Optimizing Normalizer Breakpoints

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Overview of Calibrating Normalizers Optimizing Breakpoints Example of Breakpoint Optimization Viewing the Normalizer Comparison Pane

Overview of Calibrating Normalizers

Select a normalizer in the tree display. This displays the Normalizer view, where you can calibrate the normalizers.

This section describes how you can use CAGE to space the breakpoints over the range of the normalizers.

To space the breakpoints, either click the buttons on the toolbar or select from the following options on the Normalizer menu:

• Initialize

  This spaces the breakpoints evenly along the normalizer. For more information, see Initializing Breakpoints.

• Fill

  This spaces the breakpoints by reference to the model. For example, you can place more breakpoints where the model curvature is greatest. For more information, see Optimizing Breakpoints.

• Optimize

  This moves the breakpoints to minimize the least square error over the range of the axis. To optimize normalizers, each normalizer must have a single variable input that is an input to the model (and must be different from the input to the other normalizer for 2D tables).

  For more information, see How CAGE Optimizes Normalizer Breakpoints.

Note   Fill and Optimize are only available when you are calibrating with reference to a model, when you are performing Feature calibrations.

For more information about the Normalizer view controls, see Normalizer View.

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Optimizing Breakpoints

Optimizing breakpoints spaces the breakpoints by reference to the model. For example, one method places the majority of the breakpoints where the curvature of the model is greatest. This option is only available when you are performing Feature calibrations. To learn more, see How CAGE Optimizes Normalizer Breakpoints.

For example, a model of the spark angle that produces the maximum brake torque (MBT) has the following inputs: engine speed N, relative air charge L, and air/fuel ratio A. You can space the breakpoints for engine speed and relative air charge over the range of these variables by referring to the model.

To space the breakpoints based on model curvature, perform the following steps:

1. Click or select Normalizer > Fill.

   The Breakpoint Fill Options dialog box opens.

   

2. Choose the appropriate method to space your breakpoints, from the drop-down menu in the dialog box.

   The preceding example shows ShareAveCurv. For more information about the methods for spacing the breakpoints, see Filling Methods.

3. Enter the ranges of the values for the normalizers.

   The preceding example shows Range N 500 6500, and Range L, 0.1 1.

4. Enter the ranges of the other model variables.

   CAGE spaces the breakpoints by reference to the model. It does this at selected points of the other model variables. The example shows 11 17 for the Range of A and 2 for the Number of points. This takes two slices through the model at A = 11 and A = 17. Each slice is a surface in N and L. That is, MBT(N, L, 11) and MBT(N, L, 17).

   CAGE computes the average value of these two surfaces to give an average model MBT_AV(N, L).

   If you set Number of points to one, and specify a range, then the mean of the range is chosen as the evaluation point.

5. Click OK.

   Note   If any of the breakpoints is locked, each group of unlocked breakpoints is independently spaced according to the selected algorithm.

If you increase the number of slices through the model, you increase the computing time required to calculate where to place the breakpoints.

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Example of Breakpoint Optimization

For an example of breakpoint optimization, say you have a model of the spark angle that produces the MBT (maximum brake torque). The model has the following inputs: engine speed, N, relative air charge, L, and air/fuel ratio, A. You can optimize the breakpoints for N and L over the ranges of these variables.

To optimize the breakpoints, perform the following steps:

1. Ensure that the optimization routine works over reasonable values for the table by choosing one of these methods:

   1. Select Normalizer > Initialize.

   2. Select Normalizer > Fill .

2. Click  on the toolbar or select Normalizer > Optimize.

   This opens the following dialog box.

   

3. Enter the ranges for the normalizers.

   The example shows 0.2 0.811 for the Range of L, and 750 6500 for N.

4. Enter the appropriate number of grid points for the optimization.

   This defines a grid over which the optimization works. In the preceding example, the number of grid points is 36 for both L and N. This mesh is combined using cubic splines to approximate the model.

5. Enter ranges and numbers of points for the other model variables.

   The example shows a Range of A of 14.3 and the Number of points is 1.

6. Decide whether or not to reorder deleted breakpoints, by clicking the radio button.

   If you choose to reorder deleted breakpoints, the optimization process might redistribute them between other nondeleted breakpoints (if they are more useful in a different position).

   For information about deleting breakpoints, see Editing Breakpoints.

7. Click OK.

CAGE calculates the table filled with the mesh at the current breakpoints. Then CAGE calculates the total square error between the table values and the mesh model.

The breakpoints are adjusted until this error is minimized, using nonlinear least squares optimization (See the reference page for lsqnonlin).

When optimizing the breakpoints, it is worth noting the following:

• The default range for the normalizer variable is the range of the variable.

• The default value for all other model variables is the set point of the variable.

• The default number of grid points is three times the number of breakpoints.

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Viewing the Normalizer Comparison Pane

To view or hide the comparison pane, select View > Feature/Model Comparison. Alternatively, click  , the "snapper point" at the bottom of the normalizer display panes.

The comparison pane displays a comparison between the following:

• A full factorial grid filled using these breakpoints

• The model

  Note   This is not a comparison between the current table values and the model. To compare the current table values and the model, see Comparing the Strategy and the Model.

To make full use of the comparison pane,

1. Adjust the ranges of the variables that are common to the model and table.

2. Adjust the values selected for any variables in the model that are not in the selected table.

   The default for this is the set point of the variable, as specified in the variable dictionary. For more information, see Using Set Points in the Variable Dictionary.

3. Check the number of points at which the display is calculated.

4. Check the comparison between the table and the model.

   Right-click the comparison graph to view the error display.

5. Check some of the error statistics for the comparison, and use the comparison to locate where improvements can be made.

Error Display

The comparison pane can also be used to display the error between the model and the 'generated table' (grid filled using these breakpoints).

To display the error, select one of the Error items from the Plot type drop-down list.

This changes the graph to display the error between the model and the table values at these breakpoints.

You can display the error data in one of the following ways:

• Error (Table—Model). This is the difference between the feature and the model.

• Squared Error. This is the error squared.

• Absolute Error. This is the absolute value of the error.

• Relative Error. This is the error as a percentage of the value of the table.

• Absolute Relative Error (%). This is the absolute value of the relative error.

See Also

• Comparing the Strategy and the Model

This describes the comparison made when a table node is selected in the tree display.

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Initializing Tables and Normalizers

Optimizing Table Values

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