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pce module in the pyapprox library #21

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canhuaLiu opened this issue Sep 16, 2022 · 1 comment
Open

pce module in the pyapprox library #21

canhuaLiu opened this issue Sep 16, 2022 · 1 comment

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@canhuaLiu
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Dear Dr. Jakeman,
please ask whether the pce module in the pyapprox library is only valid for continuous functions with expressions. For practical problems, I can only obtain the input variables and output results. Can I effectively use the library you developed. If it is convenient, I would be grateful if you could provide a simple example for reference.
@canhuaLiu
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Dear Dr. Jakeman,
After reading online documentation， I try to construct a polynomial chaos expansion (PCE) of a simple 2-D frame RE model with uncertain parameters using Leja sequences, the capacity of validation_samples is 200, the max_nsamples is 10000, the tolerance is 1e-10，however, the errors between pce_values and validation_values are not convergent and even increase. I would like to ask why does such a problem occur. The code is as follows：
`import numpy as np
from scipy import stats
from pyapprox.variables import IndependentMarginalsVariable
from pyapprox.interface.wrappers import evaluate_1darray_function_on_2d_array
import math
from warnings import simplefilter
from pyapprox import analysis
from pyapprox import surrogates
import openseespy.opensees as ops
simplefilter(action='ignore', category=FutureWarning)

def evaluate(NB):
ops.wipe()
ops.model('Basic', '-ndm', 2, '-ndf', 3)

h = 4
w = 3

ops.node(1, 0.0, 0.0)
ops.node(2, h, 0.0)
ops.node(3, 0.0, w)
ops.node(4, h, w)

ops.fix(1, 1, 1, 1)
ops.fix(2, 1, 1, 1)
ops.fix(3, 0, 0, 0)
ops.fix(4, 0, 0, 0)

ops.mass(3, NB[0], 0.0, 0.0)
ops.mass(4, NB[0], 0.0, 0.0)

ops.geomTransf('Linear', 1)

ops.element('elasticBeamColumn', 1, 1, 3, 0.25, NB[1], NB[2], 1)
ops.element('elasticBeamColumn', 2, 2, 4, 0.25, NB[1], NB[2], 1)
ops.element('elasticBeamColumn', 3, 3, 4, 0.25, NB[1], NB[2], 1)

ops.rayleigh(NB[3], 0, 0, 0)  # RAYLEIGH damping

dt = 0.02
ops.timeSeries('Path', 200, '-dt', dt, '-filePath', 'EI.txt', '-factor', 10)
ops.pattern('UniformExcitation', 200, 1, '-accel', 200)
ops.constraints('Transformation')
ops.numberer('RCM')
ops.system('UmfPack')
ops.test('NormDispIncr', 0.000001, 1000)
ops.algorithm('KrylovNewton')
ops.integrator('Newmark', 0.55, 0.2765625)
ops.analysis('Transient')
tCurrent = ops.getTime()
tFinal = 52
time = [tCurrent]
us = [0.0]
ax = [0.0]
ok = 0
while tCurrent < tFinal:
    while ok == 0 and tCurrent < tFinal:
        ops.analysis('Transient')
        ok = ops.analyze(1, .02)
        if ok == 0:
            tCurrent = ops.getTime()
            time.append(tCurrent)
            us.append(ops.nodeDisp(3, 1))
            ax.append(ops.nodeAccel(3, 1))
usm = abs(max(us, key=abs))
return usm

Avalues = []
def compute_l2_error(validation_samples, validation_values, pce,
relative=True):
pce_values = pce(validation_samples)
Avalues.append(pce_values)
error = np.linalg.norm(pce_values - validation_values, axis=0)
if not relative:
error /= np.sqrt(validation_samples.shape[1])
else:
error /= np.linalg.norm(validation_values, axis=0)

return error

np.random.seed(1)

def trunNor(mu, sigma):
lower, upper = mu - 2 * sigma, mu + 2 * sigma # 截断在[μ-3σ, μ+3σ]
X = stats.truncnorm((lower - mu) / sigma, (upper - mu) / sigma, loc=mu, scale=sigma)
return X

