum, I_spectral_std, and their quadrature counterparts, reveal significant group differences, highlighting that the power and variability of the frequency content are strongly modulated. Band-specific measures (I_band_50_100 Hz, I_band_100_500 Hz, Q_band_100_500 Hz) demonstrate selective sensitivity, suggesting that certain frequency ranges are more affected by the experimental conditions than others.

Envelope and peak features (I_env_mean, I_env_std, amp_mean, amp_max, I_peak_freq, I_low_freq_peak, Q_low_freq_peak) also display significant differences. These results indicate that both the amplitude envelope and peak intensities, as well as the spectral peak locations, are strongly modulated by the experimental manipulations.

It is evident from results that, the 30gr group exhibits the most pronounced differences across almost all features, suggesting a dose-dependent effect of the experimental conditions. Features capturing amplitude, variability, distribution shape, and spectral content appear to be the most sensitive indicators of group differences. These findings highlight the robustness of multi-domain signal features in differentiating experimental conditions and support their potential use in classification.

The statistical evaluation established that the extracted features systematically deviate from Gaussian assumptions, thereby justifying the use of non-parametric methods. The Kruskal–Wallis tests, complemented by ϵ2 effect sizes, revealed that a substantial number of both time- and frequency-domain features exhibit statistically significant differences across the imbalance conditions. Subsequent post-hoc pairwise comparisons with FDR correction further identified the specific feature–group interactions driving these effects. The results consistently highlight that the 30gr group demonstrates the most pronounced deviations from both the normal and lighter imbalance conditions, suggesting a clear dose-dependent effect. Across domains, features reflecting amplitude, variability, distributional shape (skewness and kurtosis), as well as spectral energy and band-specific measures, emerged as the most sensitive discriminators of imbalance severity. These findings validate the robustness of a multi-domain feature representation and provide a principled basis for feature selection and the development of downstream predictive models.

7  Feature Selection

Building on the insights from the statistical analysis, the identified discriminative features provide a natural foundation for feature selection. Features exhibiting both significant group differences and meaningful effect sizes are prioritized to reduce dimensionality, minimize redundancy, and enhance the predictive performance of ML models. Consequently, the subsequent feature selection process focuses on systematically ranking and selecting the most informative features across time-, quadrature-, and spectral-domains, thereby ensuring that the predictive models leverage the strongest indicators of imbalance severity.

The results (Table 2) indicate that a substantial subset of features exhibits highly significant variation across imbalance classes, with p-values ranging from 10−18 to 10−52. Current-domain descriptors such as Iskew, Imedian, and Qskew emerged as the strongest discriminators, achieving effect sizes in the range of 0.06–0.13, consistent with moderate to high practical significance. Prominent contributions were also observed from spectral-domain descriptors (e.g., Ispectral\_std, Ispectral\_energy, Qspectral\_centroid), underscoring that both amplitude-related and spectral-shape features are critical indicators of imbalance severity. By contrast, features such as spectral roll-off and higher-order spectral moments showed negligible effect sizes, suggesting limited utility for classification.

To complement the statistical analysis, a model-driven feature selection was conducted using RFE with a RF classifier (100 estimators, random state = 42) as the base estimator. RF was selected due to its robustness to outliers, ability to model non-linear relationships, and provision of impurity-based importance scores for feature ranking. Feature subsets ranging from 65 down to 5 were evaluated using a 70–30 stratified train-test split, with accuracy on the test set serving as the primary performance metric.

The RFE evaluation (Fig. 6) revealed that the baseline 65-feature set achieved 0.9630 accuracy. Performance remained stable above 0.96 for subsets of 50–65 features, with peak accuracy of 0.9667 observed at both 55 and 39 features. A 20-feature subset preserved the baseline performance (0.9630) while achieving a 69% reduction in dimensionality, representing the optimal trade-off between accuracy, computational efficiency, and interpretability. Accuracy degraded more noticeably below 20 features, reaching 0.9353 at 5 features.

Figure 6: Classification accuracy across feature subset sizes obtained via RFE with Random Forest

To consolidate insights from both approaches, the top 20 features were ranked by combining (i) their statistical discriminative power (ϵ2 from Kruskal–Wallis) and (ii) their RF importance scores derived from RFE. This dual perspective ensures that the selected features are not only statistically distinct across imbalance classes but also contribute materially to classification accuracy.

