The project deals with the development of active fault diagnosis (AFD) algorithms for stochastic discrete-time large-scale systems. To achieve the feasibility of the algorithms, tensor decompositions (TDs) will be employed in several components of the AFD algorithm design. In particular, the TDs will be applied for the dynamic programming responsible for the active aspect of the diagnosis, for the nonlinear Bayesian state estimation responsible for the learning, and for the information fusion responsible for merging the information learned by individual AFD nodes. To meet the requirements involved, novel TD algorithms will be developed with a special focus on non-negative variants, variants with limited sensitivity, and functional TD. Combining the components fused with the developed TDs in the decentralized, distributed or hierarchical AFD architectures exploiting structural properties of the large-scale system will lead to feasible algorithms capable of coping with the complexity of nonlinear stochastic large-scale systems.