eess.SPAug 27, 2026

Stagewise Anomaly Detection for E-Transaxle Quality Monitoring Using Wavelet and STFT Features

Authors: Mohammad N. Bisheh, Rajesh Gupta, Qian Wang, Mohammad Babakmehr, Colin Brady, Parinaz Farajiparvar, Saurabh Singh, Kamran Payanabar

Organizations: H. Milton Stewart School of Industrial & Systems Engineering Georgia Institute of Technology Atlanta, USA · Ford Motor Company USA · Amazon Web Services

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Abstract

This paper presents two interpretable machine-learning frameworks for quality screening of e-transaxle assemblies in electric vehicles: a Stagewise Wavelet Isolation Forest (SWIF) framework and a short-time Fourier transform (STFT)-based diagnostic framework. High-dimensional vibration signals acquired from front and back accelerometers are analyzed across multiple operating stages to capture stage-dependent vibration behavior. In the SWIF framework, signals are decomposed using a five-level Daubechies-4 discrete wavelet transform, and blockwise mean-squared coefficients are extracted from the selected wavelet detail level to obtain compact multiscale features. In the STFT-based framework, dominant-frequency trends are extracted from time-frequency representations and summarized through regression coefficients with respect to instantaneous motor speed. Anomaly detection models are trained using accepted production units under the assumption that only a small fraction of accepted assemblies contain latent defects, and their performance is evaluated using road-tested units with validated quality outcomes. Experiments on production and road-tested e-transaxle units show that both approaches provide interpretable diagnostic information, while SWIF achieves the most favorable balance between defect detection and false-positive control. Compared with the STFT-based method and alternative anomaly detectors, SWIF combined with Isolation Forest yields lower anomaly rates within the Accept population while identifying high-risk units from the Reject population. The stagewise structure further localizes anomalous behavior to specific operating conditions, supporting root-cause analysis and targeted process improvement.

Figures & tables

Figure 1: A sample vibration signal from E-transaxle
Figure 2: Comprehensive acceleration profiles of the E-transaxle recorded by the front sensor through four key operational phases: Speed Ramp, Drive Side Steady State, Coast Side Steady State, and Deceleration, demonstrating the dynamic response of the system
Figure 3: Spectrogram Analysis of Good and Defective E-Transaxles. This figure illustrates the vibration patterns in two operational stages (stage 1 and stage 4) of e-transaxles. Images (a) and (b) represent the vibration frequency and time distribution for a normal, functioning e-transaxle, while images (c) and (d) depict these characteristics for a defective unit. The spectrograms clearly visualize the differences in vibrational behavior, highlighting variations in frequency and timing that signal potential defects.
Figure 4: Stage-wise wavelet–Isolation-Forest (SWIF) workflow. Raw end-of-line (EOL) traces x a,s(t)\mathbf{x}^{\,a,s}(t) from four operating stages and two accelerometers undergo a 5-level DB4 decomposition. Per-level energy EjE_{j} identifies the most discriminative scale L⋆L^{\star} . Blockwise mean-squared coefficients (MSC) form feature vectors z a,s\mathbf{z}^{\,a,s} , which are scored by stage-specific Isolation Forest models. An e-transaxle is rejected if any stage score exceeds the threshold τ\tau .
Figure 5: Box plots of mean squared wavelet coefficients across four stages for each of the front and back accelerometers. Vibration profiles for four categories Accept, Reject, Accept RT, and Reject RT highlighting variability and anomaly patterns under different test conditions.
DetectorTotalTPTNFPFNPrecisionRecallF1-ScoreAccuracy
iForest1439021.0000.6000.7500.857
LOF1436320.5000.6000.5450.643
One-Class SVM1455400.5561.0000.7140.714
Table 1: Classification performance on the road-tested dataset. Models were trained using only the Accept population with a contamination rate of 0.005 and evaluated using the validated Accept RT and Reject RT units.
DetectorGroupTotalFlagged as AnomalyAnomaly Rate
iForestAccept935130.0139
iForestReject127130.1024
LOFAccept935190.0203
LOFReject127120.0945
One-Class SVMAccept9351560.1668
One-Class SVMReject127780.6142
Table 2: Anomaly rates estimated for the production Accept and Reject populations. Models were trained using the Accept population under the assumption that fewer than 0.5% of accepted units contain latent defects.
DetectorTotalTPTNFPFNPrecisionRecallF1-ScoreAccuracy
iForest1459001.0001.0001.0001.000
LOF1418140.5000.2000.2860.643
One-Class SVM1439021.0000.6000.7500.857
Table 3: Classification performance using the selected wavelet sensor–stage pair (Front S4). Models were trained using the Accept population with a contamination rate of 0.05 and evaluated using the validated Accept RT and Reject RT units.
DetectorGroupTotalFlagged as AnomalyAnomaly Rate
iForestAccept935470.0503
iForestReject127160.1260
LOFAccept935410.0439
LOFReject127170.1339
One-Class SVMAccept935570.0610
One-Class SVMReject127100.0787
Table 4: Anomaly rates estimated for the production Accept and Reject populations using the selected wavelet sensor–stage pair (Front S4).
Figure 6: Box plots of STFT–RPM regression coefficients across eight stage-accelerometer pairs. Slopes and intercepts are compared for Accept, Reject, Accept RT, and Reject RT categories. Bootstrap mean and 95% confidence intervals are overlaid to quantify uncertainty, particularly for small-sample road-test groups.
DetectorTotalTPTNFPFNPrecisionRecallF1-ScoreAccuracy
iForest1439021.0000.6000.7500.857
LOF1449011.0000.8000.8890.929
One-Class SVM1450900.3571.0000.5260.357
Table 5: Classification performance of the STFT-based anomaly detection framework using only the Back S1 frequency-intercept feature. Models were trained using the Accept population and evaluated on the road-tested Accept RT and Reject RT units.
DetectorGroupTotalFlagged as AnomalyAnomaly Rate
iForestAccept935940.1005
iForestReject127250.1969
LOFAccept935710.0759
LOFReject127250.1969
One-Class SVMAccept9353440.3679
One-Class SVMReject1271080.8504
Table 6: Estimated anomaly rates for the production Accept and Reject populations using the STFT-based framework with the Back S1 frequency-intercept feature.
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