Table 4 presents the integrated ranking. Features such as Iskew, Qskew, Imedian, and Ispectral\_std consistently rank among the most important according to both criteria. This convergence reinforces their role as robust indicators of imbalance severity. A bar plot illustrating RF importance (Fig. 7) and a pie chart summarizing domain contributions (Fig. 8) further highlight the predominance of quadrature-domain (45%) and in-phase time-domain (40%) features, with additional contributions from derived amplitude features (15%).

Figure 7: RF feature importance scores for the top 20 features selected by RFE

Figure 8: Domain distribution of the top 20 most important features

The convergence between Kruskal–Wallis effect sizes and RFE-based Random Forest importance confirms the robustness of the identified feature set. The selected 20 features are both statistically discriminative and practically effective in driving classification accuracy, supporting their use for efficient and interpretable imbalance detection.

7.1 Model Selection and Hyperparameter Optimization

The classification of motor imbalance was approached using multiple supervised learning algorithms trained on 20 discriminative features obtained through RFE. The models were selected to represent diverse learning paradigms, ensuring coverage of ensemble-based, boosting-based, kernel-based, and instance-based methods. Specifically, the algorithms considered were Random Forest (RF), ETC, Extreme Gradient Boosting (XGBoost), CatBoost, Support Vector Machine (SVM) with a radial basis function (RBF) kernel, and k-Nearest Neighbors (KNN). This diversity allowed the comparison of models that vary in interpretability, computational efficiency, and capacity to model nonlinear decision boundaries.

RF and ETC are tree-ensemble methods that construct multiple decision trees, differing in their introduction of randomness: RF employs bootstrap sampling, while ETC introduces random feature splits. XGBoost and CatBoost are boosting algorithms that sequentially correct errors from prior learners, with XGBoost utilizing gradient-based optimization and regularization, and CatBoost incorporating ordered boosting with efficient handling of categorical features. The SVM with an RBF kernel was employed for its ability to model complex nonlinear class boundaries by projecting data into a higher-dimensional space. KNN, on the other hand, is a non-parametric method that classifies based on neighborhood proximity, providing a complementary baseline perspective.

Hyperparameter tuning for each algorithm was performed using grid search with 5-fold cross-validation to ensure robust parameter estimation. Table 5 presents the key hyperparameters explored and the selected values. The grid search was designed to balance model complexity, predictive accuracy, and computational efficiency.

The hyperparameters serve distinct roles in shaping model behavior. For ensemble methods, the number of estimators defines the size of the forest, while maximum depth and minimum samples per split regulate tree complexity and generalization. In boosting algorithms, learning rate controls the contribution of each tree, while subsampling parameters in XGBoost mitigate overfitting through stochasticity. CatBoost’s depth parameter manages the bias-variance trade-off, with iterations determining boosting rounds. For SVM, the regularization constant C adjusts the trade-off between margin maximization and misclassification, while γ specifies the influence of support vectors. In KNN, the number of neighbors determines locality sensitivity, and weighting strategies adjust the effect of nearby vs. distant samples.

The grid search procedure ensured that each model was configured at near-optimal settings, thereby enhancing the reliability of classification performance for motor imbalance detection.

7.2 Algorithmic Framework for Radar-Based Motor Fault Classification

The complete framework for motor imbalance detection using radar signals is summarized in Algorithm 1. The process begins with data preprocessing, where raw in-phase (I) and quadrature (Q) signals are standardized to a fixed duration of 30 s at a sampling rate of 10 kHz, yielding 300,000 samples per trial. Truncation or zero-padding is applied when necessary, and the complex analytic signal z[n]=I[n]+jQ[n] is formed to derive amplitude and unwrapped phase, which serve as the basis for feature extraction.

From each signal, 65 features are computed across multiple domains. Time-domain statistics such as mean, variance, skewness, kurtosis, RMS, median, and MAV are extracted for both I and Q. Complex features include amplitude statistics and phase-difference measures, while frequency-domain descriptors are obtained from the Fourier spectrum, including peak frequency, spectral centroid, and band-limited energy. Envelope features are derived using the Hilbert transform, and additional energy measures are extracted from band-pass filtered signals in the range of 1–500 Hz. This multi-domain representation ensures that both statistical and spectral properties of the signals are captured.

To assess feature relevance, the Kruskal–Wallis test is applied across classes, with effect sizes and false discovery rate correction providing a ranked importance order. A recursive feature elimination strategy using Random Forest further refines the feature set by iteratively removing the least important features while monitoring classification accuracy. This process results in an optimal subset of 20 features that balances discriminative ability and dimensionality.

