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Electric_Motor_Cost_Optimization.py
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Electric_Motor_Cost_Optimization.py
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# -*- coding: utf-8 -*-
"""
Created on Tue Dec 7 11:40:41 2021
Copyright TheAmirHK
"""
import numpy as np
import sys
import time
from func_timeout import func_timeout, FunctionTimedOut
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.pyplot as plt
from scipy.stats import multivariate_normal
import math as m
import pickle
# In[] Electric motor and processing information
L=[-80, -120, 60, 80, 100, 140, 50, 30, -20, 85, -50]
s = [0.0566, 0.0133, 0.0100,0.0166, 0.0300, 0.0208,0.0208, 0.0133, 0.009]
Components_Manufacturing_cost= (5, 8, 10, 3, 2.5, 2.95, 2.95, 3.15, 4)
Components_Scraping_cost = (.5,.5,.5)
Components_Inspection_cost = (1,1.5,1)
Components_Reworking_cost = (1,1,1)
Components_Inventory_cost = (2,2,2)
Product_Scraping_cost = 10
Product_Inspection_cost = 0.5
Product_Assembly_cost = 3
Nlinear = 100 #Linearization parameter on non-linear surfaces
gap = 0.05 #Gap between surfaces
factor = 6
nmc = 1000 #Number of Monte-Carlo simulation for dynamic behaviour of the case
la = 0
al=0.0027 #Error type I
be=0.00005 #Error type II
Q = 100 # Number of Demands
Number_of_Components = 3
Partitions = 1 # Number of Partitions
Rework = 1
start_time = time.time()
# In[] Genetic algorithm
class geneticalgorithm():
#############################################################
def __init__(self, function, dimension, variable_type='bool', \
variable_boundaries=None,\
variable_type_mixed=None, \
function_timeout=100,\
algorithm_parameters={'max_num_iteration': 100,\
'population_size':100,\
'mutation_probability':0.04,\
'elit_ratio': 0.01,\
'crossover_probability': 0.7,\
'parents_portion': 0.2,\
'crossover_type':'uniform',\
'max_iteration_without_improv':None},\
convergence_curve=True,\
progress_bar=True):
self.__name__= geneticalgorithm
#############################################################
# input function
assert (callable(function)),"function must be callable"
self.f=function
#############################################################
#dimension
self.dim=int(dimension)
#############################################################
# input variable type
assert(variable_type=='bool' or variable_type=='int' or\
variable_type=='real'), \
"\n variable_type must be 'bool', 'int', or 'real'"
#############################################################
# input variables' type (MIXED)
if variable_type_mixed is None:
if variable_type=='real':
self.var_type=np.array([['real']]*self.dim)
else:
self.var_type=np.array([['int']]*self.dim)
else:
assert (type(variable_type_mixed).__module__=='numpy'),\
"\n variable_type must be numpy array"
assert (len(variable_type_mixed) == self.dim), \
"\n variable_type must have a length equal dimension."
for i in variable_type_mixed:
assert (i=='real' or i=='int'),\
"\n variable_type_mixed is either 'int' or 'real' "+\
"ex:['int','real','real']"+\
"\n for 'boolean' use 'int' and specify boundary as [0,1]"
self.var_type=variable_type_mixed
#############################################################
# input variables' boundaries
if variable_type!='bool' or type(variable_type_mixed).__module__=='numpy':
assert (type(variable_boundaries).__module__=='numpy'),\
"\n variable_boundaries must be numpy array"
assert (len(variable_boundaries)==self.dim),\
"\n variable_boundaries must have a length equal dimension"
for i in variable_boundaries:
assert (len(i) == 2), \
"\n boundary for each variable must be a tuple of length two."
