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Integrating Expert Knowledge with Domain Adaptation for Unsupervised Fault Diagnosis

Qin Wang, Cees Taal, Olga Fink

arXiv:2107.01849v2eess.SP

TL;DR

Real-world fault diagnosis is constrained by unlabeled data, few faulty examples, and a gap between synthetic and real faults. This paper combines expert-informed synthetic fault generation with imbalance-robust domain adaptation, reporting improved target-domain performance across bearing experiments, including 70.8% accuracy on the wind-turbine dataset.

  • Problem

    Real fault data is often unlabeled and dominated by healthy observations, while synthetic-only training can face a distribution gap from real faults and target classes may be severely imbalanced.

    Source: §I · p. 1, 1) Imbalance Issue for Direct Alignment · p. 5

  • Method

    The framework generates expert-informed synthetic faults from healthy samples, then adapts from labeled synthetic data to unlabeled real data using class-conditioned alignment and mixup augmentation.

    Source: §I · pp. 1–2, 2) Class Information Taken into Account · p. 6

  • Results

    The authors report that conditional alignment with feature-distribution augmentation alleviates imbalance-related performance degradation; on the wind-turbine dataset, the proposed method achieves 70.8% accuracy, almost 10% absolute improvement.

    Source: D. Wind Turbine Generator… · p. 9, E. Experiment Summary · p. 10

  • Takeaways & Limitations

    The experiments support learning bearing-fault diagnosis models without supervision from real faults by combining expert-generated synthetic faults with imbalance-robust adaptation.

    Source: §VI · p. 10

Abstract

from arXiv · show

Data-driven fault diagnosis methods often require abundant labeled examples for each fault type. On the contrary, real-world data is often unlabeled and consists of mostly healthy observations and only few samples of faulty conditions. The lack of labels and fault samples imposes a significant challenge for existing data-driven fault diagnosis methods. In this paper, we aim to overcome this limitation by integrating expert knowledge with domain adaptation in a synthetic-to-real framework for unsupervised fault diagnosis. Motivated by the fact that domain experts often have a relatively good understanding on how different fault types affect healthy signals, in the first step of the proposed framework, a synthetic fault dataset is generated by augmenting real vibration samples of healthy bearings. This synthetic dataset integrates expert knowledge and encodes class information about the fault types. However, models trained solely based on the synthetic data often do not perform well because of the distinct distribution difference between the synthetically generated and real faults. To overcome this domain gap between the synthetic and real data, in the second step of the proposed framework, an imbalance-robust domain adaptation~(DA) approach is proposed to adapt the model from synthetic faults~(source) to the unlabeled real faults~(target) which suffer from severe class imbalance. The framework is evaluated on two unsupervised fault diagnosis cases for bearings, the CWRU laboratory dataset and a real-world wind-turbine dataset. Experimental results demonstrate that the generated faults are effective for encoding fault type information and the domain adaptation is robust against the different levels of class imbalance between faults.

I. INTRODUCTION

Real fault data is often unlabeled, dominated by healthy observations, and sparse across fault types, while synthetic-only training can leave a gap to real faults. The proposed framework combines expert-informed fault generation with imbalance-robust domain adaptation to address this gap.

I. INTRODUCTION

  • The framework first augments healthy bearing vibration samples with expert-informed synthetic faults, then adapts from labeled synthetic data to unlabeled real data.The generation process uses fault-initiated pulse trains and mixes them with healthy-condition signals, reducing reliance on highly accurate physical models.Source: §I · pp. 1–2
  • Standard adversarial alignment can mismatch balanced synthetic classes with a real target dominated by healthy samples, leaving rare faults poorly adapted.Target class frequencies are unknown because the real data is unlabeled.Source: §I · p. 2
  • The proposed adaptation aligns class-conditioned distributions using pseudo-labels and mixup-based augmentation to provide more support for rare classes.The figure description contrasts this with DANN, whose discriminator does not use class information.Source: §I · p. 2, Figure 1 · p. 2
  • The framework is evaluated on the CWRU laboratory dataset and real-world wind-turbine bearing data, and the authors report good performance with domain adaptation.The synthetic-fault generation process is described as relatively simple.Source: §I · p. 2
  • The authors identify an imbalance-robust adaptation approach and a publicly available synthetic bearing-fault dataset as contributions.They also report releasing code to facilitate further research.Source: §I · p. 3

II. BACKGROUND

The background reviews synthetic fault data and domain adaptation as routes toward learning when real fault labels are scarce. It also describes adversarial alignment and related approaches that use source and target data.

