# An EWS-LSTM-Based Deep Learning Early Warning System for Industrial Machine Fault Prediction
## 2 Theoretical Background
### Early Warning System  
The monitoring system plays a crucial role in managing and controlling manufacturing processes. Its main applications include fault prediction, production improvement, cost reduction, and the development of early warning systems (EWSs). An effective EWS must ensure the timely collection of relevant information, enabling stakeholders to take preventive or corrective actions to minimise risks and optimise operational responses. The key characteristics of an efficient EWS include the following [41; 42]:  
* Monitoring: Continuous acquisition of critical data through advanced instrumentation and sensing techniques. * Data analysis: Use of statistical and machine learning algorithms to identify anomalous patterns and predictive signals. * Alerting: Implementation of automated notification systems for the timely communication of relevant information. * Response: Planning intervention strategies to mitigate the impact of adverse events. * Risk assessment: Preventive analysis of system vulnerabilities to develop proactive mitigation strategies. The integration of EWSs in the manufacturing environment has been widely studied in the literature, with a particular focus on the digitalisation of decision-making processes and the minimisation of human intervention in anomaly detection and management [43; 44; 45; 46]. However, despite significant advancements, complete automation of monitoring remains an ongoing challenge. Several approaches have been proposed to improve the effectiveness of EWSs. Classical statistical methods, such as DFA (Detrended Fluctuation Analysis) and ACF (AutoCorrelation Function), have proven effective in detecting anomalies in electronic components and industrial systems [47; 48]. Invariant-based identification models and data-driven techniques have been used for monitoring lithium-ion batteries and heat pumps [49; 50]. Additionally, fuzzy logic-based approaches have been developed to enhance predictive maintenance strategies [51]. With the evolution of artificial intelligence techniques, machine learning and, in particular, deep learning (DL) have taken on a central role in EWSs. Deep neural networks are distinguished by their ability to learn complex and non-linear patterns, making them particularly suitable for analysing multidimensional and temporal data [52]. Specifically, recurrent neural networks (RNNs) and Long Short-Term Memory (LSTM) networks have proven effective in predicting rare events and analysing time series, thanks to their ability to retain long-term dependencies [53]. Several studies have applied LSTM networks to EWSs in the manufacturing sector with promising results. In [31], an early warning system based on an LSTM-Bayes model was implemented for the predictive maintenance of steam turbines in the nuclear energy sector. Similarly, in [32], an EWS for monitoring axle box bearings in high-speed trains demonstrated advantages in analysing anomalies that could not be detected with traditional sensors. A combined approach integrating LSTM networks with Bayesian inference for anomaly detection in machinery was proposed in [54]. Table 1 provides a comparative analysis of different models adopted for early warning systems (EWSs), highlighting their applications and key findings. This overview helps to understand technological advancements and methodologies used to enhance monitoring, predictive maintenance, and risk management across various industrial sectors.