# Fault Detection in Industrial Equipment through Analysis of Time Series Stationarity
## 2 Literature Review  
Fault prediction in industrial equipment is an area of research and practice that encompasses a wide range of approaches and methodologies. Given the complexity of industrial systems and the diversity of factors that can lead to faults, there is no single approach that is universally applicable. Instead, engineers and researchers have explored a variety of techniques and strategies to anticipate, avoid, and mitigate equipment failures [10]. Statistical models aim at analysing the behaviour of random variables based on recorded data. For predictive maintenance, statistical models are used to determine the current degradation and the expected remaining life of the equipment. This type of model is often implemented in multi-model approaches [11]. [PERSON] et al. [12] presented a novel methodology that uses the Autoregressive Moving Average (ARMA). Instead of using the most common data transformation methods, they developed their own method by creating a transfer function and took the transformed sequence as the input data to build an ARMA model. They achieved a Mean Absolute Percentage Error (MAPE) 2.48%, which is lower than that of the ARMA model with traditional methods. ARIMA is the most common forecast model used in time series, due to the adaptability of its linear patterns to all time series strategies, according to [PERSON] et al. [13]. Based on daily real electricity load data for 709 individual households that were randomly chosen over an 18 month period, they compared the performance of two forecasting methods: ARIMA and an Artificial Neural Network (ANN). After tests, the ANN's MAPE was 1.80% and ARIMA's was approximately 2.61%. In order to prove the good performance, when applied to problems related to anomaly detection and technological parameter forecasting, of the ARIMA algorithm, using sparse data obtained from an urban sewer system, [PERSON] et al. [14] developed a model and obtained appealing results. Over a time span of 30 days, during which 24 days were used for training, they achieved a Mean Absolute Error (MAE) of approximately 0.0962. [PERSON] and [PERSON] [15] developed a model, aiming to study quality predictions in power grid equipment based on key inspection parameters. By gathering live monitoring data from power grid equipment and creating an intelligent predictive alerting algorithm using time series and a trend analysis, they achieved a MAPE of 5.62% for the leakage current and 4.16% for the resistive current. [PERSON] et al. [16] proposed an LSTM methodology for the predictive maintenance of railway rolling stock equipment. As the dataset contained some imperfections, they developed an algorithm for filtering the spikes found and another one for standardizing them. They also used 10-fold cross-validation and Adaptive Moment Estimation (ADAM) and obtained the following results: a 0.0184 MAE for a 60 min predicted time window, including for low- and high-severity diagnostic events (L&H). For high-severity diagnostic events only (H), they achieved 0.0008 MAE. Based on supervisory control and data acquisition (SCADA) data, [PERSON] and [PERSON] developed eight models using extreme gradient boosting (XGBoost) and LSTM to build the characteristic behaviour of critical wind turbine components [17]. They tested them on two real case studies regarding six different wind turbines with the aim of predicting the gearbox bearing temperature and obtained a MAPE between 0.8% and 6.2%. [PERSON] et al. [18] propose that RNNs have been shown to be promising options for prediction tasks, often surpassing the current state-of-the-art statistical benchmarks in the field. One of the existing types of RNNs is a GRU. [PERSON] et al. [19] have employed neural networks to develop two models aimed at predicting the behaviour of an industrial paper press. Their achievement lies in accurately forecasting the press' behaviour over a 30-day period, achieving a MAPE of less than 10% when utilizing GRU. [PERSON] et al.also developed a model using LSTM to compare it with a GRU network.