Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Shahmohammadi, Ali; McAuley, Kimberley B.

doi:10.1021/acs.iecr.8b03047

Cited by 25 publications

(32 citation statements)

References 83 publications

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“…When performing sequential MBDoE calculations, Z contains two parts 25,52 :

boldZ = ([], \begin{matrix} Z_{old} \\ Z_{new} \end{matrix})

where Z old corresponds to experimental settings and data from old experiments. The elements of Z old are fixed during sequential MBDoE and elements of Z new are determined by the optimizer.…”

Section: Background Informationmentioning

confidence: 99%

“…If modelers are interested in obtaining accurate parameter estimates for their model, A‐, D‐, or E‐optimal designs can be selected 15,16,18 . Alternatively, G‐ and V‐optimal designs focus on obtaining accurate model predictions at specified operating conditions of interest to the modeler 20,23‐25 . All of these MBDoE techniques in Table 1 require computation of the inverse of the Fisher information matrix ( FIM ) when selecting experimental settings 17,25,26 .…”

Section: Introductionmentioning

confidence: 99%

“…In this way, experiments can be designed using a well‐conditioned reduced FIM that ignores problematic parameters. Alternatively, pseudoinverse methods approximate the inverse of the FIM (e.g., using the Moore–Penrose pseudoinverse) during MBDoE calculations 25,42,52 . In Tikhonov regularization, a penalty is added to diagonal elements of the FIM to make it invertible 40,44‐46 .…”

Section: Introductionmentioning

confidence: 99%

“…In two previous articles, we considered pharmaceutical case studies involving noninvertible FIM s. Two different approaches were compared: (i) a subset‐selection‐based approach that leaves out problematic parameters (LO approach) and (ii) a simpler approach that uses a Moore–Penrose pseudoinverse in place of FIM −1 (PI approach) 25,52 . These case studies suggest that the LO approach is often superior to the PI approach for designing both A‐ and V‐optimal experiments 25,52 . A shortcoming of the LO approach is that it can be complicated and computationally expensive due to changes in the subset of parameters that is left out during MBDoE calculations.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

Shahmohammadi

McAuley

2020

AIChE Journal

Self Cite

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Sequential model-based design of experiments (MBDoE) uses information from previous experiments to select new experimental conditions. Computation of MBDoE objective functions can be impossible due to a noninvertible Fisher information matrix (FIM). Previously, we evaluated a leave-out (LO) approach that designed experiments by removing problematic model parameters from the design process. Unfortunately, the LO approach can be computationally expensive due to its iterative nature. In this study, we propose a simplified Bayesian approach that makes the FIM invertible by accounting for prior parameter information. We compare the proposed simplified Bayesian approach to the LO approach for sequential A-optimal design. Results from a pharmaceutical case study show that the proposed approach is superior, on average, for design of experiments. We suggest that simplified Bayesian MBDoE should be combined with a subset-selection-based approach for parameter estimation. This combined methodology gave the best results on average for the case study.

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“…When performing sequential MBDoE calculations, Z contains two parts 25,52 :

boldZ = ([], \begin{matrix} Z_{old} \\ Z_{new} \end{matrix})

where Z old corresponds to experimental settings and data from old experiments. The elements of Z old are fixed during sequential MBDoE and elements of Z new are determined by the optimizer.…”

Section: Background Informationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

Shahmohammadi

McAuley

2020

AIChE Journal

Self Cite

View full text Add to dashboard Cite

show abstract

“…Since the A criterion may not be accessible due to the FIM being non-invertible in some cases with a high degree of non-linearity in the model, the Q criterion may be one of the few available options for performing MBDoE. In contrast to other methods this criterion is easy to use, as it does not require a deeper mathematical understanding nor does it use approximations like pseudoinverses to calculate the A-criterion (Shahmohammadi and McAuley, 2019). However, more research with complex models is necessary to further validate this usage.…”

Section: Case Study: Enzymatic Synthesis Of Pentose-1p Using Thermostmentioning

confidence: 99%

Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design

Krausch

Barz

Sawatzki

et al. 2019

Front. Bioeng. Biotechnol.

