Research
- Functional Data Analysis
- Real-Time Optimization Using Mechanistic and Empirical Models
- Identifiability of Process Models
- Fault Detection Using Multivariate Statistical Techniques
- Sensitivity Analysis
- MITACS Project - Advanced Parameter Estimation Tools for Building Models of Chemical Processes
(project web page)
The theme of our research is the development of techniques to support dynamic modeling, analysis, estimation, monitoring and control of chemical processes. The emphasis is on the use of nonlinear process models, consisting of systems of ordinary differential, partial differential, or differential algebraic equations derived from fundamental energy and material balances, and equilibrium relationships.
Project Descriptions
Identifiability of Process Models
Given a model structure with specific parameters, is it possible to estimate unique
values for the parameters? This is the question of identifiability. The problem becomes
more acute when large-scale process models are considered. We are investigating tests for
identifiability that can be automated and applied to large-scale models. In
addition, we have developed tests of identifiability for differential-algebraic
models. Amos Ben-Zvi (now an Assistant Professor at the University of Alberta) investigated these topics for his doctoral research. A MapleTM worksheet containing our Generalized Markov Parameter test can be found here.
Functional Data Analysis
Functional data analysis is a relatively new field in statistical modeling in which the basic data objects are realizations of functions, rather than collections of points. A wide range of techniques have been developed for functional data, including functional regression, functional principal components analysis (fPCA) and Principal Differential Analysis (PDA). The overall interest is in understanding how these techniques can be effectively used for chemical process analysis. I am working with Prof. Jim Ramsay at McGill in a number of these different areas. Specific projects include: principal differential analysis for identifying dynamic structure in process behaviour, functional regression for empirical modeling of chemical processes (particular applications to polymer systems, as described below), integral equation modeling using functional data analysis, and batch trajectory analysis using principal differential analysis and functional principal component analysis.
Estimating Parameters in Process Models Using Principal Differential Analysis - Profs. Jim Ramsay, Kim McAuley (Queen's) and I are investigating the use of Principal Differential Analysis (PDA) for estimating parameters in dynamic process models. PDA involves identifying differential operators that annihilate time traces, in other words fitting the differential equations directly to time traces of process variables. PDA in one sense represents a form of principal components analysis (PCA) in which linear combinations of variables and their derivatives can be considered, in contrast to PCA which considers only linear combinations of variables. We have been investigating the effectiveness of an iterative approach, Iterative Principal Differential Analysis (iPDA), for parameter estimation. In iPDA, parameters are estimated using an iterative scheme which alternates between smoothing (typically using splines) with a model-based roughness penalty, and a parameter estimation step using the smoothed responses.
Sensitivity Analysis Using Functional Principal Component Analysis - P. Gokulakrishnan and I have been investigating the model reduction of detailed kinetic models describing combustion systems using a discretized form of functional principal components analysis to the sensitivity parameters for the reaction system, in order to identify primary reactions and species.
Functional Regression Modeling of Polymer Processes - Profs. Robin Hutchinson (Queen's), Jim Ramsay (McGill), and I are investigating the application of functional regression techniques (a subset of Functional Data Analysis) for empirical modeling of polymer reactors. Currently, we are working with simulated data for a polystyrene reactor as an initial test of the techniques. We are developing empirical models relating initiator concentration and reactor temperature to molecular weight distributions. Results of this work have been presented in May, 2003 at the Polymer Reaction Engineering conference in Quebec City, and at the ECOREP conference in Lyon, December 2003.
Impact of Model Uncertainty on Polymer Product-Property Monitoring and Control Schemes
Prof. Kim McAuley and I are developing techniques for assessing the impact of model uncertainty in polymer reaction models on product-property monitoring and control schemes. Included in these techniques are diagnostics for identifying suitable parameters for on-line updating, and estimability analysis for off-line mechanistic models.
Design of Real-Time Optimization (RTO) Systems
In a collaborative effort with Prof. Fraser Forbes (University of Alberta), we are investigating the optimal generation of information during RTO moves, and techniques for augmenting existing model information.
Fault Detection Using Multivariate Statistical Techniques
We are investigating the use of Principal Component Analysis for prognostic health management of aircraft environmental control systems. In particular, we are focusing on the special characteristics of the operation of these systems, and assessing how it can be exploited using multivariate statistical techniques. This work is being conducted in collaboration with Prof. Tom Harris at Queen's. Colin Breck and John Wong completed Master's theses on this topic.
Recent Funding
NSERC (Discovery), MITACS, Honeywell
Teaching Honours and Awards
Education and Career History
B.Sc. (Hon), Mathematics and Engineering (Process Control option), Queen's University, 1981
M.A.Sc., Chemical Engineering, University of Waterloo, 1983
Ph.D., Chemical Engineering, Queen's University, 1990
Control Applications Engineer, Petro-Canada Products Inc., Toronto, 1983-1986
Assistant Professor, Chemical Engineering, Queen's University, 1990-1995
Associate Professor, Chemical Engineering, Queen's University, 1995-2000
Cross-appointed to Mathematics and Statistics, Queen's University, 1998-present
Professor, Chemical Engineering, Queen's University, 2000-present
Acting Head, Department of Chemical Engineering, July 2002 - June 2003
Head, Department of Chemical Engineering, July 2006 - present
Last updated
September 3, 2009
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P. James McLellan, P.Eng.