Attention-gated stacked information-separation target-supervised variational autoencoder for soft sensing

Compared to the standard variational autoencoder (VAE), the Stacked VAE (SVAE) is widely recognized for its ability to extract high-level representations from strongly nonlinear data for soft sensor modeling. However, conventional stacking approaches still suffer from two key limitations: target-correlated information is not explicitly incorporated during the pretraining phase, and predictions rely exclusively on the final-layer features during fine-tuning, leaving valuable intermediate representations underutilized. To address these limitations, this paper proposes a novel soft sensor modeling framework based on an attention-gated, stacked, information-separation, target-supervised VAE (AGSISTVAE). The proposed model adopts a multi-layer VAE architecture to facilitate the progressive extraction of meaningful latent features. During layer-wise pretraining, the latent space is explicitly partitioned into output-correlated and output-irrelevant subspaces. By introducing a prior encoder to derive data-driven prior distributions conditioned on both inputs and outputs, target-correlated information is concentrated within the correlated subspace, enabling more effective extraction of predictive nonlinear features. Furthermore, an attention mechanism is incorporated during the fine-tuning stage to adaptively regulate information flow and fully exploit multi-level representations across all network depths. The proposed model is comprehensively validated on a numerical benchmark and a real-world debutanizer column industrial case study. Experimental results demonstrate that AGSISTVAE achieves superior predictive performance relative to existing state-of-the-art stacked architectures, yielding a low root-mean-square error of 0.00610 and a coefficient of determination of 0.9990 on the industrial case study. Moreover, the explicit separation and selective propagation of latent variables offer enhanced physical interpretability regarding which features are retained or discarded during the compression process.