Nonlinear programming for data reconciliation and parameter estimation

Data Reconciliation and Parameter Estimation (DRPE) is an important class of problems relevant to process industries. DRPE is often the precursor of online control strategies such as real time optimization (RTO) and model predictive control (MPC). An efficient way to perform DRPE is the simultaneous method where the DRPE problem is set up as a nonlinear programming (NLP) problem whose variables of optimization are the reconciled state variables and the estimated parameters.; Presence of gross errors and outliers in the data can reduce the efficiency of DRPE because they can bias the parameter estimates. We need to identify and compensate for gross errors while DRPE is being carried-out simultaneously. For this purpose, we examine estimators of measurement errors based on robust statistics. Robust estimators are suitable for online DRPE where we replace the objective function of the NLP by a robust estimator. In particular, we use the three-part redescending estimator of Hampel. This estimator explicitly removes the contribution of outliers toward estimation by comparing the measurement residual to a cutoff value. However, this cutoff value is often dependent upon the quality of the dataset and the order of magnitude of the measurements. For this purpose we develop a novel algorithm that uses the Akaike information criterion ($AIC$), which is a model discrimination tool, to tune the redescending estimator to the data to have the most reliable estimation. We also compare the redescending estimator to another robust estimator, the fair function, and exact minimizers of the $AIC$, the mixed-integer approaches, and demonstrate that the redescending estimators are computationally more efficient and robust.; Unobservable parameters and non-redundant measurements can make the NLP in the DRPE problem difficult to solve as the reduced Hessian matrix may become singular or ill-conditioned. If quasi-Newton approximations to the reduced Hessian are used in place of the exact Hessian, these approximations may be a very poor representation of the curvature of the problem and can cause the NLP algorithm to become extremely slow. Under the aforementioned conditions, line search based NLP algorithms may experience numerical difficulties leading to line search failures. Saddle points may attract the iterates of the NLP algorithm as well. To overcome all the above problems and yet use exact second-order information for fast convergence, we develop a successive quadratic programming (SQP) algorithm which uses trust regions to attain global convergence. (Abstract shortened by UMI.)...