The reduced feature set is then used to train several ML models, including RF, ETC, XGBoost, CatBoost, SVM-RBF, and k-Nearest Neighbors. For each classifier, hyperparameters are optimized using grid search with five-fold cross-validation. Parameters such as the number of trees and depth for ensemble models, learning rate and estimators for boosting methods, kernel width and penalty parameter for SVM, and neighbor count for KNN are systematically explored. The final model selection is based on test performance, yielding the most effective classifier for radar-based motor imbalance detection.

8  Results

The performance evaluation of the proposed radar-based motor imbalance detection framework was conducted using a stratified 70-30 train-test split to ensure representative class distribution across both training and testing sets. This partitioning strategy maintained the original class balance (0 g: 462 samples, 10 g: 464 samples, 20 g: 413 samples, 30 g: 463 samples) while providing sufficient training data for robust model development and adequate testing samples for reliable performance assessment.

Six ML algorithms were systematically evaluated using the optimal 20-feature subset identified through recursive feature elimination: RF, ETC, XGBoost, CatBoost, SVM-RBF, and KNN. Each model underwent hyperparameter optimization via grid search with 5-fold cross-validation to ensure fair comparison under optimal configurations.

8.1 Classification Performance Analysis

Table 6 presents the comprehensive performance evaluation across all tested algorithms. The results demonstrate substantial variation in both predictive accuracy and computational efficiency, with test accuracies ranging from 0.7002 to 0.9852.

ETC emerged as the superior performer, achieving the highest test accuracy of 98.52% and cross-validation accuracy of 98.00% with low standard deviation (0.0069), indicating consistent performance across different data partitions. The model demonstrated exceptional computational efficiency with a training time of only 1.01 s, making it highly suitable for real-time industrial applications. XGBoost secured the second-best performance with test accuracy of 97.41% and cross-validation accuracy of 97.39%. While exhibiting slightly higher variance (0.0115) than ETC, XGBoost maintained strong predictive consistency. However, its training time of 4.62 s represents a 4.5× computational overhead compared to ETC.

RF achieved competitive performance with 96.30% test accuracy and 96.56% cross-validation accuracy, coupled with the fastest training time (0.73 s). The model’s moderate variance (0.0082) and computational efficiency make it an attractive alternative for resource-constrained environments. Catboost demonstrated solid predictive capability (96.12% test accuracy, 97.39% CV accuracy) with the lowest cross-validation variance (0.0091), indicating highly stable performance. However, its training time of 43.55 s represents a significant computational burden, limiting practical deployment feasibility. SVM with RBF kernel achieved 95.75% test accuracy with 95.56% cross-validation performance. While computationally reasonable (1.12 s training time), the model exhibited the highest variance among competitive algorithms (0.0156), suggesting potential sensitivity to data variations.

KNN significantly underperformed with only 70.02% test accuracy and 69.12% cross-validation accuracy, accompanied by the highest variance (0.0265). Despite minimal training time (0.0036 s), the algorithm’s inability to effectively capture the complex patterns in radar-based imbalance signatures renders it unsuitable for this application.

ETC is selected as the optimal model based on its superior performance across multiple evaluation criteria. ETC achieved the highest test accuracy (98.52%) with a substantial 1.11 percentage point margin over the second-best XGBoost (97.41%). The cross-validation accuracy of 98.00% with low standard deviation (0.0069) demonstrates consistent performance across different data subsets, indicating robust generalization capability essential for industrial applications. The model’s training time of 1.01 s provides an optimal balance between accuracy and computational efficiency. While Random Forest achieves faster training (0.73 s), the 1.22 percentage point accuracy improvement justifies the marginal computational overhead. Compared to other high-performing models like XGBoost (4.62 s) and CatBoost (43.55 s), ETC offers significant time advantages.

8.2 Classification Performance of Top Models

The classification performance of the top three models, RF, XGBoost, and ETC, was evaluated using per-class precision, recall, and F1-score in addition to overall accuracy. These results provide a comprehensive assessment of each model’s ability to discriminate between imbalance severities and the normal condition. As shown in Table 7, all models demonstrate strong classification performance, with accuracies above 96%.

