A Deep Nonnegative Matrix Factorization Approach via Autoencoder for Nonlinear Fault Detection

In the era of big data, data-driven fault detection is vital for modern industrial systems. This article considers the potential complexity of fault detection and proposes a novel nonlinear method based on nonnegative matrix factorization (NMF). Motivated by an autoencoder, in this article we first utilize the input data to learn an appropriate nonlinear mapping function, which transforms the original space into a high-dimensional feature space. Then, according to the decomposition rule of NMF, we divide the learned feature space into two subspaces, and two statistics in these subspaces are designed appropriately for nonlinear fault detection. The established method, i.e., deep nonnegative matrix factorization (DNMF), is implemented by three parts: an encoder module, an NMF module, and a decoder module. Unlike conventional NMF-based nonlinear methods using implicit and predetermined kernels, DNMF provides a new nonlinear scheme applied to NMF via a deep autoencoder framework and realizes nonlinear mapping for input data automatically. Our proposed nonlinear framework can be further generalized to other linear methods. Besides, DNMF greatly expands the NMF application scope by breaking through the limitation of nonnegative input. The Tennessee Eastman process as an industrial benchmark is employed to verify the effectiveness of the proposed method.