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, which helps to improve the accuracy of fault detection. Furthermore, the online computational efficiency improves by many times compared with the conventional KPCA. Finally, the Tennessee Eastman (TE) process benchmark and wastewater treatment plant (WWTP) benchmark are employed to illustrate the effectiveness of the proposed method, where the average fault detection rates of DAE-PCA are at least 0.27% and 4.69% higher than those of other methods, and its online computational efficiency is faster 90.48% and 24.57% times than that of KPCA respectively.