A deep latent variable model for semi-supervised multi-unit soft sensing in industrial processes

Scarcity of labeled data limits the development of data-driven soft sensors for many industrial processes. However, there are often opportunities to learn stronger models by exploiting process knowledge and being more data-efficient. Two opportunities, which frequently occur in industrial data, are learning unsupervised from unlabeled data and learning supervised across similar process units. Motivated by the lack of existing methods that jointly address these opportunities, we introduce a deep latent variable model for semi-supervised multi-unit soft sensing. The hierarchical, generative model describes a data-generating process for multiple similar process units and facilitates learning from unlabeled data. An empirical study of multi-unit soft sensing is conducted using three datasets: a benchmark dataset from a simulated sulfur recovery unit, a synthetic dataset of single-phase fluid flow, and a large, real dataset of multi-phase flow in oil and gas wells. We show that by combining semi-supervised and multi-task learning across multiple process units, the proposed method achieves superior results when unlabeled data is available. In the real well data case, it outperforms a leading method for supervised multi-unit soft sensing, lowering the average test error by approximately 9 %. We also show that a trained model may be fine-tuned to previously unseen units using only a handful of data points. Interestingly, the soft sensor performance for a new unit is slightly improved by fine-tuning to unlabeled data only. This demonstrates that some unit properties that are predictive to the soft sensor task can be learned unsupervised. • A deep latent variable model is proposed for multi-unit soft sensing. • A learning method based on variational inference enables semi-supervised learning. • High data efficiency is demonstrated in a virtual flow metering case.