## 1 Introduction  
As industrial systems grow in complexity and become more interconnected, the challenge of identifying and diagnosing faults has intensified. Traditional diagnostic methods which rely heavily on fixed models or expert-driven rules often fall short in real-world environments, especially when confronted with dynamic conditions and unpredictable variables. This limitation has paved the way for more adaptable, data-driven approaches. Among the most promising of these are machine learning (ML) and deep learning (DL), which possess the unique ability to learn directly from data. These technologies can automatically detect and classify faults without needing explicitly defined models [1, 2, 3, 4, 5, 6, 7]. Machine learning encompasses a wide range of techniques for fault detection. One commonly employed approach is supervised learning, which proves especially effective when large datasets with clearly labeled fault examples are accessible. With these datasets, ML algorithms can identify patterns and correlations between system behaviorsand specific types of faults. Some widely adopted supervised learning techniques in this context include support vector machines (SVMs), decision trees, and various forms of neural networks [4; 5; 6; 7; 8]. Not all fault detection scenarios, however, provide access to labeled data. In such cases, unsupervised learning methods become invaluable. Techniques such as clustering and anomaly detection enable systems to identify unusual behaviors or deviations from normal patterns offering valuable insights even when clear fault labels are absent [3; 4; 6; 7]. Interconnected systems are made up of different parts that work together and share data or resources to make things run more smoothly, efficiently, and flexibly. For example, in smart homes, devices like thermostats, lighting, and security systems are all connected, communicating with each other to keep things comfortable and reduce energy consumption. In the human body, systems like the nervous and circulatory networks collaborate to keep everything functioning properly. In cities, smart infrastructure such as water, electricity, and transportation networks work together to manage resources in a more effective and sustainable way. These examples show just how important interconnected systems are in shaping and improving our daily lives [9; 10; 11]. Deep learning has emerged as a powerful tool in fault diagnosis. Architectures such as convolutional neural networks (CNNs) and recurrent neural networks (RNNs) are particularly well suited to handling time-series data, which are common in industrial settings. These models are capable of detecting subtle, time-dependent patterns that traditional techniques might miss [4; 5; 6; 7; 8]. This makes them especially valuable in diagnosing faults that develop progressively over time [5; 8]. Another promising advancement is reinforcement learning (RL), in which an agent learns to make decisions by interacting with its environment and receiving feedback. In the context of predictive maintenance, RL can be utilized to determine the optimal times for maintenance, predict failures in advance, and optimize system performance ultimately reducing downtime and enhancing efficiency [5; 7; 8]. Among all the applications of ML in fault diagnosis, predictive maintenance (PdM) stands out as particularly impactful. PdM focuses on forecasting equipment failures to schedule maintenance just in time avoiding unnecessary interventions and minimizing unexpected breakdowns. By using continuous streams of sensor data, ML models can identify early warning signs of failure, allowing for proactive, rather than reactive, maintenance strategies [1; 2; 6; 7]. This strategy is particularly beneficial in industries such as manufacturing, energy, and transportation, where unexpected downtime can be incredibly expensive [2; 3; 6; 7]. Despite advancements, challenges still persist. One key obstacle is the need for large, high-quality datasets.