CAGE User's Guide

Optimizing Breakpoints

Optimizing breakpoints alters the position of the table normalizers so that the total square error between the model and the table is reduced.

This routine improves the fit between your strategy and your model. The following illustration shows how the optimization of breakpoint positions can reduce the difference between the model and the table. The breakpoints are moved to reduce the peak error between breakpoints. In CAGE this happens in two dimensions across a table.

To see the difference between optimizing breakpoints and optimizing table values, compare with the illustration in Optimizing Table Values.

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:

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.

1. This opens the following dialog box.

   

3. Enter the ranges for the normalizers.

1. For the preceding example, enter 0.2 0.811 for the Range of L, and enter 750 6500 for N.

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

1. 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.

1. In the preceding example, the Range of A is 14.3 and the Number of points is 1.

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

1. 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 Deleting 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 (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.

See Also

• See the lsqnonlin reference page.
• Calibrating the Normalizers

Filling Breakpoints

Normalizer View