Virtual sample generation for soft-sensing in small sample scenarios using glow-embedded variational autoencoder

In industrial processes, limitations of the physical environment, sensors drop-out, and repetitive sampling often lead to insufficient and unevenly distributed representative instances, which greatly hinders the accuracy of soft-sensing models. This paper presents a novel virtual sample generation method based on Glow-embedded variational autoencoder (GVAE-VSG), aimed at enhancing data richness and diversity to improve the modeling performance. Specifically, GVAE-VSG embeds the Glow model from flow transformations into the variational autoencoder. This allows for the derivation of a more generalized posterior distribution without reducing sample dimensionality, thereby ensuring the generation of higher-quality virtual input samples. Subsequently, a nonlinear iterative partial least squares regression framework, incorporating a sparse constrained error matrix, is employed to generate virtual output samples that more closely resemble actual data. Finally, by a synthetic nonlinear function and an actual purification terephthalic acid (PTA) solvent system, the generative and modeling performance of the proposed method are comprehensively assessed.