Monte Carlo and RSM study

Here we will use a more complex criterion to avoid oscillations. Instead of only one constraint of the final displacement, we will also impose a constraint on the final velocity, and on the final acceleration.

This time the optimization will be performed in 3 steps.

First we will perform a few experiments in order to observe the behavior of the active suspension, when the mainDamper varies between 500 and 1500, and when the skyHookdamper varies between 200 and 1200.

Then we will compute a mathematical model that approximates the active suspension behavior. This mathematical model will be a polynomial, obtained with RSM.

The third step will consist in using the RSM with a Genetic algorithm in other to find the best values for the damper that respects the new constraints.

Step 1: Create a sampling with a Monte Carlo study

Procedure

1. Click the New button.

2. Change the study name to RSM_sampling.

3. In the Type drop-down list, select Monte Carlo.

You can also click the down arrow next to the New button and directly select Monte Carlo 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. Under Parameters, set the Number of runs to 100, and Seed to 1.

5. In the Study parameter definition pane, set up the controls as shown in the following figure.

Figure 22: Controls

Figure 23: Responses

Results

Figure 24: Sampling method

The following figures give an example of the different sampling methods. As you can see, OLH gives a more uniform sampling than the other methods.

Figure 25: Sample obtained with a random generator

Figure 26: Sample obtained with LH

Figure 27: Sample obtained with OLH

When you launch the study, a Response Surface Model (RSM) can be computed.

Step 2: Compute the Response Surface Model from the Monte Carlo study

An RSM is a mathematical model that approximates the active suspension model we are examining in Simcenter Amesim.

Procedure

1. Click the Response Surface button to create the RSM from the Monte Carlo study.

The Response Surfaces dialog box opens.

2. Select More in the Response Surface Order drop-down list and define the value as 6:

Figure 28: Response Surface Order

Figure 29: Polynomial for the RSM

Using the polynomial shown above, we can obtain a mathematical formula to compute the response we are interested in. Next we will save this RSM in order to use in an Optimization study.

3. Click Save To File to save the RSM file.

4. You can create a plot of the RSM to preview the results by clicking Add plot and then Response Surface as the Plot type.

Results

In the following example, we have selected SkyHookDamp and MainDamp as variables, and FinalDisp as the response:

Figure 30: Selecting variables and responses

Figure 31: RSM Plot

Results

Step 3: Create an optimization study from the RSM

As it is much quicker to evaluate an RSM than an Simcenter Amesim model, it is useful to do an optimization study using the RSM rather than the Simcenter Amesim model.

Procedure

1. Create an optimization study in the same way as described in Step 1: Define an optimization process.

2. Under RSM Tools, click the button to select the RSM file you created in Step 2.Make sure you select the Use RSM File check box. This means that the optimization study will not call the Simcenter Amesim model, but the RSM model computed previously. This way the study will be much faster.

Figure 32: Select your RSM Study

3. In the Optimization technique drop-down list, select Genetic algorithm and set up the Parameters as follows:

Figure 33: Parameters for Genetic algorithm

Procedure

1. In the Study parameter definition pane, set the Lower and Upper bounds as follows for SkyHookDamp and MainDamp:

Figure 34: Lower and upper bounds

Only inputs and outputs that were used when the RSM was computed are available (therefore TireSpringRate and PS_DamperRate are grayed-out). Next we will define several constraints.

2. Define the following constraints:

Figure 35: Constraints

In order to avoid oscillations at the end of the simulation, we will impose some constraints to ensure that the final values for BodyAcceleration, BodyVelocity and BodyDisplacement are "small".

3. Run the study.

Figure 36: Genetic algorithm results

The optimal parameters are found. SkyHookDamp is about 1180, MainDamp is about 805. Note The results are calculated from the RSM, and not from Simcenter Amesim, so they may be slightly different than those obtained with the Active Suspension model.

4. Click the Apply best results button.

5. Plot BodyDisplacement and BodyAcceleration in Simcenter Amesim.

Figure 37: Body Displacement

We can see that we have eliminated the oscillations. Figure 38: Body Acceleration

The acceleration is reasonable, it is kept below 8.5 m/s².