gemseo / problems / sobieski

core module

SSBJ core computations

class gemseo.problems.sobieski.core.SobieskiProblem(dtype='float64')

Bases: object

Class defining Sobieski problem and related method to the problem such as disciplines computation, constraints, reference optimum

Constructor

Parameters

dtype (str) – data type of problem, either “float64” or “complex128”.

CONTRAINTS_NAMES = ('Stress_x1', 'Stress_x2', 'Stress_x3', 'Stress_x4', 'Stress_x5', 'Twist', 'Pgrad', 'ESF', 'Temperature', 'Throttle')

CONTRAINTS_NAMES_INEQUALITY = ('c_Stress_x1', 'c_Stress_x2', 'c_Stress_x3', 'c_Stress_x4', 'c_Stress_x5', 'c_Twist_upper', 'c_Twist_lower', 'c_Pgrad', 'c_ESF_upper', 'c_ESF_lower', 'c_Throttle', 'c_Temperature')

COUPLING_VARIABLES_NAMES = ('Total weight', 'Fuel weight', 'Wing twist', 'Lift', 'Drag', 'Lift/Drag', 'SFC', 'Engine weight')

DTYPE_COMPLEX = 'complex128'

DTYPE_DOUBLE = 'float64'

DV_NAMES = ('TaperRatio', 'SectionalArea', 'Cf', 'Throttle_setting', 'eta', 'h', 'Mach', 'AR', 'Phi', 'sref')

DV_NAMES_NORMALIZED = ('x_TaperRatio', 'x_SectionalArea', 'x_Cf', 'x_Throttle_setting', 'x_eta', 'x_h', 'x_Mach', 'x_AR', 'x_Phi', 'x_sref')

ESF_LOWER_LIMIT = 0.5

ESF_UPPER_LIMIT = 1.5

PRESSURE_GRADIENT_LIMIT = 1.04

STRESS_LIMIT = 1.09

TEMPERATURE_LIMIT = 1.02

TWIST_LOWER_LIMIT = 0.8

TWIST_UPPER_LIMIT = 1.04

blackbox_aerodynamics(x_shared, y_12, y_32, x_2, true_cstr=False)

This function calculates drag and lift to drag ratio of A/C.

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_12 (ndarray) –

  shared variables coming from blackbox_structure:

  • y_12[0]: total aircraft weight

  • y_12[1]: wing twist

• y_32 (ndarray) –

  shared variables coming from blackbox_propulsion:

  • y_32[0]: engine scale factor

• x_2 (ndarray) –

  aero. design variable:

  • x_2[0]: friction coeff

• true_cstr – Default value = False)

Returns

y_2, y_21, y_23, y_24, g_2:

• y_2: aero. analysis outputs

• y_2[0]: lift

• y_2[1]: drag

• y_2[2]: lift/drag ratio

• y_21: shared variable for blackbox_structure (lift)

• y_23: shared variable for blackbox_propulsion (drag)

• y_24: shared variable for blackbox_mission (lift/drag ratio)

• g_2: aero constraint (pressure gradient)

Return type

ndarray, ndarray, ndarray, ndarray, ndarray

blackbox_mission(x_shared, y_14, y_24, y_34)

THIS SECTION COMPUTES THE A/C RANGE from Breguet’s law

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_14 (ndarray) –

  shared variables coming from blackbox_structure:

  • y_14[0]: total aircraft weight

  • y_14[1]: fuel weight

• y_24 – shared variables coming from blackbox_aerodynamics (lift/drag ratio)

• y_34 (ndarray) – shared variables coming from blackbox_propulsion (SFC)

Returns

y_4: range value

Return type

ndarray

blackbox_propulsion(x_shared, y_23, x_3, true_cstr=False)

This function calculates fuel comsumption, engine weight and engine scale factor

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_23 (ndarray) – shared variables coming from blackbox_aerodynamics (drag)

• x_3 (ndarray) – power/propulsion design variable (throttle setting)

• true_cstr (bool) – analysis returns constraint absolute value or relative value to bounds (Default value = False)

Returns

y_3, y_34, y_31, y_32, g_3:

• y_3: output variables for propulsion analysis

• y_3[0]: SFC

• y_3[1]: engine weight

• y_3[2]: engine scale factor

• y_34: shared variable for blackbox_mission (SFC)

• y_31: shared variable for blackbox_structure (engine weight)

• y_32: shared variable for blackbox_aerodynamics (ESF)

• g_3: propulsion constraints

• g_3[0]: engine scale factor constraint

• g_3[1]: engine temperature

• g_3[2]: throttle setting constraint

Return type

ndarray, ndarray, ndarray, ndarray, ndarray

blackbox_structure(x_shared, y_21, y_31, x_1, true_cstr=False)

This function calculates the weight of the aircraft by structure and adds them to obtain a total aircraft weight.

