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\begin{document}

\title{Parameter estimation and prediction uncertainties for multi-response
kinetic models with uncertain inputs}



\author[1]{Kaveh Abdi}%
\author[2]{Benoit Celse}%
\author[3]{Kimberley McAuley}%
\affil[1]{Queen's University Faculty of Engineering and Applied Science}%
\affil[2]{IFP Energies nouvelles}%
\affil[3]{Queen's University}%


\vspace{-1em}



  
  \date{June 17, 2024}


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\begin{abstract}
Error-in-variables model (EVM) methods are used for parameter estimation
when independent variables are uncertain. During EVM parameter
estimation, output measurement variances are required as weighting
factors in the objective function. These variances can be estimated
based on data from replicate experiments. However, conducting replicates
is complicated when independent variables are uncertain. Instead,
pseudo-replicate runs may be performed where the target values of inputs
for repeated runs are the same, but the true input values may be
different. Here, we propose a method to estimate output-measurement
variances for use in multivariate EVM estimation problems, based on
pseudo-replicate data. We also propose a bootstrap technique for
quantifying uncertainties in resulting parameter estimates and model
predictions. The methods are illustrated using a case study involving
n-hexane hydroisomerization in a well-mixed reactor. Case-study results
reveal that assumptions about input uncertainties can have important
influences on parameter estimates, model predictions and their
confidence intervals.%
\end{abstract}%



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