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

TL;DR

The paper addresses data scarcity in soft sensing by introducing a deep latent variable framework that jointly models multiple industrial units using semi-supervised and multi-task learning. It proposes a hierarchical generative model with latent states $z$, unit contexts $c$, and a global parameter $ heta$, trained via variational inference and an augmented ELBO to emphasize accurate $y$ inference. The method is validated on synthetic and real Virtual Flow Metering data, showing that unlabeled data provide measurable performance gains, especially when transferring to unseen units. This approach offers data-efficient, transferable soft sensors suited for information-poor industrial environments, with potential extensions to richer sensors and sequential data.

Abstract

In many industrial processes, an apparent lack of data limits the development of data-driven soft sensors. There are, however, often opportunities to learn stronger models by being more data-efficient. To achieve this, one can leverage knowledge about the data from which the soft sensor is learned. Taking advantage of properties frequently possessed by industrial data, we introduce a deep latent variable model for semi-supervised multi-unit soft sensing. This hierarchical, generative model is able to jointly model different units, as well as learning from both labeled and unlabeled data. An empirical study of multi-unit soft sensing is conducted using two datasets: 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, the proposed model achieves superior results, outperforming current leading methods for this soft sensing problem. We also show that when a model has been trained on a multi-unit dataset, it may be finetuned to previously unseen units using only a handful of data points. In this finetuning procedure, unlabeled data improve soft sensor performance; remarkably, this is true even when no labeled data are available.

Figures (11)

• Figure 1: Illustration of multi-unit data generation. The units are similar, and can be thought of as realizations of a common "prototype" unit. Each unit gives rise to a large amount of unlabeled data (red boxes), and a small amount of labeled data (green boxes).
• Figure 2: A generative model for multi-unit soft sensing. Random variables are encircled. A grey (white) circle indicates that the variable is observed (latent). The nested plates (rectangles) group variables at different levels.
• Figure 3: A graphical representation of the inference model. Arrows indicate which parameters $(\phi_y, \phi_z, \phi_c)$ and which variables (encircled) that are used in the inference of the latent variables $(y^u, z, c)$.
• Figure 4: Illustration of model architecture when $y$ is unobserved. When $y$ is observed, the encoder $q_{\varphi}(y \,|\, x, c)$ is unused, and $y$ is fed straight into the encoder $q_{\varphi_z}(z \,|\, x, y, c)$. In either case, the output is an approximation of $p_{\theta}(x, y)$.
• Figure 5: Related generative models