WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligent Diagnosis (1911.07925v3)

Abstract: Convolutional neural network (CNN), with ability of feature learning and nonlinear mapping, has demonstrated its effectiveness in prognostics and health management (PHM). However, explanation on the physical meaning of a CNN architecture has rarely been studied. In this paper, a novel wavelet driven deep neural network termed as WaveletKernelNet (WKN) is presented, where a continuous wavelet convolutional (CWConv) layer is designed to replace the first convolutional layer of the standard CNN. This enables the first CWConv layer to discover more meaningful filters. Furthermore, only the scale parameter and translation parameter are directly learned from raw data at this CWConv layer. This provides a very effective way to obtain a customized filter bank, specifically tuned for extracting defect-related impact component embedded in the vibration signal. In addition, three experimental verification using data from laboratory environment are carried out to verify effectiveness of the proposed method for mechanical fault diagnosis. The results show the importance of the designed CWConv layer and the output of CWConv layer is interpretable. Besides, it is found that WKN has fewer parameters, higher fault classification accuracy and faster convergence speed than standard CNN.

• The paper introduces WaveletKernelNet, which replaces the standard first CNN layer with a continuous wavelet convolution layer to achieve physically interpretable features.
• The methodology reduces the number of parameters and accelerates training, while simultaneously improving diagnostic accuracy across various datasets.
• Experimental results on bearings, gear faults, and aeroengine faults demonstrate significant performance gains over conventional CNN models.

An Analysis of WaveletKernelNet: An Interpretable Deep Neural Network for Industrial Intelligence Diagnosis

In the field of mechanical system fault diagnosis, convolutional neural networks (CNNs) have established themselves as a viable technology due to their adeptness at feature learning and nonlinear mapping. Despite their success, a limitation of CNNs is their reliance on a "black-box" approach, providing little interpretability of the learned features. This lack of transparency complicates the trustworthiness and applicability of CNN in industrial settings. To address this challenge, the paper presents WaveletKernelNet (WKN), a novel deep learning architecture that incorporates a continuous wavelet convolutional (CWConv) layer to enhance the physical interpretability of CNNs.

Main Contributions

The key innovation in WaveletKernelNet is the substitution of the standard first convolutional layer in a CNN with a CWConv layer. The CWConv layer is designed to learn only two parameters directly from raw data: scale and translation. By doing so, it constructs a wavelet filter bank tailored for the extraction of defect-related impacts from vibration signals. The introduction of the CWConv layer brings several significant contributions:

1. Interpretability: The model extracts fault features with clear physical meaning, making the feature maps from the first layer interpretable.
2. Reduction in Parameters: WKN reduces the number of parameters in the initial layer compared to standard CNNs, which speeds up convergence during training.
3. Accuracy Enhancement: The method improves mechanical fault diagnosis accuracy, outperforming traditional CNNs in experimental evaluations.

Experimental Validation

The authors validated WaveletKernelNet through three rigorous experiments using laboratory data. These experiments involved datasets on bearings, helical gear faults, and aeroengine bevel gear faults. In all cases, WaveletKernelNet achieved superior fault classification accuracy compared to conventional CNNs. The results demonstrated that the proposed approach not only benefits from fewer learned parameters but also achieves more effective feature representations. Notably, the LaplaceWaveletNet variant of WKN showed the highest classification accuracy across various datasets.

Implications for Future Research

The introduction of the CWConv layer paves the way for further exploration into interpretable deep learning architecture, particularly in applications beyond fault diagnosis. Future work may focus on optimizing wavelet definitions within the first layer for domain-specific applications and examining the potential benefits of wavelet filters in other types of signals.

In theoretical terms, the incorporation of wavelet theory within neural network architecture underscores a trend toward hybrid methodologies that leverage the strengths of different mathematical models for enhanced learning. Practically, this research could drive improvements in predictive maintenance systems across various industries, reducing downtime and improving operational efficiency.

In summary, WaveletKernelNet represents a meaningful progression in interpretable machine learning models for industrial applications. This work highlights the value of integrating domain-specific knowledge, such as wavelet transforms, into deep learning models to achieve more efficient, transparent, and effective solutions for complex real-world problems.