Johannesson counting method

# Import auxiliary libraries for demonstration

import matplotlib as mpl
import matplotlib.pyplot as plt
import numpy as np

plt.rcParams[ "figure.figsize" ] = [ 5, 4 ]

plt.rcParams[ "figure.dpi" ] = 80
plt.rcParams[ "font.family" ] = "Times New Roman"
plt.rcParams[ "font.size" ] = '14'

Johannesson min max counting

Function johannessonMinMaxCounting implements the Johannesson min max counting method ( Definition 2 in the reference ).

Reference:

• Johannesson, P., 1998. Rainflow cycles for switching processes with Markov structure. Probability in the Engineering and Informational Sciences, 12(2), pp.143-175.

Function help

from ffpack.lcc import johannessonMinMaxCounting
help( johannessonMinMaxCounting )

Help on function johannessonMinMaxCounting in module ffpack.lcc.johannessonCounting:

johannessonMinMaxCounting(data, aggregate=True)
    Johannesson min-max counting

    Parameters
    ----------
    data: 1d array
        Load sequence data for counting.
    aggragate: bool, optional
        if aggregate is set to False, the original sequence for internal counting,
        e.g., [ [ rangeStart1, rangeEnd1, count1 ], [ rangeStart2, rangeEnd2, count2 ], ... ],
        will be returned.

    Returns
    -------
    rst: 2d array
        Sorted counting results.

    Raises
    ------
    ValueError
        If the data dimension is not 1
        If the data length is less than 2

    Examples
    --------
    >>> from ffpack.lcc import johannessonMinMaxCounting
    >>> data = [ -0.8, 1.3, 0.7, 3.4, 0.7, 2.5, -1.4, -0.5, -2.3,
    >>>          -2.2, -2.6, -2.4, -3.3, 1.5, 0.6, 3.4, -0.5 ]
    >>> rst = johannessonMinMaxCounting( data )

Example with default values

johannessonMmcSequenceData = [ -0.8, 1.3, 0.7, 3.4, 0.7, 2.5, -1.4, -0.5, -2.3,
                               -2.2, -2.6, -2.4, -3.3, 1.5, 0.6, 3.4, -0.5 ]

johannessonMmcCountingResults = johannessonMinMaxCounting( johannessonMmcSequenceData )

print( johannessonMmcCountingResults )

[[0.1, 1.0], [0.2, 1.0], [0.9, 1.0], [1.8, 1.0], [2.1, 1.0], [4.2, 1.0], [4.8, 1.0], [6.7, 1.0]]

fig, ( ax1, ax2 ) = plt.subplots( 1, 2, figsize=( 10, 4 ) )

ax1.plot( johannessonMmcSequenceData, "o-" )

ax1.tick_params( axis='x', direction="in", length=5 )
ax1.tick_params( axis='y', direction="in", length=5 )
ax1.set_ylabel( "Load units" )
ax1.set_xlabel( "Data points" )
ax1.set_title( "Sequence data" )

ax2.barh( np.array( johannessonMmcCountingResults )[ :, 0 ],
          np.array( johannessonMmcCountingResults )[ :, 1 ] )

ax2.tick_params( axis='x', direction="in", length=5 )
ax2.tick_params( axis='y', direction="in", length=5 )
ax2.set_ylabel( "Load range units" )
ax2.set_xlabel( "Counts" )
ax2.set_title( "Rychlik rainflow counting" )

plt.tight_layout()
plt.show()