def global_wa_hyp(M, lat_hyp, lon_hyp, depth_hyp, lat_sta, lon_sta):
"""
Computed intensity prediction equation according to Wald & Allan, 2012
Parameters:
M magnitude
lat_hyp, lon_hyp, depth_hyp: coordinates of the hypocenter (latitude, longitude, depth, respectively)
lat_sta, lon_sta: coordinates of the station (latitude and longitude, respectively)
Returns:
a number
"""
#defining constants:
c0 = 2.085
c1 = 1.428
c2 = -1.402
c4 = 0.078
m1 = -0.209
m2 = 2.042
R_hyp = _threed_dist(lat_hyp, lon_hyp, depth_hyp, lat_sta, lon_sta, 0)
R_M = m1 + m2 * exp(M - 5)
I = c0 + c1 * M + c2 * log(sqrt(R_hyp**2 + R_M**2))
if R_hyp > 50:
I = I + c4 * log(R_hyp / 50)
return I
def calculate(self, distance):
xEP1, xEP2, xEP3, xEP4, xEP5 = self.__constants
M = self.m #magnitude
depth = self.depth
return xEP1 * M + xEP2 * log10(depth) + xEP3 - xEP4 * 0.5 * log10(
(distance / depth)**2 + 1) - xEP5 * (sqrt(distance**2 + depth**2) -
depth)
def global_wa_hyp(M, lat_hyp, lon_hyp, depth_hyp, lat_sta, lon_sta):
"""
Computed intensity prediction equation according to Wald & Allan, 2012
Parameters:
M magnitude
lat_hyp, lon_hyp, depth_hyp: coordinates of the hypocenter (latitude, longitude, depth, respectively)
lat_sta, lon_sta: coordinates of the station (latitude and longitude, respectively)
Returns:
a number
"""
#defining constants:
c0 = 2.085
c1 = 1.428
c2 = -1.402
c4 = 0.078
m1 = -0.209
m2 = 2.042
R_hyp = _threed_dist(lat_hyp, lon_hyp, depth_hyp, lat_sta, lon_sta, 0)
R_M = m1 + m2 * exp(M-5)
I = c0 + c1 * M + c2 * log(sqrt(R_hyp ** 2 + R_M ** 2));
if R_hyp > 50:
I = I + c4 * log(R_hyp/50)
return I
def calculate(self, distance):
c0, c1, c2, c4, m1, m2 = self.__constants
M = self.m #magnitude
R_M = m1 + m2 * exp(M - 5)
I = c0 + c1 * M + c2 * log(sqrt(distance**2 + R_M**2))
if distance > 50:
I = I + c4 * log(distance / 50)
return I
def disthyp(lat_hyp, lon_hyp, depth_hyp, lat, lon):
"""
Returns the distance, in km, from the hypocenter whose latitude, longitude
and depth are lat_hyp, lon_hyp and depth_hyp, respectively, and a generic location
whose latitude and longitude are lat and lon, respectively.
All arguments are assumed in degrees except for depth, in km
"""
chord = chorddistance(lat_hyp, lon_hyp, lat, lon)
return sqrt(depth_hyp**2 + chord**2)
def test_two_bar_truss_analysis():
"""Example of two-bar truss stress/deflection analysis"""
H = N(30, 5 / 3.0, tag="H")
B = N(60, 0.5 / 3.0, tag="B")
d = N(3, 0.1 / 3, tag="d")
t = N(0.15, 0.01 / 3, tag="t")
E = N(30000, 1500 / 3.0, tag="E")
rho = N(0.3, 0.01 / 3.0, tag="rho")
P = N(66, 3 / 3.0, tag="P")
pi = np.pi
wght = 2 * pi * rho * d * t * umath.sqrt((B / 2) ** 2 + H ** 2)
strs = (P * umath.sqrt((B / 2) ** 2 + H ** 2)) / (2 * pi * d * t * H)
buck = (pi ** 2 * E * (d ** 2 + t ** 2)) / (8 * ((B / 2) ** 2 + H ** 2))
defl = (P * ((B / 2) ** 2 + H ** 2) ** (1.5)) / (2 * pi * d * t * H ** 2 * E)
print(wght.describe("wght"))
print(strs.describe("strs"))
print(buck.describe("buck"))
print(defl.describe("defl"))
def __call__(self, lat, lon):
#TO BE IMPLEMENTED
#getting constants:
c0, c1 , c2 , c4, m1, m2 = self.__constants
#R_hyp = _threed_dist(self.lat, self.lon, self.depth, lat, lon, 0)
chord = chorddistance(self.lat, self.lon, lat, lon)
R_hyp = sqrt(self.depth**2 + chord**2)
M = self.m #magnitude
R_M = m1 + m2 * exp(M-5)
I = c0 + c1 * M + c2 * log(sqrt(R_hyp ** 2 + R_M ** 2));
if R_hyp > 50:
I = I + c4 * log(R_hyp/50)
return I
def __call__(self, lat, lon):
if not hasattr(self, "_rld"):
self._rld, self._rw = rld_rw(self.sof)(self.m)
c0, c1, c2, c3 = self.__constants
r_rup = rup_distance(lat, lon, self.lat, self.lon, self.depth, self.strike, self.dip, self._rld, self._rw)
return c0 + c1 * self.m + c2 * log (sqrt( r_rup ** 2 + (1 + c3 * exp(self.m -5)) **2 ))
def test_volumetric_gas_flow():
"""Example of volumetric gas flow through orifice meter"""
H = N(64, 0.5)
M = N(16, 0.1)
P = N(361, 2)
t = N(165, 0.5)
C = 38.4
Q = C * umath.sqrt((520 * H * P) / (M * (t + 460)))
Q.describe()
def _centralasia_emca_1(
M, depth, dist_epi_sta
): #h=Depth, dist_epi_sta=distanza in R2 tra epicentro e stazione. DISTANCES IN KM!!!!
