Drivers for SimulationΒΆ

Now that we have a functional and quick Vehicle assembly, we need to complete the problem by providing a way to simulate the acceleration and the EPA fuel economy estimates. The acceleration test requires an integration in time to match a specified velocity profile. In other words, the vehicle assembly needs to be executed at each time step to produce the instantaneous acceleration. The EPA fuel economy tests are a bit more tricky, though they also require an integration in time. For these tests, the vehicle assembly must be executed while varying the throttle and gear position inputs to match a desired acceleration for the integration segment. Both of these solution procedures were implemented in Python as drivers. The SimAcceleration driver simulates the acceleration test, and the SimEconomy driver simulates the EPA fuel economy test.

Recall that in the Optimization Tutorial, a Driver called CONMINdriver was used to optimize the Paraboloid problem. Similarly, the algorithms that perform these tests have been implemented as OpenMDAO drivers that can be found in These drivers contain OpenMDAO variables where you can specify the connections to the vehicle component that we developed in the previous section. Specifically, to drive the Vehicle assembly, the simulation driver needs to be able to set the velocity, throttle, and gear positions. Likewise, it also needs to be able to read variables from the vehicle component. For the acceleration test, the vehicle’s instantaneous acceleration is needed, and for the economy test, both the acceleration and fuel burn are needed.

You may want to examine the SimAcceleration and the SimEconomy drivers that are found in This tutorial does not cover how to create an OpenMDAO Driver, but a future tutorial will teach this. Until then, you can gain some understanding by studying these drivers, as well as the ones included in the standard library.

The simulation drivers have a variable that stores the result of the simulation:

SimAcceleration - Output:

Variable Description Units
accel_time Time for vehicle to accelerate to 60 mph from a stop. s

SimEconomy - Output:

Variable Description Units
fuel_economy Fuel economy estimate based on EPA driving profile mi/galUS

These variables can be accessed like any other component output, and can be connected to the input of another OpenMDAO component if needed.

Let’s set up a model that runs all three of these simulations to calculate these results: 0-60 acceleration time, EPA city mpg, and EPA highway mpg. To build this model, we need to learn a little more about the iteration hierarchy. In the simple example, we used the iteration hierarchy to define a problem which contained an optimizer and a simple Python component. The iteration hierarchy was defined by adding the component to the driver’s workflow with the add method. If we want to run the SimAcceleration driver on the Vehicle component, we can set up a similar iteration hierarchy where we add the Vehicle component to the SimAcceleration driver’s workflow. The top level assembly would look like this:

from openmdao.main.api import Assembly
from openmdao.examples.enginedesign.driving_sim import SimAcceleration
from openmdao.examples.enginedesign.vehicle import Vehicle

class VehicleSim(Assembly):
    """Optimization of a Vehicle."""

    def configure(self):

        # Create Vehicle instance
        self.add('vehicle', Vehicle())

        # Create 0-60 Acceleration Simulation instance
        self.add('driver', SimAcceleration())

        # Add vehicle to sim workflows.

        # Acceleration Sim setup
        self.driver.velocity_str = 'vehicle.velocity'
        self.driver.throttle_str = 'vehicle.throttle'
        self.driver.gear_str = 'vehicle.current_gear'
        self.driver.acceleration_str = 'vehicle.acceleration'
        self.driver.overspeed_str = 'vehicle.overspeed'

if __name__ == "__main__":

    my_sim = VehicleSim()

    print "Time (0-60): ", my_sim.driver.accel_time

Here, we add a SimAcceleration instance as our top level driver, and then we add our Vehicle instance to the driver’s workflow. We also specify the locations of the vehicle variables we need to manipulate and read. These are stored in Str variables, and are just strings that contain the location of the variables we need in the model hierarchy.

This is a very simple problem, and hence the workflows and iteration hierarchy are also very simple. In OpenMDAO, you can build models with arbitrary levels of complexity. To understand how this works, it is beneficial to use a diagram like this:

Diagram of process model showing the vehicle assembly, some simulation drivers, and the optimizer

Iteration Hierarchy for One Vehicle Simulation

This is the iteration hierarchy for the model we just built. The gray rounded-rectangles represent drivers, the white rounded-rectangles represent components, and the yellow rectangles represent workflows. The gray rounded-rectangle in the upper left-hand corner of a yellow rectangle is the driver that owns that workflow. The remaining items in that rectangle are the components that are contained within that workflow. Note that a workflow can also contain assemblies and drivers, though in this case it just contains a component.

The top level driver in an assembly is always called driver. If no specific driver instance (e.g., SimAcceleration in our example) is declared with the name driver, then the assembly’s default driver is used. The behavior for this default driver is to execute the components in its workflow sequentially, inferring the execution order from the data connections. If there are no data connections, then the components are executed in the order they were added to the workflow.