assert(i[0]<=i[1]),\
"\n lower_boundaries must be smaller than upper_boundaries [lower,upper]"
self.var_bound=variable_boundaries
else:
self.var_bound=np.array([[0,1]]*self.dim)
#############################################################
#Timeout
self.funtimeout=float(function_timeout)
#############################################################
#convergence_curve
if convergence_curve==True:
self.convergence_curve=True
else:
self.convergence_curve=False
#############################################################
#progress_bar
if progress_bar==True:
self.progress_bar=True
else:
self.progress_bar=False
#############################################################
#############################################################
# input algorithm's parameters
self.param=algorithm_parameters
self.pop_s=int(self.param['population_size'])
assert (self.param['parents_portion']<=1\
and self.param['parents_portion']>=0),\
"parents_portion must be in range [0,1]"
self.par_s=int(self.param['parents_portion']*self.pop_s)
trl=self.pop_s-self.par_s
if trl % 2 != 0:
self.par_s+=1
self.prob_mut=self.param['mutation_probability']
assert (self.prob_mut<=1 and self.prob_mut>=0), \
"mutation_probability must be in range [0,1]"
self.prob_cross=self.param['crossover_probability']
assert (self.prob_cross<=1 and self.prob_cross>=0), \
"mutation_probability must be in range [0,1]"
assert (self.param['elit_ratio']<=1 and self.param['elit_ratio']>=0),\
"elit_ratio must be in range [0,1]"
trl=self.pop_s*self.param['elit_ratio']
if trl<1 and self.param['elit_ratio']>0:
self.num_elit=1
else:
self.num_elit=int(trl)
assert(self.par_s>=self.num_elit), \
"\n number of parents must be greater than number of elits"
if self.param['max_num_iteration']==None:
self.iterate=0
for i in range (0,self.dim):
if self.var_type[i]=='int':
self.iterate+=(self.var_bound[i][1]-self.var_bound[i][0])*self.dim*(100/self.pop_s)
else:
self.iterate+=(self.var_bound[i][1]-self.var_bound[i][0])*50*(100/self.pop_s)
self.iterate=int(self.iterate)
if (self.iterate*self.pop_s)>10000000:
self.iterate=10000000/self.pop_s
else:
self.iterate=int(self.param['max_num_iteration'])
self.c_type=self.param['crossover_type']
assert (self.c_type=='uniform' or self.c_type=='one_point' or\
self.c_type=='two_point'),\
"\n crossover_type must 'uniform', 'one_point', or 'two_point' Enter string"
self.stop_mniwi=False
if self.param['max_iteration_without_improv']==None:
self.mniwi=self.iterate+1
else:
self.mniwi=int(self.param['max_iteration_without_improv'])
#############################################################
def run(self):
#############################################################
# Initial Population
self.integers=np.where(self.var_type=='int')
self.reals=np.where(self.var_type=='real')
pop=np.array([np.zeros(self.dim+1)]*self.pop_s)
solo=np.zeros(self.dim+1)
var=np.zeros(self.dim)
for p in range(0,self.pop_s):
for i in self.integers[0]:
var[i]=np.random.randint(self.var_bound[i][0],\
self.var_bound[i][1]+1)
solo[i]=var[i].copy()
for i in self.reals[0]:
var[i]=self.var_bound[i][0]+np.random.random()*\
(self.var_bound[i][1]-self.var_bound[i][0])
solo[i]=var[i].copy()
obj=self.sim(var)
solo[self.dim]=obj
pop[p]=solo.copy()
#############################################################
#############################################################
# Report
self.report=[]
self.report2=[]
self.test_obj=obj
self.best_variable=var.copy()
self.best_function=obj
##############################################################
t=1
counter=0
while t<=self.iterate:
if self.progress_bar==True:
self.progress(t,self.iterate,status="GA is running...")
#############################################################
#Sort
pop = pop[pop[:,self.dim].argsort()]
if pop[0,self.dim]<self.best_function:
counter=0
self.best_function=pop[0,self.dim].copy()
self.best_variable=pop[0,: self.dim].copy()
else:
counter+=1
#############################################################
# Report
self.report.append(pop[0,self.dim])
self.report2.append(pop[0,: self.dim])
##############################################################
# Normalizing objective function
normobj=np.zeros(self.pop_s)
minobj=pop[0,self.dim]
if minobj<0:
normobj=pop[:,self.dim]+abs(minobj)
else:
normobj=pop[:,self.dim].copy()
maxnorm=np.amax(normobj)
normobj=maxnorm-normobj+1
#############################################################
# Calculate probability
sum_normobj=np.sum(normobj)
prob=np.zeros(self.pop_s)
prob=normobj/sum_normobj
cumprob=np.cumsum(prob)
#############################################################
# Select parents
par=np.array([np.zeros(self.dim+1)]*self.par_s)
for k in range(0,self.num_elit):
par[k]=pop[k].copy()
for k in range(self.num_elit,self.par_s):
index=np.searchsorted(cumprob,np.random.random())
par[k]=pop[index].copy()
ef_par_list=np.array([False]*self.par_s)
par_count=0
while par_count==0:
for k in range(0,self.par_s):
if np.random.random()<=self.prob_cross:
ef_par_list[k]=True
par_count+=1
ef_par=par[ef_par_list].copy()
#############################################################
#New generation
pop=np.array([np.zeros(self.dim+1)]*self.pop_s)
for k in range(0,self.par_s):
pop[k]=par[k].copy()
for k in range(self.par_s, self.pop_s, 2):
r1=np.random.randint(0,par_count)
r2=np.random.randint(0,par_count)
pvar1=ef_par[r1,: self.dim].copy()
pvar2=ef_par[r2,: self.dim].copy()
ch=self.cross(pvar1,pvar2,self.c_type)
ch1=ch[0].copy()
ch2=ch[1].copy()
ch1=self.mut(ch1)
ch2=self.mutmidle(ch2,pvar1,pvar2)
solo[: self.dim]=ch1.copy()
obj=self.sim(ch1)
solo[self.dim]=obj
pop[k]=solo.copy()
solo[: self.dim]=ch2.copy()
obj=self.sim(ch2)
solo[self.dim]=obj
pop[k+1]=solo.copy()
#############################################################
t+=1
if counter > self.mniwi:
pop = pop[pop[:,self.dim].argsort()]
if pop[0,self.dim]>=self.best_function:
t=self.iterate
if self.progress_bar==True:
self.progress(t,self.iterate,status="GA is running...")