Among the evaluated models, ETC achieved the highest accuracy of 98.52% and exhibited the most balanced per-class metrics. Notably, ETC maintained precision and recall values above 97% across all classes, reflecting its robustness in identifying both mild and severe imbalance conditions without class-specific bias. This superior stability and consistency highlight its suitability for real-world deployment in industrial monitoring systems.

8.3 Confusion Matrices

The performance of the top three classifiers is summarized in Fig. 9. For the RF model, the total number of correct predictions across all classes is 521, with 20 misclassifications distributed among the classes. Specifically, the 10gr class had 128 correct and 11 incorrect predictions, the 20gr class had 120 correct and 4 incorrect, the 30gr class had 135 correct and 4 incorrect, and the normal class had 138 correct and 1 incorrect prediction. XGBoost improved the overall accuracy, yielding 527 correct predictions with 14 misclassifications. The 10gr class had 133 correct predictions, 20gr had 119, 30gr had 136, and normal achieved 139 correct predictions. The ETC demonstrated the highest performance, with 533 correct predictions and only 8 misclassifications. Notably, the ETC achieved nearly perfect recognition for the normal class and consistently high performance for all imbalance levels, confirming its suitability as the optimal model for this radar-based motor imbalance detection task.

Figure 9: Confusion matrices of the top three classifiers RF, XGBoost and ETC

The diagonal dominance in ETC’s confusion matrix indicates robust classification capability, while the sparse off-diagonal entries show that misclassifications are minimal and mostly limited to adjacent imbalance levels. This observation highlights ETC’s reliability for industrial deployment where precise discrimination between motor imbalance severity levels is crucial for predictive maintenance, operational safety, and cost optimization.

8.4 Comparison with Deep Learning Baseline

To validate the competitiveness of the proposed feature-based method, a one-dimensional convolutional neural network (1D-CNN) was trained directly on raw I/Q radar signals. The 1D-CNN consisted of three convolutional layers with ReLU activations, max-pooling layers, a fully connected layer, and a softmax output for the four imbalance classes. The network was trained using the same stratified 70-30 train-test split and preprocessing as the feature-based models.

Table 8 summarizes the performance of the 1D-CNN in comparison with the top feature-based models. The 1D-CNN achieved a test accuracy of 86.8%, which is slightly lower than the 98.52% achieved by the feature-based ETC model. While the CNN can automatically learn signal representations, the feature-based approach demonstrates superior accuracy and considerably faster training and inference times, highlighting its suitability for real-time industrial deployment.

8.5 Statistical Significance and Confidence Intervals

To substantiate the observed performance differences among the top feature-based models, we conducted statistical significance testing and computed confidence intervals. Paired t-tests were performed on the test accuracies and macro-averaged F1-scores obtained from five repeated stratified 70-30 train-test splits for the ETC, XGBoost, and RF models. The results indicate that the superior performance of ETC over XGBoost and RF is statistically significant (p<0.05) for both metrics.

Additionally, 95% confidence intervals were estimated using the bootstrap method with 1,000 resamples. Table 9 summarizes the mean test accuracy and macro F1-score along with their 95% confidence intervals for the top models. The results confirm that ETC consistently outperforms the other models, and the observed performance differences are statistically robust.

The confidence intervals clearly demonstrate that ETC’s superior performance is statistically significant compared to XGBoost and RF, reinforcing its suitability for reliable real-time radar-based motor imbalance detection.

8.6 Ablation Study

An ablation study was conducted to assess the impact of distinct feature groups on classification performance for RF, XGBoost, and ETC. I and Q features, as well as other statistical or envelope-derived features, were evaluated individually and in combination. Using individual groups resulted in decreased accuracy; for instance, time-domain features alone yielded 0.8965 (RF), 0.9094 (XGBoost), and 0.9168 (ETC). Quadrature-domain features performed slightly better, whereas other features alone showed limited discriminative power.

Combining multiple feature groups significantly improved results. The combination of time- and quadrature-domain features achieved 0.9578 (RF), 0.9741 (XGBoost), and 0.9795 (ETC), while the complete 20-feature set produced the highest accuracy, with ETC reaching 0.9852. These results, illustrated in Fig. 10, confirm that integrating complementary feature domains enhances motor imbalance detection and that the selected 20-feature subset provides a balanced and discriminative representation.

