def wind_EWTSII_Davenport(vave, k, T=50, n=23037):
"""
Algorithm appeared in the European Wind Turbine Standards II (EWTS II).
Davenport variation.
It uses 10-minute wind speeds to obtain the return period extreme wind
speed for the ``T`` return period defined.
**Parameters**
vave : float or int
Long term mean wind speed
k : float or int
Weibull k parameter as defined in the wind industry. To obtain the k
parameter using scipy `have a look here
<http://stackoverflow.com/questions/17481672/fitting-a-weibull-distribution-using-scipy/17498673#17498673>`_.
The `c` parameter in scipy is the k equivalent in the wind industry.
T : float or int
Return period in years. Default value is 50 (years).
n : floar or int
the number of independent events per year. Default value is 23037 for
10-min time steps and 1-yr extrema.
**Returns**
vref : float
Expected extreme wind speed at the return period defined.
**References**
Dekker JWM, Pierik JTG (1998): 'European Wind Turbine Standards II',
ECN-C-99-073, ECN Solar & Wind Energy, Netherlands.
"""
c1 = 1 - (k - 1) / (k * _np.log(n))
c2 = 1 + (_np.log(k * _gamma(1 + 1 / k) *
((_np.log(n))**(1 - 1 / k)))) / (k * _np.log(n) - k + 1)
a = ((_np.log(n))**(1 / k - 1)) / (c1 * k * _gamma(1 + 1 / k))
b = c1 * c2 * k * _np.log(n) - _np.log(-_np.log(1 - 1 / T))
res = vave * a * b
return res
def wind_EWTSII_Davenport(vave, k, T = 50, n = 23037):
"""
Algorithm appeared in the European Wind Turbine Standards II (EWTS II).
Davenport variation.
It uses 10-minute wind speeds to obtain the return period extreme wind
speed for the ``T`` return period defined.
**Parameters**
vave : float or int
Long term mean wind speed
k : float or int
Weibull k parameter as defined in the wind industry. To obtain the k
parameter using scipy `have a look here
<http://stackoverflow.com/questions/17481672/fitting-a-weibull-distribution-using-scipy/17498673#17498673>`_.
The `c` parameter in scipy is the k equivalent in the wind industry.
T : float or int
Return period in years. Default value is 50 (years).
n : floar or int
the number of independent events per year. Default value is 23037 for
10-min time steps and 1-yr extrema.
**Returns**
vref : float
Expected extreme wind speed at the return period defined.
**References**
Dekker JWM, Pierik JTG (1998): 'European Wind Turbine Standards II',
ECN-C-99-073, ECN Solar & Wind Energy, Netherlands.
"""
c1 = 1 - (k - 1) / (k * _np.log(n))
c2 = 1 + (_np.log(k * _gamma(1+1/k) * ((_np.log(n))**(1-1/k)))) / (k * _np.log(n) - k + 1)
a = ((_np.log(n))**(1/k-1)) / (c1 * k * _gamma(1+1/k))
b = c1 * c2 * k * _np.log(n) - _np.log(-_np.log(1-1/T))
res = vave * a * b
return res
def gev_momfit(data):
"""
Estimate parameters of Generalised Extreme Value distribution using the
method of moments. The methodology has been extracted from appendix A.4
on EVA (see references below).
**Parameters**
data : array_like
Sample extreme data
**Returns**
tuple
tuple with the shape, location and scale parameters. In this,
case, the shape parameter is always 0.
**References**
DHI, (2003): '`EVA(Extreme Value Analysis - Reference manual)
<http://www.tnmckc.org/upload/document/wup/1/1.3/Manuals/MIKE%2011/eva/EVA_RefManual.pdf>`_',
DHI.
"""
g = lambda n, x : _gamma(1 + n * x)
mean = _np.mean(data)
std = _np.std(data)
skew = _st.skew(data)
def minimize_skew(x):
a = -g(3, x) + 3 * g(1, x) * g(2, x) - 2 * g(1, x)**3
b = (g(2, x) - (g(1, x))**2)**1.5
c = abs(a / b - skew)
return c
c = _op.fmin(minimize_skew, 0)[0] # first guess is set to 0
scale = std * abs(c) / _np.sqrt((g(2, c) - g(1, c)**2))
loc = mean - scale * (1 - g(1, c)) / c
return c, loc, scale
def gev_momfit(data):
"""
Estimate parameters of Generalised Extreme Value distribution using the
method of moments. The methodology has been extracted from appendix A.4
on EVA (see references below).
**Parameters**
data : array_like
Sample extreme data
**Returns**
tuple
tuple with the shape, location and scale parameters. In this,
case, the shape parameter is always 0.
**References**
DHI, (2003): '`EVA(Extreme Value Analysis - Reference manual)
<http://www.tnmckc.org/upload/document/wup/1/1.3/Manuals/MIKE%2011/eva/EVA_RefManual.pdf>`_',
DHI.
