The Data Model of pyLife
pyLife stores data for calculations most often in pandas objects. Modules that want to operate on such pandas objects should use the pandas methods wherever possible.
Dimensionality of data
pandas comes with two data classes, pandas.Series for one
dimensional data and pandas.DataFrame for two dimensional data.
This dimensionality has nothing to do with mathematical or geometrical dimensions, it only relates to the dimensionality from a data structure perspective. There are two dimensions, we call them the one in row direction and the one in column direction.
In row direction, all the values represent the same physical quantity, like a stress, a length, a volume, a time. It means that it is easily thinkable to add infinitely more values in row direction. Furthermore it mostly would make sense to perform statistical operations in row direction, like the maximum stress, the average volume, etc.
An one channel time signal is an example for a one dimensional data structure in row direction. You could add infinitely more samples, every sample represents the same physical quantity, it makes sense to perform statistical operations on the whole series.
In [4]: row_direction
Out[4]:
time
0 0.497646
1 0.278503
2 0.649374
3 0.419474
4 0.614923
5 0.961856
... <infinitely more could be added>
Name: Load, dtype: float64
In column direction, the values usually represent different physical quantities. You might be able to think of adding a few more values in column direction, but not infinitely. It almost never makes sense to perform statistical operations in column direction.
A Wöhler curve is an example for a one dimensional example in column direction. All the members (columns) represent different physical quantities, it is not obvious to add more values to the data structure and it makes no sense to perform statistical operations to it.
In [8]: column_direction
Out[8]:
SD 3.000000e+02
ND 2.300000e+06
k_1 7.000000e+00
TS 1.234363e+00
TN 3.420000e+00
dtype: float64
Two dimensional data structures have both dimensions. An example would be a FEM-mesh.
In [9]: vmap.make_mesh('1', 'STATE-2').join_coordinates().join_variable('STRESS_CAUCHY').join_variable('DISPLACEMENT').to_frame()
Out[9]:
x y z S11 S22 S33 S12 S13 S23 dx dy dz
element_id node_id
1 1734 14.897208 5.269875 0.0 27.080811 6.927080 0.0 -13.687358 0.0 0.0 0.005345 0.000015 0.0
1582 14.555333 5.355806 0.0 28.319006 1.178649 0.0 -10.732705 0.0 0.0 0.005285 0.000003 0.0
1596 14.630658 4.908741 0.0 47.701195 5.512213 0.0 -17.866833 0.0 0.0 0.005376 0.000019 0.0
4923 14.726271 5.312840 0.0 27.699907 4.052865 0.0 -12.210032 0.0 0.0 0.005315 0.000009 0.0
4924 14.592996 5.132274 0.0 38.010101 3.345431 0.0 -14.299768 0.0 0.0 0.005326 0.000013 0.0
... ... ... ... ... ... ... ... ... ... ... ... ...
4770 3812 -13.189782 -5.691876 0.0 36.527439 2.470588 0.0 -14.706686 0.0 0.0 -0.005300 0.000027 0.0
12418 -13.560289 -5.278386 0.0 32.868889 3.320898 0.0 -14.260107 0.0 0.0 -0.005444 0.000002 0.0
14446 -13.673285 -5.569107 0.0 34.291058 3.642457 0.0 -13.836027 0.0 0.0 -0.005404 0.000009 0.0
14614 -13.389065 -5.709927 0.0 36.063541 2.828889 0.0 -13.774759 0.0 0.0 -0.005330 0.000022 0.0
14534 -13.276068 -5.419206 0.0 33.804211 2.829817 0.0 -14.580153 0.0 0.0 -0.005371 0.000014 0.0
[37884 rows x 12 columns]
Even though a two dimensional rainflow matrix is two dimensional from a mathematical point of view, it is one dimensional from a data structure perspective because every element represents the same physical quantity (occurrence frequency of loops). You could add infinitely more samples by a finer bin and it can make sense to perform statistical operations on the whole matrix, for example in order to normalize it to the maximum frequency value.
In order to represent mathematically multidimensional structures like a two
dimensional rainflow matrix we use pandas.MultiIndex. Example for a
rainflow matrix in a two dimensional pandas.IntervalIndex.
In [11]: rainflow_matrix
Out[11]:
from to
(-60.14656996518033, -49.911160871492996] (-50.39826857402471, -40.36454994053457] 7.0
(-40.36454994053457, -30.33083130704449] 10.0
(-30.33083130704449, -20.29711267355441] 5.0
(-20.29711267355441, -10.26339404006427] 4.0
(-10.26339404006427, -0.2296754065741311] 6.0
...
(42.20752097169333, 52.44293006538072] (9.804043226915951, 19.837761860406033] 9.0
(19.837761860406033, 29.871480493896172] 6.0
(29.871480493896172, 39.90519912738631] 5.0
(39.90519912738631, 49.93891776087639] 11.0
(49.93891776087639, 59.972636394366475] 5.0
Name: frequency, Length: 121, dtype: float64
In [12]: type(rainflow_matrix)
Out[12]: pandas.core.series.Series