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.
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.
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