The failure of a complex and safety critical industrial asset can have extremely high consequences. Close monitoring for early detection of abnormal system conditions is therefore required. Data-driven solutions to this problem have been limited for two reasons: First, safety critical assets are designed and maintained to be highly reliable and faults are rare. Fault detection can thus not be solved with supervised learning. Second, complex industrial systems usually have long lifetime during which they face very different operating conditions. In the early life of the system, the collected data is probably not representative of future operating conditions, making it challenging to train a robust model. In this paper, we propose a methodology to monitor the systems in their early life. To do so, we enhance the training dataset with other units from a fleet, for which longer observations are available. Since each unit has its own specificity, we propose to extract features made independent of their origin by three unsupervised feature alignment techniques. First, using a variational encoder, we impose a shared probabilistic encoder/decoder for both units. Second, we introduce a new loss designed to conserve inter-point spacial relationships between the input and the learned features. Last, we propose to train in an adversarial manner a discriminator on the origin of the features. Once aligned, the features are fed to a one-class classifier to monitor the health of the system. By exploring the different combinations of the proposed alignment strategies, and by testing them on a real case study, a fleet composed of 112 power plants operated in different geographical locations and under very different operating regimes, we demonstrate that this alignment is necessary and beneficial.