# Fault Detection in Industrial Equipment through Analysis of Time Series Stationarity
## 2 Literature Review
Using the same training and test data in both experiments, with changes such as different resample rates, different layer sizes, and different activation functions in the hidden layer, they concluded the existence of some instability in the LSTM model, with its results varying significantly. To examine the most efficient pre-processing approaches to predicting sensory data trends based on GRU neural networks, [PERSON] et al.developed a model that can anticipate future values with a MAPE of 1.2%. They proved that it is possible to forecast the future behaviour of industrial paper pulp presses up to 30 days in advance. [PERSON] et al. [20] also developed a model using a GRU, successfully predicting, within a 7-day timeframe and with a MAPE of 2.79%, the three states classified by a Hidden Markov Model and the observable states obtained from clustering. The methodology also involved the use of a Principal Component Analysis (PCA) and K-Means algorithm during data clustering. With a variety of models and ways to predict time series values, and, in turn, equipment failures, [PERSON] et al. [21] conducted a study on the performance of LSTM, GRU, and ARIMA models. They used data from Bitcoin transactions from a Crypto data download website. The data were normalized and forced into stationarity, and their trend and seasonality were removed. All models were tested over a time span of 500 days, yielding the following MAPE results: LSTM, 6.80%; GRU, 3.97%; and ARIMA, 2.76%, with this last being the best and taking the least amount of time. Although the introduction of stationarity tests into predictive maintenance has not yet been the subject of a more in-depth study, there are already some articles on the topic. [PERSON] and [PERSON] [22] investigated the application of tests such as the ADF and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests to detect damage in structures using Lamb wave data. This study emphasized the challenges imposed by environmental conditions, such as temperature variations, that affect wave responses. The KPSS test was found to be more sensitive in detecting damage, although it is more affected by temperature changes. Their study highlights the need to mitigate these effects for reliable detection. In this type of study, it is also very common to use techniques such as cointegration, which is capable of removing both natural and artificial common trends, and then use peak-to-peak and variance values to detect and classify damages more efficiently [23]. More recently, [PERSON] et al. [24] also introduced a new method for early fault detection through the analysis of time series stationarity across sliding windows of SCADA data with a high level of confidence. This method demonstrated some superiority over others in detecting unusual or abrupt changes and being able to monitor multiple parameters simultaneously, once again showcasing the simplicity, efficiency, and promise of such methods. Table 1 shows a comparison of some of the relevant approaches to time series prediction and fault detection, including both classical statistical models and modern approaches based on deep neural networks. As the table shows, predictive models already achieve very reasonable accuracy, with errors less than 10 %. Nonetheless, these predictions still need additional analysis in order to determine a potential failure. No studies were founded based on the analysis of the \(p\)-value to determine ongoing trends, as we aim to in the present study.