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Generation of optimal correlations by simulated annealing for ill-conditioned least-squares solution

A typical process of determining parameters of empirical correlation is collecting measurements of experiments and applying least-squares method with over-determined number of variable data. Least-squares problems occur frequently in the parameter identification of linear/nonlinear dynamic models, model fitting using dimensionless variables in flow interfacial treatment, heat transfer and pressure drop models, etc. Considering the inevitable measurement noise and careless experimental design, the ill-posedness property of the least-squares method can arise and limit the accuracy of the assumed correlation structures. In this paper, a method of simulated annealing is proposed for estimating power-law parameters of the empirical correlation of experimental data. The method is applied to the determination of the hydrogen removal correlation being used in reactor containment analysis. The analysis results show the remarkable improvement in accuracy and robustness for the noisy measurement data.