Bayesian method for state estimation of batch process with missing data

Zhao, Zhonggai; Huang, Biao; Liu, Fei

doi:10.1016/j.compchemeng.2013.01.011

Cited by 16 publications

(6 citation statements)

References 19 publications

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“…It shows that the states at the same sampling instant of all batches are dynamically related due to the dynamics along the batch dimension, and the dynamics within a single batch will make states related to the previous states. Considering that each initial state is dependent on both the initial state and the terminal state of the previous batch, Zhao et al has considered a two-dimensional state-space model for the initial state as where both the state x i , k and the measurement y i , k are double indexed by the batch number i and the sampling instant k . x i , k denotes the state at the k th sampling instant in the i th batch.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…Therefore, the two-dimensional dynamics should be considered in the design of monitoring, control, and state estimation. Two-dimensional latent variable models have been developed to improve monitoring performance, , and the feature of two-dimensional dynamics has also been used to design the two-dimensional generalized predictive controller for batch processes. , In the aspect of state estimation, taking into account that each initial state is transited from the terminal state of the previous batch, Zhao et al developed a two-dimensional state-space model for initial states and then estimated states and parameters based on Bayesian methods. , However, in this method, only the initial state is characterized by two-dimensional dynamics. The other states are estimated only along the time dimension, and the two-dimensional dynamics of other states is ignored.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

State Estimation in Batch Process Based on Two-Dimensional State-Space Model

Zhao

Huang

Liu

2014

Ind. Eng. Chem. Res.

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Most existing methods for the state estimation in batch processes are similar to those for continuous processes, and these methods usually only consider the state dynamics within a single batch and ignore the dynamics across batches. In this paper, the state estimation in batch processes is investigated based on a two-dimensional state-space model by employing the Bayesian recursive algorithm. In addition to the dynamics along the time dimension (the dynamics within a single batch), the batch process is also characterized by the dynamics along the batch dimension (batch-to-batch dynamics). In the proposed method, both the batch-to-batch dynamics and the dynamics within a single batch are taken into account. The current state is dependent on the previous states both along the time dimension and along the batch dimension, so the filtering and smoothing for previous batches should be performed before doing current state estimation. In this way, the information on measurements from the previous batches as well as from the current batch can be incorporated into the estimation. The proposed method is illustrated and evaluated through a simple numerical example as well as a simulated two-state batch reaction process.

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Section: Problem Descriptionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

State Estimation in Batch Process Based on Two-Dimensional State-Space Model

Zhao

Huang

Liu

2014

Ind. Eng. Chem. Res.

Self Cite

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“…The Bayesian method for state estimation is also used to treat missing data. 10 Kalman filtering and the data fusion technique are taken to solve the problem of irregular measurements. 11 For the primary variables, missing data are caused by a testing delay in laboratory or uneasy measurement.…”

Section: Introductionmentioning

confidence: 99%

“…Schafer and Graham propose two general approaches to handle missing data based on maximum-likelihood and Bayesian multiple imputations. The Bayesian method for state estimation is also used to treat missing data . Kalman filtering and the data fusion technique are taken to solve the problem of irregular measurements .…”

Section: Introductionmentioning

confidence: 99%

A Framework and Modeling Method of Data-Driven Soft Sensors Based on Semisupervised Gaussian Regression

Wan

Guo

Tian

et al. 2016

Ind. Eng. Chem. Res.

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Soft sensors have been widely used in industrial processes to predict uneasily measured important process variables. The core of data-driven soft sensors is to construct a soft sensor model by using recorded process data. This paper analyzes the geometry and characteristics of soft sensor modeling data and explains that soft sensor modeling is essentially semisupervised regression rather than widely used supervised regression. A framework of data-driven soft sensor modeling based on semisupervised regression is introduced so that information on all recorded data, including both labeled data and unlabeled data, is involved in the soft sensor modeling. A soft sensor modeling method based on a semisupervised Gaussian process regression is then proposed and applied to the estimation of total Kjeldahl nitrogen in a wastewater treatment process. Experimental results show that the proposed method is a promising method for soft sensor modeling.

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“…A state‐space model includes not only the unknown parameters, but also the unmeasurable system states [41]. The Kalman filter technique provides an optimal state estimation for state‐space systems with stochastic noise, but this technique assumes that the model parameters are known in advance, which is usually not the case in practice [42, 43]. To overcome this difficulty, Ding et al [44] presented a Kalman state filtering‐based least squares iterative parameter estimation algorithm for observer canonical state‐space systems using decomposition.…”

Section: Introductionmentioning

confidence: 99%