# Source code for gemseo.problems.sobieski.core.mission

```
# Copyright 2021 IRT Saint Exupéry, https://www.irt-saintexupery.com
#
# This program is free software; you can redistribute it and/or
# modify it under the terms of the GNU Lesser General Public
# License version 3 as published by the Free Software Foundation.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
# Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with this program; if not, write to the Free Software Foundation,
# Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
# Contributors:
# INITIAL AUTHORS - initial API and implementation
# and/or initial documentation
# :author: Sobieski, Agte, and Sandusky
# OTHER AUTHORS - MACROSCOPIC CHANGES
# :author: Damien Guenot
# :author: Francois Gallard
# From NASA/TM-1998-208715
# Bi-Level Integrated System Synthesis (BLISS)
# Sobieski, Agte, and Sandusky
"""Mission discipline for the Sobieski's SSBJ use case."""
from __future__ import annotations
from numpy import array
from numpy import ndarray
from numpy import zeros
from gemseo.problems.sobieski.core.discipline import SobieskiDiscipline
[docs]
class SobieskiMission(SobieskiDiscipline):
"""Mission discipline for the Sobieski's SSBJ use case."""
@staticmethod
def __compute_weight_ratio(
w_t: float,
w_f: float,
) -> float:
"""Compute the weight ratio from the Breguet formula.
Args:
w_t: The total weight.
w_f: The fuel weight.
Returns:
The weight ratio ``w_t/(w_t-w_f)``.
"""
return w_t / (w_t - w_f)
@staticmethod
def __compute_dweightratio_dwt(
w_t: float,
w_f: float,
) -> float:
"""Derive the weight ratio with respect to the total weight.
Args:
w_t: The total aircraft weight.
w_f: The fuel weight.
Returns:
The derivative of the weight ratio ``w_t/(w_t-w_f)``
with respect to the total weight.
"""
return -w_f / ((w_t - w_f) * (w_t - w_f))
@staticmethod
def __compute_dweightratio_dwf(
w_t: float,
w_f: float,
) -> float:
"""Derive the weight ratio with respect to the fuel weight.
Args:
w_t: The total aircraft weight.
w_f: The fuel weight.
Returns:
The derivative of the weight ratio ``w_t/(w_t-w_f)``
with respect to the fuel weight.
"""
return w_t / ((w_t - w_f) * (w_t - w_f))
def __compute_dlnweightratio_dwt(
self,
w_t: float,
w_f: float,
) -> float:
"""Derive the logarithm of the weight ratio with respect to the total weight.
Args:
w_t: The total aircraft weight.
w_f: The fuel weight.
Returns:
The derivative of the logarithm of the weight ratio ``w_t/(w_t-w_f)``
with respect to the total weight.
"""
return self.__compute_dweightratio_dwt(w_t, w_f) / self.__compute_weight_ratio(
w_t, w_f
)
def __compute_dlnweightratio_dwf(
self,
w_t: float,
w_f: float,
) -> float:
"""Derive the logarithm of the weight ratio with respect to the fuel weight.
Args:
w_t: The total aircraft weight.
w_f: The fuel weight.
Returns:
The derivative of the logarithm of the weight ratio ``w_t/(w_t-w_f)``
with respect to the fuel weight.
"""
return self.__compute_dweightratio_dwf(w_t, w_f) / self.__compute_weight_ratio(
w_t, w_f
)
def __compute_range(
self,
altitude: float,
mach: float,
w_t: float,
w_f: float,
cl_cd: float,
sfc: float,
) -> float:
"""Compute the range from the Breguet formula.
Args:
altitude: The altitude.
mach: The Mach number.
w_t: The total aircraft weight.
w_f: The fuel weight.
cl_cd: The lift-over-drag ratio.
sfc: The specific fuel consumption.
Returns:
The range.
"""
sqrt_theta = self.__compute_sqrt_theta(altitude)
return ((mach * cl_cd) * 661.0 * sqrt_theta / sfc) * self.math.log(
w_t / (w_t - w_f)
)
def __compute_drange_dtotalweight(
self,
mach: float,
w_t: float,
w_f: float,
cl_cd: float,
sfc: float,
sqrt_theta: float,
) -> float:
"""Derive the range with respect to the total weight.
Args:
mach: The Mach number.
w_t: The total aircraft weight.
w_f: The fuel weight.
cl_cd: The lift-over-drag ratio.
sfc: The specific fuel consumption.
sqrt_theta: The square root of the air temperature.
Returns:
The derivative of the range with respect to the total weight.
"""
return (
mach
* cl_cd
/ sfc
* 661.0
* sqrt_theta
* self.__compute_dlnweightratio_dwt(w_t, w_f)
)
def __compute_drange_dfuelweight(
self,
mach: float,
w_t: float,
w_f: float,
cl_cd: float,
sfc: float,
sqrt_theta: float,
) -> float:
"""Derive the range with respect to the fuel weight.
