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'eq_load' calculate equivalent loads using one of the two rain flow counting methods
'cycle_matrix' calculates a matrix of cycles (binned on amplitude and mean value)
'eq_load_and_cycles' is used to calculate eq_loads of multiple time series (e.g. life time equivalent load)
The methods uses the rainflow counting routines (See documentation in top of methods):
- 'rainflow_windap': (Described in "Recommended Practices for Wind Turbine Testing - 3. Fatigue Loads",
2. edition 1990, Appendix A)
or
- 'rainflow_astm' (based on the c-implementation by Adam Nieslony found at the MATLAB Central File Exchange
http://www.mathworks.com/matlabcentral/fileexchange/3026)
from __future__ import division
from __future__ import print_function
from __future__ import unicode_literals
from __future__ import absolute_import
from future import standard_library
standard_library.install_aliases()
from wetb.fatigue_tools.rainflowcounting import rainflowcount
rainflow_windap = rainflowcount.rainflow_windap
rainflow_astm = rainflowcount.rainflow_astm
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def eq_load(signals, no_bins=46, m=[3, 4, 6, 8, 10, 12], neq=1, rainflow_func=rainflow_windap):
"""Equivalent load calculation
Calculate the equivalent loads for a list of Wohler exponent and number of equivalent loads
Parameters
----------
signals : list of tuples or array_like
- if list of tuples: list must have format [(sig1_weight, sig1),(sig2_weight, sig1),...] where\n
- sigx_weight is the weight of signal x\n
- sigx is signal x\n
- if array_like: The signal
no_bins : int, optional
Number of bins in rainflow count histogram
m : int, float or array-like, optional
Wohler exponent (default is [3, 4, 6, 8, 10, 12])
neq : int, float or array-like, optional
The equivalent number of load cycles (default is 1, but normally the time duration in seconds is used)
rainflow_func : {rainflow_windap, rainflow_astm}, optional
The rainflow counting function to use (default is rainflow_windap)
Returns
-------
eq_loads : array-like
List of lists of equivalent loads for the corresponding equivalent number(s) and Wohler exponents
Examples
--------
>>> signal = np.array([-2.0, 0.0, 1.0, 0.0, -3.0, 0.0, 5.0, 0.0, -1.0, 0.0, 3.0, 0.0, -4.0, 0.0, 4.0, 0.0, -2.0])
>>> eq_load(signal, no_bins=50, neq=[1, 17], m=[3, 4, 6], rainflow_func=rainflow_windap)
[[10.311095426959747, 9.5942535021382174, 9.0789213365013932], # neq = 1, m=[3,4,6]
[4.010099657859783, 4.7249689509841746, 5.6618639965313005]], # neq = 17, m=[3,4,6]
eq_load([(.4, signal), (.6, signal)], no_bins=50, neq=[1, 17], m=[3, 4, 6], rainflow_func=rainflow_windap)
[[10.311095426959747, 9.5942535021382174, 9.0789213365013932], # neq = 1, m=[3,4,6]
[4.010099657859783, 4.7249689509841746, 5.6618639965313005]], # neq = 17, m=[3,4,6]
"""
try:
return eq_load_and_cycles(signals, no_bins, m, neq, rainflow_func)[0]
except TypeError:
return [[np.nan] * len(np.atleast_1d(m))] * len(np.atleast_1d(neq))
def eq_load_and_cycles(signals, no_bins=46, m=[3, 4, 6, 8, 10, 12], neq=[10 ** 6, 10 ** 7, 10 ** 8], rainflow_func=rainflow_windap):
"""Calculate combined fatigue equivalent load
Parameters
----------
signals : list of tuples or array_like
- if list of tuples: list must have format [(sig1_weight, sig1),(sig2_weight, sig1),...] where\n
- sigx_weight is the weight of signal x\n
- sigx is signal x\n
- if array_like: The signal
no_bins : int, optional
Number of bins for rainflow counting
m : int, float or array-like, optional
Wohler exponent (default is [3, 4, 6, 8, 10, 12])
neq : int or array-like, optional
Equivalent number, default is [10^6, 10^7, 10^8]
rainflow_func : {rainflow_windap, rainflow_astm}, optional
The rainflow counting function to use (default is rainflow_windap)
Returns
-------
eq_loads : array-like
List of lists of equivalent loads for the corresponding equivalent number(s) and Wohler exponents
cycles : array_like
