Performance comparison of parameter estimation techniques for unidentifiable models

• Published in: Computers & chemical engineering Vol. 64; pp. 24 - 40
• Main Authors: Graciano, J.E., Mendoza, D.F., Le Roux, G.A.C.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 07-05-2014; Elsevier
• Subjects: Adaptative systems; Applied sciences; Biased estimators; Chemical kinetics; Chemistry; Computer science; control theory; systems; Control theory. Systems; Electrochemistry; Exact sciences and technology; General and physical chemistry; Identifiability; Kinetics and mechanism of reactions; Modelling and identification; Parameter estimation; Parameter estimation; Identifiability; Biased estimators; Chemical kinetics; Sensitivity analysis; Differential geometry; Automatic selection; Modeling; Rotational analysis; Uncertain system; Discrimination; Chemical reaction; Observer; A priori estimation; Eigenvalue problem; System identification; Automatic analysis; Non linear effect; Biased estimation
• ISSN: 0098-1354; 1873-4375
• DOI: 10.1016/j.compchemeng.2014.01.009

•Practical unidentifiability (PU) is evidenced by near singular parameter estimation.•Biased and unbiased parameter estimation algorithms are compared in a PU framework.•Biased algorithms decreases model overfit compared to unbiased method.•Rotational discrimination shows the best performance among the methods assessed.•A validation data set must be used to evaluate the quality of the estimation.
Four different estimation approaches exploiting sensitivities, eigenvalue analysis (rotational discrimination and automatic parameter selection and estimation), reparameterization via differential geometry and the classical nonlinear least squares are assessed in terms of predictivity, robustness and speed. A Monte Carlo methodology is adopted to evaluate the statistical information required to quantify the inherent uncertainty of each approach. The results show that the rotational discrimination method presents the best characteristics among the evaluated methods, since it requires less a priori information than the reparameterization via differential geometry, uses simpler stop criteria than the automatic selection, reduces the overfitting caused by the nonlinear least squares solution and because it estimates parameters with the best predictivity among the methods tested. Additionally, results suggest that assessing the goodness of the estimated parameters solely in the calibration set can be misleading, and that the statistical information obtained from a validation set is more valuable.