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.
Authors
Related Organizations
- Bibliographic Reference
- Kaveh Abdi, Benoit Celse, Kimberley B Mcauley. Parameter estimation and prediction uncertainties for multi‐response kinetic models with uncertain inputs. AIChE Journal, 2023, 69 (6), pp.e18058. ⟨10.1002/aic.18058⟩. ⟨hal-04179994⟩
- DOI
- https://doi.org/10.1002/aic.18058
- Funding
- EUROKIN; Natural Sciences and EngineeringResearch Council of Canada, Grant/AwardNumber: RGPIN-2020-03901
- HAL Collection
- IFP Energies Nouvelles
- HAL Identifier
- 4179994
- Institution
- ["Queen's University [Kingston, Canada]", 'IFP Energies nouvelles']
- Published in
- France
Table of Contents
- Parameter estimation and prediction uncertainties for multi-response kinetic models with uncertain inputs 0
- 1 INTRODUCTION 0
- 2 BACKGROUND 0
- 2.1 Using pseudo-replicate experiments to estimate parameters and obtain output measurement variances 0
- 2.2 Parameter uncertainty quantification using bootstrapping for a single-response model with a single uncertain input 0
- 2.3 Quantifying prediction uncertainties based on uncertainties in inputs and parameter estimates 0
- 3 PROPOSED METHODOLOGY 0
- 3.1 Bootstrap method for quantifying parameter uncertainties in multi-response EVM 0
- 3.2 Bootstrap method for quantifying prediction uncertainties from EVM 0
- 4 CASE STUDY: CATALYTIC N-HEXANE HYDROISOMERIZATION IN A WELL-MIXED REACTOR 0
- 4.1 Model equations and experimental system 0
- 4.2 EVM parameter and variance estimation 0
- 4.3 Parameter and prediction uncertainty quantification 0
- 4.4 Uncertainties in predicted yield and selectivities 0
- 5 CONCLUSIONS 0
- AUTHOR CONTRIBUTIONS 0
- ACKNOWLEDGMENTS 0
- DATA AVAILABILITY STATEMENT 0
- NOMENCLATURE 0
- REFERENCES 0
