Data-driven fault diagnostics of safety-critical systems often faces the challenge of a complete lack of labeled data associated with faulty system conditions (i.e., fault types) at training time. Since an unknown number and nature of fault types can arise during deployment, data-driven fault diagnostics in this scenario is an open-set learning problem. Most of the algorithms for open-set diagnostics are one-class classification and unsupervised algorithms that do not leverage all the available labeled and unlabeled data in the learning algorithm. As a result, their fault detection and segmentation performance (i.e., identifying and separating faults of different types) are sub-optimal. With this work, we propose training a variational autoencoder (VAE) with labeled and unlabeled samples while inducing implicit supervision on the latent representation of the healthy conditions. This, together with a modified sampling process of VAE, creates a compact and informative latent representation that allows good detection and segmentation of unseen fault types using existing one-class and clustering algorithms. We refer to the proposed methodology as "knowledge induced variational autoencoder with adaptive sampling" (KIL-AdaVAE). The fault detection and segmentation capabilities of the proposed methodology are demonstrated in a new simulated case study using the Advanced Geared Turbofan 30000 (AGTF30) dynamical model under real flight conditions. In an extensive comparison, we demonstrate that the proposed method outperforms other learning strategies (supervised learning, supervised learning with embedding and semi-supervised learning) and deep learning algorithms, yielding significant performance improvements on fault detection and fault segmentation.