Vol.:(0123456789) Optimization and Engineering https://doi.org/10.1007/s11081-018-9415-4 1 3 RESEARCH ARTICLE Optimal designs of experiments for non‑isothermal kinetic rates: analysis of diferent strategies Belmiro P. M. Duarte 1,2  · Anthony C. Atkinson 3 Received: 26 July 2017 / Revised: 1 May 2018 / Accepted: 8 November 2018 © Springer Science+Business Media, LLC, part of Springer Nature 2018 Abstract We consider the dependence on the measurement schedule of optimal experiments for kinetic parameters when the rates are temperature-dependent and follow the Arrhenius law. We compare three diferent approaches using the D-optimality cri- terion: (1) a locally optimal design based on a sequence of four batches where the process is observed at a single time; (2) two batches carried out at constant tem- perature where the process is observed at a pre-defned grid of times; and (3) a sin- gle batch where the temperature profle is optimal regarding the amount of infor- mation extracted and the process is observed at a pre-defned grid of times. An extension of the generalized equivalence theorem of optimal experimental design provides insight into the structure of the designs we fnd. The local D-optimality of the designs obtained is validated using the extended theorem for the latter two approaches. Keywords Dynamic experiments · Optimal design of experiments · Kinetic rates · Non-isothermal kinetics 1 Motivation The efcient design of experiments for the estimation of kinetic parameters is essential if resources are not to be wasted. Bauer et al. (2000) give an exam- ple of an inefcient conventional design. Here we use the methods of optimal * Belmiro P. M. Duarte bduarte@isec.pt Anthony C. Atkinson a.c.atkinson@lse.ac.uk 1 Department of Chemical and Biological Engineering, ISEC, Polytechnic Institute of Coimbra, Coimbra, Portugal 2 CIEPQPF, Department of Chemical Engineering, University of Coimbra, Rua Sílvio Lima, Polo II, 3030–790 Coimbra, Portugal 3 Department of Statistics, London School of Economics, London WC2A 2AE, UK