rainflow#

Rainflow cycle counting algorithms for fatigue analysis.

Implements: - ASTM rainflow (Nieslony’s algorithm, standard practice). - Four-point rainflow (Amzallag et al. 1994).

Also includes utilities to find turning points and extrema.

References

[1] WAFO Toolbox https://www.maths.lth.se/matstat/wafo/ [2] PyWAFO wafo-project/pywafo [3] Rychlik (1987), “A new definition of the rainflow cycle counting method” [4] Amzallag et al. (1994), “Standardization of the rainflow counting method”

See also

findtp: Find indices to turning points.
findextrema: Find indices to local maxima and minima.
findcross: Find indices to level crossings.

py_fatigue.cycle_count.rainflow.rainflow(data: ndarray | list, time: ndarray | list | None = None, method: str = 'astm', extended_output: bool = True) → ndarray | Tuple#

Returns the cycle-count of the input data calculated through the rainflow method (ASTM or four-point).

Parameters:

data (Union[np.ndarray, list]) – time series or residuals sequence
time (Optional[Union[np.ndarray, list]], optional) – sampled times, by default None
method (str, optional) – “astm” or “fourpoint”
extended_output (bool, optional) – If True, also return residuals.

Return type:

Union[np.ndarray, tuple]

py_fatigue.cycle_count.rainflow.findcross(x: ndarray, v=0.0, kind=None) → ndarray#

Return indices to level v up and/or downcrossings of a vector

Parameters:

x (array_like) – vector with sampled values.
v (scalar, real) – level v.
kind (string) – defines type of crossing returned. Possible options are - ‘d’ : downcrossings only - ‘u’ : upcrossings only - None : All crossings will be returned

Returns:

ind – indices to the crossings in the original sequence x.

Return type:

array-like

Example

>>> from matplotlib import pyplot as plt
>>> import py_fatigue.wafo.misc as wm
>>> ones = np.ones
>>> np.allclose(findcross([0, 1, -1, 1], 0), [0, 1, 2])
True
>>> v = 0.75
>>> t = np.linspace(0,7*np.pi,250)
>>> x = np.sin(t)
>>> ind = wm.findcross(x,v) # all crossings
>>> np.allclose(ind, [  9,  25,  80,  97, 151, 168, 223, 239])
True

>>> ind2 = wm.findcross(x,v,'u')
>>> np.allclose(ind2, [  9,  80, 151, 223])
True
>>> ind3 = wm.findcross(x,v,'d')
>>> np.allclose(ind3, [  25,  97, 168, 239])
True

>>> t0 = plt.plot(t,x,'.',t[ind],x[ind],'r.', t, ones(t.shape)*v)
>>> t0 = plt.plot(t[ind2],x[ind2],'o')
>>> plt.close('all')

py_fatigue.cycle_count.rainflow.findextrema(x: ndarray) → ndarray#

Return indices to minima and maxima of a vector

Parameters:: x (vector with sampled values.)
Returns:: ind
Return type:: indices to minima and maxima in the original sequence x.

Examples

>>> import numpy as np
>>> import matplotlib.pyplot as plt
>>> import wafo.misc as wm
>>> t = np.linspace(0,7*np.pi,250)
>>> x = np.sin(t)
>>> ind = wm.findextrema(x)
>>> np.allclose(ind, [ 18,  53,  89, 125, 160, 196, 231])
True

>>> a = plt.plot(t,x,'.',t[ind],x[ind],'r.')
>>> plt.close('all')

py_fatigue.cycle_count.rainflow.findtp(x: ndarray) → ndarray#

Return indices to turning points (tp) of ASTM rainflow filtered data.

Parameters:: x (vector) – signal to be filtered.
Returns:: ind – indices to the turning points in the original sequence.
Return type:: Union[np.ndarray, None]

Examples

>>> import matplotlib.pyplot as plt
>>> import py_fatigue.wafo.misc as wm
>>> t = np.linspace(0,30,500).reshape((-1,1))
>>> x = np.hstack((t, np.cos(t) + 0.3 * np.sin(5*t)))
>>> x1 = x[0:100,:]
>>> itp = wm.findtp(x1[:,1])
>>> tp = x1[itp,:]
>>> np.allclose(itp, [ 5, 18, 24, 38, 46, 57, 70, 76, 91, 98, 99])
True

>>> a = plt.plot(
... x1[:,0], x1[:,1], tp[:,0], tp[:,1], 'ro')
>>> plt.close('all')

rainflow#

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