Dmodel Mixed-Variable Optimization Example

This page introduces the Dmodel_mixed_variables project.
Compared with the Dmodel project, Dmodel_mixed_variables uses the ga optimizer and eMotorSolution integration to optimize categorical and discrete variables that determine the motor configuration together with the continuous variables of the NGnet on/off method.

machine.yaml (Dmodel_mixed_variables project)

The basic machine.yaml settings are the same as in the Dmodel project, but the ems_project_filepath configuration is added to enable optimization with eMotorSolution.
The Dmodel_mixed_variables project already contains the eMotorSolution project JSON file, so specify its path.

# ems functionality link
ems_project_filepath: "Path/To/EMSOptimizer/projects/Dmodel_mixed_variables/Dmodel.json"

info

Set the file path above according to the location where EMSOptimizer is installed.

optimization.yaml (Dmodel_mixed_variables project)

The contents of optimization.yaml are shown below.
ems_shape_builder is Dmodel_mixed_builder, an implementation example that receives one categorical variable (permanent-magnet material), one discrete variable (number of coil turns), and three continuous variables (permanent-magnet dimensions), and configures them through eMotorSolution integration.
The NGnet on/off method is also configured as in the Dmodel project.

ems_shape_builder:
  name: Dmodel_mixed_builder
level_set_function:
  name: ngnet
  kwargs:
    sigma: 0.0020
    design_region: [[0.008, 0.0275], [0, 45.0]]
    coordinate: Polar

Set ga as the optimizer and specify one categorical variable and one discrete variable. The categorical variable (permanent-magnet material) is 0 (NdFeB, $B_r=1.25\text{T}$) or 1 (FerriteMagnet, $B_r=0.40\text{T}$); the discrete variable (number of coil turns) ranges from 20 to 35.
Specify the ranges of the continuous variables in bounds. Here, the lower and upper bounds of the permanent-magnet dimensions are specified.

optimizer:
  name: ga
  kwargs:
    seed: 42
    population_size: 30
    variable_type_counts:
      categorical: 1
      discrete: 1
    categorical_choices: [[0, 1]]
    discrete_values: [[20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35]]
    bounds: [[10.0, 20.0], [3.0, 13.0], [1.5, 3.5]]

optimization_problem.yaml (Dmodel_mixed_variables project)

In optimization_problem.yaml, the configuration maximizes average torque and minimizes a virtual permanent-magnet material cost (permanent-magnet area × cost coefficient).
When FerriteMagnet is selected, a coefficient of 0.2 is applied to the cost to reflect its lower cost than NdFeB.
The constraint also limits the maximum voltage to 80.0 V. Optimizing the rotor structure and number of turns balances torque and cost while keeping the voltage below the target value.

objectives:
  - function_name: average_torque
    kwargs:
      torque_scale: 4.0
    normalization_const: 2.1
    coefficient: -0.8
  - function_name: magnet_cost
    kwargs:
      physical_tag: 50000
      ferrite_coef: 0.2
    normalization_const: 4.9975e-05
    coefficient: 0.2

ineq_constraints:
  - function_name: maximum_voltage
    normalization_const: 80.0
    baseline: 80.0

Optimization Example

This example performs 50 generations of optimization. The result is shown below: average torque 2.12 Nm, permanent-magnet cost 33.4 ($\text{mm}^2$), and maximum voltage 76.9 V. NdFeB is selected as the permanent-magnet material, and the number of turns is the maximum value, 35.
The same torque is achieved with less permanent-magnet material than in the original Dmodel. The permanent magnets are closer to the rotor surface than in Dmodel, suggesting a shape that makes greater use of magnet torque.

Now change the objective-function settings as follows. Because magnet_cost has a larger weight under these settings, solutions with lower permanent-magnet cost are expected.

objectives:
  - function_name: average_torque
    kwargs:
      torque_scale: 4.0
    normalization_const: 2.1
    coefficient: -0.5
  - function_name: magnet_cost
    kwargs:
      physical_tag: 50000
      ferrite_coef: 0.2
    normalization_const: 4.9975e-05
    coefficient: 0.5

The result after changing the settings is shown below: average torque 0.87 Nm, permanent-magnet cost 5.85 ($\text{mm}^2$), and maximum voltage 69.0 V. FerriteMagnet is selected as the permanent-magnet material, and the number of turns is the maximum value, 35.
Compared with the previous result, the selection of FerriteMagnet is notable. The rotor structure also changes accordingly, suggesting a larger contribution from reluctance torque.