Chemical processes involve complex operational mechanisms and high-dimensional variables with multiscale dependencies and temporal covariate shifts, posing significant challenges for soft sensing implementation. To address these issues, a self-constrained weighted garrote ordered memory network with adaptive distribution learning is proposed for industrial soft sensor modeling. Specifically, an improved long short-term ordered memory (LSTOM) architecture with a composite hierarchical information update mechanism is designed to capture multiscale dynamic features from industrial time-series data. Meanwhile, an adaptive distribution learning module is embedded into the LSTOM architecture to match high-order feature distributions across different temporal periods via maximally dissimilar segments. With the composite hierarchical update mechanism and embedded adaptive distribution learning, the proposed approach improves generalization in soft sensor modeling under multi-timescale dependencies and temporal covariate shifts. Finally, the shrinkage coefficients of the self-constrained weighted garrote are embedded into the LSTOM’s input weights to eliminate redundant variables and promote structural sparsity. The effectiveness of the proposed approach is validated on a public industrial-scale penicillin fermentation process and a real-world flue gas desulfurization case.

Gated recurrent units (GRUs) have been successfully applied to various industrial soft-sensor tasks. However, their linear coupling constraint in the hidden-state limits information propagation, while high-dimensional inputs and structural redundancies further challenge modeling. To address these issues, a speed-adaptive gated recurrent unit (SAGRU) network with weights dual-garrote regularization (WDG-SAGRU) is proposed for product quality prediction. Specifically, a speed-adaptive gating mechanism is integrated into the GRU update gate through a nonlinear exponential transformation. This mechanism is incorporated into the hidden-state update to break the linear coupling constraint, enhancing information flow and feature extraction. Meanwhile, the dual-garrote shrinkage coefficients are embedded into SAGRU’s input and hidden weight matrices, enabling synchronized optimization of input variable selection and structural sparsity. The proposed WDG-SAGRU is validated against state-of-the-art methods on a numerical example and an operational flue gas desulfurization system in a thermal power plant.

As modern industrial processes increase in integration and scale, there exist intricate dynamic time variability and nonlinearity within process data. Deep learning-based nonlinear dynamic models, such as Transformer, are frequently applied to soft sensor modeling for industrial time sequences due to their powerful ability in learning temporal feature representations. Nevertheless, process data gathered from industrial plants are usually sampled at irregular intervals, posing a challenge for most mainstream dynamic models to handle the resulting temporally changeable relations in process sequence data. Thus, this paper proposes a time-aware rotary Transformer (TART) for soft sensor modeling of irregular sampled time series in industrial processes, which adaptively and efficiently model the temporally changeable dynamics among series data. Specifically, a sampling interval embedding layer is devised to simultaneously encode the process variables, positional information and sampling intervals, facilitating the efficient extraction of temporal dynamic features. Accordingly, a non-increasing function-based time-aware rotary attention mechanism is proposed to deal with the temporally changeable sampling intervals via assigning proper weights to the corresponding feature representations. Theoretical analysis shows that the proposed time-aware rotary attention mechanism can adaptively assign temporal similarities according to the irregular sampling intervals. The TART-based soft sensor is applied to an actual-run industrial sugar crystallization process to predict the supersaturation and purity of mother liquor. In comparison with recent predictive modeling methods, the proposed TART achieves state-of-the-art performance, demonstrating its feasibility and efficacy for soft sensing of practical industrial processes.