When we created the Vehicle component above, we used this default driver to create a sequential execution of the Transmission, Engine, and Chassis components in the order that the data connections required. The iteration hierarchy is shown in this diagram:

Diagram of process model showing the vehicle assembly, some simulation drivers, and the optimizer

Iteration Hierarchy for Vehicle Component

Notice that the workflow contains the three components that we used to build the vehicle assembly. The top level driver of the assembly is just called driver.

Now, let’s see how we can make a new assembly that performs all three simulations. Just as we did with the Vehicle assembly, we want to run these three simulations sequentially. In this case, they are drivers, but the mechanics of adding a driver to another driver’s workflow is the same as with a component. An additional level is introduced to this iteration hierarchy because each of the simulation drivers also has its own workflow. Each of these workflows contains the Vehicle instance. The iteration hierarchy for a model that performs the 0-60 accelerations test, the EPA city estimated fuel economy test, and the EPA highway estimated fuel economy test is shown in this diagram:

Diagram of process model showing the vehicle assembly, some simulation drivers, and the optimizer

Iteration Hierarchy for All Vehicle Simulations

Again, the top level driver commands a sequential execution of the SimAcceleration instance and the two SimEconomy instances. The three simulation drivers contain the same Vehicle instance in each of their workflows. That means, that when one driver finished with its simulation, the inputs and outputs of the vehicle component remain set to whatever the last values from that simulation were. The next driver then resets the velocity to 0, the throttle to idle, and the gear to first before starting its own simulation.

Now, let’s build a new assembly that includes all three simulations run sequentially.

from openmdao.main.api import Assembly
from openmdao.examples.enginedesign.driving_sim import SimAcceleration, \
from openmdao.examples.enginedesign.vehicle import Vehicle

class VehicleSim2(Assembly):
    """Optimization of a Vehicle."""

    def configure(self):

        # Create Vehicle instance
        self.add('vehicle', Vehicle())

        # Create Driving Simulation instances
        self.add('sim_acc', SimAcceleration())
        self.add('sim_EPA_city', SimEconomy())
        self.add('sim_EPA_highway', SimEconomy())

        # add Sims to default workflow
        self.driver.workflow.add(['sim_acc', 'sim_EPA_city', 'sim_EPA_highway'])

        # Add vehicle to sim workflows.

        # Acceleration Sim setup
        self.sim_acc.velocity_str = 'vehicle.velocity'
        self.sim_acc.throttle_str = 'vehicle.throttle'
        self.sim_acc.gear_str = 'vehicle.current_gear'
        self.sim_acc.acceleration_str = 'vehicle.acceleration'
        self.sim_acc.overspeed_str = 'vehicle.overspeed'

        # EPA City MPG Sim Setup
        self.sim_EPA_city.velocity_str = 'vehicle.velocity'
        self.sim_EPA_city.throttle_str = 'vehicle.throttle'
        self.sim_EPA_city.gear_str = 'vehicle.current_gear'
        self.sim_EPA_city.acceleration_str = 'vehicle.acceleration'
        self.sim_EPA_city.fuel_burn_str = 'vehicle.fuel_burn'
        self.sim_EPA_city.overspeed_str = 'vehicle.overspeed'
        self.sim_EPA_city.underspeed_str = 'vehicle.underspeed'
        self.sim_EPA_city.profilename = 'EPA-city.csv'

        # EPA Highway MPG Sim Setup
        self.sim_EPA_highway.velocity_str = 'vehicle.velocity'
        self.sim_EPA_highway.throttle_str = 'vehicle.throttle'
        self.sim_EPA_highway.gear_str = 'vehicle.current_gear'
        self.sim_EPA_highway.acceleration_str = 'vehicle.acceleration'
        self.sim_EPA_highway.fuel_burn_str = 'vehicle.fuel_burn'
        self.sim_EPA_highway.overspeed_str = 'vehicle.overspeed'
        self.sim_EPA_highway.underspeed_str = 'vehicle.underspeed'
        self.sim_EPA_highway.profilename = 'EPA-highway.csv'

if __name__ == "__main__":

    my_sim = VehicleSim2()

    print "Time (0-60): ", my_sim.sim_acc.accel_time
    print "City MPG: ", my_sim.sim_EPA_city.fuel_economy
    print "Highway MPG: ", my_sim.sim_EPA_highway.fuel_economy

First, all of the components are instantiated in the assembly, including the Vehicle instance, the SimAcceleration instance, and the two SimEconomy instances, which are named sim_EPA_city and sim_EPA_highway. Next, the three simulation component instances are added to the driver’s workflow. Multiple components can be added to a workflow with a single call to add by passing a list of the name strings. Since there are no data connections between them, they will be executed in the order they appear in this list.

Each simulation driver has a workflow, so the vehicle instance is added to each of their workflows. After that, the simulation connections are specified. The variable profilename is the name of the file that contains the EPA driving profile, which is essentially velocity as a function of time.

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