Advanced Parameter Estimation Tools for Building Mathematical Models of Chemical Processes

Project leader: Kim B. McAuley, Queen's University,

Information captured in mathematical models is used by companies that design and operate chemical and biochemical production processes. The information and models are used to improve operating profits, product quality, process safety, and environmental compliance. Fundamental models, which rely on knowledge of chemical, biological and physical phenomena, are useful for extrapolating beyond experimentally observed behaviour and for optimizing process operations. When insufficient knowledge is available to develop detailed fundamental model equations, modellers rely on empirical expressions. A major problem faced by modelers is determining appropriate values of unknown model parameters. In chemical process models, the unknown parameters are often associated with the rates of chemical reactions and with the movement of chemical species between gas and liquid phases. Good model predictions require appropriate model structure and good parameter values.

Our project team develops and tests advanced statistical tools for parameter estimation in mathematical models. Approximate maximum likelihood techniques are being developed for parameter estimation in differential-equation models that describe time-varying behaviour of industrial chemical processes. These statistical techniques account for stochastic process disturbances and for model imperfections, which are ignored in traditional estimation techniques. Our team is also developing and assessing new methods to help modelers estimate parameters in complex models when only limited data are available. Sometimes it is difficult or impossible to estimate all of the unknown parameters using the available data. Our techniques help modelers to decide which parameters to estimate and which to leave at initial guesses or to remove via model simplification. We have developed an effective algorithm to rank parameters from most estimable to least estimable and for determining how many parameters to estimate to obtain the best predictions. We also develop new models to describe chemical and biochemical processes of interest to our industrial sponsors. We use advanced statistical tools estimate parameters in these models, and we design experiments aimed at improving parameter estimates and model predictions. We examine the influence of model imperfections and parameter uncertainty on the performance of of on-line process monitoring and control systems so that the effects of statistical uncertainty on process operating decisions can be quantified.