Deep probabilistic learning networks have been applied in industrial soft sensors. However, they face significant challenges in latent variable inference, deep learning backend implementation, and labeled data scarcity. The first challenge arises when covariates directly infer the latent variable, potentially leading to inaccuracies. The second stems from discrepancies between the theoretical probabilistic distribution and practical instance-based deep learning backends. The third is commonly encountered in soft sensor applications, where unlabeled data often go unused, reducing accuracy. To address these challenges, this work proposes a novel semi-supervised probabilistic learning network (SS-PLN) for soft sensor modeling with partially labeled data. The first issue is addressed by formulating an optimization problem as the model’s learning objective. This optimization is efficiently solved by investigating the input of inference network through analyzing the optimal solution’s structure. For the second issue, mean and covariance equations are used to represent probabilistic distributions, ensuring effective deep learning backends. The third issue is addressed by integrating supervised and unsupervised probabilistic learning networks to form the SS-PLN model, thereby maximizing the use of unlabeled data and enhancing the soft sensing performance. The feasibility and effectiveness of the proposed SS-PLN are validated through comparisons with recent semi-supervised learning methods, using data from two industrial processes.

Soft sensing technique has been extensively used to predict key quality variables in industrial systems. However, due to the difficulty of quality variable acquisition, only limited labeled data samples are available, and a large number of unlabeled ones are discarded. This raises a big challenge to build a high-quality soft sensor model. In order to furthest exploit information contained in both the labeled and unlabeled data, this paper proposes a principal component-based semi-supervised extreme learning machine (referred to as PCSELM) model. Through this model, extracting latent features and learning nonlinear input-output relationship can be simultaneously performed. In this way, unlabeled samples are utilized efficiently for feature representation and model accuracy improvement. Moreover, mixed regularizations are employed to work in conjunction with the PCSELM to obtain high generality and flexibility. We also derive an efficient parameter learning algorithm with theoretically guaranteed convergence. Comprehensive experiments are conducted via an industrial process. Comparison results illustrate that the proposed PCSELM outperforms other representative semi-supervised algorithms.Note to Practitioners—Industrial processes in general incorporate unlabeled samples which are ubiquitous in real world applications. The focus of this paper is to develop a semi-supervised soft sensor model (PCSELM) that is capable to learn the nonlinear features and regression relationship efficiently with both the labeled and unlabeled samples. The proposed model can automatically implement the feature representation and the input-output relationship description. In addition, we introduce mixed norms for the model objective function to improve the final prediction performance and generalization. A feasible model optimization technique with proved convergence is also derived. Experimental results based on a real industrial dataset manifest that PCSELM achieves better prediction accuracy than its peers.

Social networks are an essential component of the Internet of People (IoP) and play an important role in stimulating interactive communication among people. Graph convolutional networks provide methods for social network analysis with its impressive performance in semi-supervised node classification. However, the existing methods are based on the assumption of balanced data distribution and ignore the imbalanced problem of social networks. In order to extract the valuable information from imbalanced data for decision making, a novel method named minority-weighted graph neural network (mGNN) is presented in this article. It extends imbalanced classification ideas in the traditional machine learning field to graph-structured data to improve the classification performance of graph neural networks. In a node feature aggregation stage, the node membership values among nodes are calculated for minority nodes’ feature aggregation enhancement. In an oversampling stage, the cost-sensitive learning is used to improve edge prediction results of synthetic minority nodes, and further raise their importance. In addition, a Gumbel distribution is adopted as an activation function. The proposed mGNN is evaluated on six social network data sets. Experimental results show that it yields promising results for imbalanced node classification.

Extreme learning machine (ELM) is suitable for nonlinear soft sensor development. Yet it faces an overfitting problem. To overcome it, this work integrates bound optimization theory with variational Bayesian (VB) inference to derive novel L1 norm-based ELMs. An L1 term is attached to the squared sum cost of prediction errors to formulate an objective function. Considering the nonconvexity and nonsmoothness of the objective function, this article uses bound optimization theory, and constructs a proper surrogate function to equivalently convert a challenging L1 norm-based optimization problem into easy one. Then, VB inference is adopted for optimizing the converted problem. Thus, an L1 norm-based ELM can be efficiently optimized by an alternating optimization algorithm with a proved convergence. Finally, a soft sensor is developed based on the proposed algorithm. An industrial case study is carried out to demonstrate that the proposed soft sensor is competitive against recent ones.