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Soft sensor for nonuniform sampling nonlinear dynamic process using irregular-time-interval latent probabilistic predictability embedding supervised deep network.

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Title: Soft sensor for nonuniform sampling nonlinear dynamic process using irregular-time-interval latent probabilistic predictability embedding supervised deep network.
Authors: Zhang, Zhengxuan1 (AUTHOR) d202110351@xs.ustb.edu.cn, Yang, Xu1,2 (AUTHOR) yangxu@ustb.edu.cn, Shardt, Yuri A.W.3 (AUTHOR) yuri.shardt@tu-ilmenau.de, Gao, Jingjing1,2 (AUTHOR) jingjing.gao@ustb.edu.cn, Cui, Jiarui1,2 (AUTHOR) cuijiarui@ustb.edu.cn
Source: ISA Transactions. Jul2026, Vol. 174, p242-258. 17p.
Subjects: Irregular sampling (Signal processing), Recurrent neural networks, Deep learning, Latent variables, Artificial neural networks, Industrial applications, Prediction models
Abstract: Dynamic latent variable (DLV) models have been widely applied in industrial soft sensing due to their ability to extract features and capture dynamic behavior. However, conventional DLV models are limited to linear feature extraction and perform poorly with nonuniformly sampled data. Thus, this paper proposes a soft sensor for a nonuniform sampling nonlinear dynamic process using irregular-time-interval latent probabilistic predictability embedding supervised deep network (ILPPSDN). First, a prediction regularization term is added to the decoding loss of the target-related autoencoder to model latent temporal dependencies and enhance feature predictability. Furthermore, the internal state derivative in the proposed irregular-time-interval variational recurrent neural network is parameterized by an ordinary differential equation network, integrating hidden-state evolution with state updates. In addition, all network components are jointly optimized through unified training. Then, an ILPPSDN-based soft sensor is developed for nonuniformly sampled nonlinear dynamic processes via pre-training and supervised fine-tuning. Finally, the results indicate that the proposed ILPPSDN can reduce the root mean square error by at least 26.1 %, 21.1 %, and 26.1 % at the uneven sampling ratios of 1/2, 2/3, and 3/4 in the debutanizer column. Correspondingly, in the sulfur recovery unit, these values are 21.1 %, 26.1 %, and 26.1 %. Additionally, in the ablation studies, the proposed method reduced the root mean square error by at least 5 % and 6 % in the two industrial cases, respectively. • An ILPPSDN-based soft sensor is established for nonuniform sampled nonlinear dynamic processes. • Irregular-time-interval variational recurrent neural network is designed to model latent probabilistic dynamics with complex distributions. • All optimizers are combined to jointly train network parameters to avoid getting stuck in local minima. • ILPPSDN is improved by up to 26.1 % and 21.2 % in two application examples, respectively, compared with the baseline ODE-RSSM. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Dynamic latent variable (DLV) models have been widely applied in industrial soft sensing due to their ability to extract features and capture dynamic behavior. However, conventional DLV models are limited to linear feature extraction and perform poorly with nonuniformly sampled data. Thus, this paper proposes a soft sensor for a nonuniform sampling nonlinear dynamic process using irregular-time-interval latent probabilistic predictability embedding supervised deep network (ILPPSDN). First, a prediction regularization term is added to the decoding loss of the target-related autoencoder to model latent temporal dependencies and enhance feature predictability. Furthermore, the internal state derivative in the proposed irregular-time-interval variational recurrent neural network is parameterized by an ordinary differential equation network, integrating hidden-state evolution with state updates. In addition, all network components are jointly optimized through unified training. Then, an ILPPSDN-based soft sensor is developed for nonuniformly sampled nonlinear dynamic processes via pre-training and supervised fine-tuning. Finally, the results indicate that the proposed ILPPSDN can reduce the root mean square error by at least 26.1 %, 21.1 %, and 26.1 % at the uneven sampling ratios of 1/2, 2/3, and 3/4 in the debutanizer column. Correspondingly, in the sulfur recovery unit, these values are 21.1 %, 26.1 %, and 26.1 %. Additionally, in the ablation studies, the proposed method reduced the root mean square error by at least 5 % and 6 % in the two industrial cases, respectively. • An ILPPSDN-based soft sensor is established for nonuniform sampled nonlinear dynamic processes. • Irregular-time-interval variational recurrent neural network is designed to model latent probabilistic dynamics with complex distributions. • All optimizers are combined to jointly train network parameters to avoid getting stuck in local minima. • ILPPSDN is improved by up to 26.1 % and 21.2 % in two application examples, respectively, compared with the baseline ODE-RSSM. [ABSTRACT FROM AUTHOR]
ISSN:00190578
DOI:10.1016/j.isatra.2025.11.001