time.sleep(2)
t+=1
self.stop_mniwi=True
#############################################################
#Sort
pop = pop[pop[:,self.dim].argsort()]
if pop[0,self.dim]<self.best_function:
self.best_function=pop[0,self.dim].copy()
self.best_variable=pop[0,: self.dim].copy()
#############################################################
# Report
self.report.append(pop[0,self.dim])
self.report2.append(pop[0,: self.dim])
D = open("Pareto_variables.dat", "wb")
E = open("Pareto_variables_cost.dat", "wb")
pickle.dump(self.report , E)
pickle.dump(self.report2 , D)
self.output_dict={'variable': self.best_variable, 'function':\
self.best_function}
if self.progress_bar==True:
show=' '*100
sys.stdout.write('\r%s' % (show))
# sys.stdout.write('\r The best solution found:\n %s' % (self.best_variable))
sys.stdout.write('\n\n Production cost:\n %0.2f\n ' % (self.best_function))
Solutions = np.append( self.best_variable, self.best_function)
F = open("results.dat", "wb")
pickle.dump(Solutions , F)
def Body_conformity_rate (process_deviation,tolerance_2_b,tolerance_2_c):
sigma = (process_deviation/factor)**2
tolerance_2_b = tolerance_2_b
tolerance_2_c = tolerance_2_c
b_coefficient = np.abs((L[10]-L[0]))*sigma
c_coefficient = np.abs((L[8]-L[0]))*sigma
cov = [[b_coefficient,0],[0,c_coefficient]]
body_conformity_rate = (multivariate_normal.cdf([ tolerance_2_b,tolerance_2_c ], [0,0] , cov) - multivariate_normal.cdf([ -tolerance_2_b,-tolerance_2_c ] , [0,0] , cov ))
body_conformity_rate = body_conformity_rate*(1-al)+(1-body_conformity_rate)*be
Component_Rework_ = (1-body_conformity_rate)*Rework/2
body_conformity_rate = body_conformity_rate + body_conformity_rate*Component_Rework_
return body_conformity_rate
def Shaft_conformity_rate (process_deviation, tolerance_3_c,tolerance_3_d,tolerance_3_e ):
sigma = (process_deviation/factor)**2
tolerance_3_c = tolerance_3_c
tolerance_3_d = tolerance_3_d
tolerance_3_e = tolerance_3_e
c_coefficient = np.abs((L[8]-L[0]))*sigma
d_coefficient = np.abs((L[2]))*sigma
e_coefficient = np.abs((L[4]-L[3]))*sigma
cov = [[c_coefficient,0,0], [0,d_coefficient,0],[0,0,e_coefficient]] + np.full((3, 3), 1e-10)
shaft_conformity_rate = (multivariate_normal.cdf([tolerance_3_c,tolerance_3_d,tolerance_3_e], [0,0,0] , cov) - multivariate_normal.cdf([-tolerance_3_c,-tolerance_3_d,-tolerance_3_e] , [0,0,0] , cov ))
shaft_conformity_rate = shaft_conformity_rate*(1-al)+(1-shaft_conformity_rate)*be
Component_Rework_ = (1-shaft_conformity_rate)*Rework/2
shaft_conformity_rate = shaft_conformity_rate + shaft_conformity_rate*Component_Rework_
return shaft_conformity_rate
def Housing_conformity_rate (process_deviation,tolerance_1_b,tolerance_1_d,tolerance_1_e ):
sigma = (process_deviation/factor)**2
tolerance_1_b = tolerance_1_b
tolerance_1_d = tolerance_1_d
tolerance_1_e = tolerance_1_e
b_coefficient = np.abs((L[10]-L[0]))*sigma
d_coefficient = np.abs((L[2]))*sigma
e_coefficient = np.abs((L[3]-L[4]))*sigma
cov = [[b_coefficient,0,0],[0,d_coefficient,0],[0,0,e_coefficient]] + np.full((3, 3), 1e-10)
housing_conformity_rate = (multivariate_normal.cdf([tolerance_1_b,tolerance_1_d,tolerance_1_e], [0,0,0] , cov) - multivariate_normal.cdf([-tolerance_1_b,-tolerance_1_d,-tolerance_1_e] , [0,0,0] , cov ))
housing_conformity_rate = housing_conformity_rate*(1-al)+(1-housing_conformity_rate)*be
Component_Rework_ = (1-housing_conformity_rate)*Rework/2
housing_conformity_rate = housing_conformity_rate + housing_conformity_rate*Component_Rework_
return housing_conformity_rate
print ("Housing conformity rate =%", "%.2f" %(Housing_conformity_rate (s[int(Solutions[0])],Solutions[3],Solutions[4],Solutions[5]) *100))
print ("Body conformity rate = %", "%.2f" %(Body_conformity_rate (s[int(Solutions[1])],Solutions[6],Solutions[7]) *100))
print ("Shaft conformity rate = %", "%.2f" %(Shaft_conformity_rate (s[int(Solutions[2])],Solutions[8],Solutions[9],Solutions[8]) *100))
