Loading…
Optimal design of mixture experiments for general blending models
Mixture models of the Scheffé polynomial class are standard in several scientific fields. For these models there is a vast literature on the optimal design of experiments to provide good estimates of the parameters with the use of minimal resources. Contrarily, the optimal design of experiments for...
Saved in:
Published in: | Chemometrics and intelligent laboratory systems 2021-10, Vol.217, p.104400, Article 104400 |
---|---|
Main Authors: | , , , |
Format: | Article |
Language: | English |
Subjects: | |
Citations: | Items that this one cites Items that cite this one |
Online Access: | Get full text |
Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
Summary: | Mixture models of the Scheffé polynomial class are standard in several scientific fields. For these models there is a vast literature on the optimal design of experiments to provide good estimates of the parameters with the use of minimal resources. Contrarily, the optimal design of experiments for general blending models, extending the class of Becker, have not been systematically addressed. Nevertheless, there are practical examples where the models relating the response variables, the parameters and the factors including nonlinear blending effects fall into a general form. We propose a general formulation to find continuous and exact D– and A–optimal designs for general blending models. First, we consider designs to estimate the regression coefficients, and then extend the formulations to find locally optimal continuous designs for estimating both the coefficients and the power exponents. The treatment relies on converting the Optimal Experimental Design (OED) problem into an optimization problem of the Nonlinear Programming (or Mixed Integer Nonlinear Programming) class. We apply this approach to quadratic and special cubic general blending models of the H2 class of polynomials introduced by Becker, and to three examples of practical interest in combustion science and in the characterization of fuel properties.
•The paper considers the optimal design of experiments (ODoE) for general blending models represented by Becker's H2 class of polynomials.•We find continuous and exact optimal designs for two setups: (i) the parametrization of regression coefficients; and (ii) the parametrization of both the regression coefficients and power coefficients.•The classic D– and A–optimality criteria are used to measure the information content.•Nonlinear Programming and Mixed Integer Nonlinear Programming formulations are proposed to systematically solve the ODoE problems, requiring a global optimization solver. |
---|---|
ISSN: | 0169-7439 1873-3239 |
DOI: | 10.1016/j.chemolab.2021.104400 |