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Especially in biomanufacturing, methods to design optimal experiments are a valuable technique to fully exploit the potential of the emerging technical possibilities that are driving experimental miniaturization and parallelization. The general objective is to reduce the experimental effort while maximizing the information content of an experiment, speeding up knowledge gain in R&D. The approach of model-based design of experiments (known as MBDoE) utilizes the information of an underlying mathematical model describing the system of interest. A common method to predict the accuracy of the parameter estimates uses the Fisher information matrix to approximate the 90% confidence intervals of the estimates. However, for highly non-linear models, this method might lead to wrong conclusions. In such cases, Monte Carlo sampling gives a more accurate insight into the parameter's estimate probability distribution and should be exploited to assess the reliability of the approximations made through the Fisher information matrix. We first introduce the model-based optimal experimental design for parameter estimation including parameter identification and validation by means of a simple non-linear Michaelis-Menten kinetic and show why Monte Carlo simulations give a more accurate depiction of the parameter uncertainty. Secondly, we propose a very robust and simple method to find optimal experimental designs using Monte Carlo simulations. Although computational expensive, the method is easy to implement and parallelize. This article focuses on practical examples of bioprocess engineering but is generally applicable in other fields.

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Model‐based design of experiments for polyether production from bio‐based 1,3‐propanediol

Shahmohammadi

McAuley

2021

AIChE Journal

Self Cite

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Sequential model-based design of experiments (MDBOE) accounts for information from previous experiments when selecting conditions for new experiments. In the current study, sequential MBDOE is used to select operating conditions for experiments in a batch-reactor that produces bio-based polytrimethylene ether glycol (PO3G). These Bayesian A-optimal experiments are designed to obtain improved estimates of 70 fundamental-model parameters, while accounting for industrial data from eight previous runs. Settings are selected for three decision variables: reactor temperature, initial catalyst level, and initial water concentration. If only one new experiment is conducted, it should be run at high temperature, with relatively high concentrations of catalyst and initial water. When two new runs are conducted, one should use an intermediate catalyst concentration. The effectiveness of the proposed MBDOE approach is tested using Monte-Carlo simulations, revealing that the selected experiments are superior compared to experiments selected randomly from corners of the permissible design space. K E Y W O R D S model-based design of experiments, parameter estimation, PO3G, polymerization model, sequential experimental design | INTRODUCTIONCerenol ® is tradename for a bio-based polytrimethylene ether glycol (PO3G) that has been commercialized by Dupont. [1][2][3] The monomer used for producing Cerenol ® is corn-based 1,3-propanediol derived from a glucose fermentation process (Bio-PDO ® ), 4 so that Cerenol ® is renewably-sourced. Cerenol ® offers a variety of value-added properties (e.g., excellent biodegradability, high reactivity, high oxidative stability) and has a wide range of applications in automotives, cosmetics, and polymer specialties. [1][2][3]5 Cerenol ® is produced in batch, semi-continuous, and continuous reactors using super-acid catalyst. Operating conditions such as catalyst concentration and temperature vary depending on the desired molecular weight and the end-use properties of the final products. 3,[6][7][8][9][10][11][12][13][14] The influences of operating conditions on product properties and production rates have been studied via several fundamental PO3G models. [15][16][17][18][19][20][21][22] Recently, we developed a series of PO3G models that account for: (a) the effects of super-acid catalyst on polycondensation reactions and side reactions in the liquid phase, (b) liquid hold-up in the condenser system, (c) the inhibitory influence of water on polycondensation kinetics, (d) the generation, consumption, and evaporation of cyclic oligomers, and (e) the effects of temperature on polycondensation kinetics and on mass-transfer rates of volatile species. [20][21][22] Our most-recent PO3G model contains a total of 49 ordinary differential equations (ODEs) and 70 kinetic, transport and thermodynamic parameters. 22 A comprehensive industrial dataset obtained from 8 batch-reactor runs, 3 which were conducted at temperatures ranging from 160 to 180 C and using super-acid catalyst levels from 0.1 to 0.25 wt%, w...

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Sequential Model-Based A-Optimal Design of Experiments When the Fisher Information Matrix Is Noninvertible

Cited by 25 publications

References 83 publications

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

Using prior parameter knowledge in model‐based design of experiments for pharmaceutical production

Monte Carlo Simulations for the Analysis of Non-linear Parameter Confidence Intervals in Optimal Experimental Design

Model‐based design of experiments for polyether production from bio‐based 1,3‐propanediol

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