Different algorithms for estimating parameters of a non-linear model for obtaining ions

Abstract

The objective of the work was to evaluate different algorithms for estimating parameters of a non linear model to obtain the concentration of nitrate and potassium ions in the soil solution. Soil water content, electrical conductivity and nitrate and potassium concentrations were monitored along time. The data were processed in different estimating computer programs. The programs had the function of estimating the parameter of the Vogeler model. The following programs were used: SAS, Statistica 7.0 and Excel. The model in the case of the Statistica program was non-linearly adjusted with the following algorithms: Simplex (SI); Simplex + Gauss-Newton (SG); Hooke & Jeeves +Pattern Moves (HJ) and Rosenbrock+ Pattern Search (RO). In the excel, the parameters were compared for the choice of the best algorithm. High determination coefficients were verified for fitting models to the data; however, the model estimates of nitrate and potassium concentrations were not equivalent to the measured ones. Moreover, high RMSE and MEN were observed for most of the algorithms. The Solver tool provided the best results for the experimental conditions. The deviation of the estimates by the Solver and measured values were close to 20%, which is acceptable.