Weights ¬

Grid Views

Reconciled Measurements

When a variable is selected for reconciliation in this grid, REX will attempt to match that measurement by optimizing the kinetic parameters. When a variable is unselected, REX does not make an attempt to match this measurement, however the weighting factors are still preserved. This allows you to conduct estimation studies with different sets of reconciled measurements, without having to change the weighting factors.

When Pressure is defined as Free in Reactor node for a reactor with one gas phase, you may reconcile the pressure measurements by selecting Pressure as a Reconciled Measurement in this node. Thus, the kinetic parameters are adjusted to match the pressure measurement. When Pressure is selected as Controlled in the Reactor node, REX calculates the value of the floated flow to match the pressure, while the other selected variables are reconciled by adjusting the kinetic parameters.

Temperature may be reconciled only if Use Energy Balance is selected for calculating temperatures in the Reactor node.

Note: A given compound can be selected to be reconciled only if that compound was included in the Measurements node. The same holds for pressure, temperature (when enery balance is enabled), pseudo-compounds and derived quantities.

Weight Generation Options

This grid is used to generate the weighting factors based on the nature of the error assumption selected. After selecting the desired error assumption option, you may generate the weighting factors by pressing the AutoGenerate button. If you choose to enter the weights manually, select the reconciled items in the Reconciled Measurements grid and then directly enter the weighting factors in the Weights → Sets node.

For all the options of error assumptions, if the Ignore Zero Values is selected, then the weighting factors are set to zero for those measurements whose values are specified as zero. These measurement points are also excluded from the unweighted deviation (LSQ Errors) as indicated in the Results: LSQ Error section.
If the Ignore Zero Values option is unchecked, the weighting factors for these zero value measurements are set to the highest value among the nonzero measurements for the corresponding compound and experimental data set.

In this grid, if you select "Generate Weights for → All Included Data", the weights are generated for:

• All Variables that are included in Reconciled Measurements
  
• All Sets that are included in Experiments

In some cases, you may have specified weights for some experiments, and then included new experiments or changed the experimental values for some sets. In order to generate weights only for the new or modified data without affecting the weights that were previously loaded, you may select the option "Generate Weights for → Only Modified / New Data". If you wish to check which sets are new/modified, please go to the Advanced tab and use the Select Modified Data Button.

After setting the above options, please click on the Autogenerate button to generate the weights.
Further details on the weighting strategies are provided below.

Explanation of Error Assumptions.

The kinetic parameters are estimated by the Weighted Least Squares method, where the objective function to be minimized is as follows:

Objective = w₁*(Exp₁ - Cal₁)² + w₂*(Exp₂ - Cal₂)² + ... w_n*(Exp_n - Cal_n)²

where w_i are the Weighting Factors for the measurements; Exp_i are the Experimental Data Values, and Cal_i are the Calculated Values at the Data Points.
REX provides the following options for the error assumptions. Select the appropriate option to generate the weighting factors. You may always fine tune them later.

• Uniform Absolute Error:
  
  In this case, w_i has the following formula:
                   w_i = 1/Exp_i⁰ = 1

This means that all measurements have same accuracy (or same absolute error). Therefore, on Autogenerate with this option, all the data points are equally weighted with a value of 1. In this case, the results from the REX estimation may show model deviations (difference between measured and calculated values), which are similar across a large range of measurement values.

As an example, lets consider two data points, with measurement values of 0.01 and 1 units, and calculated REX values of 0.02 and 1.01. In this case, both points result in a mismatch of 0.01 units. Since the weighting factors (w_i) are all 1, both of these deviations are considered to be identical by the REX estimation program. This means that this weighting method is not suitable if you are concerned about the high percentage error (100%) for the first data point. In general, with this method, large values tend to get a better match on a relative (percentage) basis, whereas smaller values may be poorly matched on a relative basis.


