Amy R. Ciric

A dual temperature simulated annealing approach for solving bilevel programming problems

This paper presents a dual temperature simulated annealing approach to bilevel programming problems. Bilevel programming problems arise when one optimization problem, the inner problem, is a constraint of a second optimization problem, the outer problem. In this paper, the inner problem is stochastically relaxed with a parameter that can be used as a temperature scale in simulated annealing. Solving the outer problem with simulated annealing as well leads to the dual temperature approach. The technique is demonstrated with several linear, nonlinear, and mixed integer nonlinear bilevel programming problems, including a safe plant layout problem that simultaneously minimizes cost and the damage caused during a worst case scenario accident.

Fault diagnosis of differential-algebraic systems

A large class of engineering systems are modeled by coupled differential and algebraic equations (DAE). Due to the singular nature of the algebraic equations, DAE systems do not satisfy the standard state-space description and require special techniques. So far, the literature has concentrated mostly on the numerical analysis and control of DAE systems. This paper investigates the problem of health monitoring and robust fault diagnosis of DAE systems. The main contributions are the design and analysis of a numerically feasible learning scheme for robust and stable fault diagnosis of DAE systems. The proposed fault diagnosis architecture monitors the physical system for any off-nominal behavior using nonlinear modeling techniques and learning algorithms. Online approximators, in the form of neural networks, are utilized in the detection of faults and in the derivation of models for the fault function, which can be used for fault isolation, fault identification, and fault accommodation. The stability and robustness properties of the fault diagnosis scheme are investigated. A simulation example illustrating the ability of the proposed fault diagnosis architecture to detect faults in a chemical reactive flash is presented.

Difference points in extractive and reactive cascades. I – Basic properties and analysis

The interactions between reaction and separation in extractive and reactive cascades are addressed through the use of difference points. It is shown how the structural elements in a generic cascade such as (side) feeds, products and chemical reactions combine to a normalized linear combination where the effect of each individual contribution is readily visualized. We derive and analyze the fundamental mathematical and geometric properties of these difference points for individual and aggregated units. Finally, it will be shown how to draw straight sectional and overall material balance lines in composition space for reacting systems through the use of pseudo-compositions.

Reactive distillation column design with vapor/liquid/liquid equilibria

This paper explores the design of reactive distillation columns with vapor/liquid/liquid equilibria. The number of phases and the phase equilibria on each tray are determined by minimizing the Gibbs free energy, allowing for a variable number of phases on each tray. The minimization problems are embedded within a larger problem that minimizes the annualized cost of the column, creating a bilevel optimization problem. A novel sequential approximation approach that can identify global solutions of the inner optimization problems is also introduced. The sequential approximation approach is employed to design reactive distillation and reactive flash processes.

Economic sensitivity analysis of waste treatment costs in source reduction projects: Continuous optimization problems

Abstract This paper presents an approach for determining the sensitivity of maximum net profits to uncertainty in the waste treatment costs in a chemical process. It is shown that a basic relationship exists between sensitivity analysis and the solution of a multiobjective optimization problem that simultaneously minimizes waste production and maximizes the profits before waste treatment. It is shown that all solutions of the sensivity problem lie on the convex hull of the tradeoff curve generated by the multiobjective optimization problem, and that the sensitivity curve can be generated from the tradeoff curve with a simple transformation. The paper presents a sequential approximation method that rapidly calculates the tradeoff curve. The method is illustrated with four examples.

Azeotropic distillation with an internal decanter

Abstract A distillation column with an internal decanter is used to separate a mixture containing five some oxygenated and hydrocarbons and having at least three carbon atoms, and water. One of the species is partially miscible with water, as well as another organic species. Both binary pairs exhibit azeotropes above the minimum bubble-point temperature. The column is very sensitive to small disturbances which can lead to flooding, poor product quality, and migration of an embedded two-liquid phase region within the column. These disturbances can cause the column to move from one steady state to another for the same specifications. Multiple operating regimes are exhibited, with unusual transitions between them. Two regions involving multiple steady states are observed, one of which involves the partial-miscibility of two organic phases. The dynamics of moving interfaces between trays having one- and two-liquid phases, as well as controllers to insure that unwanted transitions do not occur, are examined.

Nonlinear Fault Diagnosis of Differential/Algebraic Systems

Abstract This paper investigates the problem of health monitoring and robust fault diagnosis in systems described by coupled Differential and Algebraic Equations (DAE). The main objective is the development of numerically feasible on-line approximation schemes for robust and stable fault diagnosis of DAE systems. The proposed fault diagnosis architecture monitors the physical system for any off-nominal behavior using nonlinear modeling techniques and learning algorithms. The on-line approximation scheme is utilized not only to detect but also to provide a model of any faults, which is useful for fault isolation, identification and accommodation. The stability and robustness properties of the fault diagnosis scheme are investigated.