Summary of Activities/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.
B.Ch.E., University of Minnesota, Minneapolis (1972)
Ph.D., Chemical Engineering, University of Wisconsin, Madison (1976)
Assistant Professor of Chemical Engineering, University of Illinois, Urbana, Illinois, 1976-1982.
Associate Professor of Chemical Engineering, University of Illinois, Urbana, Illinois, 1982-1996.
Visiting Professor, Centre for Process Systems Engineering, Imperial College, London, UK, January-May 2001.
Professor of Chemical Engineering, University of Notre Dame, Notre Dame, Indiana, 1996-2009.
Bernard Keating-Crawford Professor of Engineering, University of Notre Dame, Notre Dame, Indiana, 2009-present.
Concurrent Professor of Applied and Computational Mathematics and Statistics, University of Notre Dame, Notre Dame, Indiana, 2010-present.
D. A. Măceș and M. A. Stadtherr, “Computing Fuzzy Trajectories for Nonlinear Dynamic Systems,” Computers & Chemical Engineering, 52: 10-25, 2013.
Y. Zhao and M. A. Stadtherr, “Global Solution of Min-Max Optimization Problems for Nonlinear Dynamic Systems,” Computer-Aided Chemical Engineering, 30: 1287-1291, 2012.
Y. Zhao, and M. A. Stadtherr, “Rigorous Global Optimization for Dynamic Systems Subject to Inequality Path Constraints,” Industrial & Engineering Chemistry Research, 48:7246-7256, 2011.
J. A. Enszer, Y. Lin, S. Ferson, G. F. Corliss and M. A. Stadtherr, “Probability Bounds Analysis for Nonlinear Dynamic Process Models,” AIChE Journal, 57:404-422, 2011.
L. D. Simoni, A. Chapeaux. J.F. Brennecke and M.S. Stadtherr, “Extraction of Biofuels and Biofeedstocks from Aqueous Solutions Using Ionic Liquids,” Computers & Chemical Engineering, 34:3893-3901, 2010.
Y. Lin and M. A. Stadtherr, “Rigorous Model-Based Safety Analysis for Nonlinear Continuous-Time Systems,” Computers & Chemical Engineering, 33:493-502, 2009. 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, “Fault Detection in Nonlinear Continuous-Time Systems with Uncertain Parameters,” AIChE Journal, 54:2335-2345, 2008. 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.
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.
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.
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.
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.
GTE Emerging Scholar Lectureship,
University of Notre Dame, Notre Dame, Indiana, November 18, 1986.
List of Teachers Ranked as Excellent by Their Students
University of Illinois, several appearances, 1976-1995.