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_21 (ndarray) – lift

• y_31 (ndarray) – engine weight

• x_1 (ndarray) –

  weight design variables:

  • x_1[0]: wing taper ratio

  • x_1[1]: wingbox x-sectional area as poly. funct

• true_cstr – Default value = False)

Returns

g_1,y_1, y_12:

• g_1 : vector of constraints for weight analysis

• g_1[0] to g_1[4]: stress on wing

• g_1[5]: wing twist as constraint

• y_1: weight analysis outputs

• y_1[0]: total aircraft weight

• y_1[1]: fuel weight

• y_1[2]: wing twist

• y_12: shared variables used for aero. computations (blackbox_aerodynamics)

• y_12[0]: total aircraft weight

• y_12[1]: wing twist

• y_14: shared variables used for range computation (blackbox_mission)

• y_14[0]: total aircraft weight

• y_14[1]: fuel weight

Return type

ndarray, ndarray, ndarray, ndarray

default_constants()

Definition of constants vector C for Sobieski problem

Returns

constant vector

Return type

ndarray

derive_blackbox_aerodynamics(x_shared, y_12, y_32, x_2)

This function calculates drag and lift to drag ratio of A/C.

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_12 (ndarray) –

  shared variables coming from blackbox_structure:

  • y_12[0]: total aircraft weight

  • y_12[1]: wing twist

• y_32 (ndarray) –

  shared variables coming from blackbox_propulsion:

  • y_32[0]: engine scale factor

• x_2 (ndarray) –

  aero. design variable:

  • x_2[0]: friction coeff

Returns

J : Jacobian matrix

Return type

dict(ndarray)

derive_blackbox_mission(x_shared, y_14, y_24, y_34)

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_14 (ndarray) –

  shared variables coming from blackbox_structure:

  • y_14[0]: total aircraft weight

  • y_14[1]: fuel weight

• y_24 – shared variables coming from blackbox_aerodynamics (lift/drag ratio)

• y_34 (ndarray) – shared variables coming from blackbox_propulsion (SFC)

Returns

J : Jacobian matrix

Return type

dict(ndarray)

derive_blackbox_propulsion(x_shared, y_23, x_3, true_cstr=False)

This function calculates the Jacobian matrix of propulsion

Parameters

• x_shared (ndarray) –

  shared design variable vector:

  • x_shared[0]: thickness/chord ratio

  • x_shared[1]: altitude

  • x_shared[2]: Mach

  • x_shared[3]: aspect ratio

  • x_shared[4]: wing sweep

  • x_shared[5]: wing surface area

• y_23 (ndarray) – shared variables coming from blackbox_aerodynamics (drag)

• x_3 (ndarray) – power/propulsion design variable (throttle setting)

• true_cstr (bool) – analysis returns constraint absolute value or relative value to bounds (Default value = False)

Returns

J : Jacobian matrix

Return type

dict(ndarray)

derive_blackbox_structure(x_shared, y_21, y_31, x_1, true_cstr=False)

Compute jacobian matrix of structural analysis y_1 is the vector of structural outputs and g_1 are the structural constraints

• y_1[0]: total aircraft weight

• y_1[1]: fuel weight

• y_1[2]: wing twist

Parameters

• x_shared (ndarray) – shared design variable vector

• x_1 (ndarray) –

  structure design variable vector:

  • x_1[0]: wing taper ratio

  • x_1[1]: wingbox x-sectional area as poly. funct

• y_21 (ndarray) – coupling variable from aerodynamics (lift)

• y_31 (ndarray) – coupling variable from propulsion (Engine weight)

• true_cstr – Default value = False)

Returns

J : Jacobian matrix

Return type

dict(ndarray)

get_bounds_by_name(variables_names)

Class method that return bounds of design variables and coupling variables

Parameters

variables_names – name of variable

Returns

lower bound and upper bound

get_constraints(design_vector, true_cstr=False)

Compute all constraints of Sobieski problem

Parameters

• design_vector (ndarray) – design variable vector

• true_cstr (bool) – indicates if user wants absolute value or relative to limits (Default value = False)

Returns

outputs : g_1,g_2,g_3:constraint values

Return type

ndarray

get_default_inputs(names=None)

Returns a set of default inputs for the different disciplines

Parameters

names (str or list(str)) – specific data names, if None, returns all inputs (Default value = None)

Returns

indata , a dict of input data

Return type

dict

get_default_inputs_equilibrium(names=None)

Returns a set of default inputs, where coupling variables are at the equilibrium (MDA) for X0

Parameters

names (str or list(str)) – specific data names, if None, returns all inputs (Default value = None)

Returns

indata , a dict of input data

Return type

dict

get_default_inputs_feasible(names=None)

