Reduced Hessian based parameter selection and estimation with simultaneous collocation approach

Parameter estimation is a critical step in the building of process models. Given the nonlinear structure and limited measurements, it is often difficult to correctly estimate all the parameters involved in the model. Linear dependence and low correlation among the parameters are the main problems to be handled in parameter estimation. The common approach is to estimate a subset of the parameters by fixing the others at reasonable values. However, it is a challenge to determine which parameters can be properly estimated. In this work, the ratio between standard deviation and estimated parameter value is introduced for evaluating the estimability. A Gauss‐Jordan elimination based approach is proposed for parameter estimability ranking. Combined with the proposed ranking approach and approximate ratio criterion, a reduced Hessian based approach is proposed for parameter selection and estimation under a simultaneous collocation framework. The proposed approach is at least as effective and more efficient than competing approaches based on multiple eigenvalue decompositions or orthogonalizations for larger problems. Three case studies with increasing complexity are presented to demonstrate the performance of the proposed approach.