print ("Housing allocated resource = M1", "%s" %(int(Solutions[0])+1))
print ("Body allocated resource = M2", "%.0f" %(int(Solutions[1])-2))
print ("Shaft allocated resource = M3", "%.0f" %(int(Solutions[2])-5))
print ("Housing allocated tolerances F11 = %.3f F12 = %.3f F13 = %.3f" %(Solutions[3],Solutions[4],Solutions[5]))
print ("Body allocated tolerances F21 = %.3f F22 = %.3f" %(Solutions[6],Solutions[7]))
print ("Shaft allocated tolerances F31 = %.3f F32 = %.3f F33 = %.3f" %(Solutions[8],Solutions[9],Solutions[8]))
Prob = np.zeros(3)
Prob_list = []
for i in range (len(self.report2)):
Prob = [Housing_conformity_rate (s[int(self.report2[i][0])],self.report2[i][3],self.report2[i][4],self.report2[i][5]),\
Body_conformity_rate (s[int(self.report2[i][1])],self.report2[i][6],self.report2[i][7]),\
Shaft_conformity_rate (s[int(self.report2[i][2])],self.report2[i][8],self.report2[i][9],self.report2[i][8])]
Prob_list.append(Prob)
PROB = open("Probabilities.dat", "wb")
pickle.dump(Prob_list , PROB)
def Assembly_functionality ():
sigma_1 = s[int(Solutions[0])]/factor
sigma_2 = s[int(Solutions[1])]/factor
sigma_3 = s[int(Solutions[2])]/factor
GI = []
# 1b 2b 2c 3c 1d 3d 1e 3e
mD = [65, 64.98, 30, 29.95, 50, 49.9, 30, 29.95]
gap_1b_2b = (np.abs(mD[1]-mD[0]) + Solutions[3] + Solutions[6])/2
gap_3c_2c = (np.abs(mD[3]-mD[2]) + Solutions[7] + Solutions[8] )/2
gap_1e_3e = (np.abs(mD[7]-mD[6]) + Solutions[5] + Solutions[8])/2
gap_1d_3d = (np.abs(mD[5]-mD[4]) + Solutions[4] + Solutions[9] )/2
#al 2b1b be 2b1b ga 2b1b u 2b1b v 2b1b w 2b1b al 3c2c be 3c2c ga 3c2c u 3c2c v 3c2c w 3c2c al 3e1e be 3e1e ga 3e1e u 3e1e v 3e1e w 3e1e u 3d1d v 3d1d#
for k in range(Nlinear) :
t = (2*(k+1)*m.pi)/Nlinear
GI.append([ -L[8]*m.cos(t), -L[8]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0, 0, 0., 0, 0,
0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ -L[0]*m.cos(t), -L[0]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0, 0, 0., 0, 0,
0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., -L[3]*m.cos(t), -L[3]*m.sin(t), 0., -m.sin(t),
m.cos(t), 0., 0, 0, 0., 0, 0, 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., -L[4]*m.cos(t), -L[4]*m.sin(t), 0., -m.sin(t),
m.sin(t), 0., 0, 0, 0., 0, 0, 0., 0., 0.])
GI.append([ 0, 0, 0., 0, 0, 0., 0., 0., 0., 0.,
0., 0., -L[10]*m.cos(t), -L[10]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0., 0.])
GI.append([ 0, 0, 0., 0, 0, 0., 0., 0., 0., 0.,
0., 0., -L[8]*m.cos(t), -L[8]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -1, 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -1])
b1_b2_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(6)))/36
c2_c3_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(6,12,1)))/36
e1_e3_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(12,18,1)))/36
d1_d3_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(18,20,1)))/36
cov = [[b1_b2_coefficient*(sigma_1*sigma_2), 0, 0, 0], [0, c2_c3_coefficient*(sigma_2*sigma_3),0,0], [0, 0,e1_e3_coefficient*(sigma_1*sigma_3),0], [0, 0,0, d1_d3_coefficient*(sigma_1*sigma_3)]]
assembly_functionality = (multivariate_normal.cdf([gap_1b_2b,gap_3c_2c,gap_1e_3e,gap_1d_3d], [0.0001,0.0001,0.0001,gap] , cov) - multivariate_normal.cdf([-gap_1b_2b,-gap_3c_2c,-gap_1e_3e,-gap_1d_3d] , [0.0001,0.0001,0.0001,gap] , cov ))
assembly_functionality = assembly_functionality*(1-al)+(1-assembly_functionality)*be
return assembly_functionality
pickle.dump(Assembly_functionality () , F)
print ("Assembly conformity rate =%", "%.2f" %(Assembly_functionality ()*100))
sys.stdout.flush()
re=np.array(self.report)
if self.convergence_curve==True:
plt.plot(re)
plt.xlabel('Iteration')
plt.ylabel('Production cost')
plt.title('Genetic Algorithm')
plt.show()
if self.stop_mniwi==True:
sys.stdout.write('\nWarning: GA is terminated due to the'+\
' maximum number of iterations without improvement was met!')