"""
g = lambda n, x: _gamma(1 + n * x)
mean = _np.mean(data)
std = _np.std(data)
skew = _st.skew(data)
def minimize_skew(x):
a = -g(3, x) + 3 * g(1, x) * g(2, x) - 2 * g(1, x)**3
b = (g(2, x) - (g(1, x))**2)**1.5
c = abs(a / b - skew)
return c
c = _op.fmin(minimize_skew, 0)[0] # first guess is set to 0
scale = std * abs(c) / _np.sqrt((g(2, c) - g(1, c)**2))
loc = mean - scale * (1 - g(1, c)) / c
return c, loc, scale
def gamma(x, alpha, beta):
'''检测一致
alpha 是 shape para
beta 是 rate para'''
return ((beta**alpha) / _gamma(alpha)) * (x**(alpha - 1)) * np.exp(
-beta * x)
def compute_mean_residence_time(self,
nb_blocks=1,
filter_artifacts=False,
per_residue=False,
return_average_time=False,
use_filtered=True):
if use_filtered: results = self.filtered_results
else: results = self.initial_results
def func(x, tau, lamda):
return _np.exp(-(x / tau)**lamda)
all_residence_time = []
all_average_time = []
block_length = int(self.nb_frames / nb_blocks)
xdata = _np.arange(1, block_length + 1)
for run in range(nb_blocks):
s = slice(run * block_length, (run + 1) * block_length, 1)
intervals = {
key: _hf.intervals_binary(results[key][s])
for key in results
}
residence_time = _np.zeros(block_length)
average_time = _np.array([0., 0.])
if per_residue:
residence_time = {}
del_res = []
average_time = {}
for pair in results:
segn, resn, resi, _, _, _ = _hf.deconst_key(pair, True)
residue_key = segn + '-' + resn + '-' + str(resi)
work_intervals = intervals[pair]
interval_lengths = _np.diff(work_intervals,
1).astype(_np.int).flatten()
if filter_artifacts:
interval_lengths = interval_lengths[(interval_lengths <
block_length)]
try:
average_time[residue_key] += _np.array(
[interval_lengths.sum(), interval_lengths.size])
except KeyError:
average_time[residue_key] = _np.array(
[interval_lengths.sum(), interval_lengths.size])
residence_time[residue_key] = _np.zeros(block_length)
for l in interval_lengths:
residence_time[residue_key][:l] += _np.arange(
1, l + 1)[::-1]
for residue_key in residence_time:
residence_time[residue_key] /= _np.arange(
1, block_length + 1)[::-1]
residence_time[residue_key] /= residence_time[residue_key][
0]
if _np.isnan(residence_time[residue_key]).any():
del_res.append(residue_key)
average_time[residue_key] = average_time[residue_key][
0] / average_time[residue_key][1]
try:
(tau,
lamda), pcov = _curve_fit(func,
xdata,
residence_time[residue_key],
p0=(10.0, 0.5))
residence_time[residue_key] = tau / lamda * _gamma(
1 / lamda)
except:
if average_time[residue_key] <= 2.0:
residence_time[residue_key] = 1.0
else:
try:
(tau, lamda), pcov = _curve_fit(
func,
xdata,
residence_time[residue_key],
p0=(block_length, 0.5))
residence_time[
residue_key] = tau / lamda * _gamma(
1 / lamda)
except:
residence_time[residue_key] = block_length
for key in del_res:
del residence_time[key]
else:
for water in results:
work_intervals = intervals[water]
interval_lengths = _np.diff(work_intervals,
1).astype(_np.int).flatten()
if filter_artifacts:
interval_lengths = interval_lengths[(interval_lengths <
block_length)]
average_time += _np.array(
[interval_lengths.sum(), interval_lengths.size])
for l in interval_lengths:
residence_time[:l] += _np.arange(1, l + 1)[::-1]
residence_time /= _np.arange(1, block_length + 1)[::-1]
residence_time /= residence_time[0]
average_time = average_time[0] / average_time[1]
try:
(tau, lamda), pcov = _curve_fit(func,
xdata,
residence_time,
p0=(10.0, 0.5))
residence_time = tau / lamda * _gamma(1 / lamda)
except:
if average_time <= 2.0:
residence_time = 1.0
else:
residence_time = block_length
all_residence_time.append(residence_time)
all_average_time.append(average_time)
if per_residue:
for key in residence_time:
temp_residence_time = []
temp_average_time = []
for residence_dict in all_residence_time:
try:
temp_residence_time.append(residence_dict[key])
except:
pass
for average_dict in all_average_time:
try:
temp_average_time.append(average_time[key])
except:
pass
residence_time[key] = (_np.mean(temp_residence_time),
_np.std(temp_residence_time) /
_np.sqrt(nb_blocks))
average_time[key] = (_np.mean(temp_average_time),
_np.std(temp_average_time) /
_np.sqrt(nb_blocks))
else:
residence_time = (_np.mean(all_residence_time),
_np.std(all_residence_time) /
_np.sqrt(nb_blocks))
average_time = (_np.mean(all_average_time),
_np.std(all_average_time) / _np.sqrt(nb_blocks))
if return_average_time: return residence_time, average_time
else: return residence_time