## 1 Introduction
The S-transform is a time-window Fourier transform that has the advantages of both the STFT and the wavelet transform. Moreover, the problem of selecting window sizes, i.e., selecting a long window for low-frequency components and a short window for high-frequency components, is balanced when using the S-transform by an adjustable window size with a tunable parameter that can yield good frequency and time localization for each signal. Discrete orthonormal Stockwell transform (DOST)-based signal stacking is proposed for pattern generation for each fault type of a bearing. In short, this study presents a new approach for bearings diagnosis under variable speed and load conditions that employs vibration signals to address two key limitations of existing methods: (1) under different operational speeds, proper feature selection requires domain-level expertise, and (2) automating optimal feature selection requires special dynamic algorithms. Instead of selecting optimal features directly from the one-dimensional (1D) signals, two-dimensional (2D) vibration images are generated by employing discrete orthonormal Stockwell transform (DOST)-based stacking to explore the patterns of different bearing states. The proposed 2D vibration imaging creates identical patterns for the same type of health, where variable operating speeds do not affect the patterns for certain health states. From these 2D images, the feature selection process is automated by employing a transfer learning (TL)-based convolutional neural network (CNN). Conventional, straightforward neural networks make the feature selection process much easier through their convoluted encoding layers compared to traditional methods [17; 31; 32]. In [33], [PERSON] et al. introduced a TL-based artificial neural network (ANN) for a bearing's raw vibration signals. However, for a raw signal, this approach cannot discover the critical features needed to transfer to the knowledge domain for further classification under different loads and speeds. Inadequate raw signal data extracted from mechanical sensors leads us to incomplete observation of critical patterns for the neural networks. To create invariant patterns, pre-processing steps are necessary since our data are limited. Due to white noise in signals, it is difficult to find out the exact information from additional properties mixed with domain data. These learnings are passed through another working condition later through transfer learning, which is how the network can learn from both working conditions and be fine-tuned by adjusting weights along with previous learning. In this study, after creating an invariance scenario with 2D DOST-based vibration imaging, a TL-based approach is executed to resolve these challenges. Details about the TL are discussed in the Methodology section along with a description of the proposed CNN architecture. Therefore, the main contributions of the current work are: (1) identical health pattern formations for different health types employing discrete orthonormal Stockwell transform (DOST)-based vibration imaging to create load-invariant and rpm-invariant scenarios, and (2) a transfer learning-based convolutional neural network approach to automate the feature extraction process from those identical health patterns in a short amount of training time. The rest of this paper is organized as follows. Section 2 describes the proposed methodology. Section 3 describes the dataset and discusses the experimental results analysis, including comparisons to establish the robustness of the proposed method. Finally, Section 4 concludes this paper.