-
Notifications
You must be signed in to change notification settings - Fork 0
/
SA_MM.py
301 lines (259 loc) · 10.1 KB
/
SA_MM.py
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
# -*- coding: utf-8 -*-
"""
Created on Fri Feb 2 11:03:57 2018
@author: zhaox
"""
import pandas as pd
import numpy as np
import matplotlib.pyplot as plt
import seaborn as sns
from SALib.sample import saltelli
from SALib.analyze import sobol
from SALib.analyze import delta
from SALib.analyze import dgsm
from SALib.sample import finite_diff
from SALib.analyze import fast
from SALib.sample import fast_sampler
from SALib.analyze.ff import analyze as ff_analyze
from SALib.sample.ff import sample as ff_sample
from SALib.analyze import morris
from SALib.sample.morris import sample as morris_sample
from SALib.sample import latin
from scipy.stats import multivariate_normal
from oct2py import octave
# Import test data
# Partial correlated test data
test_freq = pd.read_excel('Test_record_2018_01.xlsx',sheet_name=0)
test_freq.drop(test_freq.columns[-2:],axis=1,inplace=True)
test_freq.drop(test_freq.index[-7:],axis=0,inplace=True)
# Positive linear correlated test data
#test_freq = pd.read_excel('Test_record_2018_01.xlsx',sheet_name=1)
#test_freq.drop(test_freq.index[-7:],axis=0,inplace=True)
test_freq=np.array(test_freq.iloc[:,4:])
# Initilization
method_flag=7
sample_number=1000
upb_search=0.1
lob_search=-0.1
problem = {
'num_vars': 4,
'names': ['x1', 'x2', 'x3','x4'],
'groups': None,
'bounds': [[lob_search, upb_search],[lob_search, upb_search],[lob_search, upb_search],[lob_search, upb_search]]
}
## Generate samples
if method_flag==1:
param_values = saltelli.sample(problem, sample_number)
parm=(param_values+1)
elif method_flag==2:
param_values = latin.sample(problem,sample_number)
parm=(param_values+1)
elif method_flag==3:
param_values = finite_diff.sample(problem, sample_number, delta=0.001)
parm=(param_values+1)
elif method_flag==4:
param_values = fast_sampler.sample(problem, sample_number)
parm=(param_values+1)
elif method_flag==5:
param_values = ff_sample(problem)
parm=(param_values[:,:21]+1)
elif method_flag==6:
param_values = morris_sample(problem, N=sample_number, num_levels=4, grid_jump=2, \
optimal_trajectories=None)
parm=(param_values+1)
elif method_flag==7:
param_values = saltelli.sample(problem, sample_number)
parm=(param_values+1)
FEM_freq = octave.K_movingmass_fun(parm)
#%% Sensitivity analysis
order_invloved=12
test_freq=test_freq[:,:order_invloved]
FEM_freq=FEM_freq[:,:order_invloved]
#init_freq=init_freq[:,:order_invloved]
mean_test=np.mean(test_freq,axis=0)
cov_test=np.cov(test_freq,rowvar=False)
mean_FEM=np.mean(FEM_freq,axis=0)
cov_FEM=np.cov(FEM_freq,rowvar=False)
#mean_init=np.mean(init_freq,axis=0)
#cov_init=np.cov(init_freq,rowvar=False)
test_freq_normalized=np.zeros(test_freq.shape)
FEM_freq_normalized=np.zeros(FEM_freq.shape)
#init_freq_normalized=np.zeros(init_freq.shape)
for i in range(0,order_invloved):
test_freq_normalized[:,i]=(test_freq[:,i])/mean_test[i]
FEM_freq_normalized[:,i]=(FEM_freq[:,i])/mean_test[i]
# init_freq_normalized[:,i]=(init_freq[:,i])/mean_test[i]
mean_test_normalized=np.mean(test_freq_normalized,axis=0)
