An interpretable multiplication-convolution residual network for equipment fault diagnosis via time-frequency filtering

With strong feature representation ability, deep learning has been widely used in equipment fault diagnosis. Nevertheless, the "black box" nature has always been restricting its further application in the field of intelligent diagnosis. Combining the intrinsic characteristics of the time-frequency representation of vibration signals, this study proposes a multiplication -convolution residual network (MCRNet) and it consists of two substructures, including a time-frequency filtering layer (TFFLayer) and a residual learner. Different from the conventional interpreter for deep learning, multiple ex -ante interpretable time-frequency filtering kernels (TFFKs), including 2D -Wiener filtering kernel and 2D -Gaussian filtering kernel, are analytically designed with deep learning and signal processing collaborated. With the deep learning block of benchmark ResNet18 employed, each TFFK in the TFFLayer, aims to mathematically extract explainable features by dot -multiplication time-frequency operation with only three variable parameters. Finally, the residual learner is used to abstract high-level feature representations and make the final decision. Specially, to strengthen the representation capacity of TFFLayer, an antialiasing strategy is presented to force TFFKs to mine differential knowledge as much as possible. Comparisons with the existing convolution sensing models verify the effectiveness and superiority of MCRNet via one selfmade dataset and three open -source datasets. Besides, the analysis of model interpretability and anti -noise capability also demonstrate that the designed TFFKs can adaptively sense fault -sensitive time-frequency knowledge as interpretable feature representation. This further indicates that the proposed deep learning collaborated with and signal processing architecture can not only contribute novel and in-depth insights into model interpretability, but also provide trustworthy intelligent decision -making for reliable equipment maintenance.