Reliable Nonlinear Parameter Estimation Using Interval Analysis: Error-in-Variable Approachy

Parameter estimation is a key problem in the development of process models, both steadyand unsteadystate, and thus is an important issue in both process design and control. The error-in-variable approach differs distinctly from the standard approach in that measurement errors in both dependent and independent system variables are taken into account when formulating the objective function in the parameter estimation problem. It is not uncommon for the objective function in nonlinear parameter estimation problems to have multiple local optima. However, the usual methods used to solve these problems are local methods that offer no guarantee that the global optimum, and thus the best set of model parameters, has been found. We demonstrate here a technique, based on interval analysis, that can solve the error-in-variable parameter estimation problem with complete reliability, providing a mathematical and computational guarantee that the global optimum is found. As examples, we consider the estimation of parameters in both steady and unsteady-state models, including a vapor-liquid equilibrium (VLE) model, a CSTR model, and a reaction kinetics model.