This research explores the application of the Riemann–Liouville fractional sigmoid, briefly ${}^{RL}F\sigma$, activation function in modeling the chaotic dynamics of Chua’s circuit through Multilayer Perceptron (MLP) architecture. Grounded in the context of chaotic systems, the study aims to address the limitations of conventional activation functions in capturing complex relationships within datasets. Employing a structured approach, the methods involve training MLP models with various activation functions, including ${}^{RL}F\sigma$, sigmoid, swish, and proportional Caputo derivative ${}^{PC}\sigma$, and subjecting them to rigorous comparative analyses. The main findings reveal that the proposed ${}^{RL}F\sigma$ consistently outperforms traditional counterparts, exhibiting superior accuracy, reduced Mean Squared Error, and faster convergence. Notably, the study extends its investigation to scenarios with reduced dataset sizes and network parameter reductions, demonstrating the robustness and adaptability of ${}^{RL}F\sigma$. The results, supported by convergence curves and CPU training times, underscore the efficiency and practical applicability of the proposed activation function. This research contributes a new perspective on enhancing neural network architectures for system modeling, showcasing the potential of ${}^{RL}F\sigma$ in real-world applications.

Broken rotor bar faults (BRBFs) in induction motors (IMs) present significant challenges in industrial applications, particularly due to the need for large labeled datasets and fast processing. This study addresses these issues by leveraging transfer learning with classical diagnostic techniques, using experimental 3-phase current and 3-axes vibration signals. The Gramian Angular Field (GAF) technique has been utilized to transform time series data into 2D images, enabling fine-tuning of an EfficientNetB3 model, which achieved 99.83% accuracy in classifying five BRBF severity levels. The proposed strategy also outperforms the state-of-the-art methods using the same experimental data. Similarly, validation with features extracted using Continuous Wavelet Transform (CWT) and Short-Time Fourier Transform (STFT) further confirmed its reliability and superiority. This study also offers enhanced interpretability through Grad-CAM visualizations of the best model, which highlights the critical regions contributing to fault classification. These visualizations enable deeper and simpler understanding of fault mechanisms and support subsequent risk analysis, making the developed model actionable and user-friendly for industrial applications.