  Process monitoring based on neural networks is getting more and more
attention. Compared with classical neural networks, high-order neural networks
have natural advantages in dealing with heteroscedastic data. However,
high-order neural networks might bring the risk of overfitting and learning
both the key information from original data and noises or anomalies. Orthogonal
constraints can greatly reduce correlations between extracted features, thereby
reducing the overfitting risk. This paper proposes a novel fault detection
method called second-order component analysis (SCA). SCA rules out the
heteroscedasticity of pro-cess data by optimizing a second-order autoencoder
with orthogonal constraints. In order to deal with this constrained
optimization problem, a geometric conjugate gradient algorithm is adopted in
this paper, which performs geometric optimization on the combination of Stiefel
manifold and Euclidean manifold. Extensive experiments on the Tennessee-Eastman
benchmark pro-cess show that SCA outperforms PCA, KPCA, and autoencoder in
missed detection rate (MDR) and false alarm rate (FAR).
