  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.
