This chapter presents a comprehensive mathematical framework for the analysis and diagnostic application of vibration and acoustic emission (AE) signals in electrical equipment (EE). Through the development of linear random processes and multi-resonant models, it offers a detailed representation of vibration and AE signals generated by rolling bearings and laminated magnetic circuits within electrical machines. The models are designed to decipher the complex condition of equipment components by analyzing vibrations caused by mechanical interactions and AE resulting from operational stresses. Key contributions include the establishment of a vibration model that simulates the multi-resonant system's response to generating impulses, reflecting the dynamics of rolling bearings, and a model for AE that integrates continuous and discrete signal components. This dual approach allows for a nuanced analysis of EE conditions, particularly focusing on bearing vibrations and laminated magnetic circuit responses to operational defects. The proposed models are centered on the understanding that diagnostic signals can be dissected into probabilistic characteristics, offering novel diagnostic signs through the statistical estimation of signal parameters. These models are crucial for identifying defects and monitoring the condition of EE, with significant implications for enhancing reliability and extending the lifespan of such equipment. The findings propose a methodological advancement in the diagnostic domain, providing a solid foundation for future research into the application of these models in real-world diagnostics and preventive maintenance strategies.