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Adversarial adaptive 1-D convolutional neural networks for bearing fault diagnosis under varying working condition

Bo Zhang, Wei Li, Jie Hao, Xiao-Li Li, Meng Zhang

arXiv:1805.00778v3eess.SPcs.LGcs.SDeess.AS

TL;DR

Varying working conditions shift bearing data distributions, undermining fault diagnosis models trained under a shared-distribution assumption. The paper proposes A2CNN, an adversarial adaptive 1-D CNN with partially untied source and target extractors, and reports high accuracy across conditions while visualizing learned features and networks.

  • Problem

    Bearing fault diagnosis becomes difficult when working conditions change the target distribution, making labeled target data costly to obtain.

    Source: §1 · p. 1, §2 · p. 3, §2.1 · p. 4

  • Method

    A2CNN combines source and target feature extractors, a label classifier, and a domain discriminator, using adversarial training with partially untied extractor layers.

    Source: §1 · p. 3, §5 · p. 17

  • Results

    A2CNN achieves higher accuracy than WDCNN with AdaBN under different working conditions, reaching 99.21% average accuracy.

    Source: §5 · p. 17

  • Takeaways & Limitations

    The model provides strong fault-discriminative and domain-invariant capacity for bearing diagnosis across varying working conditions.

    Source: §1 · p. 3, §5 · p. 17

    The domain-adaptation setting assumes shared feature spaces and label spaces between source and target domains.

    Source: §2.1 · p. 4

Abstract

from arXiv · show

Traditional intelligent fault diagnosis of rolling bearings work well only under a common assumption that the labeled training data (source domain) and unlabeled testing data (target domain) are drawn from the same distribution. However, in many real-world applications, this assumption does not hold, especially when the working condition varies. In this paper, a new adversarial adaptive 1-D CNN called A2CNN is proposed to address this problem. A2CNN consists of four parts, namely, a source feature extractor, a target feature extractor, a label classifier and a domain discriminator. The layers between the source and target feature extractor are partially untied during the training stage to take both training efficiency and domain adaptation into consideration. Experiments show that A2CNN has strong fault-discriminative and domain-invariant capacity, and therefore can achieve high accuracy under different working conditions. We also visualize the learned features and the networks to explore the reasons behind the high performance of our proposed model.

1. Introduction

The paper addresses bearing fault diagnosis when working-condition changes make source and target data distributions differ. It proposes A2CNN, an adversarial adaptive 1-D CNN designed to learn fault-discriminative and domain-invariant features.

Problem

  • Changing working conditions can invalidate the shared-distribution assumption, making newly labeled target-domain data expensive or impractical to collect.Source: §1 · p. 2

Method

  • The model is designed to learn features that are simultaneously fault-discriminative and domain-invariant through adversarial adaptation.Source: §1 · pp. 2–3
  • A2CNN comprises source and target feature extractors, a label classifier, and a domain discriminator, with partially untied extractor layers balancing training efficiency and adaptation.Source: §1 · p. 3

Analysis

  • Learned feature maps are visualized to investigate the model’s mechanism in fault diagnosis and domain adaptation.Source: §1 · p. 3

Evaluation

  • Precision and recall are introduced alongside accuracy to assess the reliability and sensitivity of recognizing particular fault types.Source: §1 · p. 3

2. Preliminary Knowledge

The preliminary section formulates varying-condition fault diagnosis as domain adaptation and connects domain divergence estimation with adversarial learning. Its framework assumes shared feature and label spaces while input distributions may differ.

2.1. Domain Adaptation

  • Domain adaptation uses labeled source-domain knowledge to predict target-domain labels when working conditions change but the classification task remains the same.Source: §2 · p. 3, §2.1 · p. 4
  • The setting assumes identical feature spaces and label spaces across domains, while the input marginal distributions differ.Source: §2.1 · p. 4

2.2. Domain Divergence Measure

  • The dH∆H divergence is estimated through a domain classifier that distinguishes source from target instances, with ˆdH∆H(S, T) = 1 − 2ϵ(hd).Source: §2.2 · p. 4
  • A lower estimated dH∆H value indicates smaller domain divergence: overlapping domains yield approximately zero, whereas distinct domains approach one.Source: §2.2 · p. 5

2.3. Generative Adversarial Networks

  • GAN training pits a generator against a discriminator in a minimax game, with the generator making discrimination increasingly difficult.Source: §2.3 · p. 5
  • Domain adaptation and GANs share the objective of mapping different domains to a feature space where a discriminator cannot distinguish them.Source: §2.3 · p. 5

3. Proposed adversarial adaptive 1-D CNN

A2CNN adapts bearing-fault representations across differing source and target domains by combining supervised fault discrimination with adversarial domain invariance. Its partially untied source–target CNNs are pretrained, adversarially fine-tuned, and used directly for target-label prediction.

