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'''
Created on 19. dec. 2016
@author: mmpe
'''
from wetb.utils.geometry import mean_deg, rad, tand, sind, deg, cosd
import numpy as np
from scipy.signal import detrend
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def wsp_dir2uv(wsp, dir, dir_ref=None):
"""Convert horizontal wind speed and direction to u,v
Parameters
----------
wsp : array_like
Horizontal wind speed
dir : array_like
Wind direction
dir_ref : int or float, optional
Reference direction\n
If None, default, the mean direction is used as reference
Returns
-------
u : array_like
u wind component
v : array_like
v wind component
"""
if dir_ref is None:
dir = dir[:] - mean_deg(dir[:])
else:
dir = dir[:] - dir_ref
u = np.cos(rad(dir)) * wsp[:]
v = -np.sin(rad(dir)) * wsp[:]
return np.array([u, v])
def wsp_dir_tilt2uvw(wsp, dir, tilt, wsp_horizontal, dir_ref=None):
"""Convert horizontal wind speed and direction to u,v,w
Parameters
----------
wsp : array_like
- if wsp_horizontal is True: Horizontal wind speed, $\sqrt{u^2+v^2}\n
- if wsp_horizontal is False: Wind speed, $\sqrt{u^2+v^2+w^2}
dir : array_like
Wind direction
tilt : array_like
Wind tilt
wsp_horizontal : bool
See wsp
dir_ref : int or float, optional
Reference direction\n
If None, default, the mean direction is used as reference
Returns
-------
u : array_like
u wind component
v : array_like
v wind component
w : array_like
v wind component
"""
wsp, dir, tilt = wsp[:], dir[:], tilt[:]
if wsp_horizontal:
w = tand(tilt) * wsp
u, v = wsp_dir2uv(wsp, dir, dir_ref)
else:
w = sind(tilt) * wsp
u, v = wsp_dir2uv(np.sqrt(wsp ** 2 - w ** 2), dir, dir_ref)
return np.array([u, v, w])
def xyz2uvw(x, y, z, left_handed=True):
"""Convert sonic x,y,z measurements to u,v,w wind components
Parameters
----------
x : array_like
Sonic x component
y : array_like
Sonic x component
z : array_like
Sonic x component
left_handed : boolean
if true (default), xyz are defined in left handed coodinate system (default for some sonics)
if false, xyz are defined in normal right handed coordinate system
Returns
-------
u : array_like
u wind component
v : array_like
v wind component
w : array_like
w wind component
"""
x, y, z = map(np.array, [x, y, z])
if left_handed:
y *= -1
theta = deg(np.arctan2(np.mean(y), np.mean(x)))
SV = cosd(theta) * y - sind(theta) * x
Mads M. Pedersen
committed
# SUW = cosd(theta) * x + sind(theta) * y
#
# #% rotation around y of tilt
# tilt = deg(np.arctan2(np.mean(z), np.mean(SUW)))
# SU = SUW * cosd(tilt) + z * sind(tilt);
# SW = z * cosd(tilt) - SUW * sind(tilt);
SU = cosd(theta) * x + sind(theta) * y
SW = z
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return np.array([SU, SV, SW])
def abvrel2xyz_old(alpha, beta, vrel):
"""Convert pitot tube alpha, beta and relative velocity to local Cartesian wind speed velocities
Parameters
----------
alpha : array_like
Pitot tube angle of attack [rad]. Zero: Parallel to pitot tube. Positive: Flow from wind side (pressure side)
beta : array_like
Pitot tube side slip angle [rad]. Zero: Parallel to pitot tube. Positive: Flow from root side
vrel : array_like
Pitot tube relative velocity. Positive: flow towards pitot tube
Returns
-------
x : array_like
Wind component towards pitot tube (positive for postive vrel and -90<beta<90)
