"""
Optimal design of multiple clutch brakes.
Osyczka, A. (1992). Computer aided multicriterion optimization
system (CAMOS) : software package in FORTRAN.
"""
from desdeo_problem.problem.Variable import Variable
from desdeo_problem.problem.Objective import ScalarObjective
from desdeo_problem.problem.Problem import MOProblem, ProblemBase
from desdeo_problem import ScalarConstraint, problem
import numpy as np
[docs]def multiple_clutch_brakes(var_iv: np.array = np.array([67.5, 92.5, 2.25, 650, 6])) -> MOProblem:
""" Multiple clutch brake problem.
Arguments:
var_iv (np.array): Optional, initial variable values.
Defaults are [67.5, 92.5, 2.25, 650, 6].
x1 ∈ [55, 80], x2 ∈ [75, 110], x3 ∈ [1.5, 3],
x4 ∈ [300, 1000] and x5 ∈ {2, ..., 10}
Returns:
MOProblem: a problem object.
"""
# Check the number of variables
if (np.shape(np.atleast_2d(var_iv)[0]) != (5,)):
raise RuntimeError("Number of variables must be seven")
# Lower bounds
lb = np.array([55, 75, 1.5, 300, 2])
# Upper bounds
ub = np.array([80, 110, 3, 1000, 10])
# Check the variable bounds
if np.any(lb > var_iv) or np.any(ub < var_iv):
raise ValueError("Initial variable values need to be between lower and upper bounds")
def m_h(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
(2/3) * 0.5 * x[:,3] * (np.round(x[:,4])) *
((x[:,1]**3 - x[:,0]**3) / (x[:,1]**2 - x[:,0]**2))
* 0.001 # This line is from Jussi's Matlab code
# Mh = (2/3) * mu* x(5-1) * x(6-1) * ((x(3-1)^3-x(2-1)^3)/(x(3-1)^2-x(2-1)^2)) * 0.001; %convert to Nm
)
def p_rz(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 3] / (np.pi * x[:, 1]**2 - np.pi * x[:, 0]**2)
)
def v_sr(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
(np.pi * (2/3 * ((x[:, 1]**3 - x[:, 0]**3) /
(x[:, 1]**2 - x[:, 0]**2))) * 250) / 30
)
# Objective functions
def f_1(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
np.pi * ((x[:, 1]**2 - x[:, 0]**2)) * (x[:, 2] * (np.round(x[:, 4]) + 1)) * 0.0000078
)
def f_2(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
(55 * ((np.pi * 250) / 30)) / ((m_h(x)) + 3)
)
def f_3(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
np.round(x[:, 4])
)
def f_4(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 1]
)
def f_5(x: np.ndarray) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 3]
)
# Constraint functions
def g_1(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 0] - 55
)
def g_2(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
110 - x[:, 1]
)
def g_3(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 1] - x[:, 0] - 20
)
def g_4(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 2] - 1.5
)
def g_5(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
3 - x[:, 2]
)
def g_6(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
30 - (np.round(x[:, 4]) + 1) * (x[:, 2] + 0.5)
)
def g_7(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
10 - (np.round(x[:, 4]) + 1)
)
def g_8(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
np.round(x[:, 4]) - 1
)
def g_9(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
10 - p_rz(x)
)
def g_10(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
10 * 2000 - (p_rz(x) * v_sr(x))
)
def g_11(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
2000 - v_sr(x)
)
def g_12(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
15 - f_2(x)
)
def g_13(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
m_h(x) - (1.5 * 40)
)
def g_14(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
f_2(x)
)
def g_15(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
x[:, 3]
)
def g_16(x: np.ndarray, _ = None) -> np.ndarray:
x = np.atleast_2d(x)
return (
1000 - x[:, 3]
)
objective_1 = ScalarObjective(name="mass of the brake", evaluator=f_1, maximize=[False])
objective_2 = ScalarObjective(name="stopping time", evaluator=f_2, maximize=[False])
objective_3 = ScalarObjective(name="number of friction surfaces", evaluator=f_3, maximize=[False])
objective_4 = ScalarObjective(name="outer radius", evaluator=f_4, maximize=[False])
objective_5 = ScalarObjective(name="actuating force", evaluator=f_5, maximize=[False])
objectives = [objective_1, objective_2, objective_3, objective_4, objective_5]
cons_1 = ScalarConstraint("c_1", 5, 5, g_1)
cons_2 = ScalarConstraint("c_2", 5, 5, g_2)
cons_3 = ScalarConstraint("c_3", 5, 5, g_3)
cons_4 = ScalarConstraint("c_4", 5, 5, g_4)
cons_5 = ScalarConstraint("c_5", 5, 5, g_5)
cons_6 = ScalarConstraint("c_6", 5, 5, g_6)
cons_7 = ScalarConstraint("c_7", 5, 5, g_7)
cons_8 = ScalarConstraint("c_8", 5, 5, g_8)
cons_9 = ScalarConstraint("c_9", 5, 5, g_9)
cons_10 = ScalarConstraint("c_10", 5, 5, g_10)
cons_11 = ScalarConstraint("c_11", 5, 5, g_11)
cons_12 = ScalarConstraint("c_12", 5, 5, g_12)
cons_13 = ScalarConstraint("c_13", 5, 5, g_13)
cons_14 = ScalarConstraint("c_14", 5, 5, g_14)
cons_15 = ScalarConstraint("c_15", 5, 5, g_15)
cons_16 = ScalarConstraint("c_16", 5, 5, g_16)
constraints = [cons_1, cons_2, cons_3, cons_4, cons_5, cons_6, cons_7, cons_8,
cons_9, cons_10, cons_11, cons_12, cons_13, cons_14, cons_15, cons_16]
x_1 = Variable("inner radius", 67.5, 55, 80)
x_2 = Variable("outer radius", 92.5, 75, 110)
x_3 = Variable("thickness of the disc", 2.25, 1.5, 3)
x_4 = Variable("actuating force", 650, 300, 1000)
x_5 = Variable("number of friction surfaces", 6, 2, 10)
variables = [x_1, x_2, x_3, x_4, x_5]
problem = MOProblem(variables=variables, objectives=objectives, constraints=constraints)
return problem
