An Interpretable Denoising Layer for Neural Networks Based on Reproducing Kernel Hilbert Space and its Application in Machine Fault Diagnosis

Baoxuan Zhao,Qingbo He,Zhike Peng,Changming Cheng,Guang Meng,Guowei Tu

doi:10.1186/s10033-021-00564-5

Abstract

Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis, while the noise mixed in measured signals harms the prediction accuracy of networks. Existing denoising methods in neural networks, such as using complex network architectures and introducing sparse techniques, always suffer from the difficulty of estimating hyperparameters and the lack of physical interpretability. To address this issue, this paper proposes a novel interpretable denoising layer based on reproducing kernel Hilbert space (RKHS) as the first layer for standard neural networks, with the aim to combine the advantages of both traditional signal processing technology with physical interpretation and network modeling strategy with parameter adaption. By investigating the influencing mechanism of parameters on the regularization procedure in RKHS, the key parameter that dynamically controls the signal smoothness with low computational cost is selected as the only trainable parameter of the proposed layer. Besides, the forward and backward propagation algorithms of the designed layer are formulated to ensure that the selected parameter can be automatically updated together with other parameters in the neural network. Moreover, exponential and piecewise functions are introduced in the weight updating process to keep the trainable weight within a reasonable range and avoid the ill-conditioned problem. Experiment studies verify the effectiveness and compatibility of the proposed layer design method in intelligent fault diagnosis of machinery in noisy environments.

Highlights

In practical engineering, gears, shafts, bearings, and other key components in rotating machinery frequently occur various failures due to severe work conditions such as alternating load and long operational time [1, 2]
Faced with the dilemma of the current denoising method for neural networks, we proposed a novel, well-compatible, and well-interpreted denoising layer based on reproducing kernel Hilbert space (RKHS) in this paper
In order to make the RKHS based denoising method have adequate performance in bandwidth control, the fixed value of σ can be determined by cross-validation so that the adjustable bandwidth range of the system is balanced with the quality factor

Summary

Introduction

Gears, shafts, bearings, and other key components in rotating machinery frequently occur various failures due to severe work conditions such as alternating load and long operational time [1, 2]. This method requires clean signals obtained in advance, which is extremely difficult to achieve in practical engineering Another popular denoising method is to modify the network structure and using the raw data to fit it, where techniques to prevent overfitting, such as dropout in DAE [18] and pooling in CNN [19], have been widely applied in various noisy working conditions [20, 21]. These techniques can be interpreted as reducing the complex co-adaptation between neurons and following the idea of biological evolution [22]. In order to make the RKHS based denoising method have adequate performance in bandwidth control, the fixed value of σ can be determined by cross-validation so that the adjustable bandwidth range of the system is balanced with the quality factor

Interpretable Denoising Layer Design for Neural Networks

Machine Fault Diagnosis with the Denoising Layer

Procedure of Fault Diagnosis Using the Denoising Layer

Findings

Conclusions