##############################################################################
##############################################################################
def cross(self,x,y,c_type):
ofs1=x.copy()
ofs2=y.copy()
if c_type=='one_point':
ran=np.random.randint(0,self.dim)
for i in range(0,ran):
ofs1[i]=y[i].copy()
ofs2[i]=x[i].copy()
if c_type=='two_point':
ran1=np.random.randint(0,self.dim)
ran2=np.random.randint(ran1,self.dim)
for i in range(ran1,ran2):
ofs1[i]=y[i].copy()
ofs2[i]=x[i].copy()
if c_type=='uniform':
for i in range(0, self.dim):
ran=np.random.random()
if ran <0.5:
ofs1[i]=y[i].copy()
ofs2[i]=x[i].copy()
return np.array([ofs1,ofs2])
###############################################################################
def mut(self,x):
for i in self.integers[0]:
ran=np.random.random()
if ran < self.prob_mut:
x[i]=np.random.randint(self.var_bound[i][0],\
self.var_bound[i][1]+1)
for i in self.reals[0]:
ran=np.random.random()
if ran < self.prob_mut:
x[i]=self.var_bound[i][0]+np.random.random()*\
(self.var_bound[i][1]-self.var_bound[i][0])
return x
###############################################################################
def mutmidle(self, x, p1, p2):
for i in self.integers[0]:
ran=np.random.random()
if ran < self.prob_mut:
if p1[i]<p2[i]:
x[i]=np.random.randint(p1[i],p2[i])
elif p1[i]>p2[i]:
x[i]=np.random.randint(p2[i],p1[i])
else:
x[i]=np.random.randint(self.var_bound[i][0],\
self.var_bound[i][1]+1)
for i in self.reals[0]:
ran=np.random.random()
if ran < self.prob_mut:
if p1[i]<p2[i]:
x[i]=p1[i]+np.random.random()*(p2[i]-p1[i])
elif p1[i]>p2[i]:
x[i]=p2[i]+np.random.random()*(p1[i]-p2[i])
else:
x[i]=self.var_bound[i][0]+np.random.random()*\
(self.var_bound[i][1]-self.var_bound[i][0])
return x
###############################################################################
def evaluate(self):
return self.f(self.temp)
###############################################################################
def sim(self,X):
self.temp=X.copy()
obj=None
try:
obj=func_timeout(self.funtimeout,self.evaluate)
except FunctionTimedOut:
print("given function is not applicable")
assert (obj!=None), "After "+str(self.funtimeout)+" seconds delay "+\
"func_timeout: the given function does not provide any output"
return obj
###############################################################################
def progress(self, count, total, status=''):
bar_len = 50
filled_len = int(round(bar_len * count / float(total)))
percents = round(100.0 * count / float(total), 1)
bar = '|' * filled_len + '_' * (bar_len - filled_len)
sys.stdout.write('\r%s %s%s %s' % (bar, percents, '%', status))
sys.stdout.flush()
###############################################################################
###############################################################################
def f(X):
Component_Operation_ = np.zeros(Number_of_Components)
for i in range (Number_of_Components):
Component_Operation_[i]=int(X[i])
def Body_conformity_rate (process_deviation,tolerance_2_b,tolerance_2_c):
sigma = (process_deviation/factor)**2
tolerance_2_b = tolerance_2_b
tolerance_2_c = tolerance_2_c
b_coefficient = np.abs((L[10]-L[0]))*sigma
c_coefficient = np.abs((L[8]-L[0]))*sigma
cov = [[b_coefficient,0],[0,c_coefficient]]
body_conformity_rate = (multivariate_normal.cdf([ tolerance_2_b,tolerance_2_c ], [0,0] , cov) - multivariate_normal.cdf([ -tolerance_2_b,-tolerance_2_c ] , [0,0] , cov ))
body_conformity_rate = body_conformity_rate*(1-al)+(1-body_conformity_rate)*be
return body_conformity_rate, tolerance_2_b,tolerance_2_c, process_deviation
def Shaft_conformity_rate (process_deviation, tolerance_3_c,tolerance_3_d,tolerance_3_e ):
sigma = (process_deviation/factor)**2
tolerance_3_c = tolerance_3_c
tolerance_3_d = tolerance_3_d
tolerance_3_e = tolerance_3_e
c_coefficient = np.abs((L[8]-L[0]))*sigma
d_coefficient = np.abs((L[2]))*sigma
e_coefficient = np.abs((L[4]-L[3]))*sigma
cov = [[c_coefficient,0,0], [0,d_coefficient,0],[0,0,e_coefficient]] + np.full((3, 3), 1e-10)
shaft_conformity_rate = (multivariate_normal.cdf([tolerance_3_c,tolerance_3_d,tolerance_3_e], [0,0,0] , cov) - multivariate_normal.cdf([-tolerance_3_c,-tolerance_3_d,-tolerance_3_e] , [0,0,0] , cov ))
