def output(x):
#Retrieve r and k
global ite
r = x[0:m]
#k = x[m:]
cost = hp.C(A, B, r)
for i in range(m):
print(ite,
'r' + str(i + 1) + ' ',
r[i],
'k' + str(i + 1) + ' ',
k[i],
end='')
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D)
U = hp.U_scrap(cost, USY, miuY, sigmaY_Taylor, k)
print(ite, ' U=', U)
ite += 1
def obj_grad_scipy_inspect(x):
#retrieve r and k
grad = np.zeros_like(x)
r = x[0:m]
k = x[m:]
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D)
sigmaY_Taylor = lamada * sigmaY_Taylor
#Compute Unit Cost
C = hp.C(A, B, r)
for i in range(0, m): # Change this for loop to vectorization
dCi_dri_v = hp.dCi_dri(B[i], r[i])
dsigmai_dri_v = hp.dsigmai_dri(F[i], r[i])
dsigmaY_dri_v = hp.dsigmaY_dri(D, sigmaX, r, i, dsigmai_dri_v)
grad_r[i] = hp.dU_dri_scrap(USY, miuY, sigmaY_Taylor, C, k, i, lamada,
dsigmaY_dri_v, dCi_dri_v)
grad_k[i] = hp.dU_dki_scrap(USY, miuY, sigmaY_Taylor, k[i], C[i])
grad_combine = np.concatenate((grad_r, grad_k), axis=0)
grad[:] = grad_combine
return grad
def casestudy_U():
para = np.array([A, B, E, F])
result = optimize(True, para)
U_equation = result['U']
r_opt = result['r']
if scenario == INSPECT:
k_opt = result['k']
else:
k_opt = 3 * np.ones_like(r_opt)
sigma_opt = hp.sigma(E, F, r_opt)
[N, M] = hp.estimateNandM(miu, E, F, r_opt, k_opt, NSample, USY, miuY,
scenario)
U_simulation = hp.U_inspect_simulation(NSample, r_opt, A, B, E, F, k_opt,
miu, USY, miuY, Sp, Sc)
print('U Equation: ', U_equation)
print('U Simulation: ', U_simulation)
satisfactionrate = hp.satisfactionrate_component_product(
miu, E, F, r, k, NSample, USY, miuY, scenario)
print('beta: ', satisfactionrate['beta'])
print('sigmaY: ', hp.sigmaY(sigma_opt, D, scenario, k_opt))
print('opt cost:', hp.C(A, B, r_opt))
print('N: ', N)
print('M: ', M)
print('Gama', satisfactionrate['gammas'])
def obj_nlopt_noinspect(x, grad, para):
#retrieve r as the optimization variable x. (k will not be optimized, so just use const)
A = para[0]
B = para[1]
E = para[2]
F = para[3]
r = x[0:m]
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D, scenario, k)
#Compute Unit Cost
C = hp.C(A, B, r)
U = hp.U_noscrap(C, USY, miuY, sigmaY_Taylor, Sp)
for i in range(0, m): # Change this for loop to vectorization
dCi_dri_v = hp.dCi_dri(B[i], r[i])
dsigmai_dri_v = hp.dsigmai_dri(F[i], r[i])
dsigmaY_dri_v = hp.dsigmaY_dri(D, sigmaX, r, i, dsigmai_dri_v,
scenario, k)
grad_r[i] = hp.dU_dri_noscrap(USY, miuY, sigmaY_Taylor, C, k, i,
dsigmaY_dri_v, dCi_dri_v, Sp)
if grad.size > 0:
grad[:] = grad_r #Make sure to assign value using [:]
#print(U)
return U
#Scrap cost of a product Sp = np.sum(A) / 10 #Scrap costs of components Sc = A / 10 D1 = hp.dy_dx1(miu[0], miu[1], miu[2]) D2 = hp.dy_dx2(miu[0], miu[1], miu[2]) D3 = hp.dy_dx3(miu[0], miu[1], miu[2]) D = np.array([D1, D2, D3]) #r=hp.sigmator(sigmaX,E,F) r = 10 * np.random.rand(3) k = 5 * np.random.rand(3) #3 * np.ones_like(r) # sigmaX = hp.sigma(E, F, r) #Compute Unit Cost of initial value C = hp.C(A, B, r) sigmaY_Taylor = hp.sigmaY(sigmaX, D, scenario, k) #Nominal value of Y miuY = np.radians(7.0124) ##Upper specification limit USY = miuY + np.radians(2.0) #U = hp.U_scrap(C,USY,sigmaY,k) grad_numerical_r = np.zeros(m) grad_equation_r = np.zeros(m) grad_numerical_k = np.zeros(m)
def gradientcheck(x, case):
if case == SCRAP:
grad_equation = obj_grad_scipy_inspect(x)
#retrieve grad of r and k
grad_equation_r = grad_equation[0:m]
grad_equation_k = grad_equation[m:]
grad_numerical_k = np.zeros(m)
grad_numerical_r = np.zeros(m)
elif case == NOSCRAP:
grad_equation_r = obj_grad_scipy_noinspect(x)
grad_numerical_r = np.zeros(m)
C = hp.C(A, B, r)
for i in range(0, m):
ri_add_epsilon = np.copy(r)
ri_minus_epsilon = np.copy(r)
ri_add_epsilon[i] += epsilon
ri_minus_epsilon[i] -= epsilon
ki_add_epsilon = np.copy(k)
ki_minus_epsilon = np.copy(k)
ki_add_epsilon[i] += epsilon
ki_minus_epsilon[i] -= epsilon
sigmaX_plus = hp.sigma(E, F, ri_add_epsilon)
sigmaX_minus = hp.sigma(E, F, ri_minus_epsilon)
