This page was generated from docs\source\notebooks/hoffman_fit.ipynb.

Configuring the Hoffman failure criterion by fitting to experimental data

from sigmaepsilon.solid.material import HoffmanFailureCriterion
import numpy as np

inputs = [
    [-1, 0, 0, 0, 0, 0],
    [0, 1, 0, 0, 0, 0],
    [0, 0, -1, 0, 0, 0],
    [0, 0, 0, 1, 0, 0],
    [0, 0, 0, 0, -1, 0],
    [0, 0, 0, 0, 0, 1],
    [-1, 0.2, 0, 0, 0, 0],
    [0.2, 1, 0, 0, 0, 0],
    [-1, 0, 0.2, 0, 0, 0],
]
inputs = np.array(inputs, dtype=float)
outputs = np.ones(len(inputs))

failure_obj = HoffmanFailureCriterion()

Parameter fitting with a Binary Genetic Algorithm

params = failure_obj.fit(
    inputs,
    outputs,
    solver_params=dict(nPop=100, length=12),
    penalty=1e12,
    tol=0.1,
    n_iter=100,
    ranges=[[-10, 10] for _ in range(9)],
    method="bga",
)
failure_obj.params = params
params

(-0.9694749694749696,
 -3.0647130647130645,
 0.808302808302809,
 8.686202686202687,
 -4.378510378510379,
 -4.349206349206349,
 1.2380952380952372,
 -2.5274725274725274,
 1.0378510378510377)

prediction = failure_obj.utilization(stresses=inputs)
max_error = np.max(np.abs(prediction - outputs))
total_error = np.sum(np.sqrt((prediction - outputs) ** 2))
max_error, total_error

(0.6043478260869566, 1.9910851099808313)

prediction

array([1.02121238, 1.20985704, 0.40580257, 0.80769231, 0.39565217,
       0.96352941, 1.20067546, 1.01013493, 0.87811824])

Parameter fitting with Scipy’s Nelder-Mead method

params = failure_obj.fit(
    inputs,
    outputs,
    penalty=1e12,
    tol=0.1,
    method="Nelder-Mead",
    x0=[-1.0, 1.0, -1.0, 1.0, -1.0, 1.0, 0.2, 0.2, 0.2],
)
failure_obj.params = params
params

(-1.007322989181017,
 2.1576353611607075,
 -0.1541917498510884,
 0.9728903373271577,
 -0.9949634593134442,
 0.30283382032188944,
 0.35151153576340144,
 0.4327118607825844,
 0.44137317208707544)

prediction = failure_obj.utilization(stresses=inputs)
max_error = np.max(np.abs(prediction - outputs))
total_error = np.sum(np.sqrt((prediction - outputs) ** 2))
max_error, total_error

(3.311006678188673, 7.380983890058536)

prediction

array([ 0.98936093,  1.20858211,  1.02177759,  2.84485685, -2.31100668,
        2.26565651,  0.92597216,  0.35965563,  1.00409288])