In process manufacturing industries, existing semi-supervised soft sensor methods often exhibit compromised performance under low label rates due to poor generalization, underscoring the urgent need for extracting generalized and transferable features from unlabeled data. Recently, diffusion model-based self-supervised learning (SSL) has shown great potential in addressing this challenge by leveraging powerful generative mechanisms to capture complex data distributions and distill informative representations without extensive supervision. Motivated by this, this paper proposes a variational diffusion representation learning (VDRL) framework for semi-supervised soft sensing modeling under low label rates. First, we propose a self-supervised parametric terminal variational diffusion (PTVD) model for generalized feature extraction. By defining the forward process terminal of the diffusion model as parameterized learnable latent distributions and attempting to recover the original input samples in the reverse process, we successfully achieve a transformation in the role of the diffusion model from the original sample generator to the desired feature extractor. The designed pretext task of patch-level mask reconstruction further improves its capability on temporal data and allows the PTVD model to be trained in a self-supervised manner without the involvement of real labels. Subsequently, we propose a temporal-diffusion joint representation (TDJR) model for the prediction of quality variables based on the extracted generalized multi-granular features. In order to fully exploit the joint dynamic information of multi-granular features in different sequence dimensions, we innovatively extract joint representation information from both time and diffusion dimensions simultaneously and complementarily, and perform supervised training under limited label guidance. A series of experimental evaluations on two real industrial processes validate the framework’s effectiveness and stability in soft sensing applications.
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