The ultra-dense Low Earth Orbit (LEO) satellite networks can provide global coverage and high-speed communication services. However, the ultra-dense LEO satellite constellation is also faced with many different types of malfunctions, hence the importance of effective fault diagnosis technology. We apply the two-layer networks of Medium Earth Orbit (MEO) and LEO as the architecture of fault diagnosis. Confronted with the problems of massive data and limited resources of cache and calculation in each satellite node, we propose the feature selection method which combines Levy Flight and Shuffled Complex Evolution with Binary Grasshopper Optimization Algorithm (LS-BGOA) for data pre-processing. The LS-BGOA aims at reducing data dimensions by eliminating unrelated or noise data without losing the accuracy of fault recognition. Simulation results demonstrate that the transmission data of LEO satellites for fault diagnosis is validly compressed with the guarantee of diagnosis accuracy.