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#!/usr/bin/env python
#
# Author: Mike McKerns (mmckerns @caltech and @uqfoundation)
# Copyright (c) 2009-2016 California Institute of Technology.
# Copyright (c) 2016-2024 The Uncertainty Quantification Foundation.
# License: 3-clause BSD. The full license text is available at:
# - https://github.com/uqfoundation/mystic/blob/master/LICENSE
"""Original matlab code:
function A=marc_surr(x)
h=x(1)*25.4*10^(-3);
a=x(2)*pi/180;
v=x(3);
Ho=0.5794;
s=1.4004;
n=0.4482;
K=10.3963;
p=0.4757;
u=1.0275;
m=0.4682;
Dp=1.778;
v_bl=Ho*(h/(cos(a))^(n))^s;
if v<v_bl
A=0
else
A=K*((h/Dp)^p)*((cos(a))^u)*(tanh((v/v_bl)-1))^m;
end
"""
### NOTES ###
# h = thickness = [60,105]
# a = obliquity = [0,30]
# v = speed = [2.1,2.8]
# explore the cuboid (h,a,v), with
# subdivisions at h=100, a=20, v=2.2
# due to ballistic limit: v(h=100,a=20) = 2.22,
# perforation in this region should be zero.
# NOTE: 'failure' is A < = t
#
# Calculate for each of the 8 subcuboids:
# * probability mass, i.e. the product of the normalized side-lengths,
# since we're taking h, a and v to be uniformly distributed in their
# intervals
# * McDiarmid diameter of the perforation area A when restricted to that
# cuboid or subcuboid
# * the mean value of the perforation area A on each (sub)cuboid
from math import pi, cos, tanh
def ballistic_limit(h,a):
"""calculate ballistic limit
Inputs:
- h = thickness in (unknown) units
- a = obliquity in (unknown) units
Outputs:
- v_bl = velocity (ballistic limit) in (unknown) units
"""
#h = x[0] * 25.4 * 1e-3
#a = x[1] * pi/180.0
Ho = 0.5794
s = 1.4004
n = 0.4482
return Ho * ( h / cos(a)**n )**s
def marc_surr(x):
"""calculate perforation area using a tanh-based model surrogate
Inputs:
- x = [thickness, obliquity, speed] in (unknown) units
Outputs:
- A = performation area in (unknown) units
"""
# h = thickness = [60,105]
# a = obliquity = [0,30]
# v = speed = [2.1,2.8]
h = x[0] * 25.4 * 1e-3
a = x[1] * pi/180.0
v = x[2]
K = 10.3963
p = 0.4757
u = 1.0275
m = 0.4682
Dp = 1.778
# compare to ballistic limit
v_bl = ballistic_limit(h,a)
if v < v_bl:
return 0
return K * (h/Dp)**p * (cos(a))**u * (tanh((v/v_bl)-1))**m
# EOF
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