Welcome From The Chair

Message From The Director of Graduate Admissions

Faculty

Mark Stadtherr, Keating-Crawford Professor

Education
B.Ch.E., University of Minnesota, Minneapolis (1972)
Ph.D., Chemical Engineering, University of Wisconsin, Madison (1976)


Research Interests

The focus of our research is on the development and application of strategies for reliable engineering computing. In many applications of interest in chemical engineering, it is necessary to deal with nonlinear models of complex physical phenomena, on scales ranging from the macroscopic to the molecular. Frequently these are problems that require solving a nonlinear equation system (algebraic and/or differential) or finding the global optimum of a nonconvex function. Thus, the reliability with which these computations can be done is often an important issue. For example, if there are multiple solutions to the model, have all been located? If there are multiple local optima, has the global optimum been found? The goal is to develop the tools needed to resolve these issues with mathematical and computational certainty, thus providing a degree of problem-solving reliability not available when using standard methods, and to apply these tools to problems of interest. Since, in some cases, this approach is computationally intense, strategies that take good advantage of parallel computing architectures are also of significant interest.

In recent years, our group has shown that strategies based on the use of interval mathematics can be used to reliably solve a wide variety of global optimization and nonlinear equation solving problems of interest in chemical and biomolecular engineering. Some problems of current interest in the group include: 1) Verified solution of uncertain dynamic systems, i.e., problems in which there are uncertainties in model parameters and/or initial conditions, including applications in ecology, physiology, epidemiology and chemical engineering; 2) Parameter estimation in modeling of phase equilibrium, including the implications of using locally vs. globally optimal parameters in subsequent computations; 3) Location of equilibrium states and bifurcations of equilibria in ecosystem models used to assess the risk associated with the introduction of new chemicals into the environment; 4) Molecular modeling, including transition state analysis and the calculation of molecular conformations; and 5) Global optimization, including problems involving dynamic models. Also of special interest (in collaboration with Professor Joan Brennecke and the Notre Dame Energy Center) are modeling problems that arise in the development of sustainable, energy-efficient and environmentally-conscious processing technology, in particular the use of supercritical carbon dioxide and room-temperature ionic liquids as environmentally-benign replacements for traditional organic solvents.

Publications

C. R. Gwaltney, W. Luo and M. A. Stadtherr. Computation of Equilibrium States and Bifurcations Using Interval Analysis: Application to Food Chain Models. Ecological Modelling, 203:495-510, 2007. view abstract // link Food chains and webs in the environment are highly nonlinear and interdependent systems. When these systems are modeled using simple sets of ordinary differential equations, these models can exhibit very rich and complex mathematical behaviors. We present here a new equation-solving technique for computing all equilibrium states and bifurcations of equilibria in food chain models. The method used is based on interval analysis, in particular an interval-Newton/generalized-bisection algorithm. Unlike the continuation methods often used in this context, the interval method provides a mathematical and computational guarantee that all roots of a nonlinear equation system are located. The technique is demonstrated using three different food chain models, and results of the computations are used to compare the models.

Y. Lin and M. A. Stadtherr. Fault Detection in Nonlinear Continuous-Time Systems with Uncertain Parameters. AIChE Journal, 54:2335-2345, 2008. view abstract // link In model-based fault diagnosis for dynamic systems with uncertain parameters, an envelope of all fault-free behaviors can be determined from the model and used as a reference for detecting faults. We demonstrate here a method for generating an envelope that is rigorously guaranteed to be complete, but without significant overestimation. The method is based on an interval approach, but uses Taylor models to reduce the overestimation often associated with interval methods. To speed fault detection, a method that uses bounded-error measurement data and a constraint propagation procedure is proposed for shrinking the envelope. Several fault detection scenarios involving nonlinear, continuous-time systems are used to evaluate this approach.

