Calculation
The calculation procedure includes, if possible, data reconciliation,
computation of unknown quantities and calculation of uncertainties using error
propagation. At the beginning, the plausibility of the system is checked and in
the end statistical tests are performed to evaluate whether the performed data
reconciliation is tolerable or not.
Here you find information about the following topics:
Select which of the defined layers shall be considered for calculation.
 On the Edit menu, select Layers and Periods.
 On the Layers tab, in column Calculation select which
layer shall be considered for calculation.
 Click OK.
Select which of the defined periods shall be considered for calculation.
 On the Edit menu, select Layers and Periods.
 On the Periods tab, select the first and the last period of
the interval to be considered for calculation.
 Click OK.
If only those input and output flows of process are modeled that contain a
certain substance, the balancing on the layer of goods (law of material
conservation, transfer coefficient equations) does not make sense. Those
processes have to be marked.
 Select a process.
 On the Properties window, select the Process tab.
 Remove the tick in front of Balancing.
Note:
 In the system diagram, the name of processes that are not balanced during
calculation on the layer of goods is written in brackets.
Additional linear relation between similar data types (e.g. two flows) can be
added.
 On the Edit menu, select Edit Relations.
 Click on [Enter new relation] and then .
 Choose the Value Type (e.g. Masses, Volumes, Concentrations,
Transfer coefficients), Layer, Period and Source of the
variables A and B.
 Define the proportion factor
 Confirm with OK.
Note:
 You can delete defined relations by clicking the relation in the list and
pressing DEL.
 If relations between different layers have been defined, scaling will be
switched of during calculation out of technical reasons.
The coarse (mass) balance of processes (sum of known input flows minus
sum of known output flows) can be displayed as a number inside of the
process icons.
 On the Extras menu, select Options and click the
Processes & Flows tab.
 On the Process pane, select Display coarse balance of
processes.
Note: This feature is already available before a
calculation has even been started. Thus, it facilitates the detection of gross
imbalances (due to missing flows or wrong input data) that could lead to
problems during calculation.
 For a quick start of the calculation, click in the Data Input
toolbar or press F5.
or
 To set additional calculation options (calculation method, trace level),
choose Calculation dialog from Edit menu or press ALT +
F5:
 Choose the calculation method (Cencic 2012 or IALIMPL2013)
 Optional: Settings to change parameters of the calculation methods. For
options refer to Options Calculation Module Cencic 2012 and IALIMPL2013
 Optional: Choose the trace level (none < errors < warning <
information < details) of logging.
 Click Start.
 After the calculation, click Close to display the results in the
system diagram.
Note:
 After the calculation, in the Trace Output window, a list of
information, warnings and errors is displayed. Click any entry in this list to
highlight the corresponding object in the system diagram.
 The Trace Output window offers the following options:
Show message grid
Show text messages.
Output is dependent on trace level
Show/Hide
Groupbybox: To group the listed messages by certain fields pull the
according column descriptions into the grey grouping area above.
Clear all messages
 The Degree of overdetermination states how many equations
without unknown variables could be found by transformation of the given
equation system.
 The Value of objective function refers to the minimized
value of the objective function of the weighted least squares approach used in
STAN.
 The Quality of data reconciliation will be displayed if no gross
errors are detected. It ranges between between 0 (i.e. the mean values of all
variables contained gross errors) and 1 (i.e. the mean values of the
measurements fitted perfectly and no adjustment were necessary at all).
 The Summary (histogram data) of the standard scores of the reconciled
values (= (measured value  reconciled value) / standard uncertainty of
measured value) is displayed.
This module was developed by Oliver Cencic. It offers the following
calculation options:
 Convergence tolerance: If the 2norm of the changes in the variable vector
is less than this tolerance the iterative calculation will be stopped. Default
= 1E10.
 Zero values tolerance: All absolute values less than this tolerance will
be considered zero during update of vectors and matrices.
 Observability tolerance: Matrix entries (absolute) smaller than this
tolerance will be considered zero during variable classification according to
Madron. Default = 1E10.
 Contradiction Check: Untick this option only if in the Trace Output
window potential problems with the contradiction check are
indicated.
 Short variable keys: Use short variable keys (e.g. FV:123 instead of
F1_m_G_2000 to represent the mass flow of Flow 1 on the layer of
goods for the period 2000) when displaying detailed results of the calculation
procedure.
 Display equations: Displays used equations after computation.
Note:
 The setting of option 5 and 6, together with the chosen trace level,
influence what is displayed in the Trace Output window when
clicking .
