Associate Professor Office: SH 440 Tel: (216) 687 3526 Email: r.lustig@csuohio.edu Ph.D., Mechanical Engineering Ruhr-University Bochum Diploma, Mechanical Engineering, 1994 Technical University Hannover

Thermodynamics, Statistical Mechanics, Molecular Simulations

• Research Groups
• Selected Publications

Research Groups

Process Modeling

Process models are considered in multiscale cell-space by representing the evolution of process as a set of stochastic or deterministic cell mappings with temporal and scale dependent parameters on multiscale cell networks. Data are considered as collections of cells wrapped in observational and modeling uncertainty according to the scale of observation. Processes with wide ranging time constants and multirate sampled systems can be treated in this general framework. We are developing multiscale online system identification methods for nonstationary nonlinear models based on spectral analysis and sinusoidal modulation. Time-frequency localized modulation is implemented via Fourier/wavelet transforms. Efforts are underway to extend these approaches to wider classes of models with trancendental nonlinearities, discrete time and stochastic systems. These developments are also geared towards fault detection and diagnosis. Several industrial applications are under investigation including, tracking of microbial growth parameters, catalyst deactivation rates and heat exchanger fouling coefficients as well as modeling kinetics in polymerization reactors. Investigations are in progress for multiscale rectification and cerebral response modeling in functional magnetic resonance (fMR) imaging, a technique to identify patterns of cerebral activity in series of MR images. The image analysis is a combination of denoising, establishing model structures for pixel dynamics and estimating the parameters.

Process Data Analysis

Current research is focused on the development of data rectification methods by means of Bayesian inference in a multiresolution framework for linear and nonlinear systems. Spectral decomposition of noisy data using orthonormal wavelets separates the deterministic components into a scaled signal and captures the stochastic features into approximately decorrelated wavelet coefficients at multiple scales. Data is rectified according to the statistical properties of the features isolated at each scale. Dynamic systems are characterized by temporal and scale evolution of probability distributions which necessitates simultaneous rectification and modeling. The generalized multiscale data rectification approach incorporates previously untapped issues (a) applications to nonstationary nonlinear/non-Gaussian processes with random and gross errors, (b) time-scale recursive moving horizon and error-in-variables algorithms and (c) reconciliation with process constraints and dynamic models. Industrial applications include rectification and fusion of multirate or irregularly sampled data, for example, in sheet manufacturing processes and the development of "software sensors" for the estimation of unmeasured variables in bioprocess. Investigations are also in progress for the removal of non-Gaussian signal dependent noise and Gibbs artifacts in magnetic resonance (MR) images.

Process Monitoring

The theory of process integrity combines estimation, historical data and global analysis to define dynamic safety levels. This information is vital to assess the strength of failure conditions and the sphere of their influence, which can be used to design feedback integrity control systems. For a given set of parameters, nonlinear systems can exhibit several attractors - equilibrium points, periodic motions and chaotic behavior. A complete understanding of the behavior of nonlinear processes must include knowledge of the attractors, the domains of attraction (DOA) and the effects of external perturbations and parameter changes on the nature of the boundaries. The cell to cell mapping analysis is recursively refined in a multiscale framework to locate attractors and DOA's. Coarse descriptions are generated with large cells and finer cell spaces are defined for analyzing cell clusters capturing long term dynamics. The approach shows parallels with multigrid and wavelet methods for solving differential equations. By augmenting cell space with parameter space, parametric sensitivity and coagulation of domains are investigated. The broader aims of the theory of process integrity are the safe design and retrofit of chemical process equipment to guarantee safe and economic operation. Investigations are underway to analyze reactor thermal runaway and identify regions of safe and runaway conditions, and flooding in distillation columns.

Selected Publications

• A. Friedrich and R. Lustig: Thermodynamics of fluid benzene from molecular dynamics simulations, Journal of Molecular Liquids, to appear (2001)
• T. Breitenstein and R. Lustig: Boyle temperatures, Joule-Thomson inversion temperatures, and critical points of highly symmetrical multi-center Lennard-Jones molecules, Journal of Molecular Liquids, to appear (2001)
• R. Lustig: Microcanonical Monte Carlo simulation of thermodynamic properties, Journal of Chemical Physics, 109: 8816-8828 (1998)
• A. Friedrich and R. Lustig: Thermodynamic properties of model molecules with hexagonal symmetry from statistical mechanical theory, Journal of Chemical Physics, 105: 9597-9614 (1996)
• R. Lustig: Thermodynamics of fluid sulfur hexafluoride from molecular dynamics simulations, Berichte der Bunsengesellschaft Physikalische Chemie, 99: 1462-1468 (1995)
• R. Lustig: Thermodynamics of liquid oxygen from molecular dynamics simulations, Berichte der Bunsengesellschaft Physikalische Chemie, 98: 706-711 (1994)
• R. Lustig: Statistical thermodynamics in the classical molecular dynamics ensemble. III. Numerical results, Journal of Chemical Physics, 100: 3068-3078 (1994)
• R. Lustig: Statistical thermodynamics in the classical molecular dynamics ensemble. II. Application to computer simulation, Journal of Chemical Physics, 100: 3060-3067 (1994)
• R. Lustig: Statistical thermodynamics in the classical molecular dynamics ensemble. I. Fundamentals, Journal of Chemical Physics, 100: 3048-3059 (1994)