Efficient numerical methods for the optimisation of large kinetic reaction mechanisms

Optimisation of detailed combustion mechanisms means that the corresponding kinetic model is fitted to experimental data via optimising their important rate and thermodynamic parameters within their domain of uncertainty. Typically, several dozen parameters are fitted to several hundred to several thousand data points. Many numerical optimisation methods have been used, but the efficiency of these methods has not been compared systematically. In this work, parameters of an H2/O2/NO x mechanism (214 reaction steps of 35 species) were fitted to 1552 indirect (ignition delay times measured in shock tubes and concentrations measured in flow reactors) and 755 direct measurements. Three test cases were investigated: (1) fitting the Arrhenius parameters of 2 reaction steps to 732 data points; (2) fitting the Arrhenius parameters of 4 reaction steps to 1077 data points; (3) fitting the Arrhenius parameters of 10 reaction steps to 2307 data points. All 3 cases were investigated in 2 ways: fitting the A-parameters only and fitting all Arrhenius parameters (5, 11 and 29 parameters, respectively). A series of global (FOCTOPUS, genetic algorithm, simulated annealing, particle swarm optimisation, covariance matrix adaptation evolutionary strategy (CMA-ES)) and local (simplex, pattern search, interior-point, quasi-Newton, BOBYQA, NEWUOA) optimisation methods were tested on these cases, some of them in two variants. The methods were compared in terms of the final error function value and number of error function evaluations. The main conclusions are that the FOCTOPUS resulted in the lowest final error value in all cases, but this method required relatively many error function evaluations. As the task became more difficult, more and more methods failed. A variant of the BOBYQA method looked stable and efficient in all cases.