2d array with shape = (no_ampl_bins, no_mean_bins)
ampl_bin_mean : array_like
mean amplitude of the bins
ampl_bin_edges
Edges of the amplitude bins
"""
cycles, ampl_bin_mean, ampl_bin_edges, _, _ = cycle_matrix(signals, no_bins, 1, rainflow_func)
if 0: #to be similar to windap
ampl_bin_mean = (ampl_bin_edges[:-1] + ampl_bin_edges[1:]) / 2
cycles, ampl_bin_mean = cycles.flatten(), ampl_bin_mean.flatten()
eq_loads = [[((np.sum(cycles * ampl_bin_mean ** _m) / _neq) ** (1. / _m)) for _m in np.atleast_1d(m)] for _neq in np.atleast_1d(neq)]
return eq_loads, cycles, ampl_bin_mean, ampl_bin_edges
def cycle_matrix(signals, ampl_bins=10, mean_bins=10, rainflow_func=rainflow_windap):
"""Markow load cycle matrix
Calculate the Markow load cycle matrix
Parameters
----------
Signals : array-like or list of tuples
Mads M. Pedersen
committed
- if array-like, the raw signal\n
- if list of tuples, list of (weight, signal), e.g. [(0.1,sig1), (0.8,sig2), (.1,sig3)]\n
ampl_bins : int or array-like, optional
if int, Number of amplitude value bins (default is 10)
if array-like, the bin edges for amplitude
mean_bins : int or array-like, optional
if int, Number of mean value bins (default is 10)
if array-like, the bin edges for mea
rainflow_func : {rainflow_windap, rainflow_astm}, optional
The rainflow counting function to use (default is rainflow_windap)
Returns
-------
cycles : ndarray, shape(ampl_bins, mean_bins)
A bi-dimensional histogram of load cycles(full cycles). Amplitudes are\
histogrammed along the first dimension and mean values are histogrammed along the second dimension.
ampl_bin_mean : ndarray, shape(ampl_bins,)
The average cycle amplitude of the bins
ampl_edges : ndarray, shape(ampl_bins+1,)
The amplitude bin edges
mean_bin_mean : ndarray, shape(ampl_bins,)
The average cycle mean of the bins
mean_edges : ndarray, shape(mean_bins+1,)
The mean bin edges
Examples
--------
>>> signal = np.array([-2.0, 0.0, 1.0, 0.0, -3.0, 0.0, 5.0, 0.0, -1.0, 0.0, 3.0, 0.0, -4.0, 0.0, 4.0, 0.0, -2.0])
>>> cycles, ampl_bin_mean, ampl_edges, mean_bin_mean, mean_edges = cycle_matrix(signal)
>>> cycles, ampl_bin_mean, ampl_edges, mean_bin_mean, mean_edges = cycle_matrix([(.4, signal), (.6,signal)])
"""
if isinstance(signals[0], tuple):
Mads M. Pedersen
committed
weights, ampls, means = np.array([(np.zeros_like(ampl)+weight,ampl,mean) for weight, signal in signals for ampl,mean in rainflow_func(signal[:]).T], dtype=np.float64).T
else:
ampls, means = rainflow_func(signals[:])
weights = np.ones_like(ampls)
if isinstance(ampl_bins, int):
Mads M. Pedersen
committed
ampl_bins = np.linspace(0, 1, num=ampl_bins + 1) * ampls[weights>0].max()
cycles, ampl_edges, mean_edges = np.histogram2d(ampls, means, [ampl_bins, mean_bins], weights=weights)
ampl_bin_sum = np.histogram2d(ampls, means, [ampl_bins, mean_bins], weights=weights * ampls)[0]
ampl_bin_mean = np.zeros_like(cycles)
mask = (cycles > 0)
ampl_bin_mean[mask] = ampl_bin_sum[mask] / cycles[mask]
mean_bin_sum = np.histogram2d(ampls, means, [ampl_bins, mean_bins], weights=weights * means)[0]
Mads M. Pedersen
committed
mean_bin_mean = np.zeros_like(cycles)+np.nan
mean_bin_mean[cycles > 0] = mean_bin_sum[cycles > 0] / cycles[cycles > 0]
cycles = cycles / 2 # to get full cycles
return cycles, ampl_bin_mean, ampl_edges, mean_bin_mean, mean_edges
if __name__ == "__main__":
signal1 = np.array([-2.0, 0.0, 1.0, 0.0, -3.0, 0.0, 5.0, 0.0, -1.0, 0.0, 3.0, 0.0, -4.0, 0.0, 4.0, 0.0, -2.0])
signal2 = signal1 * 1.1
print (eq_load(signal1, no_bins=50, neq=17, rainflow_func=rainflow_windap))
print (eq_load(signal1, no_bins=50, neq=17, rainflow_func=rainflow_astm))
# Cycle matrix with 4 amplitude bins and 4 mean value bins
print (cycle_matrix(signal1, 4, 4, rainflow_func=rainflow_windap))
print (cycle_matrix(signal1, 4, 4, rainflow_func=rainflow_astm))
# Cycle matrix where signal1 and signal2 contributes with 50% each
print (cycle_matrix([(.5, signal1), (.5, signal2)], 4, 8, rainflow_func=rainflow_astm))