cov_test_normalized=np.cov(test_freq_normalized,rowvar=False)
mean_FEM_normalized=np.mean(FEM_freq_normalized,axis=0)
cov_FEM_normalized=np.cov(FEM_freq_normalized,rowvar=False)
#mean_init_normalized=np.mean(init_freq_normalized,axis=0)
#cov_init_normalized=np.cov(init_freq_normalized,rowvar=False)
rv = multivariate_normal(mean_FEM_normalized, cov_FEM_normalized)
Y1 = rv.logpdf(FEM_freq_normalized)
rv = multivariate_normal(mean_test_normalized, cov_test_normalized)
Y2 = rv.logpdf(FEM_freq_normalized)
#rv = multivariate_normal(mean_init_normalized, cov_init_normalized)
#Y3 = rv.logpdf(FEM_freq_normalized)
Y=Y2
Y_con=Y1
#list_parm=list()
#for index,y in enumerate(Y):
# if y > -400:
# list_parm.append(parm[index,:])
# Y[index]=1
# else:
# Y[index]=0
# KDE
#mean_test=np.mean(test_freq,axis=0)
#cov_test=np.cov(test_freq,rowvar=False)
#mean_FEM=np.mean(FEM_freq,axis=0)
#cov_FEM=np.cov(FEM_freq,rowvar=False)
#
#test_freq=test_freq[:,:17]
#FEM_freq=FEM_freq[:,:17]
#
#test_freq_normalized=np.zeros(test_freq.shape)
#FEM_freq_normalized=np.zeros(FEM_freq.shape)
#for i in range(0,17):
# test_freq_normalized[:,i]=(test_freq[:,i]-mean_test[i])/mean_test[i]
# FEM_freq_normalized[:,i]=(FEM_freq[:,i]-mean_test[i])/mean_test[i]
#
#mean_test_normalized=np.mean(test_freq_normalized,axis=0)
#cov_test_normalized=np.cov(test_freq_normalized,rowvar=False)
#
#kernel = stats.gaussian_kde(test_freq_normalized.T)
#Y=kernel.logpdf(FEM_freq_normalized.T)
## Log function
#mean_test_freq=np.mean(test_freq,axis=0)
#Y=np.zeros(FEM_freq[:,0].shape)
#for i in range(0,20):
# Y+=np.log(np.abs(((FEM_freq[:,i]-mean_test_freq[i])/mean_test_freq[i])))
#Y=np.abs(Y)
# Draw the scatter of Frequencies
#g = sns.PairGrid(pd.DataFrame(test_freq[:,:]), diag_sharey=False)
#g.map_lower(sns.kdeplot, cmap="Blues_d")
#g.map_upper(plt.scatter)
#g.map_diag(sns.kdeplot, lw=3)
#
## Perform analysis
if method_flag==1:
Si = sobol.analyze(problem, Y, print_to_console=False)
figure_keys={'ax1_title':'S1',
'ax2_title':'S1_conf',
'ax2_lable':'Parameter index',
'ax3_title':'ST',
'ax4_title':'ST_conf',
'ax4_lable':'Parameter index',
'ax5_parm':'S2',
'ax5_title':'Second order sensitivity',
'ax5_lable':'Parameter index',
}
elif method_flag==2:
Si = delta.analyze(problem, param_values, Y, num_resamples=10, conf_level=0.95, print_to_console=False)
figure_keys={'ax1_title':'S1',
'ax2_title':'S1_conf',
'ax2_lable':'Parameter index',
'ax3_title':'delta',
'ax4_title':'delta_conf',
'ax4_lable':'Parameter index',
}
Si_con = delta.analyze(problem, param_values, Y_con, num_resamples=10, conf_level=0.95, print_to_console=False)
f1,(ax1,ax2)=plt.subplots(2,1,sharex=True)
SS1=(Si_con['S1'][1:])/Si['S1'][1:]
SS2=(Si_con['delta'][1:])/Si['delta'][1:]
sns.barplot(np.arange(1,5),np.abs(SS1),ax=ax1)
sns.barplot(np.arange(1,5),np.abs(SS2),ax=ax2)
ax1.set_title('SS1')
ax2.set_title('SDelta')
ax2.set_xlabel('Sensitivity')
elif method_flag==3:
Si = dgsm.analyze(problem, param_values, Y, conf_level=0.95, print_to_console=False)
figure_keys={'ax1_title':'dgsm',
'ax2_title':'dgsm_conf',
'ax2_lable':'Parameter index',
'ax3_title':'vi',