C_plus = hp.C(A, B, ri_add_epsilon)
C_minus = hp.C(A, B, ri_minus_epsilon)
sigmaY_Taylor_plus = hp.sigmaY(sigmaX_plus, D)
sigmaY_Taylor_minus = hp.sigmaY(sigmaX_minus, D)
if case == SCRAP:
sigmaY_Taylor_p = lamada * sigmaY_Taylor
#Varify dr
sigmaY_Taylor_plus *= lamada
sigmaY_Taylor_minus *= lamada
#gradient computed by numerical estimation
grad_numerical_r[i] = (
hp.U_scrap(C_plus, USY, miuY, sigmaY_Taylor_plus, k) -
hp.U_scrap(C_minus, USY, miuY, sigmaY_Taylor_minus, k)) / (
2 * epsilon)
#varify dk
grad_numerical_k[i] = (
hp.U_scrap(C, USY, miuY, sigmaY_Taylor_p, ki_add_epsilon) -
hp.U_scrap(C, USY, miuY, sigmaY_Taylor_p,
ki_minus_epsilon)) / (2 * epsilon)
print('Numerical_scrap_' + 'dr' + str(i), '=', grad_numerical_r[i])
print('Equation_scrap_' + 'dr' + str(i), '=', grad_equation_r[i])
print('Numerical_scrap_' + 'dk' + str(i), '=', grad_numerical_k[i])
print('Equation_scrap_' + 'dk' + str(i), '=', grad_equation_k[i])
elif case == NOSCRAP:
#gradient computed by numerical estimation
grad_numerical_r[i] = (hp.U_noscrap(
C_plus, USY, miuY, sigmaY_Taylor_plus) - hp.U_noscrap(
C_minus, USY, miuY, sigmaY_Taylor_minus)) / (2 * epsilon)
print('Numerical_No scrap_' + 'dr' + str(i), '=',
grad_numerical_r[i])
print('Equation_No scrap_' + 'dr' + str(i), '=',
grad_equation_r[i])
distance12_r = distance.euclidean(grad_equation_r, grad_numerical_r)
length1_r = distance.euclidean(grad_equation_r,
np.zeros_like(grad_equation_r))
length2_r = distance.euclidean(grad_numerical_r,
np.zeros_like(grad_numerical_r))
graderror_r = distance12_r / (length1_r + length2_r)
print('error of dr=', graderror_r)
if case == SCRAP:
distance12_k = distance.euclidean(grad_equation_k, grad_numerical_k)
length1_k = distance.euclidean(grad_equation_k,
np.zeros_like(grad_equation_k))
length2_k = distance.euclidean(grad_numerical_k,
np.zeros_like(grad_numerical_k))
graderror_k = distance12_k / (length1_k + length2_k)
print('error of dk=', graderror_k)
for i in range(m):
print(ite,
'r' + str(i + 1) + ' ',
r[i],
'k' + str(i + 1) + ' ',
k[i],
end='')
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D)
U = hp.U_scrap(cost, USY, miuY, sigmaY_Taylor, k)
print(ite, ' U=', U)
ite += 1
#Unit cost of initial values
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D)
cost = hp.C(A, B, r)
SCIPY = 0
NLOPT = 1
opt_lib = NLOPT
if opt_lib == SCIPY:
if case == SCRAP: #Scrap
#Define Upper and Lower boundaries
#The order is ([lower bnd for x1, lower bnd for x2], [Higher bnd for x1, Higher bnd for x2])
mbounds = Bounds([
smallvalue, smallvalue, smallvalue, smallvalue, smallvalue,
smallvalue
], [
# -*- coding: utf-8 -*- """ Created on Sun May 26 10:04:08 2019 @author: wyue """ #import packages import numpy as np import helpers as hp epsilon = 1e-7 rMin = 1e-2 # Lower bound is 0, to prevent dividing by zero, set lower bond to a small value rMax = 100 rRst = np.array([20, 20, 20]) A = np.array([0.87, 1.71, 3.54]) #np.array([5.0, 3.0, 1.0]) B = np.array([2.062, 1.276, 1.965]) #np.array([20.0, 36.7, 36.0]) F = np.array([0.001798 / 3, 0.001653 / 3, 0.002 / 3]) #E = sigmaX_init - np.multiply(F,np.power(r,2)) #np.array([sigmaX_init1-1, sigmaX_init2-1, sigmaX_init3-1]) E = np.array([0.083, 0.096, 0.129]) sigmaMin = hp.sigma(E, F, rMin) sigmaMax = hp.sigma(E, F, rMax) simgaRst = hp.sigma(E, F, rRst)
for i in range(m):
print(ite,
'r' + str(i + 1) + ' ',
r[i],
'k' + str(i + 1) + ' ',
k[i],
end='')
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D)
U = hp.U_scrap(cost, USY, miuY, sigmaY_Taylor, k, Sp, Sc)
print(ite, ' U=', U)
ite += 1
#Unit cost of initial values
sigmaX = hp.sigma(E, F, r)
sigmaY_Taylor = hp.sigmaY(sigmaX, D)
cost = hp.C(A, B, r)
SCIPY = 0
NLOPT = 1
opt_lib = NLOPT
if opt_lib == SCIPY:
if scenario == INSPECT: #Scrap
#Define Upper and Lower boundaries
#The order is ([lower bnd for x1, lower bnd for x2], [Higher bnd for x1, Higher bnd for x2])
mbounds = Bounds([
smallvalue, smallvalue, smallvalue, smallvalue, smallvalue,
smallvalue
], [