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

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.

Quo vadis artificial intelligence?

“…The theoretical support is provided by Mercer's Theorem, which proves that any semipositive function is a valid candidate. Therefore, by using DNN, it can achieve a learnable and faster realization of the kernel function where the explicit form and the coefficients of the nonlinear mapping function can be obtained [129,130]. Nevertheless, it is worth noting that the learned functions based on DNN vary greatly during each training epoch.…”