Variational Bayesian Learning With Reliable Likelihood Approximation for Accurate Process Quality Evaluation

The accurate depiction of the intricate probability distribution of industrial data in high-dimensional space is crucial for various process quality evaluation (PQE) tasks. The substantial potential of deep generative models (DGMs) in addressing this challenge originates from their integration of deep neural networks into the generative frameworks. However, despite the potential of DGMs in PQE tasks, several challenges persist, e.g., the inexact inference, intractable likelihood approximation, and large inductive bias. In this article, aiming at the DGMs for accurate PQE, a novel DGMs framework with unbiased and reliable likelihood approximation is proposed based on variational Bayesian learning (VBL). The VBL offers a solid mathematical basis to our framework, based on which our works are two-fold: first, we refine the Gaussian posterior inference of VBL by neural ordinary differential equations, which can eliminate the vague inference caused by unreasonable Gaussian assumption and the large inductive bias caused by structured Jacobian matrix; Second, we introduce an unbiased and reliable likelihood approximation method based on Markov chain Monte Carlo and simulated annealing to achieve an accurate PQE. Two typical industrial PQE case studies are conducted to verify the performance of the proposed framework.