With the rapid development of deep learning methods, the variational auto-encoder (VAE) has been utilized for nonlinear process monitoring. However, most VAE-based methods hardly consider the inner independent and related relationship of each variable. To overcome this problem, a novel VAE named independent and related variable information concentrated variational auto-encoder (IRVIC-VAE) is proposed. To concentrate the independent and related information, a loading weight matrix regularization based on the mutual information of variables with gaussian distribution is introduced so that the variables can separate into two subspaces that contain independent and related information in latent variables. The original data space decomposed via IRVIC-VAE is orthogonal and approximate to normal distribution. For process monitoring, the independent variable space and related variable space are combined to establish two statistics according to Kullback-Leibler divergence and 2-norm. Finally, the performance and effectiveness of IRVIC-VAE are testified by Tennessee Eastman (TE) process.

Meta-Learning, or so-called Learning to learn, has become another important research branch in Machine Learning. Different from traditional deep learning, meta-learning can be used to solve one-to-many problems and has a better performance in few-shot learning which only few samples are available in each class. In these tasks, meta-learning is designed to quickly form a relatively reliable model through very limited samples. In this paper, we propose a modified LSTM-based meta-learning model, which can initialize and update the parameters of classifier (learner) considering both short-term knowledge of one task and long-term knowledge across multiple tasks. We reconstruct a Compound loss function to make up for the deficiency caused by the separate one in original model aiming for a quick start and better stability, without taking expensive operation. Our modification enables meta-learner to perform better under few-updates. Experiments conducted on the Mini-ImageNet demonstrate the improved accuracies.