# Fault Detection in Industrial Equipment through Analysis of Time Series Stationarity
## 1 Introduction  
Stopping the industrial equipment used on production lines is normally detrimental to companies. Downtime means a loss of production, plus costs due to stopping and restarting the equipment. This underscores the importance of predictive approaches to anticipate behaviours corresponding to potential failures that could trigger these stoppages. In this context, predictive modelling emerges as a fundamental tool, allowing companies to anticipate equipment failures based on historical and real-time data. By employing advanced data analysis and machine learning techniques, organizations can identify hidden patterns in equipment's operational data and develop accurate predictive models that alert operators about potential impending failures. This way it is possible to minimize unexpected equipment downtime, improve service quality for customers, and also reduce the additional costs caused by over-maintenance in preventive maintenance policies [1]. There are a variety of approaches to this, each with its advantages and disadvantages [2], but in all of them it is essential to follow the best practices for data preparation, model training, and validation to ensure the accuracy and reliability of their predictions. Some approaches stand out for their ability to capture temporal dependencies in sequential data, which is essential for predicting equipment failures over time. Outstanding state-of-the-art models include recurrent neural networks, namely Long Short-Term Memory (LSTM) and Gated Recurrent Units (GRUs) [3, 4]. Other models are effective in modelling linear and stationary relationships in time series data, such as the Autoregressive Integrated Moving Average (ARIMA) or the Seasonal Autoregressive Integrated Moving Average (SARIMA), although these models are normally more efficient in short-term prediction [5, 6]. It is also common to use ensemble approaches, which combine multiple models, such as Random Forests (RFs) and Gradient BoostingMachines (GBMs) [7; 8]. However, each model should be developed according to the specific needs and characteristics of a problem. The prediction of future sensor values alone is not sufficient to identify trends automatically. Predictive models only forecast the future, but additional tools are needed to classify features and determine whether the patterns that are being anticipated are normal or abnormal. This classification is normally accomplished through classical machine learning models, such as neural networks, Support Vector Machines, and other classifiers [9]. The present work aims to detect possible failures in an industrial wood chip pump. The methodology consisted of analysing the \(p\)-value produced by the Augmented Dickey-Fuller (ADF) test for stationarity. The ADF test establishes that a \(p\)-value above a certain level, typically 0.05, indicates a possibly non-stationary time series. In industrial equipment, vibration should be eliminated or contained as much as possible, so that the equipment's vibration signature will have a profile similar to that recommended by the manufacturer. Over time, however, it normally increases at some point because screws, joints, and fragile parts in general start to become loose. When it reaches a certain value, maintenance interventions are required to fix the problem and reduce vibration again. Hence, the hypothesis is that a trend which may lead to an equipment failure might be detected by the observation of the \(p\)-value of a time series in near real time using a rolling window for the test. Specific patterns of increase or decrease or large amplitude variations might reveal a possibly approaching failure in the equipment. These patterns must, therefore, be analysed, aiming to prevent failures from happening and reduce downtime and maintenance costs. To the best of the authors' knowledge, no previous predictive maintenance study has been reported using the ADF test on chip pump time series.