Use of sensitivity analysis methods in the modelling of electrochemical transients - Part 3. Statistical error uncertainty propagation in simulation and in nonlinear least-squares parameter estimation

Sensitivity information obtained by means of a local direct method can be useful in performing various tasks associated with the analysis of the statistical error propagation in the solution of forward and inverse problems in the modelling of electrochemical transients. First- and second-order sensitivity coefficients of the transient curves with respect to model parameters play a crucial role in the formalism presented, which links errors of known parameters, errors of parameters estimated by single or multiresponse nonlinear least-squares fitting of the entire transient curves or their features, and errors of the transient curves. Uncertainty analysis of the simulated transient curves, so far unpractised in electrochemical kinetics, can be performed. Error analysis of parameters estimated using direct search (e.g, simplex) or other types of least-squares minimisation, pointwise analysis of the variances of estimated parameters, least-squares gradient-based minimisation, or identification of deterministic correlations between parameters, can be performed easily, and/or more efficiently or reliably compared with formerly used techniques. Some of these features are demonstrated by making a detailed error/uncertainty analysis of linear potential scan and cyclic voltammetric transients for a quasi-reversible charge-transfer reaction, assuming one known but uncertain parameter (charge-transfer coefficient), and two unknown parameters (heterogeneous electron transfer rate constant and formal potential). (C) 1998 Elsevier Science S.A. All rights reserved.