A Novel GAN-based Fault Diagnosis Approach for Imbalanced Industrial Time Series

This paper proposes a novel fault diagnosis approach based on generative adversarial networks (GAN) for imbalanced industrial time series where normal samples are much larger than failure cases. We combine a well-designed feature extractor with GAN to help train the whole network. Aimed at obtaining data distribution and hidden pattern in both original distinguishing features and latent space, the encoder-decoder-encoder three-sub-network is employed in GAN, based on Deep Convolution Generative Adversarial Networks (DCGAN) but without Tanh activation layer and only trained on normal samples. In order to verify the validity and feasibility of our approach, we test it on rolling bearing data from Case Western Reserve University and further verify it on data collected from our laboratory. The results show that our proposed approach can achieve excellent performance in detecting faulty by outputting much larger evaluation scores

Atomic and magnetic structures of (CuCl)LaNb2_2O7_7 and (CuBr)LaNb2_2O7_7: Density functional calculations

The atomic and magnetic structures of (Cu$X$)LaNb$_2$O$_7$ ($X$=Cl and Br) are investigated using the density-functional calculations. Among several dozens of examined structures, an orthorhombic distorted $2\times 2$ structure, in which the displacement pattern of $X$ halogens resembles the model conjectured previously based on the empirical information is identified as the most stable one. The displacements of $X$ halogens, together with those of Cu ions, result in the formation of $X$-Cu-$X$-Cu-$X$ zigzag chains in the two materials. The nearest-neighbor interaction within the zigzag chains are determined to be antiferromagnetic (AFM) for (CuCl)LaNb$_2$O$_7$ but ferromagnetic (FM) for (CuBr)LaNb$_2$O$_7$. On the other hand, the first two neighboring interactions between the Cu cations from adjacent chains are found to be AFM and FM respectively for both compounds. The magnitudes of all these in-plane exchange couplings in (CuBr)LaNb$_2$O$_7$ are evaluated to be about three times those in (CuCl)LaNb$_2$O$_7$. In addition, a sizable AFM inter-plane interaction is found between the Cu ions separated by two NbO$_6$ octahedra. The present study strongly suggests the necessity to go beyond the square $J_1-J_2$ model in order to correctly account for the magnetic property of (Cu$X)$LaNb$_2$O$_7$.Comment: 24 pages, 7 figure

Kahler submanifolds and the Umehara algebra

We show that an indefinite Euclidean complex space is not a relative of an indefinite non-flat complex space form. We further study whether two compact Fubini-Study spaces are relatives or not