###### Abstract
Regarding maintenance improvement, many different policies for industrial maintenance are available, but one of the most promising is predictive maintenance (PdM), which is generally defined as the use of prediction techniques and tools to estimate the remaining useful life (RUL) of a device or machinery, i.e., when repairs and corrections are needed in order for the production machinery to continue functioning properly [16]. Instead, [PERSON]. [17] proposed a risk-based predictive maintenance approach for multi-state production systems, using mission reliability as the primary criterion considering three types of operational risks--fundamental, explicit, and implicit--to optimize maintenance strategies and minimize overall production costs. Several older approaches used to identify linear relationships in time series are based on statistical methods. Some of them are the autoregressive integrated moving average (ARIMA) [18], a prediction method based on past observations which differs in ensuring stationarity and residuals; seasonal ARIMA (SARIMA) [19], which allows one to include seasonal components; and Seasonal ARIMA with exogenous variables (SARIMAX) [20], which allows one to incorporate exogenous variables that exert influence over the series, thus enabling the modeling of external actors for more precise forecasts. Some noteworthy approaches are based on machine learning (ML) techniques to estimate the time remaining before a production line no longer functions properly [21; 22]. Although this may sound attractive, it requires the availability of labeled or experimental data and complex mathematical or logical models, which makes their practical implementation difficult [23]. A further, often effective, approach is anomaly detection (AD). It not only focuses on predicting RUL, but it is based on detecting the first signs of a malfunction, or an anomaly, based on the analysis of time series collected from the machinery, which could indicate an impending failure. It can be used to discover interesting and unusual patterns and events [24]. However, most of the literature on the subject focuses mainly on the maintenance of power generation systems, such as wind farms [25; 26; 27], ocean wave farms [28], and so on, in order to improve their performances [29]. Although time series are widely used for AD purposes on production lines, to the authors' knowledge, an AD method using DeepESN to support energy-saving maintenance for production lines by acquiring data directly from the field has not yet been investigated. Only a few works analyze online data streaming [30; 31; 32]. Furthermore, parts of the literature try to model complex system dynamic behaviors [33; 34], requiring additional computational resources. The vehicle sector could also benefit from AD related to energy consumption, but their physical modeling is still very complex, e.g., Refs. [35; 36], and poses serious limitations to traditional techniques, which could alternatively be addressed with new approaches based on data, as, for example, has been done for other equally complex systems such as robots [37]. Finally, there are still few ML solutions that can be trained and tested at the edge, i.e., on an embedded devices or on devices close to the data source, enabling processing at higher speeds and volumes [38] and in real time [39]. In this context, this paper proposes a method based on DeepESN for anomaly prediction in non-linear dynamical systems. Compared with traditional prediction methods such as the long short-term memory (LSTM) and recurrent neural networks (RNN), although both models show a similar trend in the time-series, the DeepESN-based method presents timelier error detection and achieves a higher prediction accuracy. Furthermore, the time-series prediction made by the DeepESN-based method proved to be more accurate, with the ability to predict the occurrence of a fault as clearly as the LSTM.