# [ot-users] constraint error FORM

Anita Laera anita.laera87 at gmail.com
Wed Mar 15 09:47:46 CET 2017

```Hi Regis,

I am going to explain how I address this problem, to understand if it is
correct.

I have five input parameters and, every time the function _exec(x) is
executed, I print the value of each variable and the result obtained from
that combination of input values. The values I print are in the physical
space.
At the end of the FORM analysis, I get the value of the design point in the
physical space and I search for that combination of parameters in the list
of printed input variables. The result associated to these parameters is
the one that I compare with the threshold to calculate the constraint error.

To make an example with numbers, I have 5 input parameters with
distributions:
param_1 = TruncatedNormal(20, 1, 16, 24)
param_2 = TruncatedNormal(17.5, 0.88, 14, 21)
param_3 = TruncatedNormal(20, 1, 16, 24)
param_4 = TruncatedNormal(20, 1, 16, 24)
param_5 = TruncatedNormal(20, 1, 16, 24)

The threshold of the criterion I have chosen is 850.

Every time _exec() is called (at each evaluation), I have a list of input
parameters and the corresponding result, for example:
[20.0673673248819, 17.3184136978776, 19.9079471477259,
20.1402093633652, 20.0223766740268]
and the result is [825.665964705004]

At the end of the analysis, the design point is:

standard_space_point: ['param_1 = 0.1997867549606676', 'param_2 =
-0.055279300017051544', 'param_3 = -0.0628992654226241', 'param_4 =
0.5183599165842491', 'param_5 = -0.10839510883000002']

physical_space_point: ['param_1 = 20.199773930262452', 'param_2 =
17.451357610548104', 'param_3 = 19.937104724030977', 'param_4 =
20.518323977607277', 'param_5 = 19.89161178413688']

I take the values corresponding to the physical space point and I find the
corresponding result, i.e. 845.307471892986. Does this correspond to
f(x_opt)?
Then I calculate the constraint error as |845.307471892986 - 850|
= 4.692528107014

Is this the correct procedure? If not, how do I get the constraint error
without using getConstraintError()?
In this example, the value that is returned by getConstraintError()
is 4.59252810701402 and I want to understand how this is calculated.

2017-03-14 17:48 GMT+01:00 regis lebrun <regis_anne.lebrun_dutfoy at yahoo.fr>:

> Hi Anita,
>
> You are right, the constraint error is an obsolute error on the
> constraint. It is equal to |f(x_opt) - s| = |f(T(u_opt)) - s| where f is
> your code, T the inverse iso-probabilistic transformation that maps the
> standard space into the physical space, u_opt the design point (so in the
> standard space) and x_opt = T(u_opt) its image in the physical space.
>
> Are you 100% sure that you compute f at the correct point in your
> verification? If you compare f(u_opt) with s, it is wrong (and I suspect
> that you did it ;-)). Otherwise there is a bug and we need more input from
> your side in order to catch it.
>
> Cheers
>
> Régis
>
>
>
> ________________________________
> De : Anita Laera <anita.laera87 at gmail.com>
> À : users at openturns.org
> Envoyé le : Mardi 14 mars 2017 15h25
> Objet : [ot-users] constraint error FORM
>
>
>
> Hi all,
> I have a simple question regarding the constraint error of a FORM
> analysis, the constraint error is defined as |f(u_n) - s| , i.e. the
> absolute difference between the result and the threshold.
>
> In my case, the result in the design point is 845.307471892986 and the
> threshold is 850 (in the physical space).
> I would expect the constraint error to be about 4.69, but the value
> obtained with the method getConstraintError() is 4.59. Why?
>
> If I calculate the difference between the result and the threshold for
> each performed evaluation, I never find 4.59.
>
> Could it be different because it is calculated in the standard space u?
> How could I verify the value?
>
> Thank you for your time!
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>
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