'ax4_title':'vi_std',
'ax4_lable':'Parameter index',
}
Si_con = dgsm.analyze(problem, param_values, Y_con, conf_level=0.95, print_to_console=False)
f1,(ax1,ax2)=plt.subplots(2,1,sharex=True)
SS1=(Si_con['dgsm'][1:])/Si['dgsm'][1:]
SS2=(Si_con['vi'][1:])/Si['vi'][1:]
sns.barplot(np.arange(1,5),np.abs(SS1),ax=ax1)
sns.barplot(np.arange(1,5),np.abs(SS2),ax=ax2)
ax1.set_title('Sdgsm')
ax2.set_title('Svi')
ax2.set_xlabel('Sensitivity')
elif method_flag==4:
Si = fast.analyze(problem, Y, print_to_console=False)
figure_keys={'ax1_title':'S1',
'ax2_title':'ST',
'ax2_lable':'Parameter index',
}
Si_con = fast.analyze(problem, Y_con, print_to_console=False)
f1,(ax1,ax2)=plt.subplots(2,1,sharex=True)
SS1=(np.array(Si_con['S1'][1:]))/np.array(Si['S1'][1:])
SS2=(np.array(Si_con['ST'][1:]))/np.array(Si['ST'][1:])
sns.barplot(np.arange(1,5),np.abs(SS1),ax=ax1)
sns.barplot(np.arange(1,5),np.abs(SS2),ax=ax2)
ax1.set_title('SS1')
ax2.set_title('SST')
ax2.set_xlabel('Sensitivity')
elif method_flag==5:
Si = ff_analyze(problem, param_values, Y, second_order=True, print_to_console=False)
elif method_flag==6:
Si = morris.analyze(problem, param_values, Y, conf_level=0.95,
print_to_console=False,
num_levels=4, grid_jump=2, num_resamples=100)
figure_keys={'ax1_title':'mu',
'ax2_title':'sigma',
'ax2_lable':'Parameter index',
'ax3_title':'mu_star',
'ax4_title':'mu_star_conf',
'ax4_lable':'Parameter index',
}
elif method_flag==7:
Si_con = sobol.analyze(problem, Y_con, print_to_console=False)
Si = sobol.analyze(problem, Y, print_to_console=False)
figure_keys={'ax1_title':'S1',
'ax2_title':'S1_conf',
'ax2_lable':'Parameter index',
'ax3_title':'ST',
'ax4_title':'ST_conf',
'ax4_lable':'Parameter index',
'ax5_parm':'S2',
'ax5_title':'Second order sensitivity',
'ax5_lable':'Parameter index',
}
SST=(Si_con['ST'])/Si['ST']
SS1=(Si_con['S1'])/Si['S1']
# f1,(ax1,ax2)=plt.subplots(2,1,sharex=True)
# sns.barplot(np.arange(2,22),np.abs(SST),ax=ax1,color="gray")
# sns.barplot(np.arange(2,22),np.abs(SS1),ax=ax2,color="gray")
# ax1.set_title('SST')
# ax2.set_title('SS1')
# ax2.set_xlabel('Sensitivity')
f1,(ax1)=plt.subplots(1,1,sharex=True)
sns.barplot(np.arange(1,5),np.abs(SST),ax=ax1,color="gray")
ax1.set_xlabel('Parameter number')
ax1.set_ylabel('Composite sensitivity indices')
# Plot the figure
f1,(ax1,ax2)=plt.subplots(2,1,sharex=True)
sns.barplot(np.arange(1,5),Si[figure_keys['ax1_title']],ax=ax1)
sns.barplot(np.arange(1,5),Si[figure_keys['ax2_title']],ax=ax2)
ax1.set_title(figure_keys['ax1_title'])
ax2.set_title(figure_keys['ax2_title'])
ax2.set_xlabel(figure_keys['ax2_lable'])
f2,(ax3,ax4)=plt.subplots(2,1,sharex=True)
sns.barplot(np.arange(1,5),Si[figure_keys['ax3_title']],ax=ax3)
sns.barplot(np.arange(1,5),Si[figure_keys['ax4_title']],ax=ax4)
ax3.set_title(figure_keys['ax3_title'])
ax4.set_title(figure_keys['ax4_title'])
ax4.set_xlabel(figure_keys['ax4_lable'])
f3=plt.figure()
ax5=f3.add_axes()
g_S2=sns.heatmap(Si[figure_keys['ax5_parm']],ax=ax5,xticklabels=np.arange(1,5), yticklabels=np.arange(1,5))
g_S2.set_title(figure_keys['ax5_title'])
g_S2.set_xlabel(figure_keys['ax5_lable'])
g_S2.set_ylabel(figure_keys['ax5_lable'])