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
|
#!/usr/bin/env python
import openturns as ot
import openturns.testing as ott
import persalys
ot.RandomGenerator.SetSeed(0)
myStudy = persalys.Study("myStudy")
persalys.Study.Add(myStudy)
R = persalys.Input(
"R", 700e6, ot.LogNormalMuSigma(750e6, 11e6).getDistribution(), "Parameter R"
)
C = persalys.Input("C", 2500e6, ot.Normal(2750e6, 250e6), "Parameter C")
gamma = persalys.Input("gam", 8.0, ot.Normal(10, 2), "Parameter gamma")
dist_strain = ot.Uniform(0, 0.07)
strain = persalys.Input("strain", 0.0, dist_strain, "Strain")
sigma = persalys.Output("sigma", "Stress (Pa)")
fakeSigma = persalys.Output("fakeSigma", "Stress (Pa)")
formula = ["R + C * (1 - exp(-gam * strain))", "2*(R + C * (1 - exp(-gam * strain)))"]
model = persalys.SymbolicPhysicalModel(
"model1", [R, C, gamma, strain], [sigma, fakeSigma], formula
)
myStudy.add(model)
# generate observations
nbObs = 100
strainObs = dist_strain.getSample(nbObs)
strainObs.setDescription(["strain"])
stressSampleNoise = ot.Normal(0.0, 40.0e6).getSample(nbObs)
stressSample = ot.ParametricFunction(
model.getFunction("sigma"), [0, 1, 2], [750e6, 2750e6, 10.0]
)(strainObs)
stressObs = stressSample + stressSampleNoise
stressObs.setDescription(["sigma"])
observations = persalys.Observations("obs1", model, strainObs, stressObs)
myStudy.add(observations)
# Least Squares linear
analysis = persalys.CalibrationAnalysis("myAnalysis", observations)
analysis.run()
myStudy.add(analysis)
print("analysis=", analysis)
thetaMAP = analysis.getResult().getCalibrationResult().getParameterMAP()
ott.assert_almost_equal(thetaMAP, [7.47009e+08, 2.73521e+09, 10.1291], 1e-2, 1)
print("isBayesian=", analysis.getResult().getCalibrationResult().isBayesian())
# Least Squares Non linear
analysis2 = persalys.CalibrationAnalysis("myAnalysis2", observations)
analysis2.setMethodName("LeastSquaresNonlinear")
analysis2.setCalibratedInputs(["R", "C"], ot.Dirac([700e6, 2400e6]), ["gam"], [7.0])
analysis2.run()
myStudy.add(analysis2)
print("analysis=", analysis2)
print("isBayesian=", analysis2.getResult().getCalibrationResult().isBayesian())
# Gaussian linear calibration
analysis3 = persalys.CalibrationAnalysis("myAnalysis3", observations)
sigmaStress = 1.0e7 # (Pa)
errorCovariance = ot.CovarianceMatrix(1)
errorCovariance[0, 0] = sigmaStress**2
analysis3.setMethodName("GaussianLinear")
analysis3.setErrorCovariance(errorCovariance)
analysis3.run()
myStudy.add(analysis3)
print("analysis=", analysis3)
print("isBayesian=", analysis3.getResult().getCalibrationResult().isBayesian())
# Gaussian non linear calibration
analysis4 = persalys.CalibrationAnalysis("myAnalysis4", observations)
analysis4.setMethodName("GaussianNonlinear")
analysis4.setErrorCovariance(errorCovariance)
analysis4.setBootStrapSize(50)
analysis4.setConfidenceIntervalLength(0.99)
optimizationAlgo = analysis4.getOptimizationAlgorithm()
optimizationAlgo.setMaximumCallsNumber(50)
optimizationAlgo.setMaximumAbsoluteError(1e-6)
analysis4.setOptimizationAlgorithm(optimizationAlgo)
analysis4.run()
myStudy.add(analysis4)
print("analysis=", analysis4)
print("isBayesian=", analysis4.getResult().getCalibrationResult().isBayesian())
# analysis check
# - check two outputs
stressObs.stack(stressObs * 2)
stressObs.setDescription(["sigma", "fakeSigma"])
observations2 = persalys.Observations("obs2", model, strainObs, stressObs)
analysis5 = persalys.CalibrationAnalysis("myAnalysis5", observations2)
