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

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.