Nonlinear ill-posed problem analysis in model-based parameter estimation and experimental design

• We discuss nonlinear ill-posed problems in parameter estimation and experiment design.
• Identifiability is analyzed by the singular value spectrum of the sensitivity matrix.
• Three different regularization techniques are applied to exemplary problems.
• We show how regularization and experiment design optimization improve the spectrum.
• We link common alphabetic experiment design criteria to the singular values.

Discrete ill-posed problems are often encountered in engineering applications. Still, their sound analysis is not yet common practice and difficulties arising in the determination of uncertain parameters are typically not assigned properly. This contribution provides a tutorial review on methods for identifiability analysis, regularization techniques and optimal experimental design. A guideline for the analysis and classification of nonlinear ill-posed problems to detect practical identifiability problems is given. Techniques for the regularization of experimental design problems resulting from ill-posed parameter estimations are discussed. Applications are presented for three different case studies of increasing complexity.