rainflow#

The following code is based on the Python [1] Rainflow algorithm implemented in the WAFO toolbox [2]. The method gives the following definition of rainflow cycles, in accordance with Rychlik (1987) [3]:

From each local maximum M_k one shall try to reach above the same level, in the backward (left) and forward (right) directions, with an as small downward excursion as possible. The minima, m^-_k and m⁺_k, on each side are identified. The minimum that represents the smallest deviation from the maximum M_k is defined as the corresponding rainflow minimum m^RFC_k. The k:th rainflow cycle is defined as (m^RFC_k, M_k).

See also

findtp(): Find indices to turning points.
findextrema(): Find indices to local maxima and minima.
findrfc_astm(): Find rainflow cycles.

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')

See also

findextrema()

py_fatigue.cycle_count.rainflow.findrfc_astm(tp: ndarray, t: ndarray | None = None) → ndarray#

Return rainflow counted cycles

Nieslony’s Matlab implementation of the ASTM standard practice for rainflow counting ported to a Python C module.

Parameters:

tp (array-like) – vector of turning-points (NB! Only values, not sampled times)
t (array-like, optional) – vector of sampled times

Returns:

sig_rfc – array of shape (n,3) or (n, 5) with: sig_rfc[:,0] Cycles amplitude sig_rfc[:,1] Cycles mean value sig_rfc[:,2] Cycle type, half (=0.5) or full (=1.0) sig_rfc[:,3] cycle_begin_time (only if t is given) sig_rfc[:,4] cycle_period_time (only if t is given)

Return type:

array-like

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')