Improving Convolutional Neural Networks for Fault Diagnosis by Assimilating Global Features

Deep learning techniques have become prominent in modern fault diagnosis for complex processes. In particular, convolutional neural networks (CNNs) have shown an appealing capacity to deal with multivariate time-series data by converting them into images. However, existing CNN techniques mainly focus on capturing local or multi-scale features from input images. A deep CNN is often required to indirectly extract global features, which are critical to describe the images converted from multivariate dynamical data. This paper proposes a novel local-global CNN (LG-CNN) architecture that directly accounts for both local and global features for fault diagnosis. Specifically, the local features are acquired by traditional local kernels whereas global features are extracted by using 1D tall and fat kernels that span the entire height and width of the image. Both local and global features are then merged for classification using fully-connected layers. The proposed LG-CNN is validated on the benchmark Tennessee Eastman process (TEP) dataset. Comparison with traditional CNN shows that the proposed LG-CNN can greatly improve the fault diagnosis performance without significantly increasing the model complexity. This is attributed to the much wider local receptive field created by the LG-CNN than that by CNN. The proposed LG-CNN architecture can be easily extended to other image processing and computer vision tasks.

Unifying Theorems for Subspace Identification and Dynamic Mode Decomposition

This paper presents unifying results for subspace identification (SID) and dynamic mode decomposition (DMD) for autonomous dynamical systems. We observe that SID seeks to solve an optimization problem to estimate an extended observability matrix and a state sequence that minimizes the prediction error for the state-space model. Moreover, we observe that DMD seeks to solve a rank-constrained matrix regression problem that minimizes the prediction error of an extended autoregressive model. We prove that existence conditions for perfect (error-free) state-space and low-rank extended autoregressive models are equivalent and that the SID and DMD optimization problems are equivalent. We exploit these results to propose a SID-DMD algorithm that delivers a provably optimal model and that is easy to implement. We demonstrate our developments using a case study that aims to build dynamical models directly from video data.