Combining just‐in‐time modelling and batch‐wise unfolded PLS model for the derivative‐free batch‐to‐batch optimization

Jia, Runda; Mao, Zhizhong; Wang, Fuli

doi:10.1002/cjce.23050

Cited by 6 publications

(5 citation statements)

References 35 publications

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“…The dynamic model of the cobalt oxalate synthesis can be expressed by the ordinary differential equation as follows [ 1 ] :

\begin{array}{l} \frac{dV}{dt} goodbreak= F_{B} \\ \frac{d μ_{0}}{dt} goodbreak= B goodbreak- \frac{F_{B} μ_{0}}{V} \\ \frac{d μ_{r}}{dt} goodbreak= italicrG μ_{r - 1} goodbreak- \frac{F_{B} μ_{r}}{V} r goodbreak= 1, 2 \\ \frac{dC}{dt} goodbreak= \frac{F_{B} C_{B} V_{A 0}}{{((), V_{A 0} goodbreak+ F_{B} t)}^{2}} goodbreak- 3 ρ_{p} k_{v} G μ_{2} goodbreak- \frac{F_{B} C}{V} \end{array}

where

F_{B}

represents ammonium oxalate feed rate,

V

is the volume of the suspension,

u_{0}

is the crystal size of cobalt oxalate at the initial moment,

B

is the crystallization nucleation rate,

u_{r}

is the crystal size of cobalt oxalate at time r ,

G

is the growth rate,

C

is the concentration of the solution,

V_{A 0}

is the initial volume of cobalt chloride,

k_{v}

represents shape factor,

ρ_{p}

is the crystal density.

B

and

G

can be obtained from the following empirical formulas [ 33 ] :…”

Section: Simulation Research and Results Analysismentioning

confidence: 99%

“…The dynamic model of the cobalt oxalate synthesis can be expressed by the ordinary differential equation as follows [1] :…”

Section: Description Of the Cobalt Oxalate Synthesis Processmentioning

confidence: 99%

“…Batch production processes have a high degree of flexibility compared to continuous production processes. [ 1 ] Recently, the modern process industry is more inclined to perform batch processes for high value‐added products. [ 2–5 ] Accurate prediction of product quality for batch production is of great significance.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Multi‐source domains transfer learning strategy based on similarity measurement for batch process quality prediction

et al. 2022

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Generally, when multiple source processes are available for transfer modelling, an inappropriate transfer learning strategy may lead to the deterioration of model accuracy and even cause negative transfer. For this issue, a multi-source domains transfer learning strategy based on similarity measurement is proposed in this work for selecting the optimal transfer modelling strategy according to different scenarios. By counting the data amount and judging the similarity between each source domain and the target domain, the rich information contained in multiple source processes is well utilized to assist the modelling process in the target domain. The proposed strategy provides three alternative specific transfer mechanisms by setting the judgement conditions so that the possibility of negative transfer can get reduced and the accuracy of prediction can be guaranteed. To ensure the reliability of the transfer model and adapt to the change in conditions, the updating scheme based on online data is adopted. Finally, the mixed-effects Gaussian processes modelling method is taken as an example to verify the effectiveness of the proposed multi-source transfer learning strategy through the simulation experiment of the cobalt oxalate synthesis process.

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“…The dynamic model of the cobalt oxalate synthesis can be expressed by the ordinary differential equation as follows [ 1 ] :

\begin{array}{l} \frac{dV}{dt} goodbreak= F_{B} \\ \frac{d μ_{0}}{dt} goodbreak= B goodbreak- \frac{F_{B} μ_{0}}{V} \\ \frac{d μ_{r}}{dt} goodbreak= italicrG μ_{r - 1} goodbreak- \frac{F_{B} μ_{r}}{V} r goodbreak= 1, 2 \\ \frac{dC}{dt} goodbreak= \frac{F_{B} C_{B} V_{A 0}}{{((), V_{A 0} goodbreak+ F_{B} t)}^{2}} goodbreak- 3 ρ_{p} k_{v} G μ_{2} goodbreak- \frac{F_{B} C}{V} \end{array}

where

F_{B}

represents ammonium oxalate feed rate,

V

is the volume of the suspension,

u_{0}

is the crystal size of cobalt oxalate at the initial moment,

B

is the crystallization nucleation rate,

u_{r}

is the crystal size of cobalt oxalate at time r ,

G

is the growth rate,

C

is the concentration of the solution,

V_{A 0}

is the initial volume of cobalt chloride,

k_{v}

represents shape factor,

ρ_{p}

is the crystal density.

