Note
Go to the end to download the full example code.
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]](../../../_images/sphx_glr_plot_variable_influence_001.png)
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)