analysis5.run()
fakeIn = persalys.Input("fakeIn")
model.addInput(fakeIn)
# - check fixed input order
analysis6 = persalys.CalibrationAnalysis("myAnalysis6", observations)
analysis6.setCalibratedInputs(
["R", "C"], ot.Dirac([700e6, 2500e6]), ["fakeIn", "gam"], [0.0, 7.0]
)
analysis6.run()
# - check calibrated input order
analysis7 = persalys.CalibrationAnalysis("myAnalysis7", observations)
analysis7.setCalibratedInputs(
["C", "R"], ot.Dirac([2500e6, 700e6]), ["gam", "fakeIn"], [7.0, 0.0]
)
analysis7.run()
# - check observed input order
strainObs2 = ot.Normal().getSample(nbObs)
strainObs2.stack(strainObs)
strainObs2.setDescription(["fakeIn", "strain"])
observations3 = persalys.Observations("obs3", model, strainObs2, stressObs)
analysis8 = persalys.CalibrationAnalysis("myAnalysis8", observations3)
analysis8.setCalibratedInputs(["R", "C"], ot.Dirac([700e6, 2500e6]), ["gam"], [7.0])
analysis8.run()
# - check exceptions
try:
analysis6.setCalibratedInputs(
["R", "C"], ot.Dirac([700e6, 2400e6]), ["gam", "fakeIn"], [7.0, 0.0]
)
except Exception as e:
print(
"InvalidArgumentException occurred: %s" % ("InvalidArgumentException" in str(e))
)
try:
analysis6.setCalibratedInputs(
["R", "C", "fakeIn"], ot.Dirac([700e6, 2400e6, 4.0]), ["gam"], [7.0]
)
except Exception as e:
print(
"InvalidArgumentException occurred: %s" % ("InvalidArgumentException" in str(e))
)
try:
analysis6.setCalibratedInputs(
["R", "C"], ot.Dirac([700e6, 2400e6, 4.0]), ["gam", "C"], [7.0, 1e9]
)
except Exception as e:
print(
"InvalidArgumentException occurred: %s" % ("InvalidArgumentException" in str(e))
)
try:
analysis6.setCalibratedInputs(["R", "C"], ot.Normal(3), ["gam"], [7.0])
except Exception as e:
print(
"InvalidArgumentException occurred: %s" % ("InvalidArgumentException" in str(e))
)
print("\nthetaMAP=", analysis.getResult().getCalibrationResult().getParameterMAP())
print("thetaMAP CI=\n", analysis.getResult().getConfidenceInterval())
# print("\nthetaMAP=", analysis2.getResult().getCalibrationResult().getParameterMAP())
# print("thetaMAP CI=\n", analysis2.getResult().getConfidenceInterval())
thetaMAP = analysis2.getResult().getCalibrationResult().getParameterMAP()
ott.assert_almost_equal(thetaMAP, [7.73108e08, 3.55285e09], 1e-2, 1)
print("\nthetaMAP=", analysis3.getResult().getCalibrationResult().getParameterMAP())
print("thetaMAP CI=\n", analysis3.getResult().getConfidenceInterval())
# print("\nthetaMAP=", analysis4.getResult().getCalibrationResult().getParameterMAP())
# print("thetaMAP CI=\n", analysis4.getResult().getConfidenceInterval())
thetaMAP = analysis4.getResult().getCalibrationResult().getParameterMAP()
ott.assert_almost_equal(thetaMAP, [7.47517e08, 2.83374e09, 9.58942], 1e-2, 1)
print("\nthetaMAP=", analysis5.getResult().getCalibrationResult().getParameterMAP())
print("thetaMAP CI=\n", analysis5.getResult().getConfidenceInterval())
print("\nthetaMAP=", analysis6.getResult().getCalibrationResult().getParameterMAP())
print("thetaMAP CI=\n", analysis6.getResult().getConfidenceInterval())
print("\nthetaMAP=", analysis7.getResult().getCalibrationResult().getParameterMAP())
print("thetaMAP CI=\n", analysis7.getResult().getConfidenceInterval())
print("\nthetaMAP=", analysis8.getResult().getCalibrationResult().getParameterMAP())
print("thetaMAP CI=\n", analysis8.getResult().getConfidenceInterval())
# script
script = myStudy.getPythonScript()
print(script)
exec(script)
|