A. The Use of Synthetic Data for Fault Diagnosis

  • Prior fault-diagnosis work uses synthetic faults as substitutes for unavailable real faults, but synthetic-to-real distribution gaps remain a concern.Some approaches use a small labeled real-fault set, unlike methods trained solely on synthetic data.Source: A. The Use of Synthetic Data for Fault… · p. 3

B. Domain Adaptation

  • Domain adaptation uses labeled source data and unlabeled target data; DANN adversarially aligns features, while CDAN conditions adaptation on classifier predictions.Other reviewed approaches include discrepancy-based alignment, normalization-layer alignment, input-space adaptation, and self-training.Source: B. Domain Adaptation · p. 3

C. Domain Adaptation for Fault Diagnosis

The section places synthetic-to-real adaptation within fault-diagnosis research, where many methods address operating-condition shifts. It describes the proposed method as combining fault generation with augmented conditional alignment.

C. Domain Adaptation for Fault Diagnosis

  • The method overview depicts fault generation followed by conditional alignment, where a multi-linear map combines features and class information and mixup augments rare-class support.The figure contrasts the proposed alignment with DANN, whose discriminator lacks class information.Source: Figure 2 · p. 4
  • Existing fault-diagnosis domain-adaptation work commonly addresses operating-condition shifts, while synthetic-to-real adaptation with imbalanced faults is described as underexplored.The review names adversarial alignment, GAN-based fault generation, optimal transport, and methods accounting for individual sample contributions.Source: C. Domain Adaptation for Fault Diagnosis · pp. 3–4

III. PROPOSED METHODOLOGY

The framework combines expert-informed synthetic fault generation from healthy bearing recordings with imbalance-robust adaptation to unlabeled real data. It assumes access to real healthy samples and uses them to retain operating and environmental information in generated signals.

A. Overview of the Proposed Framework

  • The two-stage framework generates synthetic faults using expert knowledge, then adapts from synthetic source data to real target data to address their feature-distribution gap.The adaptation is designed for differing source and target class distributions and does not depend on a specific fault-generation process.Source: A. Overview of the Proposed Framework · p. 4

B. Bearing Fault Generation

  • Real healthy bearing samples are the base signals for injecting expert-informed fault patterns, preserving operating and environmental conditions in the generated data.The method assumes access to healthy recordings, such as early asset recordings before faults emerge.Source: B. Bearing Fault Generation · pp. 4–5
  • The generated vibration signal models periodic impacts and modulation, adds healthy-bearing vibration as background noise, and uses expert-derived bearing kinematics and speed to set defect periods.A band-pass filter is used because the transfer function is unknown; side-band amplitudes are chosen to represent a typical decaying pattern rather than optimized using real fault labels.Source: B. Bearing Fault Generation · p. 5
  • Standard adversarial adaptation performance declines more rapidly as the target rolling-element fault class becomes more imbalanced.The figure compares different rare-fault sample levels with a fully balanced dataset and a source-only baseline.Source: Figure 3 · p. 5

C. Augmented Conditional Adversarial Alignment

The formulation treats synthetic faults as a balanced source and unlabeled, imbalanced real recordings as the target. Its goal is to improve model performance on that real target domain.

C. Augmented Conditional Adversarial Alignment

1) Imbalance Issue for Direct Alignment:

Direct alignment can be undermined by the mismatch between balanced synthetic source classes and a real target dominated by healthy states. The proposed alignment conditions on class information to address that mismatch.