"""
Computed intensity prediction equation for central asia
given a Magnitude M, the hypocenter depth and the distance between epicenter and station
"""
#computed intensity for Central Asia
#Epicentral and EXtended distances;
#Input: mag,depth,distance values
#distance can be a vector
xEP1 = 1.0074538
xEP2 = -2.0045088
xEP3 = 3.2980663
xEP4 = 2.6920855
xEP5 = 4.2344195e-04
return xEP1 * M + xEP2 * log10(depth) + xEP3 - xEP4 * 0.5 * log10(
(dist_epi_sta / depth)**2 +
1) - xEP5 * (sqrt(dist_epi_sta**2 + depth**2) - depth)
def calculate(self, distance):
c0, c1, c2, c3 = self.__constants
I = c0 + c1 * self.m + c2 * log(
sqrt(distance**2 + (1 + c3 * exp(self.m - 5))**2))
return I
def _threed_dist(lat1, lon1, depth1, lat2, lon2, depth2):
"""
Returns the 3D distance from point1 to point2
"""
return sqrt((lat1 - lat2)**2 + (lon1 - lon2)**2 + (depth1 - depth2)**2)
def _threed_dist(lat1, lon1, depth1, lat2, lon2, depth2):
"""
Returns the 3D distance from point1 to point2
"""
return sqrt( (lat1-lat2)**2 + (lon1-lon2)**2 + (depth1-depth2)**2 )
def __call__(self, lat, lon):
#TO BE IMPLEMENTED
#getting constants:
xEP1, xEP2, xEP3, xEP4, xEP5 = self.__constants
dist_epi_sta = deg2km(greatarc_dist(self.lat, self.lon, lat, lon))
M = self.m #magnitude
depth = self.depth
return xEP1*M + xEP2*log10(depth) + xEP3 - xEP4*0.5*log10((dist_epi_sta/depth)**2 + 1) - xEP5*(sqrt(dist_epi_sta**2 + depth**2)-depth)
from mcerp import * # N, U, Gamma, Beta, correlate, etc.
import mcerp.umath as umath
import numpy as np
sp = 2 # deviation standard pour le rayon
# une deviation standard de 2 m en rayon sur chaque coin correspond a une deviation standard en x ou y de stv/sqrt(2)
sp = sp / umath.sqrt(2)
x1 = N(0, sp)
y1 = N(0, sp)
x2 = N(100, sp)
y2 = N(0, sp)
x3 = N(0, sp)
y3 = N(50, sp)
x4 = N(100, sp)
y4 = N(50, sp)
# calcul des surfaces
'''# approximatif
surface = umath.sqrt((x2-x1)**2+(y2-y1)**2)*umath.sqrt((x3-x1)**2+(y3-y1)**2)/2+umath.sqrt((x4-x2)**2+(y4-y2)**2)*umath.sqrt((x4-x3)**2+(y4-y3)**2)/2
'''
# exact
v12 = [x2 - x1, y2 - y1]
v13 = [x3 - x1, y3 - y1]
v14 = [x4 - x1, y4 - y1]
surface = np.cross(v12, v14) / 2 + np.cross(v14, v13) / 2
surface.describe()
print('surface.mean : ', surface.mean, ' stv : ', np.sqrt(surface.var))
'''
surface.mean : 4999.957807386318 stv : 157.22298079
print('*' * 80)
print('Example of a three part assembly')
x1 = N(24, 1)
x2 = N(37, 4)
x3 = Exp(2) # Exp(mu=0.5) is the same
Z = (x1 * x2**2) / (15 * (1.5 + x3))
Z.describe()
print('*' * 80)
print('Example of volumetric gas flow through orifice meter')
H = N(64, 0.5)
M = N(16, 0.1)
P = N(361, 2)
t = N(165, 0.5)
C = 38.4
Q = C * umath.sqrt((520 * H * P) / (M * (t + 460)))
Q.describe()
print('*' * 80)
print('Example of manufacturing tolerance stackup')
# for a gamma distribution we need the following conversions:
# shape = mean**2/var
# scale = var/mean
mn = 1.5
vr = 0.25
k = mn**2 / vr
theta = vr / mn
x = Gamma(k, theta)
y = Gamma(k, theta)
z = Gamma(k, theta)
w = x + y + z
def _centralasia_emca_1(M, depth, dist_epi_sta): #h=Depth, dist_epi_sta=distanza in R2 tra epicentro e stazione. DISTANCES IN KM!!!!
"""
Computed intensity prediction equation for central asia
given a Magnitude M, the hypocenter depth and the distance between epicenter and station
"""
#computed intensity for Central Asia
#Epicentral and EXtended distances;
#Input: mag,depth,distance values
#distance can be a vector
xEP1 =1.0074538
xEP2 = -2.0045088
xEP3 = 3.2980663
xEP4 = 2.6920855
xEP5 = 4.2344195e-04
return xEP1*M + xEP2*log10(depth) + xEP3 - xEP4*0.5*log10((dist_epi_sta/depth)**2 + 1) - xEP5*(sqrt(dist_epi_sta**2 + depth**2)-depth)
