Optimal experimental design for ill-posed problems
In: W. Marquardt, C. C. Pantelides (Eds.): 16th European Symposium on Computer Aided Process Engineering and 9th International Symposium on Process Systems Engineering, 173-178
Modern high-resolution measurement techniques offer the possibility to determine unknown functional dependencies directly from the data. The underlying inverse problems, however, are much more demanding than standard parameter estimation. Still, systematic strategies for experimental design of such ill-posed problems are missing. A new approach is proposed here that in particular achieves the sound integration of the bias-variance trade-off critical to the solution of ill-posed problems. The new design approach is based on the minimization of the expected total error (ETE) between true and estimated function. The ETE design approach is exemplified for the classical example of determination of reaction rates from measured data.
experimental design, inverse problem, parameter estimation, reaction kinetics, numerical differentiation