3.1. Problem Formalization

  • A2CNN jointly uses source and target feature extractors, a label classifier, and a domain discriminator to predict class and domain labels.The feature extractors are optimized to minimize source label loss while maximizing domain classification loss.Source: §3.1 · p. 5
  • The source extractor uses five 1-D convolutional layers and two fully connected layers, with its K-neuron label layer feeding the classifier.FFT spectrum amplitudes enter the network, while pooling and wide initial kernels support robust signal representations.Source: §3.1 · p. 6
  • The target extractor is initialized from the source extractor and partially untied so shared layers preserve efficiency while adaptive layers accommodate domain differences.The paper contrasts partial untying with fully tied mappings, which may be poorly conditioned when domains differ.Source: Figure 1 · p. 6, §3.1 · p. 7

3.2. Model Learning

  • Training first pretrains the source extractor on labeled data, then adversarially fine-tunes the target extractor so the discriminator cannot reliably identify source versus target features.The target domain is unlabeled, and domain instances receive pseudo-labels indicating source or target origin.Source: §3.1 · pp. 5, 7, §3.2 · p. 8

3.3. Classifier Construction

  • After training, target predictions come from the target extractor’s final fully connected output by selecting the class with maximum probability.The target extractor output is converted into class probabilities, and the highest-probability class becomes the prediction.Source: §3.3 · p. 8

4. Experimental analysis of proposed A2CNN model

The experiments address bearing diagnosis when load conditions create different data distributions. They use unlabeled data from another condition to rebuild a classifier trained under one condition.

  • Different load conditions can produce different data distributions, making cross-condition classifier rebuilding practically significant.Source: §4 · p. 8
  • The proposed A2CNN is evaluated using unlabeled data under another load condition to adapt a classifier trained under one load condition.Source: §4 · p. 8
  • The CWRU bearing database is used to investigate A2CNN under this cross-working-condition scenario.Source: §4 · p. 8

4.1. Datasets and Preprocessing

The study uses CWRU vibration data from three motor load and speed conditions, converts signals into FFT inputs, and constructs six directed domain-adaptation tasks.

  • The CWRU test bed contains bearings with inner-race, outer-race, ball, and normal conditions measured at 12kHz across three loads and speeds.Fault sizes are 0.007in, 0.014in, 0.021in, and 0.028in; the loads are 1hp/1772rpm, 2hp/1750rpm, and 3hp/1730rpm.Source: §4.1 · p. 8
  • Each sample is a randomly selected 4096-point vibration signal transformed by FFT, with the first 2048 coefficients retained because the spectrum is symmetric.Source: §4.1 · p. 8
  • The three conditions form domains A, B, and C, each containing ten classes and 8000 samples.Source: §4.1 · p. 8
  • Six adaptation problems are created by selecting two of the three domains and assigning one as source and the other as target.For A → B, domain A supplies source data and domain B supplies target data.Source: §4.1 · p. 10

4.2. Experimental setup

The experiments compare A2CNN with conventional and adaptive baselines using a configurable convolutional architecture. The model unties between one and seven target layers and evaluates accuracy across six adaptation problems.

4.2.1. Baseline Methods

  • Baselines include FFT-based SVM and MLP, a three-hidden-layer DNN using frequency features, and WDCNN with Adaptive Batch Normalization.Source: §4.2.1 · p. 10

4.2.2. Parameters of the proposed A2CNN

  • A2CNN feature extractors use five convolutional and pooling layers followed by two fully connected layers, while the discriminator has fully connected layers of 500, 500, and 1 neurons.Adam optimization is used, and the final l target layers are untied with l ∈[1, 7].Source: §4.2.2 · p. 10
  • The evaluation reports accuracy (%) on six domain adaptation problems and examines target predictions produced from the target extractor’s output.Source: Figure 2 · p. 11, §4.2.2 · p. 11

4.3. Accuracy across different domains

Across six domain-adaptation scenarios, A2CNN outperformed the comparison methods, with especially strong gains when source and target distributions differed substantially.

  • SVM, MLP, and DNN achieved average accuracies of around 65%, 80%, and 80%, respectively, under domain adaptation.These results support distribution differences across working conditions and limited cross-condition suitability of models trained on one condition.Source: §4.3 · p. 11
  • A2CNN achieved 99.21% average accuracy, exceeding WDCNN with AdaBN, which achieved 95.95% average accuracy.The passage states that A2CNN learned more domain-invariant features than the other methods.Source: §4.3 · pp. 11–12
  • A2CNN outperformed A2CNNS in every domain-adaptation scenario, indicating a benefit from adversarial adaptation training.Source: §4.3 · p. 12
  • A2CNN's advantage was modest for A→B, B→A, B→C, and C→B, but significant for A→C and C→A.The authors relate the larger gains to greater source-target distribution differences.Source: §4.3 · p. 12

4.4. Sensitivity Analysis of Faults

The fault-level analysis evaluates A2CNN and A2CNNS with precision and recall, showing that adversarial fine-tuning improves classwise detection while reducing false and missed alarms.

