Multirate Dynamic Process Monitoring Based on Multirate Linear Gaussian State-Space Model

This paper proposes a novel dynamic latent structure with time-varying parameters for virtual sensing of industrial process with irregular missing data. The proposed latent structure is based on the linear dynamic system (LDS) model. In order to capture the time-varying process characteristics, a Karman filter based parameter updating method is developed and a virtual sensor is constructed to predict hard-tomeasure quality variables. The latent variable structure of the improved model enables the virtual sensor to capture the variable cross-correlation and autocorrelation in the missing data by considering both spatial and temporal information, so that the information in the missing data can be learned from those not missing in the samples as well as the Markov process in the temporal stream. Incorporation of both spatial and temporal information renders more flexibility, resulting in a virtual sensor with higher prediction accuracy even with irregular missing data. The better performance of the proposed method is verified by two industrial applications with different ratios of irregular missing data.INDEX TERMS Data-driven process monitoring, Virtual sensors, Irregularly missing data, Linear dynamic systems (LDS), Linear time-varying parameters, Kalman filtering, EM algorithm.

“…The EM algorithm is an efficient optimization strategy for latent variable estimation and parameter learning, which operates E-step and M-step iteratively [33].…”

Section: B Model Parameter Solution Using Emmentioning

confidence: 99%

“…The LDS can be modified to accommodate missing values as well as multi-sampling rate data using Kalman filtering [31,32]. In addition, Cong et al [33] proposed a dynamic multi-sampling rate linear Gaussian state space model to handle data samples with three sampling rates, whose parameters are estimated using the EM algorithm. Also, Ref.…”

Section: Introductionmentioning

confidence: 99%

A Dynamic Latent Structure With Time-Varying Parameters for Virtual Sensing of Industrial Process With Irregular Missing Data

Ying

Wang

et al. 2021

“…This experiment assessed recoverability of various Symmetric NMF algorithms when the parts of a symmetric structural data matrix were unobserved. Such phenomena frequently occurred in similarity matrices if partial instances were unavailable [34], [35]. Continuous blocks without values may cause problems in further computation.…”

Section: A Reconstruction Errormentioning

confidence: 99%

Symmetric Nonnegative Matrix Factorization Based on Box-Constrained Half-Quadratic Optimization

Chen

2020

Nonnegative Matrix Factorization (NMF) based on half-quadratic (HQ) functions was proven effective and robust when dealing with data contaminated by continuous occlusion according to the half-quadratic optimization theory. Nonetheless, state-of-the-art HQ NMF still cannot handle symmetric data matrices, and this caused problems when applications require processing symmetric matrices, e.g., similarity matrices. In view of such, this study presents HQ Symmetric NMF along with HQ optimization algorithms that can solve symmetric matrix decomposition and avoid oscillations during alternating updates. Moreover, variants of HQ Symmetric NMF are proposed and examined in this study -The direct method and the asymmetry penalty constrained method. Both show their distinct advantages. Experiments on open datasets were conducted for comparison with other methods. Experimental results showed that the proposed HQ Symmetric NMF was more robust against continuous occlusion than the baselines. Both root-mean-squared errors and coefficients of determination were better than those of the baselines, thereby demonstrating effectiveness of the proposed method.INDEX TERMS Half-quadratic optimization, symmetric nonnegative matrix factorization, similarity matrix.

“…But these models based on dualrate system cannot be extended to three or more sampling rate systems. Furthermore, as a dynamic extension of the MRFA model, Cong et al [32] proposed a multi-rate linear Gaussian state space model (MLGSS) for dynamic process monitoring. Although MLGSS can effectively extract dynamic latent variables in the multi-rate process, the model does not consider any output information.…”

Section: Introductionmentioning

confidence: 99%

A Multi-Rate Probabilistic Slow Feature Regression Model for Dynamic Feature Learning and Industrial Soft Sensor Development

Zhang

Zhang²,

Zhou

2022

Self Cite

In practical process industries, the measurements coming from different sources are collected at different sampling rates, thereby soft sensors developed using uniformly sampled measurements may result in poor prediction performance. Besides, industrial processes are inherently stochastic and most of them present dynamic characteristic. To cope with these issues, a multi-rate probabilistic slow feature regression (MR-PSFR) model is proposed in this paper for dynamic feature learning and soft sensor development in industrial processes. In the MR-PSFR, both input and output observation datasets with different sampling rates are used to extract the slow features, which can separate slowly and fast changing features and have a better interpretation of the outputs. Then, the expectation-maximization algorithm is modified to derive the model parameters of MR-PSFR and the quality prediction strategy for multi-rate processes is constructed. Finally, the proposed method is investigated through a numerical example and a real industrial process. The simulation results show that the extracted slow features better represent the intrinsic characteristics of the processes and the proposed model has better prediction performance for multi-rate dynamic processes than other methods.INDEX TERMS Soft sensor, feature learning, multi-rate probabilistic slow feature regression, expectationmaximization algorithm; multi-rate dynamic process.