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Learnable Faster Kernel-PCA for Nonlinear Fault Detection: Deep Autoencoder-Based Realization

Zelin Ren, Xuebing Yang, Yuchen Jiang, Wensheng Zhang

TL;DR

The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs.

Abstract

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs. Furthermore, the online computational efficiency improves by approximately 100 times compared with the conventional KPCA. With the Tennessee Eastman (TE) process benchmark, the effectiveness and superiority of the proposed method is illustrated.

Learnable Faster Kernel-PCA for Nonlinear Fault Detection: Deep Autoencoder-Based Realization

TL;DR

The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs.

Abstract

Kernel principal component analysis (KPCA) is a well-recognized nonlinear dimensionality reduction method that has been widely used in nonlinear fault detection tasks. As a kernel trick-based method, KPCA inherits two major problems. First, the form and the parameters of the kernel function are usually selected blindly, depending seriously on trial-and-error. As a result, there may be serious performance degradation in case of inappropriate selections. Second, at the online monitoring stage, KPCA has much computational burden and poor real-time performance, because the kernel method requires to leverage all the offline training data. In this work, to deal with the two drawbacks, a learnable faster realization of the conventional KPCA is proposed. The core idea is to parameterize all feasible kernel functions using the novel nonlinear DAE-FE (deep autoencoder based feature extraction) framework and propose DAE-PCA (deep autoencoder based principal component analysis) approach in detail. The proposed DAE-PCA method is proved to be equivalent to KPCA but has more advantage in terms of automatic searching of the most suitable nonlinear high-dimensional space according to the inputs. Furthermore, the online computational efficiency improves by approximately 100 times compared with the conventional KPCA. With the Tennessee Eastman (TE) process benchmark, the effectiveness and superiority of the proposed method is illustrated.
Paper Structure (23 sections, 40 equations, 7 figures, 3 tables)

This paper contains 23 sections, 40 equations, 7 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. KPCA
  4. DAE
  5. Methodology
  6. DAE-FE Framework
  7. Encoder Module
  8. LFE Module
  9. Decoder Module
  10. DAE-PCA Method
  11. PCA Module
  12. Regularization Term ${\Omega _\mathbf{T}}$
  13. DAE-PCA Based Nonlinear Fault Detection
  14. Case Study
  15. Simulation Setup
  16. ...and 8 more sections

Figures (7)

  • Figure 1: The whole network structure of DAE-FE framework.
  • Figure 2: The whole network structure of DAE-PCA, where the PCA module is shown with a solid blue border and the acquisition of $\mathbf{P}$ is in a solid green border.
  • Figure 3: The flowchart of nonlinear fault detection based on DAE-PCA.
  • Figure 4: The diagram of the TE process.
  • Figure 5: The online detection time (s) of all methods. Here, the detection time refers to all time of 960 samples in a fault.
  • ...and 2 more figures

Theorems & Definitions (1)

  • proof