Fault diagnosis is important for industrial processes because it permits to determine the necessity of emergency stops in a process and/or to propose a maintenance plan. Two strategies for fault diagnosis are compared in this work. On the one hand, the data are preprocessed using the independent components analysis for dimension reduction, then the wavelet transform is used in order to highlight the faulty signals, with this information an artificial neural network was fed. On the other hand, the second strategy, the main contribution of this work, is the implementation of a long short term memory. This memory is fed with the most representative variables selected by an elastic net to use both, the L1 and L2 norms. These strategies are applied in the Tennessee Eastman process, a benchmark widely used for fault diagnosis. The fault isolation had better results than those reported in the literature.