## 1 Introduction  
With the rapid development of industrialization and intelligent technologies, modern industrial equipment and mechanical systems are increasingly evolving towards greater complexity, precision, and integration. These systems are widely applied in fields such as manufacturing, transportation, energy production, and intelligent logistics, playing an indispensable role in ensuring the efficient operation of the national economy and social activities [1]. However, as system complexity and operational loads continue to increase, the probability of faults and their unpredictability also rise. This not only poses significant challenges to the safe operation of equipment but may also lead to substantial economic losses and safety risks [2]. Unexpected failures of industrial equipment are phenomena that are difficult to completely avoid, and their impacts often go beyond production downtime, potentially causing cascading system damage. For instance, in the field of energy production, issues such as turbine blade wear, cracks, or excessive vibrations can significantly reduce power generation efficiency and even lead to catastrophic shutdown accidents. In the transportation sector, abnormal temperature rises or fatigue cracks in train bearings may become critical triggers for operational failures, thereby endangering passenger safety [3]. Consequently, ensuring the safe and efficient operation of mechanical systems has become a core requirement for modern industrial development. To achieve this, the timely prediction of potential equipment failures and the implementation of preventive maintenance measures have become critical technological approaches to mitigate operational risks and control maintenance costs [4]. The core of fault prediction technology lies in real-time monitoring of the operating states of industrial equipment to establish a mapping relationship between equipment characteristics and health conditions. This enables the prediction of potential fault modes and the estimation of fault occurrence times. In recent years, this field has garnered significant attention from both industry and academia, achieving rapid advancements in areas such as intelligent manufacturing, the Industrial Internet of Things (IIoT), and Prognostics and Health Management (PHM). However, traditional fault diagnosis methods--such as rule-based periodic maintenance or diagnostic analysis relying on human expertise--often exhibit considerable limitations when dealing with complex and diverse industrial equipment. These limitations arise mainly due to the following distinctive challenges associated with modern industrial equipment:  
* High Complexity: Industrial equipment typically consists of multiple highly coupled subsystems, with operating states characterized by strong nonlinearity and dynamic coupling. This makes it challenging to accurately describe the overall system behavior using simple physical models. * High Dynamism: Industrial equipment operates in complex and ever-changing environments, and its operating parameters (e.g., vibration, temperature, and current) fluctuate significantly over time. Traditional static analysis methods struggle to capture these dynamic variations effectively. * Fault Concealment: Certain potential faults (e.g., early-stage cracks and minor wear) have minimal impact on the operational state in their initial stages, making them difficult to detect through conventional monitoring techniques. To address the aforementioned challenges, machine learning and deep learning technologies offer novel research avenues for fault prediction in complex equipment. These techniques can automatically extract critical features from massive sensor data and construct nonlinear, multi-layered fault prediction models. Monitoring data from industrial equipment are typically presented as time-series data, encompassing various physical quantities collected by multiple sensors, such as vibration signals, current, voltage, and temperature.