17 A Framework for Dynamic Simulation of Interconnected …
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dependencies may be either pre-defined correlations (e.g. polynomic functions), or
lookup tables, that are directly visualized in the material database graphical interface.
For each dependency a valid range has to be defined. If the function is evaluated outside of this range, a nearest neighbour value inside the valid range is selected instead.
In addition, the user can define properties that describe the interaction between two
compounds, like surface tension at a phase boundary.
8 Units and Solvers Library
In Table 2, the units available in the Dyssol unit library are presented. The shown list
is complemented by a set of service units, like basic inlet, mixer, or splitter, which are
not described in detail. The available custom solvers from the Dyssol solver library
are listed in Table 3. Additional modules, implemented in Dyssol, are described in
Table 4.
9 Numerical Process Optimization and Parameter
Adjustment
To allow for global optimization of unit and process parameters for dynamical processes, a genetic algorithm has been implemented according to Weicker [65]. Its
flowchart is shown in Fig. 20.
The main optimization parameters are the number of the so-called parent solutions
n parent and the number of child solutions per parent n child . During initialization stage,
a number of n parent solutions are generated randomly within the defined bounds of
the solution space. In the main loop, for each parent solution n child solutions are
generated by mutation of the respective parent solution. The mutation is achieved by
addition of a random value from a gaussian function with zero mean and standard
deviation σ . The standard deviation σ determines the size of the search space in
which the child solutions may lie and influences the convergence of the optimizer.
In one iteration of the main loop, a total of n parent × n child solutions are generated by
mutation, for which the flowsheet model is simulated. The deviation of the variables,
received from the flowsheet simulation, to the target values is evaluated using rootmean-square error (RMSE) function. Following, the n parent best solutions are selected
according to the lowest RMSE as start values for the next iteration. Additionally, if
chosen via user input, the best parent solution may be taken to this list of selected
solutions, if its RMSE is lower than the best child solutions. After a user-defined
number of iterations, the standard deviation σ of the mutation function is adjusted.
If the RMSE is not decreasing, the value of σ is reduced—and vice versa—to adjust
the size of the solution space and therefore the convergence.
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dependencies may be either pre-defined correlations (e.g. polynomic functions), or
lookup tables, that are directly visualized in the material database graphical interface.
For each dependency a valid range has to be defined. If the function is evaluated outside of this range, a nearest neighbour value inside the valid range is selected instead.
In addition, the user can define properties that describe the interaction between two
compounds, like surface tension at a phase boundary.
8 Units and Solvers Library
In Table 2, the units available in the Dyssol unit library are presented. The shown list
is complemented by a set of service units, like basic inlet, mixer, or splitter, which are
not described in detail. The available custom solvers from the Dyssol solver library
are listed in Table 3. Additional modules, implemented in Dyssol, are described in
Table 4.
9 Numerical Process Optimization and Parameter
Adjustment
To allow for global optimization of unit and process parameters for dynamical processes, a genetic algorithm has been implemented according to Weicker [65]. Its
flowchart is shown in Fig. 20.
The main optimization parameters are the number of the so-called parent solutions
n parent and the number of child solutions per parent n child . During initialization stage,
a number of n parent solutions are generated randomly within the defined bounds of
the solution space. In the main loop, for each parent solution n child solutions are
generated by mutation of the respective parent solution. The mutation is achieved by
addition of a random value from a gaussian function with zero mean and standard
deviation σ . The standard deviation σ determines the size of the search space in
which the child solutions may lie and influences the convergence of the optimizer.
In one iteration of the main loop, a total of n parent × n child solutions are generated by
mutation, for which the flowsheet model is simulated. The deviation of the variables,
received from the flowsheet simulation, to the target values is evaluated using rootmean-square error (RMSE) function. Following, the n parent best solutions are selected
according to the lowest RMSE as start values for the next iteration. Additionally, if
chosen via user input, the best parent solution may be taken to this list of selected
solutions, if its RMSE is lower than the best child solutions. After a user-defined
number of iterations, the standard deviation σ of the mutation function is adjusted.
If the RMSE is not decreasing, the value of σ is reduced—and vice versa—to adjust
the size of the solution space and therefore the convergence.