Simultaneous State and Parameter Estimation Using Maximum Relative Entropy with Nonhomogenous Differential Equation Constraints

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For historic reasons, industrial knowledge of reproducibility and restrictions imposed by regulations, open-loop feeding control approaches dominate in industrial fed-batch cultivation processes. In this study, a generic gray box biomass modeling procedure uses relative entropy as a key to approach the posterior similarly to how prior distribution approaches the posterior distribution by the multivariate path of Lagrange multipliers, for which a description of a nuisance time is introduced. The ultimate purpose of this study was to develop a numerical semi-global convex optimization procedure that is dedicated to the calculation of feeding rate time profiles during the fed-batch cultivation processes. The proposed numerical semi-global convex optimization of relative entropy is neither restricted to the gray box model nor to the bioengineering application. From the bioengineering application perspective, the proposed bioprocess design technique has benefits for both the regular feed-forward control and the advanced adaptive control systems, in which the model for biomass growth prediction is compulsory. After identification of the gray box model parameters, the options and alternatives in controllable industrial biotechnological processes are described. The main aim of this work is to achieve high reproducibility, controllability, and desired process performance. Glucose concentration measurements, which were used for the development of the model, become unnecessary for the development of the desired microbial cultivation process.

where the index

is equal to 1 for the first-stage model and equal to 2 for the second-stage model, and

is the time when the cumulative glucose consumption

for the k -th oscillation cycle has been calculated.…”

Section: Identification Of Biomass Growth Modelmentioning

confidence: 99%

From Physics to Bioengineering: Microbial Cultivation Process Design and Feeding Rate Control Based on Relative Entropy Using Nuisance Time

Urniezius

Galvanauskas

Survyla

et al. 2018

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“…Convex optimization uses the maximization of entropy as an indicator of local extremum detections [38]. Equation (18) helps with identification of stoichiometry parameters and Equation (25) does the same for the product model fitting: Model fitting uses Equation (24) for a prediction value 〈P 〉 and observed product concentrations P inside convex optimization.…”

Section: Identification Of E Coli Parameters By Convex Optimizationmentioning

confidence: 99%

“…Figure 2 depicts the workflow of the optimization procedure. Convex optimization uses the maximization of entropy as an indicator of local extremum detections [38]. Equation (18) helps with identification of stoichiometry parameters and Equation (25) does the same for the product model fitting:…”

Section: Identification Of E Coli Parameters By Convex Optimizationmentioning

confidence: 99%

Identification of Functional Bioprocess Model for Recombinant E. Coli Cultivation Process

Urniezius

Survyla

2019

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The purpose of this study is to introduce an improved Luedeking–Piret model that represents a structurally simple biomass concentration approach. The developed routine provides acceptable accuracy when fitting experimental data that incorporate the target protein concentration of Escherichia coli culture BL21 (DE3) pET28a in fed-batch processes. This paper presents system identification, biomass, and product parameter fitting routines, starting from their roots of origin to the entropy-related development, characterized by robustness and simplicity. A single tuning coefficient allows for the selection of an optimization criterion that serves equally well for higher and lower biomass concentrations. The idea of the paper is to demonstrate that the use of fundamental knowledge can make the general model more common for technological use compared to a sophisticated artificial neural network. Experimental validation of the proposed model involved data analysis of six cultivation experiments compared to 19 experiments used for model fitting and parameter estimation.

“…Machine learning has a wide spectrum of applications in different science disciplines [1][2][3][4][5][6][7][8][9]. Advanced computational methods, including artificial neural networks (ANN), process input data in the context of previous training history on a defined sample database to produce relevant output [7].…”

Section: Introductionmentioning

confidence: 99%

Entropy Ensemble Filter: A Modified Bootstrap Aggregating (Bagging) Procedure to Improve Efficiency in Ensemble Model Simulation

Foroozand

Weijs

2017

Over the past two decades, the Bootstrap AGGregatING (bagging) method has been widely used for improving simulation. The computational cost of this method scales with the size of the ensemble, but excessively reducing the ensemble size comes at the cost of reduced predictive performance. The novel procedure proposed in this study is the Entropy Ensemble Filter (EEF), which uses the most informative training data sets in the ensemble rather than all ensemble members created by the bagging method. The results of this study indicate efficiency of the proposed method in application to synthetic data simulation on a sinusoidal signal, a sawtooth signal, and a composite signal. The EEF method can reduce the computational time of simulation by around 50% on average while maintaining predictive performance at the same level of the conventional method, where all of the ensemble models are used for simulation. The analysis of the error gradient (root mean square error of ensemble averages) shows that using the 40% most informative ensemble members of the set initially defined by the user appears to be most effective.