1) Imbalance Issue for Direct Alignment:

  • A balanced synthetic source and a real target dominated by healthy states create mismatched class distributions, and stronger target imbalance worsens direct adaptation performance.For the CWRU rolling-element fault experiment, performance declines more steeply than in the fully balanced case.Source: 1) Imbalance Issue for Direct Alignment · p. 5
  • Aligning only unconditional feature distributions may be insufficient when source and target joint feature-class distributions differ, especially with target classes skewed toward healthy states.Confusing the discriminator does not guarantee identical distributions in this setting.Source: 1) Imbalance Issue for Direct Alignment · p. 6

2) Class Information Taken into Account:

  • The method fuses features with predicted pseudo-labels for the discriminator, allowing alignment to use class information and target class-conditional distributions.The pseudo-labels are combined with features through a multi-linear map.Source: 2) Class Information Taken into Account · p. 6
  • Conditional alignment is presented as especially suitable for fault diagnosis, unlike prior conditional approaches described as not focusing on severe class imbalance.The passage names conditional GANs [56] and CDAN as related approaches.Source: 2) Class Information Taken into Account · p. 6

3) Augmented Distributions:

Even class-conditioned alignment may be unstable when rare fault classes have few samples. The proposed augmentation interpolates target features and pseudo-labels to add support for rare-class conditional distributions.

3) Augmented Distributions:

  • Few samples from rare fault classes can make optimization of the class-conditioned discriminator unstable and potentially reduce alignment performance.Source: 3) Augmented Distributions · p. 6
  • Real and synthetic inner-ring fault spectra differ in BPFI frequencies and sidebands, motivating domain adaptation to address the remaining domain gap.Source: Figure 4 · p. 6
  • The method augments target feature embeddings and pseudo-labels by interpolating samples within a batch before supplying their multi-linear combination to the discriminator.The interpolation coefficient is sampled from a beta distribution, with α = 1 in the experiments.Source: 3) Augmented Distributions · p. 6
  • Feature mixing aims to expand rare-class conditional distributions and provide more rare-fault training examples, making discriminator learning more stable.Source: 3) Augmented Distributions · p. 6

IV. DATASETS

The evaluation uses the CWRU benchmark and a real-world wind-turbine bearing dataset. The CWRU synthetic and real fault spectra differ, motivating domain adaptation.

A. CWRU Bearing Data

  • The CWRU dataset uses four classes and 4,800 real samples, with 1,200 segments per class and 4,096 points per segment.Half of the real healthy samples are split into the synthetic source data; healthy classes are up-sampled to 1,200 in both domains.Source: A. CWRU Bearing Data · p. 7
  • CWRU synthetic and real inner-race fault spectra differ in side-bands, harmonic presence, and defect-frequency position, motivating domain adaptation.Their BPFI and first harmonic are roughly aligned, but the real defect has more side-bands, lacks the second harmonic, and has slightly higher defect frequencies.Source: A. CWRU Bearing Data · p. 7

B. Wind turbine bearing data

  • The wind-turbine dataset contains healthy, outer-ring-defect, and inner-ring-defect samples collected from generator bearings across turbines.The recordings span 3–5 years, with two daily recordings per turbine, 1.28-second signals sampled at 12.8 kHz, and rotational speeds of 900–1,700 RPM.Source: B. Wind turbine bearing data · p. 7
  • The wind-turbine labels were assigned using vibration and process data, bearing-replacement knowledge, and anonymized customer feedback.The diagnosis method uses only a single vibration recording, whereas labeling also drew on additional information sources.Source: B. Wind turbine bearing data · p. 7

V. EVALUATION

The evaluation uses a shared neural architecture and preprocessing pipeline, and reports balanced accuracy alongside F1 and Cohen’s kappa.

1) Model Architecture:

  • The network comprises a feature extractor, classifier, and discriminator, with the feature extractor and classifier architecture taken from.The architecture details are summarized in Table I.Source: 1) Model Architecture · p. 7

2) Data Preprocessing:

  • All data are normalized, converted to full-wave rectified envelope spectra, and interpolated onto a speed-normalized axis of 1,000 values from 0–30 repetition orders.The signals are band-pass filtered between 500–4,000 Hz before conversion.Source: 2) Data Preprocessing · p. 7

3) Evaluation Metric:

  • Balanced accuracy is reported because the classes are imbalanced, with F1 score and Cohen’s kappa also reported.Balanced accuracy uses per-class correct predictions over test samples in that class and is averaged over ten runs.Source: 3) Evaluation Metric · pp. 7–8

4) Training and Test Details:

The CWRU experiments test adaptation under differing levels of target fault imbalance. The proposed method remains near balanced-setting performance even at 1% rolling-element-fault balance.

