# Unsupervised Anomaly Detection for Time Series Data of Spacecraft Using Multi-Task Learning
## 1 Introduction  
The number of orbiting spacecrafts has increased in recent years, followed by the number of occasional spacecraft failures. As such, spacecraft constitute complex in-orbit systems, a single failure in a component or subsystem may cause irreparable damage, especially if not detected in time [1]. A reasonable approach towards failure monitoring involves anomaly detection using the vast amount of telemetry data continuously produced by a number of spacecraft system components; these data constitute a multi-dimensional time series [2]. By definition, anomalies are patterns in data that do not conform to a well-defined notion of normal behavior, and anomaly detection refers to the problem of finding such patterns [3]. Anomaly detection methods for spacecraft include the out-of-limits, expert system-based, and data-driven methods [4], which have been widely studied. Although some success has been achieved in detecting spacecraft failures, the tens of thousands of parameters pertaining to the complex spacecraft structure and spatial-temporal correlations between those parameters pose various challenges for the abovementioned anomaly detection methods, as detailed below. 1. The expert system-based method has clear rules and strong interpretability; however, it relies heavily on expert knowledge and, thus, anomalies beyond the scope of priorknowledge cannot be detected [5]. In addition, with the continuous increase in spacecraft parameters and their increasingly complex spatial and temporal dependencies, summarizing and refining a large volume of credible expert knowledge is becoming more difficult. 2. For data-driven methods, anomaly detection seems to be a classification problem. However, the abnormal condition is rare for the spacecraft compared with the normal condition; thus, the available training data exhibits an extreme imbalance. In addition, it is not easy for users to label each item of training data, especially those pertaining to anomalies. Thus, supervised and semi-supervised methods do not work well, and an unsupervised learning method is required to handle the imbalanced and unlabeled data in a principle-based manner. 3. To distinguish anomalies from the normal data through an unsupervised method, a proxy task is typically designed and implemented; this can be a prediction [6; 7] or reconstruction [8; 9] task. The prediction task detects anomalies based on the errors between the predicted and real values, whereas the reconstruction task detects anomalies based on the errors between the reconstructed and real values. However, a single proxy task usually yields a suboptimal result because the individual task is not well aligned with anomaly detection. For instance, the principal component analysis [10], k-means [11], one-class support vector machine [12], and autoencoder (AE) [13] methods are unable to simultaneously capture spatial and temporal correlations optimally [14]. While it is necessary to model the inter-metric and temporal dependency for multivariate time series simultaneously to get better performance [15]. To overcome the above three challenges, this study proposes a multi-task learning-based time series anomaly detection method (MTAD) that trains models jointly on several different proxy tasks using high-dimensional and time series data from the spacecraft. The overall method framework is shown in Figure 1, including a multi-task model (MTAD\({}_{\text{mt}}\)) and error evaluation and anomaly detection model (MTAD\({}_{\text{ad}}\)). In the training stage, the following proxy tasks are first jointly trained via the data characterization of the complex spatial-temporal patterns for feature extraction: (1) the long short-term memory (LSTM)-based data prediction task; (2) the AE-based latent representation learning and data reconstruction task; (3) the variational autoencoder (VAE)-based latent representation learning and data reconstruction task; and (4) the joint latent representation-based data prediction task.