  • Precision measures reliable positive fault alarms, whereas recall measures the proportion of faults detected without indicating false alarms.Precision uses TP and FP; recall uses TP and FN.Source: §4.4 · p. 12
  • Tables 3 and 4 report precision and recall for A2CNNS and A2CNN across six domain-adaptation problems.Source: §4.4 · p. 12, Table 3 · p. 13, Table 4 · p. 13
  • A2CNNS precision for 0.014-in. IF faults was 49.63% on B→C and 57.55% on C→A, making about half of those alarms unreliable.Source: §4.4 · p. 12
  • A2CNNS recall for 0.007-in. IF faults was 1.13% on B→C and 26.75% on C→A, leaving many failures undetected.Source: §4.4 · p. 12
  • A2CNN generally achieved higher precision and recall than A2CNNS across fault classes, with nearly all classes correctly classified except two BF cases.The exceptions were BF faults with sizes 0.014 in. and 0.021 in.Source: §4.4 · p. 12

4.5. Parameter Sensitivity

Parameter sensitivity shows that increasing the number of untied target-extractor layers generally improves recognition, but the required degree of untuning depends on the adaptation direction.

  • The parameter l denotes the number of untied layers in the target feature extractor during adversarial adaptive fine-tuning, ranging from 1 to 7.A2CNN1 unties only FC2, while A2CNN7 unties all seven layers from Conv1 to FC2.Source: §4.5 · p. 13
  • Recognition accuracy generally increased as more target-extractor layers were untied, although sensitivity to l varied across adaptation problems.Source: §4.5 · p. 13, Figure 3 · p. 14
  • For A→B and B→A, A2CNNS already achieved 99.86% and 97.89% accuracy, respectively, only slightly below A2CNN7.Precision and recall were also similar between A2CNNS and A2CNN7 in these cases.Source: §4.5 · pp. 13–14
  • A2CNN2 matched the highest accuracy for A→C and C→B, whereas C→A and B→C required six and four untied layers, respectively, for almost-best results.The results indicate asymmetric distribution differences between domains.Source: §4.5 · p. 14

4.6. Networks visualizations

Network visualizations connect A2CNN's performance to strong fault separability and progressive alignment of source and target features during adversarial fine-tuning.

  • Features from MS on source samples, MS on target samples, and fine-tuned MT on target samples were each classifiable when diagnosed separately.This supports the strong fault-discriminative capacity of the 1-D CNN feature extractors.Source: §4.6 · p. 14
  • The 0.007/IF fault distribution differed completely across domains before adaptation, consistent with A2CNNS's 1.13% recall for B→C.Source: §4.6 · p. 14
  • With more adversarial iterations, source and target feature distributions gradually became consistent.The supplied passage identifies this progressive alignment as an observation during fine-tuning.Source: §4.6 · p. 15
  • Applying MS and MT to fault detection yielded accuracies of 99.75% and 99.90%, respectively, indicating improved domain-adaptation capacity from the adversarial network.Source: §4.6 · p. 15
  • Source and target features were visualized with t-SNE, using colored points for ten fault types and square symbols for target-domain samples.The B→C analysis compares source features, target features from MS, and target features from MT during fine-tuning.Source: §4.6 · p. 14, Figure 4 · p. 15
  • For B→C, the first three convolutional layers produced similar features, while differences emerged from Conv4, matching the need to untie the last four layers.Source: §4.6 · p. 15
  • For a 0.007/IF sample from domain C, MS-based features led to a 0.014/IF misdiagnosis, whereas MT-based features correctly identified 0.007/IF.FC2 outputs are passed to the softmax label classifier for class-posterior estimation.Source: §4.6 · p. 15

5. Conclusion

A2CNN is an adversarial adaptive 1-D CNN for bearing fault diagnosis under varying working conditions, combining domain adaptation with feature visualization to explain its performance.

  • The paper presents A2CNN as an adversarial adaptive 1-D CNN for fault diagnosis under varying working conditions and identifies it as a first use of adversarial networks for this domain.Source: §5 · pp. 15, 17
  • A2CNN uses source and target feature extractors, a label classifier, and a domain discriminator, with partially untied extractor layers during training.The architecture is designed to support adversarial adaptation while balancing training efficiency and domain adaptability.Source: §5 · p. 17
  • Compared with WDCNN (AdaBN), A2CNN achieves higher accuracy under different working conditions.Source: §5 · p. 17
  • Adversarial training improves classification performance across fault classes, producing high precision and recall with fewer false alarms and missed alarms.Source: §5 · p. 17
  • Feature-map visualization explores the model’s fault-diagnosis and domain-adaptation mechanisms and verifies the use of partially untied extractor layers.Source: §5 · p. 17
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