Information-theoretic continuously indexed domain adaptation network with wavelet-scale-wise convolution for fault diagnosis under continuously varying working conditions

Research on fault diagnosis methods based on deep transfer learning is of great significance to both measurement science and automation engineering, with an increasing number of studies adopting wavelet-based neural network frameworks in combination with domain adaptation for cross-condition fault diagnosis. However, existing domain adaptation methods generally assume discrete domains, while real working conditions such as speed and load vary continuously, and this mismatch limits the effectiveness of domain adaptation. Meanwhile, for fault feature extraction in wavelet time-frequency diagrams, few studies consider the unique frequency distribution characteristics of different faults to design networks. Therefore, we propose a dual innovation fault diagnosis framework. Firstly, we introduce the Wavelet-Scale-Wise Convolution Network (WSWCN) to explicitly extract frequency-dependent fault features through a scale-wise convolution structure tailored for the directional sensitivity of wavelet time-frequency diagrams. Secondly, we propose a continuously indexed domain adaptation method based on Multi-Kernel Mutual Information Estimation (MKME), which leverages a variational form of mutual information and kernel-based function approximation to enable direct use of continuous working condition information for domain adaptation without adversarial training. To validate our approach, a series of experiments are conducted on gearbox and bearing fault datasets collected under time-varying working conditions to demonstrate the superiority of the proposed WSWCN and MKME.