Figure 10: Ablation study showing test accuracy of top three classifiers on different feature groups

8.7 Inference Time

The inference time of the proposed models was measured by randomly selecting five signal trials from the dataset and results are visualized in Fig. 11. For each trial, the complete pipeline from feature extraction to classification was executed on the top three models. The ETC demonstrated the fastest performance with an average inference time of 70.176 ms per trial, followed by XGBoost at 90.941 ms, and RF at 92.990 ms. These results indicate that the ETC can provide near real-time imbalance detection, with offering the most computationally efficient solution while maintaining high classification accuracy.

Figure 11: Comparison of inference times for the top three classification models

8.8 Comparison with Existing Studies

A comparative analysis (Table 10) of the proposed radar-based motor imbalance detection framework with existing studies in the literature highlights its advantages in terms of diagnostic accuracy, robustness, and practicality. Traditional vibration- and current-based approaches have reported high classification performance; however, they often require direct-contact sensors, are sensitive to noise and load variations, and face challenges with data imbalance. For example, CNN-based vibration analysis in [24] achieved 95%–96% accuracy with balanced data, but performance declined under imbalanced datasets, even after augmentation with deep DCGANs, which improved accuracy only to 90%. Similarly, the ResNet-CNN method in [25] reached 99.23% for binary classification but dropped to 95.15% for multiclass unbalance levels.

Alternative noninvasive methods such as antenna-based S11 measurements [26] and electrostatic sensing [32] demonstrated accuracies of 98.2% and error rates within ±0.6%, respectively, but remain constrained by setup complexity and susceptibility to environmental conditions. Generative adversarial network (GAN)-based harmonic drive diagnosis [27] and wavelet threshold denoising with ensemble AdaBoost decision tree (EADT) [28] also reported accuracies near 98.5%, though both approaches depend on extensive vibration or current datasets. In contrast, the proposed radar-based method achieved a test accuracy of 98.52% with the ETC, surpassing most related works while eliminating the need for contact-based sensors. Moreover, the framework demonstrated near real-time inference capability with an average detection time of 70 ms, which further enhances its applicability for online monitoring in industrial environments.

The comparative results in Table 10 indicate that the radar-based framework achieves competitive or superior classification accuracy compared to state-of-the-art methods. Importantly, it addresses key limitations of existing approaches by offering a noncontact sensing solution, strong robustness against imbalance-induced variations, and low inference latency suitable for real-time industrial deployment. This positions the framework as a practical advancement in motor fault diagnosis research.

9  Discussion

The achieved classification accuracy of 98.52% with the ETC represents a significant advancement in radar-based motor fault diagnosis. This performance is comparable or superior to existing contact-based methods while eliminating their inherent limitations. The framework’s near real-time inference capability, with an average processing time of 70 ms, supports integration into industrial monitoring systems for continuous condition assessment. The non-contact operation avoids issues related to sensor mounting, mechanical coupling, and measurement artifacts that frequently compromise accelerometer-based approaches.

Analysis of the selected features indicates that current-domain descriptors, such as I_skew, I_median, and Q_skew, emerged as the most discriminative indicators, achieving effect sizes of 0.06–0.13 with p-values ranging from 10−18 to 10−52. This aligns with rotor dynamics theory, where mass imbalance generates periodic forcing functions reflected as amplitude and distributional variations in radar returns. Spectral features, including I_spectral_std, I_spectral_energy, and Q_spectral_centroid, further validate the multi-domain feature approach, confirming that time-domain amplitude variations and frequency-domain harmonic content provide complementary information for imbalance characterization.

To strengthen the clarity of novelty and competitiveness, a more explicit quantitative and qualitative comparison with related studies has been integrated. CNN-based vibration analysis methods typically achieve 95%–96% accuracy and up to 99.23% in binary settings, but require physical sensor contact and exhibit sensitivity to mounting conditions. Antenna-based S11 radar methods reach approximately 98.2% accuracy but depend heavily on precise antenna alignment. Electrostatic sensing approaches, while achieving errors within ±0.6%, are constrained by shaft geometry and grounding conditions. In contrast, the proposed radar-based method achieves 98.52% accuracy using a simple non-contact configuration that is less susceptible to installation variability, highlighting its practical advantages for industrial environments.

The experimental design ensures dataset representativeness under realistic operating conditions, with controlled variation of motor speeds and load torques. Balanced class representation minimizes bias and provides sufficient statistical power for reliable model evaluation. The comprehensive feature extraction captures multiple aspects of motor dynamics, including amplitude statistics, spectral harmonics, and envelope modulation patterns, enhancing discriminative capability.

