Direct least-squares estimation and prediction of rational systems: Application to food storage

Generally, system parameters that are nonlinear in the model output are estimated by nonlinear least-squares (NLS) optimization algorithms. As an alternative, for nonlinear discrete-time models with a so-called rational structure in input, output, and parameters, in this paper a method is proposed to re-parameterize the model such that the model becomes linear in its new parameters. Consequently, the new parameters can then be estimated by direct least-squares methods. However, most often the model becomes of the form Ax≈bAx≈b, so that the parameter estimation problem becomes a so-called errors-in-variables (EIV) problem for which a total least-squares (TLS) approach provides a natural solution. Retrieving the predictor form after estimation leads to a nonlinear predictor that is based on the re-parameterized model with its original regressor functions so that prior system’s knowledge is preserved. The objective of this paper is (i) to show some properties of rational systems, which is illustrated to a biochemical example, (ii) to evaluate the estimation results and prediction performance of an original physical model estimated with NLS and re-parameterized models estimated with ordinary least-squares (OLS) and generalized TLS, with or without bias compensation. A storage facility, containing biological products and for which experimental data sets were available, is used here as a real life example.