Application of stepwise regression for dynamic parameter estimation

• New stepwise regression algorithm for dynamic parameter estimation has been developed.
• The method is for cases where estimation of all parameters may be impossible.
• The parameters hierarchy in the model is defined and considered in the algorithm.
• Guidelines for the selection of a minimal initial basic parameter set are provided.
• Parameters are added in stepwise fashion until reaching an unstable set.

Dynamic parameter estimation in cases where it may be impossible to identify all the model parameters is considered. The objective is to obtain reliable estimates to the maximal number of physical parameters in a stable regression model where the modeling of the noise in the data is avoided. The modifications required in the stepwise regression algorithm to accommodate various nonlinear terms in the regression model are investigated and a new algorithm is presented. The algorithm considers the hierarchy among the parameters, the initial trends of the experimental data curves and the initial values of the state variables in order to establish a minimal initial set of parameters to be included in the model. Additional parameters are then added in a stepwise manner, while considering the hierarchy of the parameters and the associated reduction of the objective function value. The process continues as long as significant and physically feasible values for the parameters are obtained. The new method is demonstrated with several examples from the literature. Additional issues investigated include the proper combination of the simultaneous and sequential solution methods in the stepwise regression algorithm, the preferred method for the estimation of the derivatives and the effect of variable scaling.