Table of Links Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 3. Methodology 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 6. Conclusions Appendix and References 4.3. Case study 2: JNU dataset 4.3.1. Dataset description This dataset was provided by Jiangnan University (JNU) [80]. Two types of roller bearings were artificially injected with inner race defects (bearing N205), outer race defects and ball defects (bearing NU205) by a wire-cutting machine. Three different rotation speeds (600rpm, 800rpm, 1000rpm) were implemented to test the bearings. The sampling rate was set to 50KHz, resulting in signal segments of 20 seconds each. This dataset is one of the more difficult datasets in the field of bearing fault diagnosis [71]. To facilitate varying rotation speed classification, we organized the data into ten classes. These classes encompass three fault types across the three different speeds, along with a healthy class. Furthermore, compared to the PU dataset, the JNU dataset is characterized by a limited data volume. Consequently, we adopted an overlapping strategy to extract signal segments, with a stride of 100. The final dataset configuration involved allocating the last 25% of the data as the test set. Prior to this, the remaining data were randomly partitioned into training and validation sets, maintaining an 80:20 split ratio. In summary, the dataset statistics are as follows: 54,064 samples in the training set, 13,517 samples in the validation set, and 22,269 samples in the test set. Also, we introduce four SNR levels: -10 dB, -8 dB, -6 dB, and -4 dB for evaluation. 4.3.2. Classification results The classification results, as summarized in Table 5, yield valuable insights. Notably, the ClassBD model consistently outperforms its competitors across various noisy conditions. Overall, The ClassBD achieves an impressive F1 score exceeding 96%, surpassing the second-best method, EWSNet, which attains an average F1 score of 92.75%. To be specific, even in the presence of severe noise (at -10 dB), our method maintains a commendable 93% F1 score. This remarkable performance underscores the ClassBD’s excellent anti-noise capabilities. In comparison, under the same noisy conditions, other methods, excluding EWSNet, experience significant degradation. At last, the JNU dataset experiment substantiates that our approach effectively realizes bearing fault diagnosis across varying rotational speeds, even in challenging high-noise environments. Authors:
(1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China;
(3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China;
(4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China;
(6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. Table of Links Abstract and 1. Introduction Abstract and 1. Introduction 2. Preliminaries and 2.1. Blind deconvolution 2. Preliminaries and 2.1. Blind deconvolution 2.2. Quadratic neural networks 2.2. Quadratic neural networks 3. Methodology 3. Methodology 3.1. Time domain quadratic convolutional filter 3.1. Time domain quadratic convolutional filter 3.2. Superiority of cyclic features extraction by QCNN 3.2. Superiority of cyclic features extraction by QCNN 3.3. Frequency domain linear filter with envelope spectrum objective function 3.3. Frequency domain linear filter with envelope spectrum objective function 3.4. Integral optimization with uncertainty-aware weighing scheme 3.4. Integral optimization with uncertainty-aware weighing scheme 4. Computational experiments 4.1. Experimental configurations 4.1. Experimental configurations 4.2. Case study 1: PU dataset 4.2. Case study 1: PU dataset 4.3. Case study 2: JNU dataset 4.3. Case study 2: JNU dataset 4.4. Case study 3: HIT dataset 4.4. Case study 3: HIT dataset 5. Computational experiments 5.1. Comparison of BD methods 5.1. Comparison of BD methods 5.2. Classification results on various noise conditions 5.2. Classification results on various noise conditions 5.3. Employing ClassBD to deep learning classifiers 5.3. Employing ClassBD to deep learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.4. Employing ClassBD to machine learning classifiers 5.5. Feature extraction ability of quadratic and conventional networks 5.5. Feature extraction ability of quadratic and conventional networks 5.6. Comparison of ClassBD filters 5.6. Comparison of ClassBD filters 6. Conclusions 6. Conclusions Appendix and References Appendix and References 4.3. Case study 2: JNU dataset 4.3.1. Dataset description 4.3.1. Dataset description 4.3.1. Dataset description This dataset was provided by Jiangnan University (JNU) [80]. Two types of roller bearings were artificially injected with inner race defects (bearing N205), outer race defects and ball defects (bearing NU205) by a wire-cutting machine. Three different rotation speeds (600rpm, 800rpm, 1000rpm) were implemented to test the bearings. The sampling rate was set to 50KHz, resulting in signal segments of 20 seconds each. This dataset is one of the more difficult datasets in the field of bearing fault diagnosis [71]. To facilitate varying rotation speed classification, we organized the data into ten classes. These classes encompass three fault types across the three different speeds, along with a healthy class. Furthermore, compared to the PU dataset, the JNU dataset is characterized by a limited data volume. Consequently, we adopted an overlapping strategy to extract signal segments, with a stride of 100. The final dataset configuration involved allocating the last 25% of the data as the test set. Prior to this, the remaining data were randomly partitioned into training and validation sets, maintaining an 80:20 split ratio. In summary, the dataset statistics are as follows: 54,064 samples in the training set, 13,517 samples in the validation set, and 22,269 samples in the test set. Also, we introduce four SNR levels: -10 dB, -8 dB, -6 dB, and -4 dB for evaluation. 4.3.2. Classification results 4.3.2. Classification results 4.3.2. Classification results The classification results, as summarized in Table 5, yield valuable insights. Notably, the ClassBD model consistently outperforms its competitors across various noisy conditions. Overall, The ClassBD achieves an impressive F1 score exceeding 96%, surpassing the second-best method, EWSNet, which attains an average F1 score of 92.75%. To be specific, even in the presence of severe noise (at -10 dB), our method maintains a commendable 93% F1 score. This remarkable performance underscores the ClassBD’s excellent anti-noise capabilities. In comparison, under the same noisy conditions, other methods, excluding EWSNet, experience significant degradation. At last, the JNU dataset experiment substantiates that our approach effectively realizes bearing fault diagnosis across varying rotational speeds, even in challenging high-noise environments. Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. Authors: Authors: (1) Jing-Xiao Liao, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China and School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (2) Chao He, School of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing, China; (3) Jipu Li, Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China; (4) Jinwei Sun, School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (5) Shiping Zhang (Corresponding author), School of Instrumentation Science and Engineering, Harbin Institute of Technology, Harbin, China; (6) Xiaoge Zhang (Corresponding author), Department of Industrial and Systems Engineering, The Hong Kong Polytechnic University, Hong Kong, Special Administrative Region of China. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. This paper is available on arxiv under CC by 4.0 Deed (Attribution 4.0 International) license. available on arxiv

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How ClassBD Achieved High Accuracy in Bearing Fault Detection Despite High Noise

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