Variables influence#

In this example, we illustrate the use of the VariableInfluence plot on the Sobieski's SSBJ problem.

from __future__ import annotations

from gemseo import configure_logger
from gemseo import create_discipline
from gemseo import create_scenario
from gemseo.problems.mdo.sobieski.core.design_space import SobieskiDesignSpace

Import#

The first step is to import some high-level functions and a method to get the design space.

configure_logger()
<RootLogger root (INFO)>

Description#

The VariableInfluence post-processing performs first-order variable influence analysis.

The method computes \(\frac{d f}{d x_i} \cdot \left(x_{i_*} - x_{initial_design}\right)\), where \(x_{initial_design}\) is the initial value of the variable and \(x_{i_*}\) is the optimal value of the variable.

Create disciplines#

At this point, we instantiate the disciplines of Sobieski's SSBJ problem: Propulsion, Aerodynamics, Structure and Mission

disciplines = create_discipline([
    "SobieskiPropulsion",
    "SobieskiAerodynamics",
    "SobieskiStructure",
    "SobieskiMission",
])

Create design space#

We also create the SobieskiDesignSpace.

design_space = SobieskiDesignSpace()

Create and execute scenario#

The next step is to build an MDO scenario in order to maximize the range, encoded 'y_4', with respect to the design parameters, while satisfying the inequality constraints 'g_1', 'g_2' and 'g_3'. We can use the MDF formulation, the SLSQP optimization algorithm and a maximum number of iterations equal to 100.

scenario = create_scenario(
    disciplines,
    "y_4",
    design_space,
    formulation_name="MDF",
    maximize_objective=True,
)
scenario.set_differentiation_method()
for constraint in ["g_1", "g_2", "g_3"]:
    scenario.add_constraint(constraint, constraint_type="ineq")
scenario.execute(algo_name="SLSQP", max_iter=10)
WARNING - 00:56:34: Unsupported feature 'minItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
WARNING - 00:56:34: Unsupported feature 'maxItems' in JSONGrammar 'SobieskiMission_discipline_output' for property 'y_4' in conversion to SimpleGrammar.
   INFO - 00:56:34:
   INFO - 00:56:34: *** Start MDOScenario execution ***
   INFO - 00:56:34: MDOScenario
   INFO - 00:56:34:    Disciplines: SobieskiAerodynamics SobieskiMission SobieskiPropulsion SobieskiStructure
   INFO - 00:56:34:    MDO formulation: MDF
   INFO - 00:56:34: Optimization problem:
   INFO - 00:56:34:    minimize -y_4(x_shared, x_1, x_2, x_3)
   INFO - 00:56:34:    with respect to x_1, x_2, x_3, x_shared
   INFO - 00:56:34:    subject to constraints:
   INFO - 00:56:34:       g_1(x_shared, x_1, x_2, x_3) <= 0
   INFO - 00:56:34:       g_2(x_shared, x_1, x_2, x_3) <= 0
   INFO - 00:56:34:       g_3(x_shared, x_1, x_2, x_3) <= 0
   INFO - 00:56:34:    over the design space:
   INFO - 00:56:34:       +-------------+-------------+-------+-------------+-------+
   INFO - 00:56:34:       | Name        | Lower bound | Value | Upper bound | Type  |
   INFO - 00:56:34:       +-------------+-------------+-------+-------------+-------+
   INFO - 00:56:34:       | x_shared[0] |     0.01    |  0.05 |     0.09    | float |
   INFO - 00:56:34:       | x_shared[1] |    30000    | 45000 |    60000    | float |
   INFO - 00:56:34:       | x_shared[2] |     1.4     |  1.6  |     1.8     | float |
   INFO - 00:56:34:       | x_shared[3] |     2.5     |  5.5  |     8.5     | float |
   INFO - 00:56:34:       | x_shared[4] |      40     |   55  |      70     | float |
   INFO - 00:56:34:       | x_shared[5] |     500     |  1000 |     1500    | float |
   INFO - 00:56:34:       | x_1[0]      |     0.1     |  0.25 |     0.4     | float |
   INFO - 00:56:34:       | x_1[1]      |     0.75    |   1   |     1.25    | float |
   INFO - 00:56:34:       | x_2         |     0.75    |   1   |     1.25    | float |
   INFO - 00:56:34:       | x_3         |     0.1     |  0.5  |      1      | float |
   INFO - 00:56:34:       +-------------+-------------+-------+-------------+-------+
   INFO - 00:56:34: Solving optimization problem with algorithm SLSQP:
   INFO - 00:56:34:     10%|█         | 1/10 [00:00<00:00, 24.16 it/sec, obj=-536]
   INFO - 00:56:34:     20%|██        | 2/10 [00:00<00:00, 18.80 it/sec, obj=-2.12e+3]
WARNING - 00:56:34: MDAJacobi has reached its maximum number of iterations, but the normalized residual norm 5.741449586530469e-06 is still above the tolerance 1e-06.
   INFO - 00:56:34:     30%|███       | 3/10 [00:00<00:00, 15.34 it/sec, obj=-3.46e+3]
   INFO - 00:56:34:     40%|████      | 4/10 [00:00<00:00, 14.74 it/sec, obj=-3.96e+3]
   INFO - 00:56:34:     50%|█████     | 5/10 [00:00<00:00, 15.09 it/sec, obj=-4.61e+3]
   INFO - 00:56:35:     60%|██████    | 6/10 [00:00<00:00, 16.11 it/sec, obj=-4.5e+3]
   INFO - 00:56:35:     70%|███████   | 7/10 [00:00<00:00, 16.67 it/sec, obj=-4.26e+3]
   INFO - 00:56:35:     80%|████████  | 8/10 [00:00<00:00, 17.13 it/sec, obj=-4.11e+3]
   INFO - 00:56:35:     90%|█████████ | 9/10 [00:00<00:00, 17.53 it/sec, obj=-4.02e+3]
   INFO - 00:56:35:    100%|██████████| 10/10 [00:00<00:00, 17.86 it/sec, obj=-3.99e+3]
   INFO - 00:56:35: Optimization result:
   INFO - 00:56:35:    Optimizer info:
   INFO - 00:56:35:       Status: None
   INFO - 00:56:35:       Message: Maximum number of iterations reached. GEMSEO stopped the driver.
   INFO - 00:56:35:       Number of calls to the objective function by the optimizer: 12
   INFO - 00:56:35:    Solution:
   INFO - 00:56:35:       The solution is feasible.
   INFO - 00:56:35:       Objective: -3463.120411437138
   INFO - 00:56:35:       Standardized constraints:
   INFO - 00:56:35:          g_1 = [-0.01112145 -0.02847064 -0.04049911 -0.04878943 -0.05476349 -0.14014207
   INFO - 00:56:35:  -0.09985793]
   INFO - 00:56:35:          g_2 = -0.0020925663903177405
   INFO - 00:56:35:          g_3 = [-0.71359843 -0.28640157 -0.05926796 -0.183255  ]
   INFO - 00:56:35:       Design space:
   INFO - 00:56:35:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 00:56:35:          | Name        | Lower bound |        Value        | Upper bound | Type  |
   INFO - 00:56:35:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 00:56:35:          | x_shared[0] |     0.01    | 0.05947685840242058 |     0.09    | float |
   INFO - 00:56:35:          | x_shared[1] |    30000    |   59246.692998739   |    60000    | float |
   INFO - 00:56:35:          | x_shared[2] |     1.4     |         1.4         |     1.8     | float |
   INFO - 00:56:35:          | x_shared[3] |     2.5     |   2.64097355362077  |     8.5     | float |
   INFO - 00:56:35:          | x_shared[4] |      40     |  69.32144380869019  |      70     | float |
   INFO - 00:56:35:          | x_shared[5] |     500     |  1478.031626737187  |     1500    | float |
   INFO - 00:56:35:          | x_1[0]      |     0.1     |         0.4         |     0.4     | float |
   INFO - 00:56:35:          | x_1[1]      |     0.75    |  0.7608797907508461 |     1.25    | float |
   INFO - 00:56:35:          | x_2         |     0.75    |  0.7607584987262048 |     1.25    | float |
   INFO - 00:56:35:          | x_3         |     0.1     |  0.1514057659459843 |      1      | float |
   INFO - 00:56:35:          +-------------+-------------+---------------------+-------------+-------+
   INFO - 00:56:35: *** End MDOScenario execution (time: 0:00:00.565809) ***