shaft_conformity_rate = shaft_conformity_rate*(1-al)+(1-shaft_conformity_rate)*be
return shaft_conformity_rate, tolerance_3_c,tolerance_3_d,tolerance_3_e, process_deviation
def Housing_conformity_rate (process_deviation,tolerance_1_b,tolerance_1_d,tolerance_1_e ):
sigma = (process_deviation/factor)**2
tolerance_1_b = tolerance_1_b
tolerance_1_d = tolerance_1_d
tolerance_1_e = tolerance_1_e
b_coefficient = np.abs((L[10]-L[0]))*sigma
d_coefficient = np.abs((L[2]))*sigma
e_coefficient = np.abs((L[3]-L[4]))*sigma
cov = [[b_coefficient,0,0],[0,d_coefficient,0],[0,0,e_coefficient]] + np.full((3, 3), 1e-10)
housing_conformity_rate = (multivariate_normal.cdf([tolerance_1_b,tolerance_1_d,tolerance_1_e], [0,0,0] , cov) - multivariate_normal.cdf([-tolerance_1_b,-tolerance_1_d,-tolerance_1_e] , [0,0,0] , cov ))
housing_conformity_rate = housing_conformity_rate*(1-al)+(1-housing_conformity_rate)*be
return housing_conformity_rate,tolerance_1_b,tolerance_1_d,tolerance_1_e, process_deviation
housing_conformity_rate,t_1_b,t_1_d,t_1_e,process_deviation_1 = Housing_conformity_rate (s[int(X[0])],X[3],X[4],X[5])
body_conformity_rate, t_2_b,t_2_c,process_deviation_2 = Body_conformity_rate (s[int(X[1])],X[6],X[7])
shaft_conformity_rate, t_3_c,t_3_d,t_3_e,process_deviation_3 = Shaft_conformity_rate (s[int(X[2])],X[8],X[9],X[8])
def Assembly_functionality ():
sigma_1 = s[int(X[0])]/factor
sigma_2 = s[int(X[1])]/factor
sigma_3 = s[int(X[2])]/factor
GI = []
# 1b 2b 2c 3c 1d 3d 1e 3e
mD = [65, 64.98, 30, 29.95, 50, 49.9, 30, 29.95]
gap_1b_2b = (np.abs(mD[1]-mD[0]) + X[3] + X[6])/2
gap_3c_2c = (np.abs(mD[3]-mD[2]) + X[7] + X[8] )/2
gap_1e_3e = (np.abs(mD[7]-mD[6]) + X[5] + X[8])/2
gap_1d_3d = (np.abs(mD[5]-mD[4]) + X[4] + X[9] )/2
#al 2b1b be 2b1b ga 2b1b u 2b1b v 2b1b w 2b1b al 3c2c be 3c2c ga 3c2c u 3c2c v 3c2c w 3c2c al 3e1e be 3e1e ga 3e1e u 3e1e v 3e1e w 3e1e u 3d1d v 3d1d#
for k in range(Nlinear) :
t = (2*(k+1)*m.pi)/Nlinear
GI.append([ -L[8]*m.cos(t), -L[8]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0, 0, 0., 0, 0,
0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ -L[0]*m.cos(t), -L[0]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0, 0, 0., 0, 0,
0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., -L[3]*m.cos(t), -L[3]*m.sin(t), 0., -m.sin(t),
m.cos(t), 0., 0, 0, 0., 0, 0, 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., -L[4]*m.cos(t), -L[4]*m.sin(t), 0., -m.sin(t),
m.sin(t), 0., 0, 0, 0., 0, 0, 0., 0., 0.])
GI.append([ 0, 0, 0., 0, 0, 0., 0., 0., 0., 0.,
0., 0., -L[10]*m.cos(t), -L[10]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0., 0.])
GI.append([ 0, 0, 0., 0, 0, 0., 0., 0., 0., 0.,
0., 0., -L[8]*m.cos(t), -L[8]*m.sin(t), 0., -m.sin(t), m.cos(t), 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -1, 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., -1])
b1_b2_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(6)))/36
c2_c3_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(6,12,1)))/36
e1_e3_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(12,18,1)))/36
d1_d3_coefficient = np.sqrt(sum((GI[i][j])**2 for i in range(Nlinear*6+2) for j in range(18,20,1)))/36
cov = [[b1_b2_coefficient*(sigma_1*sigma_2), 0, 0, 0], [0, c2_c3_coefficient*(sigma_2*sigma_3),0,0], [0, 0,e1_e3_coefficient*(sigma_1*sigma_3),0], [0, 0,0, d1_d3_coefficient*(sigma_1*sigma_3)]]
assembly_functionality = (multivariate_normal.cdf([gap_1b_2b,gap_3c_2c,gap_1e_3e,gap_1d_3d], [0.0001,gap,gap,gap] , cov) - multivariate_normal.cdf([-gap_1b_2b,-gap_3c_2c,-gap_1e_3e,-gap_1d_3d] , [0.0001,gap,gap,gap] , cov ))
return assembly_functionality
Assembly_Conformity_with_Failure = Assembly_functionality ()
gp = [body_conformity_rate,shaft_conformity_rate, housing_conformity_rate] # before reworking
Component_Rework_ = np.zeros(Number_of_Components)
sr = np.zeros(Number_of_Components)
Conformity_with_reworking = np.zeros(Number_of_Components)
for i in range (Number_of_Components):
Component_Rework_[i] = (1-gp[i])*Rework/2
sr[i]= (1-(gp[0]+Component_Rework_[0]))
Conformity_with_reworking[i] = gp[i] + gp[i]*Component_Rework_[i]
Manufacturing_cost = sum((Components_Manufacturing_cost[int(X[i])])/Conformity_with_reworking[i] for i in range(Number_of_Components))