X1 = trunNor(20, 2)
X2 = trunNor(2e5, 2e4)
X3 = trunNor(5.21e-3, 5e-4)
X4 = trunNor(0.05, 0.005)
univariate_variables = [X1, X2, X3, X4]
variable = IndependentMarginalsVariable(univariate_variables)
nsamples = 150
validation_samples = variable.rvs(nsamples)

np.savetxt("SS.txt", validation_samples.T)

def pyapprox_fun_0(validation_samples):
values = evaluate_1darray_function_on_2d_array(evaluate, validation_samples)
return values

validation_values = pyapprox_fun_0(validation_samples)
errors = []
num_samples = []

def callback(pce):
error = compute_l2_error(validation_samples, validation_values, pce)
errors.append(error)
num_samples.append(pce.samples.shape[1])

max_num_samples = 200

opts = {"method": "leja", "options": {"max_nsamples": 1000, "tol": 1e-10, "callback": callback}}
pce = surrogates.adaptive_approximate(pyapprox_fun_0, variable, "polynomial_chaos", opts).approx

res = analysis.gpc_sobol_sensitivities(pce.pce, variable)
print(res.main_effects[:, 0])

S = np.size(errors)
np.savetxt("R.txt", validation_values)
Avalues = np.array(Avalues)
Avalues = np.reshape(Avalues, (S, -1))
np.savetxt("V.txt", Avalues.T)

`

The EI file data is as follows：
-0.002865497 -0.022105263 -0.020672515 -0.018011696 -0.019444444 -0.024561404 -0.029064326 -0.026198831 -0.02251462 -0.01739766 -0.01739766 -0.026812866 -0.036023392 -0.039707601 -0.033157895 -0.029473683 -0.022105263 -0.016783625 -0.008596491 -0.013508771 -0.026812866 -0.038888887 -0.040116959 -0.013508771 0.006140351 0.028859649 -0.01002924 -0.026198831 -0.029473683 -0.041549706 -0.053216373 -0.066520467 -0.062631578 -0.035204679 -0.040321638 -0.033362571 -0.03356725 -0.01371345 0.005116959 0.030701753 0.048304094 0.051578948 0.068771925 0.094766079 0.100701753 0.085760235 0.073479533 0.055467835 0.048099414 0.069385966 0.084327484 0.108479529 0.130789473 0.149824551 0.133450284 0.122602338 0.081871344 0.081871344 0.012894737 -0.105409354 -0.161081861 -0.123421048 -0.099064329 -0.051169589 -0.012076023 0.027426899 0.063040932 0.102134504 0.145321633 0.203654973 0.249707605 0.313157878 0.296783609 0.237426903 0.191374265 0.182573089 0.189532156 0.171725146 0.184415197 0.203245616 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0.04482456 0.049327486 0.139795325 0.141023391 0.270175441 0.276315792 0.417543844 -0.190555548 -0.268128658 -0.141637416 -0.111754381 0.014736841 0.138157892 -0.21900585 -0.304970743 -0.21900585 -0.237426903 -0.155964902 -0.114415206 -0.044005846 -0.025789474 -0.137953216 -0.06631579 -0.068976609 -0.02230994 0.003479532 0.061198829 0.099883036 0.12444444 0.045438597 -0.006549707 -0.050146197 0.015760233 0.043187135 0.116257305 0.169064321 0.247660821 0.30292396 0.356140335 0.086169586 0.005935673 0.053011694 0.059970757 -0.01125731 -0.030087718 0.029269006 0.042163743 0.102134504 0.132017541 0.195877183 0.231286552 0.296783609 0.333625715 0.399122791 0.380701738 0.405263142 0.362280686 0.255847956 -0.247660821 -0.110935672 -0.078596492 -0.063654969 -0.229239769 -0.339766065 -0.503508757 -0.41549706 -0.376608171 -0.270175441 -0.196491224 -0.066520467 0.031520466 0.167017538 0.270175441 0.372514604 -0.011871345 -0.034590642 0.058333332 0.091491227 0.201198833 0.290643258 0.378654955 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