This module was developed by Jeffrey Dean Kelly from Industrial Algorithms.
It offers the following calculation options:
 Maximum number of nonzeros in any working matrix.
 Multiplier needed for sparse matrix operations.
 Scaling factor
 Scaling type: 0 (none), 1 (rows only), 2 (rows and columns =
default), 3 (columns only).
 Gamma: A regularization parameter for B'*B to increase the numerical
stability of the iterative solution especially when solving illconditioned
systems => B'*B + gamma*Iy. Default = 1E12.
 Epsilon: A regularization parameter for A'*Q*A + lambda*B*B' to increase
the numerical stability if a row is vacuous => A'*Q*A + lambda*B*B' +
epsilon*Ig. Default = 1E12.
 Lambda: Estimated variance of the unmeasured variables used as a
regularization parameter in A*Q*A' + lambda*B*B'. Default = 1E6. Will be used
if no values for Lambda1 and Lambda2 are given.
 Lambda1 and Lambda2: for improved calculation of estimated raw
variance of the unmeasured variables => w(i) = Lambda1 * (abs(y(i)) +
Lambda2)^2. If Lambda1 or Lambda2 is less or equal 0, Lambda will be used
instead. default = 100.
 Convergence tolerance: Convergence tolerance for constraint closure. If
the constraint or function residuals have a 2norm less than this tolerance
then the iterative calculation is stopped.
 Zero values tolerance: All absolute values less than this tolerance will
be considered zero during update of vectors and matrices.
 Observability tolerance: All entries in o.dat with an absolute value less
than this tolerance will be considered zero (= observable).
 Method 1: Sparse matrix factorization technique or method
used in the reconciliation solver. Valid values: 1,2,3,4
 Method 2: Sparse matrix factorization
technique or method used in the postreconciliation sensitivity solver to
compute the observability and redundancy metrics. Valid values:
1,2.
Note:

Compared to the standard calculation
algorithm Cencic 2012, IALIMPL 2013 is superior in calculation speed (factor
10 to 50) when dealing with large models (number of equations + variables >
4000), and offers a higher numerical stability. It operates with sparse
matrices.

The triallicense of IALIMPL
2013 included in STAN is limited to a number of 200 equations +
variables. If you are interested in an unlimited version, please contact
Jeffrey Dean Kelly at Industrial Algorithms (jdkelly@industrialgorithms.ca)
to get an unlimited 7daystriallicense or to purchase an unlimited perpetual
version for $100 (USD) for academic, noncommercial (nonconsulting,
noncontracting, etc.) and home use only. The price for a commercial
license of IMPL can be sent upon request. The license file has to be installed
by clicking Install license.
Goal of the automatic scaling procedure is to reduce the condition number of
the equation system (matrices) thus reducing the influence
of disturbed input data (e.g. due to rounding errors) on the results. If
scaling is not desirable or possible (e.g. use of subgood layers => scaling
is switched off automatically), it can be switched off manually.
 On the Extras menu, select Options and then tab
Calculation.
 Set/Delete the tick under Enable Scaling.
To iteratively solve nonlinear equation systems, it is necessary to assign
initial values to unknown variables. In STAN this procedure is performed
automatically with the assistance of a random number generator. In some
problems, the choice of random numbers influences the results what is not
desirable. Because of that, STAN offers the possibility to change
the start value of the random numbers generator, thus generating a
different set of random numbers. If the calculation with different start
values delivers the same results, the problem can be considered stable.
 On the Extras menu, select Options and then tab
Calculation.
 Enter a value between 0 and 999 as start value for generation of
random numbers.
 On the ModelExplorer window, click the name of the system.
 On the Properties window, enter scaling unit (e.g. capita) and
scaling factor (e.g. 100.000, meaning the entered data refer to 100.000
inhabitants).
Note:
 The same settings can be edited in the Data Explorer on tab
System.
 How to apply the scaling factor look at Scale Data.
 On the Extras menu, select Options and click the
Scaling tab.
 On the Scaling pane, select the reference entity (scaling basis,
sum of imports, sum of exports).
Note:
 On the Extras menu, click Calculation Modules.
 Click Install New Modules.
 Select the new module and click Open.
 Close the window.
Note:
 Copy the new calculation module (extension = .dll) to the subfolder
"CalcModules" in the STAN directory ".
 The existing default calculation module "CalcModules.dll" must not be
removed.
 To remove installed modules requires a restart of STAN.