Scrap_cost = sum (Components_Scraping_cost[i]*sr[i]/Conformity_with_reworking[i] for i in range (Number_of_Components))
Inspection_cost = sum (Components_Inspection_cost[i]/Conformity_with_reworking[i] for i in range (Number_of_Components))
Reworking_cost = sum (Component_Rework_[i]*Rework*Components_Reworking_cost[i]/Conformity_with_reworking[i] for i in range (Number_of_Components))
CIP = (Product_Inspection_cost *Q /Assembly_Conformity_with_Failure)
CA = (Product_Assembly_cost*Q /(Assembly_Conformity_with_Failure))
CSP = Product_Scraping_cost*Q*(1-Assembly_Conformity_with_Failure)
pen = Manufacturing_cost + Scrap_cost + Inspection_cost + Reworking_cost+ CIP + CA + CSP
mD = [65, 64.98, 30, 29.95, 50, 49.9, 30, 29.95]
pen1 = 0
if ((np.abs(mD[1]-mD[0]) + X[3] + X[6]) > (2)*gap) \
or ((np.abs(mD[3]-mD[2]) + X[7] + X[8]) > (2)*gap) \
or ((np.abs(mD[7]-mD[6]) + X[5] + X[8]) > (2)*gap) \
or ((np.abs(mD[5]-mD[4]) + X[4] + X[9]) > (3)*gap):
pen1= 5e50
return pen + pen1
varbound=np.array([[0,2],[3,5],[6,8],[0.001,0.1],[0.001,0.1],[0.001,0.1],[0.001,0.1],[0.001,0.1],[0.001,0.1],[0.001,0.1]])
vartype=np.array([['int'],['int'],['int'],['real'],['real'],['real'],['real'],['real'],['real'],['real']])
model=geneticalgorithm(function=f,dimension=10,variable_type_mixed=vartype,variable_boundaries=varbound)
model.run()
print("--- Optimization RunTime = %s seconds ---" % int(round((time.time() - start_time))))
######################################################################## plot Body deviation distribution
#Parameters to set
sigma = (results[1]/factor)**2
mu_x = 0
variance_x = np.abs((L[10]-L[0]))*sigma
mu_y = 0
variance_y = np.abs((L[8]-L[0]))*sigma
#Create grid and multivariate normal
x = np.linspace(-0.1,0.1,1000)
y = np.linspace(-0.1,0.1,1000)
X, Y = np.meshgrid(x,y)
pos = np.empty(X.shape + (2,))
pos[:, :, 0] = X; pos[:, :, 1] = Y
rv = multivariate_normal([mu_x, mu_y], [[variance_x, 0], [0, variance_y]])
#Make a 3D plot
fig = plt.figure()
ax = fig.gca(projection='3d')
ax.plot_surface(X, Y, rv.pdf(pos),cmap='viridis',linewidth=0)
ax.set_xlabel('Deviation D22 axis')
ax.set_ylabel('Deviation D21 axis')
ax.set_zlabel('Body conformity axis')
# Plot 2D contour
pos = np.dstack((X, Y))
fig2 = plt.figure()
ax2 = fig2.add_subplot(111)
plt.axhline(y=results[7],linewidth = 1, linestyle ="--",color ='white',label="Tolerances on the Body")
plt.axhline(y=-results[7],linewidth = 1, linestyle ="--",color ='white')
plt.axvline(x=results[6],linewidth = 1, linestyle ="--",color ='white')
plt.axvline(x=-results[6],linewidth = 1, linestyle ="--",color ='white')
plt.legend(loc="upper right")
cmap=ax2.contourf(X, Y, rv.pdf(pos))
fig2.colorbar(cmap)
ax2.set_xlabel('Deviation D22 axis')
ax2.set_ylabel('Deviation D21 axis')
plt.show()
#################################################################################
from lpsolve55 import *
import numpy as np
import openturns as ot
def create_lp(dimension, nb_Cc, nb_Ci, nb_Cieq):
# compute the total number of constraints
nb_eq = nb_Cc + nb_Ci + nb_Cieq
# create the lp object
lp = lpsolve('make_lp', nb_eq, dimension)
# set the verbose so as to return nothing
lpsolve('set_verbose', lp, NEUTRAL)
# tell that this is minimization problem
lpsolve('set_maxim', lp)
# set the type of the constraints in a vector
e = []
e.extend([0]*nb_Cc)
e.extend([-1]*nb_Ci)
for i in range(nb_eq):
if e[i] < 0:
con_type = 'LE'
elif e[i] == 0:
con_type = 'EQ'
else:
con_type = 'GE'
lpsolve('set_constr_type', lp, i + 1, con_type)
# set large bounds for the gaps
lpsolve('set_bounds', lp, [-100]*dimension, [100]*dimension)
return lp
def solve_lp(f, a, b, criterion):
lpsolve('set_mat', lp, a)
lpsolve('set_rh_vec', lp, b)
lpsolve('set_obj_fn', lp, f)
result = lpsolve('solve', lp)
# optimal solution found
if result == 0:
[obj, x, duals, ret] = lpsolve('get_solution', lp)
# compute the functional condition
# print(x)
fc = criterion -obj
status = 0
# infeasible problem
else:
fc = np.Infinity
status = 1
return fc, status
def compute_mod(X, Nlinear,j):
"""
Compute the compatibility equations and interface constraints
for a given vector of realizations and number of linearizations.
