## 2 Related Works  
For fault detection in systems, components, or sensors, autoencoder-based models are used in a wide range of applications such as bearing fault classification [25], smart grids [26], industrial processes [27], and healthcare [28]. Based on the number of features utilized in forecasting and the number of features in the output, time series forecasting tasks can be grouped into three categories: univariate, covariate, and multivariate. Considering the forecasting window, a time series forecasting problem can be categorized into single-step or multi-step scenarios. A single-step forecasting model predicts only a single time step in the future, whereas, in a multi-step scenario, the forecasting horizon comprises multiple time steps as depicted in Figure 2.  
Both multivariate and univariate schemes are addressed in the literature for multi-step time series forecasting. [PERSON] and [PERSON] in Liu (2019) proposed a bidirectional LSTM (Bi-LSTM) model using multiple features to analyze how COVID-19 impacts electricity demand. Those authors achieved good performance while forecasting demand for a 20-day duration in terms of root mean square error (RMSE) and mean squared logarithmic error (MSLE). A modified encoder-decoder architecture was proposed in [PERSON] and [PERSON] (2019), where the encoder section is based on LSTM cells, and the decoder section is based on Bi-LSTM cells. Between the encoder and decoder, a temporal attention layer is included to obtain the latent space variables. The model was tested on five different datasets to predict up to six time steps in the future. The authors in [PERSON] and [PERSON] (2019) proposed a novel deep learning architecture called the Spatiotemporal Attention Mechanism (STAM) for multivariate time series prediction and interpretation. Spatial and temporal embeddings are computed using feed-forward networks and LSTM networks, respectively. Autoencoder-based deep learning models are particularly suitable for anomaly or fault detection in sensor signals, which is a semi-supervised approach where only normal signals are used; later, the reconstruction error is used to identify faults. Fault detection in a diesel engine of a maritime vessel using an LSTM-based variational autoencoder (VAE) was proposed in [PERSON] and [PERSON] (2019). The authors used a modified parameter (log reconstruction probability) as the anomaly score to detect faults in an engine component. The drift detection of a chemical vapor deposition process in a semiconductor manufacturing system was studied in [PERSON] and [PERSON] (2019) using a variational autoencoder. The autoencoder model was trained to learn the normal process drift, and it later detected abnormal process drift from the sensor data by comparing the reconstruction error. An end-to-end framework for sensor fault analysis was presented in [PERSON] and [PERSON] (2019), in which the authors implemented two deep learning architectures: a CNN and a convolutional autoencoder (CAE). The CNN model was used to detect faults that occur in a single sensor within a collection of 10 sensors. Upon fault detection, the CAE is used to reconstruct a normal estimation of the faulty sample. Detecting unusual patterns in time series data utilizing the concept of multi-step forecasting was implemented in several works. [PERSON] and [PERSON] (2019) proposed a multi-variable transformer architecture to predict incipient faults in chemical processes. Their model predicts the target process variable multiple steps in advance by utilizing multiple transformer models, and the multi-horizon prediction is compared with a fault threshold to detect faults in the process. In [PERSON] and [PERSON] (2019), anomalous pattern detection in internet traffic data is carried out using an LSTM-based encoder-decoder model. The authors predicted different horizons from three to twelve time steps with increments of three steps. An ANN-based multi-step forecasting model is described in [PERSON] and [PERSON] (2019) to detect leaks in a water distribution network.