PanOptimizer for Property Optimization
PanOptimizer is a C/C++ software package for evaluating thermodynamic,
kinetic and thermo-physical model parameters from experimental measurements.
PanOptimizer is dynamically linked with PanEngine, a powerful tool for
calculating multicomponent phase equilibria and other related properties.
PanOptimizer is seamlessly integrated into Pandat as a specific module,
which allows user to make real-time calculation and evaluation by comparing
the experimental data with the calculated values using the instantly
optimized parameters.
In addition, a set of windows-based graphical user
interfaces are deliberately designed for easy input of the experimental data
and automatic tracking of the optimization progress. It should also be
pointed out that the PanOptimizer is designed as a general optimization tool
not only to be used in optimization of thermodynamic model parameters, but
also in that of thermo-physical and kinetic model parameters. More detailed
information about PanOptimizer can be found in reference [2008Cao
].
The major features are:
- Seamless integration with Pandat that allows user real time
calculation and comparison based on the instantly-obtained optimized
parameters.
- Versatile algorithms implemented in PanOptimizer leads to quick
convergence to experimental data.
- User-friendly windows interfaces for easy communication between
users and program.
- Two types of optimization process were implemented in PanOptimizer:
rough search and
normal optimization.
Graphical User Interface of
PanOptimizer
Figure 1. Control panel of PanOptimizer.
Figure 2. Dialog window of model parameters.
Figure 3. Dialog window of experimental data.
Rough search
Rough search is used to obtain a rough topology of a phase diagram based
on the given experimental data. It is useful for quick estimation of the
initial values of the model parameters at the beginning stage of the
optimization procedure. The algorithm to do rough search implemented in
PanOptimizer is based on the condition of equilibrium between any two
specified phases in a closed system at constant P and T.
Figure 4. (a) The phase diagram and (b) the enthalpy of
the liquid phase of the binary Al-Zn system
before the optimization (from
2008Cao
).
Figure 5. The calculated Al-Zn phase diagram compared with
the experimental data
after rough search with a) global search
option and b) local search option (from
2008Cao
).
Normal optimization
Normal optimization is used to obtain the best set of model parameters
that can produce the best fit of experimental data. Derived from the
maximum likelihood principle, when the discrepancies between
model-calculated and experimental values are assumed to be independent,
identically distributed with a normal distribution function, a set of model
parameters with the best fit to the given experimental data can be obtained
by minimizing the sum of squares or the least square method. In the real
modeling process the experimental data may come from different
sub-populations for which an independent estimate of the error variance is
available. In this case, a better estimate than the ordinary least squares (OLS)
can be obtained using weighted least squares (WLS), also called generalized
least squares (GLS).
Figure 6. (a) The phase diagram and (b) the enthalpy of
the liquid phase of the binary Al-Zn system
after the normal optimization (from
2008Cao
).