"""
d = X[:8]
E = X[8:]
T1a1 = [0, 0, 0, 0, 0, 0]
T1b1 = [E[0], E[1], 0, 0, 0, 0]
T1d1 = [E[2], E[3], 0, E[16], E[17], 0]
T1e1 = [E[4], E[5], 0, E[18], E[19], 0]
T2a2 = [0, 0, 0, 0, 0, 0]
T2b2 = [E[6], E[7], 0, 0, 0, 0]
T2c2 = [E[8], E[9], 0, E[20], E[21], 0]
T3c3 = [E[10], E[11], 0, E[22], E[23], 0]
T3d3 = [E[12], E[13], 0, E[24], E[25], 0]
T3e3 = [E[14], E[15], 0, E[26], E[27], 0]
L=[-80, -120, 60, 80, 100, 140, 0, 30, -20, 85, -50]
# """Gaps Variables : C1a2a, u1a2a, v1a2a, A2b1b, B2b1b, C2b1b, u2b1b, v2b1b, w2b1b, A3c2c, B3c2c, C3c2c,
# u3c2c, v3c2c, w3c2c, A3e1e, B3e1e, C3e1e, u3e1e, v3e1e, w3e1e, u3d1d, v3d1d """
#
G = []; D = []
# Boucle 1/2
# Matrice rassemblant les coefficients multipliant les valeurs des torseurs jeux dans les équations de compatibilité
G.append([ 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 0., 0., -1., 0., 0., 0., 0., 0., -1., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., 1., 0., 0., 0.])
G.append([ 0., 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., 1., 0., 0.])
G.append([ -1., 0., 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0.])
G.append([ 0., -1., 0., 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0.])
G.append([ 0., 0., -1., 0., 0., 0., 0., 0., -1., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0.])
G.append([0., 0., 0., 0., 0., 0., 0., -L[7], 0., -1., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0.])
G.append([0., 0., 0., 0., 0., 0., L[7], 0., -L[6], 0., -1., 0., 0., 0., 0., 0., 0., 0., 0., 1.])
# Le vecteur contenant les valeurs des torseurs écarts ligne par ligne des équations de compatibilité
D = [-(-T2b2[3]+T1b1[3]), -T1b1[4], -(-T1a1[5] + T2a2[5]), -(-T1a1[0] + T2a2[0] + T1b1[0]), \
-(-T1a1[1] +T2a2[1] - T2b2[1] + T1b1[1]),-(-T2b2[2]),\
-(-T1b1[3] + T2b2[3] - T2c2[3] + T3c3[3] - T3e3[3] + T1e1[3]),
-(-T1b1[4] + T2b2[4] -T2c2[4] + T3c3[4] - T3e3[4] + T1e1[4]),\
0., -(-T1b1[0] + T2b2[0] -T2c2[0] + T3c3[0] - T3e3[0] + T1e1[0]), \
-(-T1b1[1] + T2b2[1] - T2c2[1] + T3c3[1] - T3e3[1] + T1e1[1]),\
0,
-(-L[7]*T1a1[1] + L[7]*T2a2[1] -T2c2[3] - L[7]*T2c2[1] + T3c3[3] + L[7]*T3c3[1] - T3d3[3] + T1d1[3]),\
-(L[7]*T1a1[0] -L[7]*T2a2[0] - T2c2[4] + L[7]*T2c2[0] + T3c3[4] + L[7]*T3c3[0] - T3d3[4] + T1d1[4])]
""" Les écarts de diamètres et leur tolérance à considérer dans les équations """
DI1 = (d[2]-d[3])/2 # liaison 3c/2c
DI2 = (d[6]-d[7])/2 # liaison 3e/1e
DI3 = (d[0]-d[1])/2 # liaison 2b/1b
""" GI estla matrice contenant les coefficients multipliant les paramètres des torseurs au niveau
des équations d'interface """
GI = []
for k in range(Nlinear) :
t = (2*(k+1)*m.pi)/Nlinear
GI.append([ 0., 0., 0., 0., 0., 0., -L[8]*m.sin(t), L[8]*m.cos(t), 0., m.cos(t), m.sin(t),
0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., -L[0]*m.sin(t), L[0]*m.cos(t), 0., m.cos(t), m.sin(t),
0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., -L[3]*m.sin(t), L[3]*m.cos(t), 0., m.cos(t), m.sin(t), 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,
0., 0., -L[4]*m.sin(t), L[4]*m.cos(t), 0., m.cos(t), m.sin(t), 0., 0., 0.])
GI.append([ -L[10]*m.sin(t), L[10]*m.cos(t), 0., m.cos(t), m.sin(t), 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ -L[8]*m.sin(t), L[8]*m.cos(t), 0., m.cos(t), m.sin(t), 0., 0., 0., 0., 0.,
0., 0., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,-1., 0., 0., 0., 0., 0., 0., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 1., 0., 0.])
GI.append([ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0.,-1., 0., 0.])
IL = 0.1
DI = [DI1, DI1, DI2, DI2, DI3, DI3] * (Nlinear)
DI4 = [IL, IL, IL, IL]
G.extend(GI)
D.extend(DI)
D.extend(DI4)
""" the objective function"""
if j == 1:
# f1 represents the vector representing the gaps coefficients
Objf = [ 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0., 0, 0., 0., 1., 0.] # u