gemseo / problems / sobieski / core

problem module

The Sobieski’s SSBJ problem.

class gemseo.problems.sobieski.core.problem.SobieskiProblem(dtype='float64')[source]

Bases: object

The Sobieski’s SSBJ problem.

This problem seeks to maximize the range of a super-sonic business jet (SSBJ) over a bounded design space whilst satisfying inequality constraints.

The objective and constraint functions come from a system of four disciplines:

  1. the structure, computing the total aircraft mass \(y_{1,4,0}\) and \(y_{1,2,0}\), the fuel mass \(y_{1,4,1}\), the wing twist \(y_{1,2,1}\) and the five stress constraints \(g_{1,0},\ldots,g_{4,0}\).

  2. the aerodynamics discipline, computing the lift \(y_{2,1}\), drag \(y_{2,3}\), lift-to-drag ratio and pressure gradient constraint \(g_2\),

  3. the propulsion, computing the engine mass \(y_{3,1,0}\), the engine scale factor \(y_{3,2,0}\), which is also the constraint \(g_{3,0}\), the specific fuel consumption \(y_{3,4,0}\), the engine temperature constraint \(g_{3,1}\), and the throttle setting constraint \(g_{3,2}\)

  4. the mission, computing the range \(y_{4,0}\).

Notes

  • The structure, aerodynamics, propulsion and mission disciplines are numbered from 1 to 4.

  • The variable \(y_{i,j,k}\) is a coupling variable from the discipline \(i\) to the discipline \(j\).

  • The aerodynamics, structure and propulsion disciplines are strongly coupled, i.e. each of them depends directly or indirectly on the others, and provide inputs to the mission discipline.

The design variables can be classified into four groups:

  • the design variables which are inputs to at least two disciplines,

    • \(x_{0,0}\): the thickness-to-chord ratio,

    • \(x_{0,1}\): the altitude (ft),

    • \(x_{0,2}\): the Mach number,

    • \(x_{0,3}\): the aspect ratio,

    • \(x_{0,4}\): the wing sweep (deg),

    • \(x_{0,5}\): the wing surface area (ft 2),

  • the design variables which are inputs of the structure discipline only:

    • \(x_{1,0}\): the wing taper ratio,

    • \(x_{1,1}\): the wingbox x-sectional area

  • the design variables which are inputs of the aerodynamics discipline only:

    • \(x_{2,0}\): the skin friction coefficient,

  • the design variables which are inputs of the propulsion discipline only:

    • \(x_{3,0}\): the throttle setting (engin mass flow).

Lastly, this problem is based on five constants:

  • \(c_0\): the minimum fuel weight,

  • \(c_1\): the miscellaneous weight,

  • \(c_2\): the maximum load factor,

  • \(c_3\): the reference engine weight,

  • \(c_4\): the minimum drag coefficient.

Parameters

dtype (str) –

The data type for the NumPy arrays, either “float64” or “complex128”.

By default it is set to float64.

Return type

None

get_bounds_by_name(variables_names)[source]

Return the lower and upper bounds of variables.

Parameters

variables_names (Sequence[str]) – The names of the variables.

Returns

The lower and upper bounds of the variables; the array components keep the order of the variables.

Return type

tuple[numpy.ndarray, numpy.ndarray]

get_constraints(design_vector, true_cstr=False)[source]

Compute all the constraints.

Parameters

  • design_vector (numpy.ndarray) – The design vector.

  • true_cstr (bool) –

    If True, return the value of the constraint outputs. Otherwise, return the distance to the corresponding constraint thresholds.

    By default it is set to False.

Returns

The value of the constraints \(g_1\), \(g_2\) and \(g_3\).

Return type

tuple[numpy.ndarray, numpy.ndarray, numpy.ndarray]

get_default_inputs(names=None)[source]

Return the default variable values at the default initial point.

Parameters

names (str | Iterable[str] | None) –

The names of the variables of interest. If None, use all the variables of the problem.

By default it is set to None.

