Non-Gaussian Industrial Process Monitoring With Probabilistic Independent Component Analysis

Abstract

Independent component analysis (ICA) is widely used for modeling and monitoring non-Gaussian process. However, traditional ICA lacks probabilistic representation of process uncertainties. In this study, a probabilistic ICA (PICA) model is proposed for non-Gaussian process modeling and monitoring. The independent latent spaces are specified with Student’s <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm t}$</tex></formula> formulation to account for both Gaussian and non-Gaussian data characteristics while the additional noise term is further served as a complement for explaining underlying process uncertainties. The Student’s <formula formulatype="inline" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex Notation="TeX">${\rm t}$</tex></formula> distribution with adjustable tails is essentially an infinite mixture of Gaussians with various scaling variances. In order to monitor retained variations, the noise space is further extracted and analyzed with probabilistic principal component analysis (PPCA). Simulation results show that compared with the deterministic ICA-based method, the proposed two-stage probabilistic extraction method is more effective for monitoring non-Gaussian industrial processes.