5 - Nonlinear Steady-State Data Reconciliation

Abstract

This chapter deals with nonlinear steady-state data reconciliation. Nonlinear models are often used to accurately describe most chemical processes. The chapter discusses various techniques used for solving the nonlinear reconciliation problem. Some are based on successive linearization, while others are derived from general nonlinear programming techniques. The chapter presents the most efficient and widely used solution methods. The sequential quadratic programming technique solves a nonlinear optimization problem by successively solving a series of quadratic programming problems. The generalized reduced gradient (GRG) optimization technique solves a nonlinear optimization problem essentially by solving a series of successive linear programming problems. At each iteration, a linear program (LP) approximation is obtained by linearizing the objective function and constraints. This chapter also analyzes decomposition techniques for nonlinear. In order to obtain a feasible solution, inequality constraints, such as bounds on variables are often imposed with nonlinear models. The constraints of a nonlinear data reconciliation problem can contain equality constraints and inequality constraints. Nonlinear data reconciliation problems, which contain only equality constraints, can be solved using iterative techniques based on successive linearization and analytical solution of the linear data reconciliation problem. Nonlinear data reconciliation problems containing inequality constraints can be solved, only using nonlinear constrained optimization techniques.