4) Training and Test Details:

  • Training uses labeled source data to update the classifier and both synthetic and real data to train the feature extractor and discriminator.Models are trained end-to-end for 100 epochs with batch size 128 and learning rate 0.001; inference does not require the discriminator.Source: 4) Training and Test Details · p. 8

B. CWRU Synthetic-to-Real Experiments with Different

  • The imbalance experiment varies rolling-element-fault samples in the unlabeled target data while other classes retain 1,200 samples.For example, 1% balance gives 12 rolling-element-fault samples, while 10% gives 120.Source: B. CWRU Synthetic-to-Real Experiments… · p. 8
  • At 1% rolling-element-fault balance, the proposed method achieves performance similar to the fully balanced standard DANN setup and remains robust across imbalance levels.The authors report that its improvement over standard DANN increases as imbalance grows.Source: B. CWRU Synthetic-to-Real Experiments… · pp. 8–9
  • The source-only baseline achieves 59.55% accuracy in the four-class CWRU task, above the 25% random-guess level.This supports that the synthetic faults encode fault information meaningfully.Source: B. CWRU Synthetic-to-Real Experiments… · p. 8

C. CWRU Synthetic-to-Real Experiment with a More Realistic Class Imbalance among Faults

Under severe, differing imbalance among CWRU fault classes, the proposed method improves alignment over DANN. It also outperforms IAST across the reported metrics.

C. CWRU Synthetic-to-Real Experiment with a More Realistic Class Imbalance among Faults

  • The experiment removes target labels and sets different imbalance levels for outer-ring, inner-ring, and rolling-element faults.The target data includes 10% outer-ring, 5% inner-ring, and 1% rolling-element-fault samples relative to 1,200 healthy samples.Source: C. CWRU Synthetic-to-Real Experiment… · p. 9
  • The proposed methodology achieves 82.3% on the target data, a 9.7% absolute improvement over the DANN baseline; its overall performance is similar to DANN in the ideal fully balanced case.Source: C. CWRU Synthetic-to-Real Experiment… · p. 9
  • The proposed method outperforms IAST by a large margin on balanced accuracy, F1-score, and Cohen’s kappa under severe imbalance.IAST combines adversarial learning and self-training.Source: C. CWRU Synthetic-to-Real Experiment… · p. 9

D. Wind Turbine Generator Synthetic-to-Real Experiment

On real-world wind-turbine bearings, the proposed method reached 70.8% accuracy and outperformed IAST on all four reported metrics. The experiments and conclusions emphasize imbalance-robust adaptation from expert-generated synthetic faults, while leaving semi-supervised settings for future work.

D. Wind Turbine Generator Synthetic-to-Real Experiment

  • 70.8% accuracy was achieved by the proposed method on the wind-turbine dataset, an almost 10% absolute improvement over the source-only baseline.The proposed method also outperformed IAST on all four reported metrics.Source: D. Wind Turbine Generator… · p. 9
  • Target fault labels were not used; fault-class information came from expert knowledge encoded in synthetic data.The framework combines fault generation with synthetic-to-real adaptation designed for imbalanced target data.Source: D. Wind Turbine Generator… · pp. 9–10

E. Experiment Summary

  • Popular domain-adaptation methods can suffer as class imbalance grows, while class information for the discriminator and feature augmentation alleviate this effect.The authors identify feature-distribution augmentation as important for conditional alignment, likely because it counters discriminator bias from class imbalance.Source: E. Experiment Summary · p. 10

VI. CONCLUSIONS

  • The framework is evaluated on benchmark CWRU and wind-turbine bearings, but this work considers only unsupervised diagnosis; semi-supervised adaptation is left for future research.The proposed approach is described as robust across imbalance levels and as requiring no assumption about the degree of underlying class imbalance.Source: §VI · p. 10
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