Robust error-in-variables estimation using nonlinear programming techniques

For steady-state systems described by algebraic or differential equation models where all variables are subject to error, the error-in-variables method (EVM) for parameter estimation has been shown to be superior to standard least-squares techniques. In EVM, measurement errors in all variables are treated in the calculation of regression coefficients, whereas the least-squares method only considers errors in the dependent variables. Previous EVM algorithms were developed assuming linear (or linearized) model equations. Unfortunately, many chemical engineering processes operate in strongly nonlinear regions where linear approximations may be inaccurate. In this dissertation, new algorithms using nonlinear programming techniques for the error-in-variables methods were proposed. In addition, a method for discerning when these methods are necessary was developed. The proposed algorithms were compared to the least-squares method and traditional error-in-variable approaches. Improved parameter estimates for several steady-state nonlinear processes were demonstrated.; For the estimation of parameters in the laboratory water gas shift reactor, the least squares method and the error-in-variables method were compared. The prediction of the temperature profiles through the bed by the EVM was more accurate than that by the least squares method. Also the true estimated values of the variables can be used to check the systematic measurement errors through a t-test.; For nonlinear dynamic systems, a sequential optimization and solution strategy for data reconciliation and parameter estimation was investigated. Specifically, numerical integration was nested within numerical optimization to comprise the nonlinear dynamic error-in-variables method (NDEVM) for on-line and off-line parameter estimation. NDEVM provided improved estimates over conventional least-squares techniques for both on-line and off-line applications. In addition, NDEVM was able to provide reliable estimates even in the presence of measurement bias under certain conditions.; Finally, three aspects regarding the rigorous treatment of adsorption data for multicomponent adsorption equilibria were investigated: (1) choice of pure-component model for the ideal adsorbed solution theory; (2) variable sensitivity analysis for the choice of independent variable sets; and (3) parameter estimation techniques for binary interaction parameters.