🔥 Physics-informed Interpretable Wavelet Weight Initialization and Balanced Dynamic Adaptive Threshold for Intelligent Fault Diagnosis of Rolling Bearings

The pytorch implementation of the paper Physics-informed interpretable wavelet weight initialization and balanced dynamic adaptive threshold for intelligent fault diagnosis of rolling bearings

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Brief introduction

Intelligent fault diagnosis of rolling bearings using deep learning-based methods has made unprecedented progress. However, there is still little research on weight initialization and the threshold setting for noise reduction. An innovative deep triple-stream network called EWSNet is proposed, which presents a wavelet weight initialization method and a balanced dynamic adaptive threshold algorithm. Initially, an enhanced wavelet basis function is designed, in which a scale smoothing factor is defined to acquire more rational wavelet scales. Next, a plug-and-play wavelet weight initialization for deep neural networks is proposed, which utilizes physics-informed wavelet prior knowledge and showcases stronger applicability. Furthermore, a balanced dynamic adaptive threshold is established to enhance the noise-resistant robustness of the model. Finally, normalization activation mapping is devised to reveal the effectiveness of Z-score from a visual perspective rather than experimental results. The validity and reliability of EWSNet are demonstrated through four data sets under the conditions of constant and fluctuating speeds.

Highlights

• A novel deep triple-stream network called EWSNet is proposed for fault diagnosis of rolling bearings under the condition of constant or sharp speed variation.
• An enhanced wavelet convolution kernel is designed to improve the trainability, in which a scale smoothing factor is employed to acquire rational wavelet scales.
• A plug-and-play and physics-informed wavelet weight initialization is proposed to construct an interpretable convolution kernel, which makes the diagnosis interpretable.
• Balanced dynamic adaptive threshold is specially devised to improve the antinoise robustness of the model.
• Normalization activation mapping is designed to visually reveal that Z-score can enhance the frequency-domain information of raw signals.

Paper

Physics-informed Interpretable Wavelet Weight Initialization and Balanced Dynamic Adaptive Threshold for Intelligent Fault Diagnosis of Rolling Bearings

Chao He^a,b, Hongmei Shi^a,b,*, Jin Si^c and Jianbo Li^a,b

^aSchool of Mechanical, Electronic and Control Engineering, Beijing Jiaotong University, Beijing 100044, China

^bCollaborative Innovation Center of Railway Traffic Safety, Beijing 100044, China

^cKey laboratory of information system and technology, Beijing institute of control and electronic technology, Beijing 100038, China

Journal of Manufacturing Systems

EWSNet

Wavelet initialization

Balanced Dynamic Adaptive Thresholding

where $\alpha$ and $\eta$ are differentiable($\alpha \in \left( {0,1} \right),\alpha \ne 0,1$). When $\alpha$=0 or 1, Eq. respectively degenerates into hard threshold and soft threshold, and thus we can adjust $\alpha$ appropriately to make $y$ closer to the genuine wavelet coefficient.

Normalization Activation Mapping

Data normalization can accelerate the process of convergence. Also, Z-score makes CNN get better accuracy. Unlike experimental methods, we notice that Z-score enhances frequency-domain information of signals so that CNN can learn these features better.

FAM illustrates the frequency-domain information by utilizing the weights of the classification layer and extracted features, but it can not reveal the influence of normalization methods. Therefore in NAM, the weight of the correct label is $1.0$, and the features are signals processed by the normalization methods and it can visualize which normalization method possesses more frequency-domain knowledge.

where ${l_{real}}$ is the real label and ${l_{target}}$ is the tested label.

Example:

class CNNNet(nn.Module):

    def __init__(self, init_weights=False):
        super(CNNNet, self).__init__()
        self.conv1 = nn.Conv1d(1, 64, 60, padding=2)
        self.conv2 = nn.Conv1d(32, 32, 3, padding=1)
        self.conv3 = nn.Conv1d(16, 48, 3, padding=1)
        #self.sage = sage(channel=16, gap_size=1)
        self.conv4 = nn.Conv1d(24, 64, 3, padding=1)
        self.pool = nn.MaxPool2d(2)
        self.fc1 = nn.Linear(32*60, 512)
        self.fc2 = nn.Linear(512, 4)
        if init_weights:
            self._initialize_weights()


    def _initialize_weights(self):
        for m in self.modules():
            if isinstance(m, nn.Conv1d):
                if m.kernel_size == (60,):
                    m.weight.data = fast(out_channels=64, kernel_size=60, eps=0.2, mode='sigmoid').forward()
                    nn.init.constant_(m.bias.data, 0.0)

    def forward(self, x):
        x = self.pool(F.relu(self.conv1(x)))
        x = self.pool(F.relu(self.conv2(x)))
        #x = x + self.sage(x)
        x = self.pool(F.relu(self.conv3(x)))
        x = self.pool(F.relu(self.conv4(x)))
        x = x.view(x.shape[0], -1)
        x = F.relu(self.fc1(x))
        x = self.fc2(x)
        return x

Citation

@article{HE,  
title = {Physics-informed interpretable wavelet weight initialization and balanced dynamic adaptive threshold for intelligent fault diagnosis of rolling bearings},  
journal = {Journal of Manufacturing Systems},  
volume = {70},  
pages = {579-592},  
year = {2023},  
issn = {1878-6642},  
doi = {https://doi.org/10.1016/j.jmsy.2023.08.014},  
author = {Chao He and Hongmei Shi and Jin Si and Jianbo Li} 

C. He, H. Shi, J. Si, J. Li, Physics-informed interpretable wavelet weight initialization and balanced dynamic adaptive threshold for intelligent fault diagnosis of rolling bearings, Journal of Manufacturing Systems 70 (2023) 579-592, https://doi.org/10.1016/j.jmsy.2023.08.014.

Ackowledgements

The authors are grateful for the supports of the Fundamental Research Funds for the Central Universities (Science and Technology Leading Talent Team Project) (2022JBXT005), and the National Natural Science Foundation of China (No.52272429).

References

• von Rueden L, Mayer S, Beckh K, Georgiev B, Giesselbach S, Heese R, et al Informed Machine Learning – A Taxonomy and Survey of Integrating Prior Knowledge into Learning Systems. IEEE Trans Knowl Data Eng 2023;35(1):614–633. https://doi.org/10.1109/TKDE.2021.3079836

• Vollert S, Atzmueller M, Theissler A. Interpretable Machine Learning: A brief survey from the predictive maintenance perspective. In: 26th IEEE International Conference on Emerging Technologies and Factory Automation, ETFA 2021, Vasteras, Sweden, September 7-10, 2021 IEEE; 2021. p. 1–8. https://doi.org/10.1109/ETFA45728.2021.9613467

• Li T, Zhao Z, Sun C, Cheng L, Chen X, Yan R, et al WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis. IEEE Trans Syst Man Cybern Syst 2022;52(4):2302–2312. https://doi.org/10.1109/TSMC.2020.3048950

• Zhao M, Zhong S, Fu X, Tang B, Pecht M. Deep Residual Shrinkage Networks for Fault Diagnosis. IEEE Trans Industr Inform 2020;16(7):4681–4690. https://doi.org/10.1109/TII.2019.2943898

• Kim MS, Yun JP, Park P. An Explainable Neural Network for Fault Diagnosis With a Frequency Activation Map. IEEE Access 2021;9:98962–98972. https://doi.org/10.1109/ACCESS.2021.3095565

  Contact

  • Chao He
  • chaohe#bjtu.edu.cn (please replace # by @)

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