Unsupervised neural networks (NNs) specialize in mining potential patterns from unlabeled data in a self-organizing manner. Recently, they have also been employed as observers for process monitoring using the generated residual signals. However, few studies have explained the model behavior and analyzed the monitoring performance of unsupervised NNs awing to their multilayer nonlinear structure. The interpretability of NN covers the analysis of its working principle to seek better network design and achieve improved performance. Thus, this paper develops explainable residual generators based on unsupervised NNs, which are applicable to deep autoencoder (DAE) and variational autoencoder (VAE). Through Taylor expansion, the residual deviation caused by the fault signal, a.k.a. the fault-affected term, is proven not to disappear in the presence of a non-zero Hessian matrix. Then, the consistency of achieving the optimal monitoring performance and the training loss of NNs is presented. A new indicator function is established based on the sum martingale, a representative of a weakly dependent stochastic process. Freedman’s inequality is first applied to describe the reliability of the learned thresholds during fault evaluation, which requires a smaller sample size for training. Finally, simulations on the continuous stirred tank reactor verify the effectiveness of the proposed methods.
