In cell culture bioprocessing, real-time batch process monitoring (BPM) refers to the continuous tracking and analysis of key process variables such as viable cell density, nutrient levels, metabolite concentrations, and product titer throughout the duration of a batch run. This enables early detection of deviations and supports timely control actions to ensure optimal cell growth and product quality. BPM plays a critical role in ensuring the quality and regulatory compliance of biopharmaceutical manufacturing processes. However, the development of accurate soft sensors for BPM is hindered by key challenges, including limited historical data, infrequent feedback, heterogeneous process conditions, and high-dimensional sensory inputs. This study presents a comprehensive benchmarking analysis of machine learning (ML) methods designed to address these challenges, with a focus on learning from historical data with limited volume and relevance in the context of bioprocess monitoring. We evaluate multiple ML approaches including feature dimensionality reduction, online learning, and just-in-time learning across three datasets, one in silico dataset and two real-world experimental datasets. Our findings highlight the importance of training strategies in handling limited data and feedback, with batch learning proving effective in homogeneous settings, while just-in-time learning and online learning demonstrate superior adaptability in cold-start scenarios. Additionally, we identify key meta-features, such as feed media composition and process control strategies, that significantly impact model transferability. The results also suggest that integrating Raman-based predictions with lagged offline measurements enhances monitoring accuracy, offering a promising direction for future bioprocess soft sensor development.

This letter presents a model-agnostic meta-learning (MAML) based framework for simultaneous and accurate estimation of human gait phase and terrain geometry using a small set of fabric-based wearable soft sensors, with efficient adaptation to unseen subjects and strong generalization across different subjects and terrains. Compared to rigid alternatives such as inertial measurement units, fabric-based soft sensors improve comfort but introduce nonlinearities due to hysteresis, placement error, and fabric deformation. Moreover, inter-subject and inter-terrain variability, coupled with limited calibration data in real-world deployments, further complicate accurate estimation. To address these challenges, the proposed framework integrates MAML into a deep learning architecture to learn a generalizable model initialization that captures subject- and terrain-invariant structure. This initialization enables efficient adaptation (i.e., adaptation with only a small amount of calibration data and a few fine-tuning steps) to new users, while maintaining strong generalization (i.e., high estimation accuracy across subjects and terrains). Experiments on nine participants walking at various speeds over five terrain conditions demonstrate that the proposed framework outperforms baseline approaches in estimating gait phase, locomotion mode, and incline angle, with superior accuracy, adaptation efficiency, and generalization.

Data-driven soft sensors help in process operations by providing real-time estimates of otherwise hard- to-measure process quantities, e.g., viscosities or product concentrations. Currently, soft sensors need to be developed individually per plant. Using transfer learning, machine learning-based soft sensors could be reused and fine-tuned across plants and applications. However, transferring data-driven soft sensor models is in practice often not possible, because the fixed input structure of standard soft sensor models prohibits transfer if, e.g., the sensor information is not identical in all plants. We propose a topology-aware graph neural network approach for transfer learning of soft sensor models across multiple plants. In our method, plants are modeled as graphs: Unit operations are nodes, streams are edges, and sensors are embedded as attributes. Our approach brings two advantages for transfer learning: First, we not only include sensor data but also crucial information on the plant topology. Second, the graph neural network algorithm is flexible with respect to its sensor inputs. This allows us to model data from different plants with different sensor networks. We test the transfer learning capabilities of our modeling approach on ammonia synthesis loops with different process topologies. We build a soft sensor predicting the ammonia concentration in the product. After training on data from one process, we successfully transfer our soft sensor model to a previously unseen process with a different topology. Our approach promises to extend the data-driven soft sensors to cases to leverage data from multiple plants.

Data-driven soft sensors (DDSS) have become mainstream methods for predicting key performance indicators in process industries. However, DDSS development requires complex and costly customized designs tailored to various tasks during the modeling process. Moreover, DDSS are constrained to a single structured data modality, limiting their ability to incorporate additional contextual knowledge. Furthermore, DDSSs' limited representation learning leads to weak predictive performance with scarce data. To address these challenges, we propose a general framework named LLM-TKESS (large language model for text-based knowledge-embedded soft sensing), harnessing the powerful general problem-solving capabilities, cross-modal knowledge transfer abilities, and few-shot capabilities of LLM for enhanced soft sensing modeling. Specifically, an auxiliary variable series encoder (AVS Encoder) is proposed to unleash LLM's potential for capturing temporal relationships within series and spatial semantic relationships among auxiliary variables. Then, we propose a two-stage fine-tuning alignment strategy: in the first stage, employing parameter-efficient fine-tuning through autoregressive training adjusts LLM to rapidly accommodate process variable data, resulting in a soft sensing foundation model (SSFM). Subsequently, by training adapters, we adapt the SSFM to various downstream tasks without modifying its architecture. Then, we propose two text-based knowledge-embedded soft sensors, integrating new natural language modalities to overcome the limitations of pure structured data models. Furthermore, benefiting from LLM's pre-existing world knowledge, our model demonstrates outstanding predictive capabilities in small sample conditions. Using the thermal deformation of air preheater rotor as a case study, we validate through extensive experiments that LLM-TKESS exhibits outstanding performance.