B

and

G

can be obtained from the following empirical formulas [ 33 ] :…”

Section: Simulation Research and Results Analysismentioning

confidence: 99%

“…The dynamic model of the cobalt oxalate synthesis can be expressed by the ordinary differential equation as follows [1] :…”

Section: Description Of the Cobalt Oxalate Synthesis Processmentioning

confidence: 99%

See 1 more Smart Citation

Multi‐source domains transfer learning strategy based on similarity measurement for batch process quality prediction

et al. 2022

Self Cite

View full text Add to dashboard Cite

show abstract

“…The operation state of batch process will change with the process parameters' drift and environmental disturbances, which results in the deviation of manipulated variables from the optimal working point. [ 1 ] Thus, it is quite significant to grasp the process operation state timely and accurately for improving the production efficiency and economic benefits of the enterprise and facilitating the production adjustment. [ 2 ] However, it will be impractical for a new process to build a data‐driven process model because of limited running time, which brings about the insufficient accumulated data.…”

Section: Introductionmentioning

confidence: 99%

Integrated operation optimization strategy for batch process based on process transfer model under disturbance

Chu

Wang

et al. 2022

Can J Chem Eng

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An integrated operation optimization strategy based on the process transfer model (PTM) is proposed in this work, which combines the batch-to-batch optimization method and the within-batch optimization method. The datadriven tool with the joint-Y partial least squares (JYPLS) model is utilized to transfer rich information from a similar old process to the new process to assist the establishment of the model of the new process. However, differences invariably exist between similar batch processes, which can bring about a fateful necessary condition of optimality (NCO) mismatch. Although the traditional batch-to-batch optimization method can overcome the problem of plantmodel mismatch between batches, it is helpless to deal with the problem of mismatch and disturbance during a single batch operation. For the sake of settlement of problems, the within-batch optimization method is introduced. The main advantages of the integrated operation optimization strategy are (i) the plant-model mismatch and disturbances within the batch or during batches can be solved, (ii) the suboptimal results of batch-to-batch optimization can be further compensated, and (iii) the optimization performance is better by discretizing the control profile into several intervals. Taking the cobalt oxalate synthesis process as a simulation study, the superior performance of the proposed strategy is illustrated.

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“…The traditional PLS is a linear modeling technique that has limited representation if process variables are relative in a strongly nonlinear way. There are several nonlinear PLS methods, such as Kernel Partial Least Squares (KPLS) [26], Quadratic Partial Least Squares (QPLS) [27] and Neural Network Partial Least Squares (NNPLS) [28]. These nonlinear PLS approaches more and less suffer from the high computational complexity.…”

Section: Introductionmentioning

confidence: 99%

Narrow Operating Space Based on the Inversion of Latent Structures Model for Glycosylation Process

et al. 2020

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N-linked glycan distribution plays a significant role in the generation of therapeutic proteins. It is challenging to determine the operating conditions when developing a new biopharmaceutical product with the desired glycan distributions. The glycosylation is a high complex nonlinear system, and it is difficult to develop a reliable first-principle model that heavily relies on experimentation. Our goal is to develop a nonlinear data-driven model and find an appropriate operating space included kinds of input combination from process variables based on this model to ensure the desired product quality. A methodology is proposed based on the inversion of a nonlinear latent-variable model (locality preserving projection to latent structures, LPPLS) to identify a subspace of the knowledge space. The normal operating points of the input variables are designed based on the LPPLS inversion, and the range of operating conditions are expanded around the normal operation points through the prediction uncertainty analysis of forward and inversion model simultaneously. Finally, the designated operation space from LPPLS inversion is applied in an benchmark glycosylation model.

show abstract

Combining just‐in‐time modelling and batch‐wise unfolded PLS model for the derivative‐free batch‐to‐batch optimization

Cited by 6 publications

References 35 publications

Multi‐source domains transfer learning strategy based on similarity measurement for batch process quality prediction

Multi‐source domains transfer learning strategy based on similarity measurement for batch process quality prediction

Integrated operation optimization strategy for batch process based on process transfer model under disturbance

Narrow Operating Space Based on the Inversion of Latent Structures Model for Glycosylation Process

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