• Uniform Percentage Error:
  
  In this case w_i has the following formula:
                    w_i = 1/Exp_i ²

This means that the measurements have uniform percentage errors. For the example shown above, the weighting factor would be 10000 and 1 for the first and second data points respectively. This means that REX will place 10000 times more importance on the square of model deviations for the first point versus the second point. Thus, selecting this option will usually result in smaller measurements getting significantly higher weighting factors, since REX attempts to ensure that the model predictions preserve the uniform percentage error assumptions. This may not be desirable if the small measurements are considered unreliable, which may be true for some chemical systems.


• Hybrid:
  
  In this case w_i has the following formula:
                    w_i = 1/Exp_i

While the uniform absolute error assumption tends to overweight larger measurements, and the uniform percentage error assumption tends to overweight smaller measurements, the hybrid option offers an intermediate alternative to the above two options. This is the recommended and most commonly used option.

Grid Views

Select Sets and Variables

Here, you may select the variables and sets for which the weights will be generated.
The following columns are available:

• The Data Series column indicates whether the variables belong to Total Moles or some Phase.
  
• The Set Name denotes the set.
  
• The Compound Name is used to select the variable whose weights are to be modified in this tab.
  

Advanced

The actions grid allows to specify the collection of items to be chosen for modification. The options available are:

• Check All: All variables for all sets in the Select Sets and Variables grid are included.
• Clear All: This action un-includes all variables for all sets in the Select Sets and Variables grid.
• Select Modified Data: This options selects the sets and variables for which either the weights have not been generated, or whose experimental data was changed in Experiments → Measurements → Sets node. This provides a clear collection of the variables that may need to have their weights (re)generated.
• Modification Type: Here, you may select the appropriate options for the following fields :
  
• The Modification Type combo, where you can select the type of modification to be done. The available options are:
• To Custom Weight: The present weight values for the items and sets selected will be replaced with your new value.
• Multiply By Custom Weight: The present weight values for the items and sets selected will be multiplied by a given value.
• Measurement Error Assumptions: The same option selected in the Weight Generation Options grid view is applied here. If the default options are selected in that view, it will be "Hybrid - Ignore Zero". This is equivalent to generating the default weights for a specified collection of items.
  If you want to change to another weighting strategy, you must do the change in the Weight Generation Options view and then return here to proceed.
• Adjust by Atom Balance Error - Auto: The weights values may be modified by a factor whose value depends on the atom error for each set and datapoint, as reported in Check Atom Balance node. This option allows to change weights for variables in Total Moles only. Weights for measurements in the phases are never affected.
  The weights are reduced by a percentage that is same as the atom balance error (in absolute terms) for the corresponding experimental set and datapoint of the selected variables.
  For example, when selecting Carbon in the Atom combo, if for a given set and datapoint there is a carbon error of +10%, the selected variables for that set and datapoint will have their weights reduced by 10%. The same 10% reduction will be applied if the carbon error were -10%.
  
• Adjust by Atom Balance Error - Manual: The weights values may be modified by a factor whose value depends on the atom error for each set and datapoint, as reported in Check Atom Balance node. This option allows to change weights for variables in Total Moles only. Weights for measurements in the phases are never affected.
  Here, a factor will multiply the weights for a given range of atom error.
  You must specify a lower bound and upper bound of the atom balance error first. For this range, you must then provide a factor to be used to multiply the weights. Thus, the selected variables will have their weights affected by the user-entered factor if the atom error (in absolute terms) for a given set and datapoint is within the error range defined here. With this feature, for example, if the errors are between 5% and 20%, you can reduce the weights by 10%. You may again make a second request to reduce the weights by 20%, if the error is between 20% and 30%.
  

Depending on the selections above, more information is requested by REX as follows:
• The Custom Weight field only appears when Multiply to Custom Weight or Custom Weight is selected in Modification type. In Custom Weight, you may enter a real number. This number will multiply the present weights or will replace them, according to the option selected in Modification Type.
  
• The Atom combo appears only if Adjust by Atom Balance Error is selected. It lists all atoms that are shown in Formula node.
  The weights adjustment will be done based on the experimental error for the selected atom. For manual adjustment based on atom balance error additional information on error ranges will be requested here.
  After setting the options, you may execute the modification with the Apply button.