Returns a set of default inputs for the different disciplines

Parameters

names (str or list(str)) – specific data names, if None, returns all inputs (Default value = None)

Returns

indata , a dict of input data

Return type

dict

get_default_x0()

Function that returns a default initial value for design variables

Returns

i_0 , initial design variables

Return type

ndarray

get_random_input(names=None, seed=None)

Get a randomized starting point with specified variables names

Parameters

• names (str or list(str)) – specific data names, if None, returns all inputs (Default value = None)

• seed – the seed for random number generation (Default value = None)

Returns

values of specified design variable name

Return type

ndarray

get_sobieski_bounds()

Set the input design bounds and return them as 2 ndarrays

Returns

ub,lb: upper and lower bounds

Return type

ndarray,ndarray

get_sobieski_constraints(g_1, g_2, g_3, true_cstr=False)

Compare the constraints to their limits for Sobieski problem

Parameters

• g_1 (ndarray) –

  vector of constraints for weight analysis:

  • g_1[0] to g_1[4]: stress on wing

  • g_1[5]: wing twist as constraint

• g_2 (ndarray) –

  vector of constraints for aerodynamics analysis:

  • g_2[0]: pressure gradient

• g_3 (ndarray) –

  vector of constraints for propulsion analysis:

  • g_3[0]: engine scale factor constraint

  • g_3[1]: engine temperature

  • g_3[2]: throttle setting constraint: must be, at least, requested throttle

• true_cstr (bool) – choice for true value of constraints or comparison to bounds (Default value = False)

Returns

constraints_values or comparison to bounds

Return type

ndarray

get_sobieski_optimum()

Optimum by Sobieski with BLISS

Returns

array of x optimum x_1, x_2, x_3, x_shared concatenated

Return type

ndarray

get_sobieski_optimum_range()

Return range value by Sobieski with BLISS

Returns

optimal range value

Return type

ndarray

get_x0_feasible(names=None)

Gets a feasible starting point with specified variables names

Parameters

names (str or list(str)) – specific data names, if None, returns all inputs (Default value = None)

Returns

values of specified design variable name

Return type

ndarray

normalize_inputs(input_vector)

This function normalizes design variables w.r.t lower and upper bounds of these design variables They will be defined in [0,1]

Parameters

input_vector (ndarray) – real design variables vector

Returns

normalized vector of design variables

Return type

ndarray

read_design_space()

Reads the sobieski design space file and creates a DesignSpace instance

systemanalysis_gauss_seidel(design_vector, true_cstr=False, accuracy=0.001)

This subfunction uses Gauss-Seidel iterations on the A/C range optimization model to compute behavior variables, given a set of design variables. Black boxes WEIGHT, DRAGPOLAR, and POWER are called

Parameters

• design_vector (ndarray) – design variable vector

• true_cstr (bool) – return constraint value or compare it to bounds (Default value = False)

• accuracy (float) – system resolution accuracy (Default value = 1e-3)

Returns

y_1, y_2, y_3, y_4, y_12, y_14, y_21, y_23, y_24, y_31, y_32, y_34, g_1, g_2, g_3:

• y_1: weight analysis outputs

• y_1[0]: total aircraft weight

• y_1[1]: fuel weight

• y_1[2]: wing twist

• y_2: aero. analysis outputs

• y_2[0]: lift

• y_2[1]: drag

• y_2[2]: lift/drag ratio

• y_3: output variables for propulsion analysis

• y_3[0]: SFC

• y_3[1]: engine weight

• y_4: range computation output

• y_12: shared variables from blackbox_structure for blackbox_aerodynamics

• y_12[0]: total aircraft weight

• y_12[1]: wing twist

• y_14: shared variables coming from blackbox_structure for blackbox_mission

• y_14[0]: total aircraft weight

• y_14[1]: fuel weight

• y_21: lift from blackbox_aerodynamics for blackbox_structure

• y_23: drag from blackbox_aerodynamics for blackbox_propulsion

• y_24: lift/drag ratio coming from blackbox_aerodynamics for blackbox_mission

• y_31: engine weight coming from blackbox_propulsion for blackbox_structure

• y_32: engine scale factor coming from BlackBoxPower for blackbox_aerodynamics

• y_34:SFC coming from blackbox_propulsion for blackbox_mission

• g_1: vector of constraints for weight analysis

• g_1[0] to g_1[4]: stress on wing

• g_1[5]: wing twist as constraint

• g_2: aero constraint (pressure gradient)

• g_3: propulsion constraints

• g_3[0]: engine scale factor constraint

• g_3[1]: engine temperature

• g_3[2]: throttle setting constraint

Return type

ndarray

unnormalize_inputs(input_vector)

This function unnormalizes design variables

Parameters

input_vector (ndarray) – normalized design variables vector

Returns

real vector of design variables

Return type

ndarray