canhuaLiu
commented
2 years ago 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 usmAvalues = [] 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 errornp.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：
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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.