Benchmark solution
=====================


Baseline calculation
-------------------

A reference NON_REGRESSION is used to test the various quantities calculated at the level of the obstacles.

The calculation procedure is as follows, on:


* Calculate the modal base,


* Create an interspectral matrix (or DSP) from complex functions,


* Generates random efforts,


* Calculate the transient dynamic response,


* Test the values of the response (movements and efforts) at the level of obstacles.


Reference quantity
---------------------

Components of the interspectral matrix obtained from complex functions.


.. csv-table::

    "Size", "Component", "Comments"
    "DEPL_X "," MOYEN ", "Average value of the next move :math:`X`, at the point of shock, in their local coordinate system,"
    "DEPL_Y "," ECART_TYPE ", "Value of the standard deviation of the next displacement :math:`Y`, at the point of shock, in their local coordinate system,"
    "DEPL_RADIAL "," RMS ", "Value RMSsur the shock time of the "radial displacement" at the point of shock."
    "DEPL_ANGULAIRE "," MAXI ", "Maximum value of the "angular displacement" at the point of shock."
    "FORCE_NORMALE "," RMS_T_TOTAL ", "Value RMSsur the total time of the normal force at the point of shock."
    "FORCE_TANG_1 "," MOYEN ", "Average value of the tangent force in the plane of the obstacle."
    "FORCE_TANG_2 "," ECART_TYPE ", "Value of the standard deviation of the tangent force orthogonal to the plane of the obstacle."
    "STAT_CHOC ", "T_ CHOC_MOYEN ", "Average shock time"
    "STAT_USURE "," PUIS_USURE ", "Wear power calculated according to ARCHARD."



Benchmark result
---------------------


+--------------------+----------------------+---------------------------+
|                    |Component             |Reference                  |
+--------------------+----------------------+---------------------------+
|Interspectral matrix|:math:`(\mathrm{1,1})`|:math:`0.1000+\mathrm{0.j}`|
+                    +----------------------+---------------------------+
|                    |:math:`(\mathrm{2,2})`|:math:`0.025+\mathrm{0.j}` |
+--------------------+----------------------+---------------------------+

*Note:**the behavior of the random number generator (module*RANDOM*) has changed since the python version*:math:`2.3`*. The results are a bit affected. For tests on the transient dynamic response, we therefore test with different magnitudes and reference results depending on the Python version. *


+-------------------------------------+-----------+---------+------------------------------+
|Python version lower than :math:`2.3`                                                     |
+-------------------------------------+-----------+---------+------------------------------+
|Grandeur                             |Component  |Point    |Reference                     |
+-------------------------------------+-----------+---------+------------------------------+
|DEPL_X                               |MOYEN      |:math:`D`|:math:`0.5m`                  |
+-------------------------------------+-----------+---------+------------------------------+
|DEPL_Y                               |ECART_TYPE |:math:`D`|:math:`2.57\times {10}^{-5}m` |
+-------------------------------------+-----------+---------+------------------------------+
|DEPL_RADIAL                          |RMS        |:math:`D`|:math:`2.573\times {10}^{-5}m`|
+-------------------------------------+-----------+---------+------------------------------+
|FORCE_NORMALE                        |RMS_T_TOTAL|:math:`D`|:math:`25.73N`                |
+-------------------------------------+-----------+---------+------------------------------+


+---------------------------------------+-------------+---------+------------------------------+
|Python version greater than :math:`2.3`                                                       |
+---------------------------------------+-------------+---------+------------------------------+
|Grandeur                               |Component    |Point    |Reference                     |
+---------------------------------------+-------------+---------+------------------------------+
|DEPL_X                                 |MOYEN        |:math:`D`|:math:`0.5m`                  |
+---------------------------------------+-------------+---------+------------------------------+
|DEPL_Y                                 |ECART_TYPE   |:math:`D`|:math:`2.456\times {10}^{-5}m`|
+---------------------------------------+-------------+---------+------------------------------+
|DEPL_RADIAL                            |RMS          |:math:`D`|:math:`2.456\times {10}^{-5}m`|
+---------------------------------------+-------------+---------+------------------------------+
|FORCE_NORMALE                          |RMS_T_TOTAL  |:math:`D`|:math:`24.56N`                |
+---------------------------------------+-------------+---------+------------------------------+
|DEPL_ANGULAIRE                         |MAXI         |:math:`C`|:math:`180.\mathrm{rad}`      |
+---------------------------------------+-------------+---------+------------------------------+
|FORCE_TANG_1                           |MOYEN        |:math:`D`|:math:`0.`                    |
+---------------------------------------+-------------+---------+------------------------------+
|FORCE_TANG_2                           |ECART_TYPE   |:math:`D`|:math:`0.`                    |
+---------------------------------------+-------------+---------+------------------------------+
|STAT_CHOC                              |T_ CHOC_MOYEN|:math:`C`|:math:`0.`                    |
+---------------------------------------+-------------+---------+------------------------------+
|STAT_USURE                             |PUIS_USURE   |:math:`C`|:math:`0.`                    |
+---------------------------------------+-------------+---------+------------------------------+