However, several limitations should be noted. All experiments were conducted under controlled laboratory conditions on a single motor type with controlled imbalance masses, which may limit generalizability to other motors or industrial settings. Variations in motor size, load conditions, bearing stiffness, and rotor dynamics could affect radar signal characteristics and feature distributions. Additionally, the current standoff distance of 30 cm was optimized for the lab setup and may require adaptation for space-constrained industrial installations. Furthermore, the framework focuses exclusively on mass imbalance, necessitating extension for comprehensive fault diagnosis, including misalignment, bearing defects, and electrical anomalies.

The radar-based framework offers substantial potential for industrial implementation, particularly in environments where traditional sensor placement is challenging or unsafe, such as chemical plants, high-temperature settings, or explosive atmospheres. The computational efficiency of the optimized 20-feature set and the ETC supports embedded deployment on industrial controllers or edge devices. The 70 ms inference time enables continuous monitoring without significant computational burden, and integration with existing condition monitoring systems can be achieved using standard communication protocols.

Future research directions include extending the approach to multi-fault diagnosis, validating performance across different motor types and operating conditions, and optimizing radar frequencies for enhanced fault sensitivity. Advanced signal processing, machine learning-based feature learning, and deep neural networks could further improve diagnostic accuracy and fault coverage. Distributed radar sensor networks may enable improved spatial resolution and fault localization, while long-term studies under varying environmental conditions would address robustness and reliability. Incorporating adaptive thresholds and uncertainty quantification could further strengthen industrial applicability. Overall the demonstrated effectiveness of radar-based motor imbalance detection establishes a foundation for broader exploration of microwave sensing in industrial condition monitoring, offering a non-invasive approach that could transform predictive maintenance practices.

10  Conclusion

This research demonstrates the effectiveness of a non-contact radar-based framework for motor imbalance detection, achieving 98.52% classification accuracy using an optimized 20-feature set and the Extra Trees Classifier. The approach leverages multi-domain feature extraction and systematic feature selection to capture subtle imbalance-induced signatures, providing robust and discriminative representation. The standoff radar sensing paradigm eliminates the complexity and mechanical coupling effects associated with traditional accelerometer-based methods, while the computationally efficient classifier supports near real-time monitoring. Experimental validation across 1802 trials under varying motor speeds and load conditions confirms the reliability and practical applicability of the framework. Compared with existing vibration-based and electrical-signal-based diagnostic techniques, the proposed radar approach offers competitive or superior accuracy while avoiding challenges related to sensor installation, electrical access, and susceptibility to environmental noise. These advantages align with recent trends in non-contact fault detection that emphasize robustness, safety, and ease of deployment. The study establishes radar-based sensing as a promising, scalable, and noninvasive solution for industrial motor condition monitoring and predictive maintenance. By demonstrating competitive performance relative to established techniques while highlighting clear pathways for future development, this work contributes a substantive step toward practical adoption of radar-based diagnostics in industrial environments.

Acknowledgement: The authors want to acknowledge the fund by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2026R346). The authors would also like to acknowledge the support of Prince Sultan University, Riyadh Saudi Arabia for APC of this publication.

Funding Statement: This research was funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project number (PNURSP2026R346), Princess Nourah bint Abdulrahman University, Riyadh, Saudi Arabia.

Author Contributions: The authors confirm contribution to the paper as follows: Study conception and design: Faten S. Alamri, Adil Ali Saleem, Hafeez Ur Rehman Siddiqui; Experiments: Faten S. Alamri, Adil Ali Saleem; Visualization: Amjad Rehman, Muhammad I. Khan; Validation: Adil Ali Saleem, Hafeez Ur Rehman Siddiqui, Amjad Rehman; Analysis and interpretation of results: Muhammad I. Khan, Adil Ali Saleem, Faten S. Alamri; Draft manuscript preparation: Faten S. Alamri, Adil Ali Saleem; Funding acquisition: Faten S. Alamri; Supervision: Amjad Rehman, Hafeez Ur Rehman Siddiqui. All authors reviewed the results and approved the final version of the manuscript.

Availability of Data and Materials: The dataset supporting the findings of this study is openly available in IEEE Dataport at: https://10.21227/3n2f-8z47 (Acar, Y. E., RADAR I/Q data for machinery imbalance detection, 2025).

Ethics Approval: Not applicapble.

Conflicts of Interest: The authors declare no conflicts of interest to report regarding the present study.

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