Returns

The default values of some variables at the default initial point.

Return type

dict[str, ndarray]

get_default_inputs_equilibrium(names=None)[source]

Return the default variable values at a multidisciplinary feasible point.

The coupling variables are at the equilibrium, in the sense of the multidisciplinary analysis (MDA).

Parameters

names (str | Iterable[str] | None) –

The names of the variables of interest. If None, use all the variables of the problem.

By default it is set to None.

Returns

The default values of some variables at a multidisciplinary feasible point.

Return type

dict[str, ndarray]

get_default_inputs_feasible(names=None)[source]

Return the default variable values at the default initial feasible point.

Parameters

names (str | Iterable[str] | None) –

The names of the variables of interest. If None, use all the variables of the problem.

By default it is set to None.

Returns

The default values of some variables at the default initial feasible point.

Return type

dict[str, ndarray]

get_random_input(names=None, seed=None)[source]

Return a randomized starting point related to some input variables.

Parameters

  • names (str | Iterable[str] | None) –

    The names of the variables. If None, use all the input variables.

    By default it is set to None.

  • seed (int | None) –

    The seed for the random number generation. If None, do not set the seed.

    By default it is set to None.

Returns

The randomized starting point.

Return type

ndarray

get_sobieski_constraints(g_1, g_2, g_3, true_cstr=False)[source]

Return either the value of the constraints or the distance to the thresholds.

Parameters

  • g_1 (numpy.ndarray) – The constraints from the structure discipline: g_1[0] to g_1[4] are the stresses on wing and g_1[5] is the wing twist.

  • g_2 (numpy.ndarray) – The constraint (pressure gradient) from the aerodynamics discipline.

  • g_3 (numpy.ndarray) –

    The constraints from the propulsion discipline: g_3[0] is the engine scale factor,

    g_3[1] is the engine temperature and g_3[2] is the throttle setting constraint.

  • true_cstr (numpy.ndarray) –

    If True, return the value of the outputs. Otherwise, return the distance to the corresponding constraint thresholds.

    By default it is set to False.

Returns

The constraints or the distance to the thresholds, according to true_cstr.

Return type

numpy.ndarray

get_x0_feasible(names=None)[source]

Return a feasible starting point related to some input variables.

Parameters

names (str | Iterable[str] | None) –

The names of the variables. If None, use all the input variables.

By default it is set to None.

Returns

The feasible starting point.

Return type

ndarray

normalize_inputs(input_vector)[source]

Normalize an input vector with respect to the variable bounds.

Parameters

input_vector (numpy.ndarray) – The input vector.

Returns

The normalized input vector with components in \([0,1]\).

Return type

numpy.ndarray

unnormalize_inputs(input_vector)[source]

Unnormalize an input vector with respect to the variable bounds.

Parameters

input_vector (numpy.ndarray) – The normalized input vector.

Returns

The input vector in the variable space.

Return type

numpy.ndarray

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')
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
property aerodynamics: gemseo.problems.sobieski.core.aerodynamics.SobieskiAerodynamics

The aerodynamics discipline.

property constants: numpy.ndarray

The constant vector.

property design_bounds: tuple[numpy.ndarray, numpy.ndarray]

The lower and upper bounds of the design variables.

property design_space: gemseo.algos.design_space.DesignSpace

The design space.

property design_space_with_physical_naming: gemseo.algos.design_space.DesignSpace

The design space with physical naming.

property initial_design: numpy.ndarray

The initial design \(x\).

property mission: gemseo.problems.sobieski.core.mission.SobieskiMission

The mission discipline.

property optimum_design: numpy.ndarray

The optimal design vector found by Sobieski with BLISS.

property optimum_range: numpy.ndarray

The optimal range found by Sobieski with BLISS.

property propulsion: gemseo.problems.sobieski.core.propulsion.SobieskiPropulsion

The propulsion discipline.

property structure: gemseo.problems.sobieski.core.structure.SobieskiStructure

The structure discipline.