Post-process scenario#

Lastly, we post-process the scenario by means of the VariableInfluence plot.

Tip

Each post-processing method requires different inputs and offers a variety of customization options. Use the high-level function get_post_processing_options_schema() to print a table with the options for any post-processing algorithm. Or refer to our dedicated page: Post-processing algorithms.

scenario.post_process(post_name="VariableInfluence", save=False, show=True)
9 variables explain 99% of -y_4, 5 variables explain 99% of g_1[0], 5 variables explain 99% of g_1[1], 5 variables explain 99% of g_1[2], 5 variables explain 99% of g_1[3], 5 variables explain 99% of g_1[4], 4 variables explain 99% of g_1[5], 4 variables explain 99% of g_1[6], 1 variables explain 99% of g_2, 7 variables explain 99% of g_3[0], 7 variables explain 99% of g_3[1], 3 variables explain 99% of g_3[2], 3 variables explain 99% of g_3[3]
    INFO - 00:56:35: Output name; most influential variables to explain 0.99% of the output variation
    INFO - 00:56:35:    -y_4; x_1[1], x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[3], x_shared[4], x_shared[5]
    INFO - 00:56:35:    g_1[0]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_1[1]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_1[2]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_1[3]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_1[4]; x_1[0], x_1[1], x_shared[0], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_1[5]; x_1[0], x_1[1], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_1[6]; x_1[0], x_1[1], x_shared[3], x_shared[5]
    INFO - 00:56:35:    g_2; x_shared[0]
    INFO - 00:56:35:    g_3[0]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
    INFO - 00:56:35:    g_3[1]; x_2, x_3, x_shared[0], x_shared[1], x_shared[2], x_shared[4], x_shared[5]
    INFO - 00:56:35:    g_3[2]; x_3, x_shared[1], x_shared[2]
    INFO - 00:56:35:    g_3[3]; x_3, x_shared[1], x_shared[2]

<gemseo.post.variable_influence.VariableInfluence object at 0x7f193b7bb140>

Total running time of the script: (0 minutes 1.831 seconds)

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