Parameter estimation and prediction uncertainties for multi-response kinetic models with uncertain inputs

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.

Automated summary

Error-in-variables model (EVM) methods are used to estimate parameters when independent variables are uncertain. This study proposes a method to estimate output measurement variances based on pseudo-replicate data for multivariate EVM estimation problems. Additionally, a bootstrap technique is proposed to quantify uncertainties in resulting parameter estimates and model predictions. A case study on n-hexane hydroisomerization is presented to illustrate the methods, showing the influence of input uncertainties on parameter estimates, model predictions, and confidence intervals.