Training data-driven approaches for complex industrial system health monitoring is challenging. When data on faulty conditions are rare or not available, the training has to be performed in a unsupervised manner. In addition, when the observation period, used for training, is kept short, to be able to monitor the system in its early life, the training data might not be representative of all the system normal operating conditions. In this paper, we propose five approaches to perform fault detection in such context. Two approaches rely on the data from the unit to be monitored only: the baseline is trained on the early life of the unit. An incremental learning procedure tries to learn new operating conditions as they arise. Three other approaches take advantage of data from other similar units within a fleet. In two cases, units are directly compared to each other with similarity measures, and the data from similar units are combined in the training set. We propose, in the third case, a new deep-learning methodology to perform, first, a feature alignment of different units with an Unsupervised Feature Alignment Network (UFAN). Then, features of both units are combined in the training set of the fault detection neural network. The approaches are tested on a fleet comprising 112 units, observed over one year of data. All approaches proposed here are an improvement to the baseline, trained with two months of data only. As units in the fleet are found to be very dissimilar, the new architecture UFAN, that aligns units in the feature space, is outperforming others.