Prof. Neima Brauner

Considering precision of experimental data in construction of optimal regression models.

In this research project the construction of optimal (stable and of the highest possible accuracy) regression models comprising of linear combination of independent variables and their non-linear functions is being considered. It has been shown that estimates of the experimental error, which are most often available for engineers and experimental scientists, are useful in identifying the set of variables to be included in an optimal regression model. Two diagnostic indicators, which are based on experimental error estimates, have been incorporated in an orthogonalized-variable-based stepwise regression (SROV) procedure. This procedure has been utilized to determine the number of terms (parameters) to be included in optimal regression models, to identify the most influential terms and to detect the dominant cause limiting the precision of the model. Various correlations and regression models, published in the literature, have been examined using the SROV procedure and in most cases the accuracy and stability of the models could be considerably improved using this new technique. The SROV algorithm was implemented as a collection of MATLAB m-files. For additional information see conference proceedings and relevant journal articles Press here to download the SROV program.

Solution of linear algebraic non-linear algebraic, differential-algebraic and ordinary differential systems of equations.

A new method for solving mixed systems of differential and algebraic equations has been developed. This method is based on the use of a feedback controller to adjust the value of a variable, so that the residual of the non-linear algebraic equation is kept very close to zero during integration. Any standard integration algorithm can be used to solve the mixed system of equations. This new method has been applied to index one problems (such as batch distillation and batch reactor simulation) as well as to a high index problem (ideal pendulum) and yielded very accurate results. A new "continuing homotopy" type method for finding all solutions of a system of non-linear algebraic equations has been developed. The unique feature of this method is that standard, widely available numerical software can be used for its implementation and it does not require dedicated software.
A new technique for solving non-linear equations with discontinuities has been developed and a web-based library for testing performance of numerical software has been prepared.

Prediction and prevention of chemical reaction hazards - learning by simulation.

Dynamic simulation assignments, based on of batch and a semi-batch reactors in which exothermic reactions are conducted have been developed. These assignments are used to teach students the various aspects of process safety. The students can observe temperature runaway taking place because of incidents, such as overcharging, cooling water failure, pipe blockage and excessive initial heating. They can derive various strategies to prevent temperature runaway developing as the result of such incidents and suggest operational and structural changes of the process to make it more resilient to component failures and incidents.

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