L. D. Simoni, A. Chapeaux, J. F. Brennecke and M. A. Stadtherr. Asymmetric Framework for Predicting Liquid−Liquid Equilibrium of Ionic Liquid−Mixed-Solvent Systems. Industrial & Engineering Chemistry Research, 48:7246-7265, 2009. view abstract // link A new approach for modeling liquid−liquid equilibrium in electrolyte/mixed-solvent systems is presented, with particular focus on systems involving a dilute aqueous solution of an ionic liquid (IL). This new approach involves an asymmetric framework in which different phases have different degrees of electrolyte dissociation, and are thus represented by different Gibbs free energy models. As a first case, we consider the situation in which the electrolyte is either completely dissociated or completely paired (molecular), with its state depending on the dielectric constant of the mixed solvent and on the concentration of the salt in the phase in question. The theory underlying this asymmetric framework is developed, and a rigorous approach for phase stability analysis is presented. It is explained how to formulate and solve the parameter estimation problem for determining model parameters from binary data, and this process is demonstrated using examples. An immediate goal is to use this approach to predict liquid−liquid equilibrium for ternary IL/solvent/water systems, using parameters obtained from binary and pure component data only.

Y. Lin and M. A. Stadtherr. Rigorous Model-Based Safety Analysis for Nonlinear Continuous-Time Systems. Computers & Chemical Engineering, 33:493-502, 2009. view abstract // link A method is presented for the quantitative, model-based safety analysis of nonlinear continuous-time hybrid systems. This method uses the region-transition-model (RTM) framework of [Huang, H., Adjiman, C. S., & Shah, N. (2002). Quantitative framework for reliable safety analysis. AIChE Journal, 48, 78–96], together with a recently developed technique [Lin, Y., & Stadtherr, M. A. (2007). Validated solutions of initial value problems for parametric ODEs. Applied Numerical Mathematics, 57, 1145–1162] for the rigorous global analysis of nonlinear, continuous-time systems with uncertain initial conditions and/or parameters. Given an operating region described by bounds on possible initial conditions, inputs and model parameters, and a finite time horizon, the method can determine which operating subregions lead to safe operation. Numerical examples are presented that demonstrate the effectiveness of the method. This approach can supplement and complement the more qualitative techniques that are widely used for hazard identification and safety analysis.

Y. Lin and M. A. Stadtherr. Deterministic Global Optimization of Nonlinear Dynamic Systems. AIChE Journal, 53:866-875, 2007. view abstract // link A new approach is described for the deterministic global optimization of dynamic systems, including optimal control problems. The method is based on interval analysis and Taylor models and employs a type of sequential approach. A key feature of the method is the use of a new validated solver for parametric ODEs, which is used to produce guaranteed bounds on the solutions of dynamic systems with interval-valued parameters. This is combined with a new technique for domain reduction based on the use of Taylor models in an efficient constraint propagation scheme. The result is that an -global optimum can be found with both mathematical and computational certainty. Computational studies on benchmark problems are presented showing that this new approach provides significant improvements in computational efficiency, well over an order of magnitude in most cases, relative to other recently described methods.

Y. Lin and M. A. Stadtherr. Validated Solutions of Initial Value Problems for Parametric ODEs. Applied Numerical Mathematics, 58:1145-1162, 2007. view abstract // link In initial value problems for ODEs with interval-valued parameters and/or initial values, it is desirable in many applications to be able to determine a validated enclosure of all possible solutions to the ODE system. Much work has been done for the case in which initial values are given by intervals, and there are available software packages that deal with this case. However, less work has been done on the case in which parameters are given by intervals. We describe here a new method for obtaining validated solutions of initial value problems for ODEs with interval-valued parameters. The method also accounts for interval-valued initial values. The effectiveness of the method is demonstrated using several numerical examples involving parametric uncertainties.

Awards

Computing in Chemical Engineering Award

Given on November 17, 1998 by the American Institute of Chemical Engineers. This is the top national award for outstanding contributions in the field of computing in chemical engineering.

Excellence in Teaching Award

Given on August 21, 1978 by the University of Illinois at Urbana-Champaign, School of Chemical Sciences. This award recognizes excellence in teaching in the School of Chemical Sciences.

James A. Burns, C.S.C., Award

Given on May 17, 2008 by the University of Notre Dame, Graduate School. This award recognizes exemplary contributions to graduate research and education.

Xerox Award for Faculty Research

Given on May 14, 1982 by the University of Illinois at Urbana-Champaign, College of Engineering. This award recognizes the most outstanding research by an Assistant Professor in the College of Engineering.

Courses

Images

No images have been uploaded yet.