y : array_like
Wind component in alpha plane (positive for positive alpha)
z : array_like
Wind component in beta plane (positive for negative beta)
"""
alpha = np.array(alpha, dtype=np.float)
beta = np.array(beta, dtype=np.float)
vrel = np.array(vrel, dtype=np.float)
sign_vsx = -((np.abs(beta) > np.pi / 2) * 2 - 1) # +1 for |beta| < 90, -1 for |beta|>90
sign_vsy = np.sign(alpha) #+ for alpha > 0
sign_vsz = -np.sign(beta) #- for beta>0
x = sign_vsx * np.sqrt(vrel ** 2 / (1 + np.tan(alpha) ** 2 + np.tan(beta) ** 2))
m = alpha != 0
y = np.zeros_like(alpha)
y[m] = sign_vsy[m] * np.sqrt(vrel[m] ** 2 / ((1 / np.tan(alpha[m])) ** 2 + 1 + (np.tan(beta[m]) / np.tan(alpha[m])) ** 2))
m = beta != 0
z = np.zeros_like(alpha)
z[m] = sign_vsz[m] * np.sqrt(vrel[m] ** 2 / ((1 / np.tan(beta[m])) ** 2 + 1 + (np.tan(alpha[m]) / np.tan(beta[m])) ** 2))
return x, y, z
def abvrel2xyz(alpha, beta, vrel):
"""Convert pitot tube alpha, beta and relative velocity to local Cartesian wind speed velocities
x : parallel to pitot tube, direction pitot tube root to tip, i.e. normal flow gives negative x\n
y : component in alpha plane
z : component in beta plane
For typical usage where pitot tube is mounted on leading edge:\n
x: Opposite rotational direction\n
y: Direction of mean wind\n
z: From blade root to tip\n
Parameters
----------
alpha : array_like
Pitot tube angle of attack [rad]. Zero for flow towards pitot tube. Positive around z-axis. I.e.
negative alpha (normal flow) gives positive y component
beta : array_like
Pitot tube side slip angle [rad]. Zero for flow towards pitot tube. Positive around y-axis. I.e.
Positive beta (normal flow due to expansion and position in front of blade) gives positive z
vrel : array_like
Pitot tube relative velocity. Positive: flow towards pitot tube
Returns
-------
x : array_like
Wind component away from pitot tube (positive for postive vrel and -90<beta<90)
y : array_like
Wind component in alpha plane (positive for positive alpha)
z : array_like
Wind component in beta plane (positive for negative beta)
"""
alpha = np.array(alpha, dtype=np.float)
beta = np.array(beta, dtype=np.float)
vrel = np.array(vrel, dtype=np.float)
sign_vsx = ((np.abs(beta) > np.pi / 2) * 2 - 1) # -1 for |beta| < 90, +1 for |beta|>90
sign_vsy = -np.sign(alpha) #- for alpha > 0
sign_vsz = np.sign(beta) # for beta>0
x = sign_vsx * np.sqrt(vrel ** 2 / (1 + np.tan(alpha) ** 2 + np.tan(beta) ** 2))
m = alpha != 0
y = np.zeros_like(alpha)
y[m] = sign_vsy[m] * np.sqrt(vrel[m] ** 2 / ((1 / np.tan(alpha[m])) ** 2 + 1 + (np.tan(beta[m]) / np.tan(alpha[m])) ** 2))
m = beta != 0
z = np.zeros_like(alpha)
z[m] = sign_vsz[m] * np.sqrt(vrel[m] ** 2 / ((1 / np.tan(beta[m])) ** 2 + 1 + (np.tan(alpha[m]) / np.tan(beta[m])) ** 2))
return np.array([x, y, z]).T
Mads M. Pedersen
committed
def detrend_uvw(u, v=None, w=None):
# def _detrend(wsp):
# if wsp is None:
# return None
# dwsp = np.atleast_2d(wsp.copy().T).T
# t = np.arange(dwsp.shape[0])
# A = np.vstack([t, np.ones(len(t))]).T
# for i in range(dwsp.shape[1]):
# trend, offset = np.linalg.lstsq(A, dwsp[:, i])[0]
# dwsp[:, i] = dwsp[:, i] - t * trend + t[-1] / 2 * trend
# return dwsp.reshape(wsp.shape)
def _detrend(y):
if y is None:
return None
return detrend(y)
return [_detrend(uvw) for uvw in [u, v, w]]