Graph Low-rank Non-negative Matrix Factorization with Auto-encoders for Fault Detection

Yabing Liu

TL;DR: This paper presents a new method for fault detection using a novel non-negative matrix decomposition model

Abstract:

Abstract—Fault detection is the process of detecting and
diagnosing faults or abnormalities in a system by analyzing
its operational data. However, with the complexity of
modern industrial processes, some faults are difficult to
be detected in a timely manner due to various factors
such as noise and data nonlinearity. Therefore, data-driven
Fault Detection (FD) has become a widely used method to
detect abnormal events in functional modules. Non-negative
Matrix Factorization (NMF), as an efficient dimensionality
reduction technique, has not had potential applications
in fault detection (FD) thoroughly explored. In order to
improve the FD methods based on NMF, we have developed
a new approach, named graph low-rank non-negative
matrix Factorization with auto-encoders (GLNMFA). GLNMFA integrates the Laplacian operator effectively identifies the local structure among data points, enhancing
the performance of dimensionality reduction algorithms.
It also introduces the nuclear norm to find a low-rank
approximation to the original matrix, thereby constraining
sparsity. Additionally, auto-encoders are incorporated to
learn a low-dimensional representation of the data and
extract key features, which are subsequently applied for
fault detection purposes. We employ an optimization algorithm based on Alternating Direction Method of Multipliers
(ADMM) to optimize this model. Two test statistics T
2
(Hotelling’s T-squared), SPE (Squared Prediction Error)
are used to evaluate detection efficiency. Kernel Density
Estimation (KDE) are used to estimate control limits for
fault detection. The effectiveness of GLNMFA is validated
on two benchmark datasets.

Submission Number: 66