Optimization

Optimization technique

We are now going to try to set the damper rate so that the performance is in some sense optimal. To do this we have to:

• Define one or more quantities which the optimization process will try to minimize. These are objectives objectives .

• Set restriction on quantities which we want to impose. These are called constraints constraints .

Results

If you have experience with optimization, you know that setting objectives is not easy and several attempts are often necessary before reasonable objectives are defined. When this exercise was developed, the first objectives resulted in very soft damper settings. These gave impressively low acceleration and the wheel stayed on the road. The problem was the car was still bouncing with a significant amplitude at the end of the run (2 seconds). It is necessary to avoid this.

Step 1: Define an optimization process

Procedure

1. Click the New button.

2. Change the study name to AS_NLPQL.

3. In the Type drop-down list, select Optimization.

You can also click the down arrow next to the New button and directly select Optimization in the drop-down list that appears. To rename the study, double-click its name on the left hand side list. Warning The new name will only be saved if you click OK on the Study Manager.

4. Keep NLPQL selected for the Optimization technique.

5. In the Study parameter definition pane, select the check boxes for SkyHookDamp and MainDamp to declare them as inputs for the algorithm.

6. Set the values of upper and lower bounds as well as the default values as shown in the following figure. Note that the default for SkyHookDamp has been changed from 200 to 700. The NLPQL algorithm is sensitive to starting values, and it is often better not to use a starting value on the boundary of the range.

Figure 16: The inputs for the optimization process are now complete

7. Click on the Outputs/Responses tab.

8. Select the Objective check box for MaxBodyAcc to declare it as an objective. This means that we want to make the absolute value of this output as small as possible.

9. Select the Constraint check box for MinTireComp and click twice on the Lower bound cell to edit it, and enter the value 0.0.

This way, you add a constraint to this output: you want it not to exceed 0.0.

10. In a similar way make the Upper bound for FinalDisp 0.01.

This means that we constrain the final value for the body displacement to be within 10 mm of the equilibrium position.

Figure 17: Outputs for the optimization process

Results

Leave all the other values empty.

Step 2: Run and observe the optimization process

Procedure

1. Click the Start Run button.

The run is fast and the algorithm gives the following solution after 51 runs. Figure 18: The Active Suspension with NLPQL

Note The most common error that you may experience using NLPQL, is the error number 4: The line search could not be terminated successfully. This is often a problem of accuracy which can be cured by adjusting the relative gradient step and the desired final accuracy. However, even with this error, the results obtained are often good enough to be used as they are.

With a main damper setting of about 760 N/(m/s) and a skyhook damper setting of about 700 N/(m/s) the maximum acceleration is very reasonable at 8.6 m/s/s. The constraints are respected: the tire stays in contact with the road and the car body is within 10 mm of the equilibrium position at the end of the run.

2. When the run is complete or even while it is running, it is instructive to plot some quantities. You can do normal plots and set an automatic update.Click the Add plot button.

The Design Exploration Plots dialog box appears.

3. Keep History plot in the plot type drop-down list.

4. Select MaxBodyAcc on the left hand side list and click on the >> button.

MaxBodyAcc appears on the right hand side list.

5. Click OK.

Figure 19: Evolution of Body Acceleration

6. Apply the values in Simcenter Amesim. Click the Apply best results button.

7. Perform a run in Simcenter Amesim. When the run is complete, plot the body displacement and the tire compression from the sketch.

Figure 20: Optimized body displacement

Figure 21:

Following this study, there are two main points to clarify:

• NLPQL does not ensure that the solution found is the global best solution. NLPQL may stop on local minima. We can check if the minimum found is a global one with a Genetic algorithm.

• This first result is not exactly what we were expecting. It seems that this system is not in a stable state at the end of the simulation, and does have some oscillations.

In the next section we will perform this study using some better constraints.