Args:
mach: The Mach number.
w_t: The total aircraft weight.
w_f: The fuel weight.
cl_cd: The lift-over-drag ratio.
sfc: The specific fuel consumption.
sqrt_theta: The square root of the air temperature.
Returns:
The derivative of the range with respect to the fuel weight.
"""
return (
mach
* cl_cd
/ sfc
* 661.0
* sqrt_theta
* self.__compute_dlnweightratio_dwf(w_t, w_f)
)
@staticmethod
def __compute_dtheta_dh(altitude: float) -> float:
"""Derive the square root of the air temperature wrt the altitude.
Args:
altitude: The altitude of the aircraft.
Returns:
The derivative of the square root of the air temperature wrt the altitude.
"""
if altitude < 36089.0:
return -0.000006875
return 0.0
def __compute_sqrt_theta(self, altitude: float) -> float:
"""Compute the square root of the air temperature.
Args:
altitude: The altitude of the aircraft.
Returns:
The square root of the air temperature.
"""
if altitude < 36089.0:
return self.math.sqrt(1 - 0.000006875 * altitude)
return self.math.sqrt(0.7519)
[docs]
def execute(
self,
x_shared: ndarray,
y_14: ndarray,
y_24: ndarray,
y_34: ndarray,
) -> ndarray:
"""Compute the range.
Args:
x_shared: The shared design variables.
y_14: The total aircraft weight ``y_14[0]`` and the fuel weight ``y_14[1]``.
y_24: The lift-over-drag ratio.
y_34: The specific fuel consumption.
Returns:
The range.
"""
return self._execute(
x_shared[1], x_shared[2], y_14[0], y_14[1], y_24[0], y_34[0]
)
def _execute(
self,
altitude: float,
mach: float,
w_t: float,
w_f: float,
cl_cd: float,
sfc: float,
) -> ndarray:
"""Compute the range.
Args:
altitude: The altitude.
mach: The Mach number.
w_t: The total aircraft weight.
w_f: The fuel weight.
cl_cd: The lift-over-drag ratio.
sfc: The specific fuel consumption.
Returns:
The range.
"""
return array(
[self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)],
dtype=self.dtype,
)
def __initialize_jacobian(self) -> dict[str, dict[str, ndarray]]:
"""Initialize the Jacobian.
Returns:
The empty Jacobian.
"""
jacobian = {"y_4": {}}
jacobian["y_4"]["x_shared"] = zeros((1, 6), dtype=self.dtype)
jacobian["y_4"]["y_14"] = zeros((1, 2), dtype=self.dtype)
jacobian["y_4"]["y_24"] = zeros((1, 1), dtype=self.dtype)
jacobian["y_4"]["y_34"] = zeros((1, 1), dtype=self.dtype)
return jacobian
[docs]
def linearize(
self,
x_shared: ndarray,
y_14: ndarray,
y_24: ndarray,
y_34: ndarray,
) -> dict[str, dict[str, ndarray]]:
"""Derive the discipline with respect to its inputs.
Args:
x_shared: The shared design variables.
y_14: The total aircraft weight ``y_14[0]`` and the fuel weight ``y_14[1]``.
y_24: The lift-over-drag ratio.
y_34: The specific fuel consumption.
Returns:
The Jacobian of the discipline.
"""
return self._linearize(
x_shared[1], x_shared[2], y_14[0], y_14[1], y_24[0], y_34[0]
)
def _linearize(
self,
altitude: float,
mach: float,
w_t: float,
w_f: float,
cl_cd: float,
sfc: float,
) -> dict[str, dict[str, ndarray]]:
"""Derive the discipline with respect to its inputs.
Args:
altitude: The altitude.
mach: The Mach number.
w_t: The total aircraft weight.
w_f: The fuel weight.
cl_cd: The lift-over-drag ratio.
sfc: The specific fuel consumption.
Returns:
The Jacobian of the discipline.
"""
jacobian = self.__initialize_jacobian()
sqrt_theta = self.__compute_sqrt_theta(altitude)
dtheta_dh = self.__compute_dtheta_dh(altitude)
ac_range = self.__compute_range(altitude, mach, w_t, w_f, cl_cd, sfc)
# dR_d(h)
jacobian["y_4"]["x_shared"][0, 1] = (
0.5 * ac_range * dtheta_dh / (sqrt_theta * sqrt_theta)
)
# dR_dM
jacobian["y_4"]["x_shared"][0, 2] = ac_range / mach
# dR_dWt
jacobian["y_4"]["y_14"][0, 0] = self.__compute_drange_dtotalweight(
mach, w_t, w_f, cl_cd, sfc, sqrt_theta
)
# dR_dWf
jacobian["y_4"]["y_14"][0, 1] = self.__compute_drange_dfuelweight(
mach, w_t, w_f, cl_cd, sfc, sqrt_theta
)
# dR_d(L/D)
jacobian["y_4"]["y_24"][0, 0] = ac_range / cl_cd
# dR_d(SFC)
jacobian["y_4"]["y_34"][0, 0] = -ac_range / sfc
return jacobian
```