Data-driven soft sensors are crucial in predicting key performance indicators in industrial systems. However, current methods predominantly rely on the supervised learning paradigms of parameter updating, which inherently faces challenges such as high development costs, poor robustness, training instability, and lack of interpretability. Recently, large language models (LLMs) have demonstrated significant potential across various domains, notably through In-Context Learning (ICL), which enables high-performance task execution with minimal input-label demonstrations and no prior training. This paper aims to replace supervised learning with the emerging ICL paradigm for soft sensor modeling to address existing challenges and explore new avenues for advancement. To achieve this, we propose a novel framework called the Few-shot Uncertainty-aware and self-Explaining Soft Sensor (LLM-FUESS), which includes the Zero-shot Auxiliary Variable Selector (LLM-ZAVS) and the Uncertainty-aware Few-shot Soft Sensor (LLM-UFSS). The LLM-ZAVS retrieves from the Industrial Knowledge Vector Storage to enhance LLMs' domain-specific knowledge, enabling zero-shot auxiliary variable selection. In the LLM-UFSS, we utilize text-based context demonstrations of structured data to prompt LLMs to execute ICL for predicting and propose a context sample retrieval augmentation strategy to improve performance. Additionally, we explored LLMs' AIGC and probabilistic characteristics to propose self-explanation and uncertainty quantification methods for constructing a trustworthy soft sensor. Extensive experiments demonstrate that our method achieved state-of-the-art predictive performance, strong robustness, and flexibility, effectively mitigates training instability found in traditional methods. To the best of our knowledge, this is the first work to establish soft sensor utilizing LLMs.

Soft sensing of hard-to-measure variables is often crucial in industrial processes. Current practices rely heavily on conventional modeling techniques that show success in improving accuracy. However, they overlook the non-linear nature, dynamics characteristics, and non-Euclidean dependencies between complex process variables. To tackle these challenges, we present a framework known as a Knowledge discovery graph Attention Network for effective Soft sensing (KANS). Unlike the existing deep learning soft sensor models, KANS can discover the intrinsic correlations and irregular relationships between the multivariate industrial processes without a predefined topology. First, an unsupervised graph structure learning method is introduced, incorporating the cosine similarity between different sensor embedding to capture the correlations between sensors. Next, we present a graph attention-based representation learning that can compute the multivariate data parallelly to enhance the model in learning complex sensor nodes and edges. To fully explore KANS, knowledge discovery analysis has also been conducted to demonstrate the interpretability of the model. Experimental results demonstrate that KANS significantly outperforms all the baselines and state-of-the-art methods in soft sensing performance. Furthermore, the analysis shows that KANS can find sensors closely related to different process variables without domain knowledge, significantly improving soft sensing accuracy.

Higher-order sensor networks are more accurate in characterizing the nonlinear dynamics of sensory time-series data in modern industrial settings by allowing multi-node connections beyond simple pairwise graph edges. In light of this, we propose a deep spatio-temporal hypergraph convolutional neural network for soft sensing (ST-HCSS). In particular, our proposed framework is able to construct and leverage a higher-order graph (hypergraph) to model the complex multi-interactions between sensor nodes in the absence of prior structural knowledge. To capture rich spatio-temporal relationships underlying sensor data, our proposed ST-HCSS incorporates stacked gated temporal and hypergraph convolution layers to effectively aggregate and update hypergraph information across time and nodes. Our results validate the superiority of ST-HCSS compared to existing state-of-the-art soft sensors, and demonstrates that the learned hypergraph feature representations aligns well with the sensor data correlations. The code is available at https://github.com/htew0001/ST-HCSS.git

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.

Executing flow estimation using Deep Learning (DL)-based soft sensors on resource-limited IoT devices has demonstrated promise in terms of reliability and energy efficiency. However, its application in the field of wastewater flow estimation remains underexplored due to: (1) a lack of available datasets, (2) inconvenient toolchains for on-device AI model development and deployment, and (3) hardware platforms designed for general DL purposes rather than being optimized for energy-efficient soft sensor applications. This study addresses these gaps by proposing an automated, end-to-end solution for wastewater flow estimation using a prototype IoT device.

With the rise of deep learning, there has been renewed interest within the process industries to utilize data on large-scale nonlinear sensing and control problems. We identify key statistical and machine learning techniques that have seen practical success in the process industries. To do so, we start with hybrid modeling to provide a methodological framework underlying core application areas: soft sensing, process optimization, and control. Soft sensing contains a wealth of industrial applications of statistical and machine learning methods. We quantitatively identify research trends, allowing insight into the most successful techniques in practice. We consider two distinct flavors for data-driven optimization and control: hybrid modeling in conjunction with mathematical programming techniques and reinforcement learning. Throughout these application areas, we discuss their respective industrial requirements and challenges. A common challenge is the interpretability and efficiency of purely data-driven methods. This suggests a need to carefully balance deep learning techniques with domain knowledge. As a result, we highlight ways prior knowledge may be integrated into industrial machine learning applications. The treatment of methods, problems, and applications presented here is poised to inform and inspire practitioners and researchers to develop impactful data-driven sensing, optimization, and control solutions in the process industries.