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Titrate:
Operator INFO_FONCTION


Date:
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:
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Organization (S): EDF-R & D/AMA, DeltaCAD

Handbook of Utilization
U4.3- booklet: Function
Document: U4.32.05

Operator INFO_FONCTION

1 Goal

To carry out mathematical operations on structures of data of the function type.

The following operations are currently available:

·
the search of the maxima of a function,
·
the calculation of the standard L 2d' a function,
·
the standard deviation of a function,
·
value RMS of a function,
·
the value of the indicator of harmfulness of seism.

Product a structure of data counts.
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

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Titrate:
Operator INFO_FONCTION


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Count

matters

1 Goal ......................................................................................................................................................... 1
2 Syntax .................................................................................................................................................. 3
3 Operands ............................................................................................................................................. 5
3.1 Key word MAX ...................................................................................................................................... 5
3.2 Key word NORME ................................................................................................................................. 5
3.3 Key word ECART_TYPE ....................................................................................................................... 5
3.4 Key word RMS ...................................................................................................................................... 6
3.5 Key word NOCI_SEISME .................................................................................................................... 6
3.6 Operand TITRATES ............................................................................................................................. 8
3.7 Operand INFORMATION ............................................................................................................................... 8
4 Examples ............................................................................................................................................... 9
4.1 Seek extrema of a function ........................................................................................... 9
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

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Operator INFO_FONCTION


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2 Syntax

Fr
= INFO_FONCTION

(
/MAX
= _F (
FONCTION = F, [function]






),
/NORME
=_F (
FONCTION
=
F
,
[function]
),
/
ECART_TYPE
=
(identical to the key word
RMS
)
[function]
/
RMS
=
_F (

FONCTION
= F,
[function]








METHODE =
/“TRAPEZE”,


[DEFAUT]
/
“SIMPSON”,








INST_INIT= tdeb,
[R]








INST_FIN
= tfin,
[R]








CRITERION =/“RELATIVE”,


[DEFAUT]
/
“ABSOLU”,







PRECISION=/0.001,
[DEFAUT]
/
prec,
[R]
),
/
NOCI_SEISME
=
_F (





/FONCTION =
F
,
[function]







OPTION
=








I “ALL”
,
[DEFAUT]








I “MAXIMUM”,









COEFF =/0, [DEFECT]
/r1
,
[R]










INST_INIT = tdeb,

[R]










INST_FIN = tfin,

[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]








I “INTE_ARIAS”,









INST_INIT = tdeb,

[R]










INST_FIN = tfin,

[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]








I “POUV_DEST”,









COEF =
/

0, [DEFAUT]


/
r1
,
[R]









INST_INIT = tdeb,

[R]










INST_FIN = tfin,

[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]








I “VITE_ABSO_CUMU”,









INST_INIT = tdeb,

[R]










INST_FIN = tfin,

[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

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I “DUREE_PHAS_FORT”,









INST_INIT = tdeb,

[R]










INST_FIN = tfin,

[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]









BORNE_INF =/0.05,


[DEFAUT]


/
binf,
[R]









BORNE_SUP =/0.95,


[DEFAUT]


/
bsup,
[R]








I “INTE_SPEC”,










AMOR_REDUIT
=
amndt,
[R]









FREQ_INIT
=/0.4,
[DEFAUT]


/
fdeb,
[R]










FREQ_FIN
=/10.,
[DEFAUT]


/
end,
[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]









NORME
=
/
1., [DEFAUT]


/
r2
,
[R]








I “ACCE_SUR_VITE”,









COEF =
/
0,
[DEFAUT]


/
r1
,
[R]
/
SPEC_OSCI
=
sro
,
[function]







OPTION
=








I “INTE_SPEC”,

[DEFAUT]










AMOR_REDUIT
=
amndt,
[R]









NATURE
=
/
“ACCE”,
[DEFAUT]


/
“VITE”,


/
“DEPL”,









NORME
=
/
1., [DEFAUT]


/
r2
,
[R]









FREQ_INIT
=/0.4,
[DEFAUT]


/
fdeb,
[R]










FREQ_FIN
=/10.,
[DEFAUT]


/
end,
[R]










CRITERION =/“RELATIVE”, [DEFECT]


/
“ABSOLU”,










PRECISION =/0.001,

[DEFAUT]


/
prec,
[R]









FREQ =
lfre, [l_R]









LIST_FREQ
=
lfreq,
[listr8]










),



TITER
= T,
[l_Kn]



INFO
=
/
1,
[DEFAUT]





/
2,

)

Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

Code_Aster ®
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3 Operands
3.1 Word
key
MAX

/MAX
=

Seek X-coordinates where the maximum and the minimum are reached.
This operation is available on functions of nature function or tablecloth.


FONCTION = F

Name of the function of which one seeks the maxima.
If F is a function, the produced concept is a table whose parameters of access are:

FONCTION, TYPE, the NOM_PARA of the function, the NOM_RESU of the function.

where one respectively finds the name of the function, MAXI or MINI, the X-coordinate of the minimum maximum/,
the value of the minimum maximum/.

If F is a tablecloth, the produced concept is a table whose parameters of access are:

FONCTION, TYPE, the NOM_PARA of the tablecloth, the name of the parameter of the functions
(NOM_PARA_FONC), the NOM_RESU of the functions.

3.2 Word
key
NORME

This key word makes it possible to follow convergence in accordance with the standard L 2d' a continuation of function F given
NR
in the form of a tablecloth. The table result comprises a line by function, the parameters of input
are NORME and FONCTION.

FONCTION = F

Name of the tablecloth whose standard must be evaluated.

3.3 Word
key
ECART_TYPE

/ECART_TYPE
=

One calculates the standard deviation of the function F (T) which is defined by:

1
=
(
2
tfin
T
F () - F)
(
where F is the average on [tdeb, tfin]
tfin - tdeb)
dt
tdeb

The key words are identical to those provided under the key word factor RMS.

The produced concept is a table whose parameters of access are:

FUNCTION, METHOD, AVERAGE, INST_INIT, INST_FIN, ECART_TYPE.

Handbook of Utilization
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3.4 Word
key
RMS

/RMS
=

One calculates value RMS of the function F (T) which is defined by:

1
tfin
RMS =
2
(
F

tfin - tdeb)
(T) dt
tdeb


FONCTION = F

Name of the function which one calculates value RMS.
Do not apply to the concepts of the tablecloth type.



METHODE =

Name of the METHODE which one uses to calculate the integral.

Two methods are available: method of the “TRAPEZE” (by defect) and method of
“SIMPSON”.



INST_INIT = tdeb,


INST_FIN = tfin,

Limits lower and higher of the interval of integration.
If these values are not indicated, the points of discretization inferior and superior (
relation of command being defined compared to the parameter in X-coordinate) are taken as limits
the interval of integration.



PRECISION =/0.001,
/
prec,



CRITERE =
/“ABSOLU”,
/
“RELATIVE”, [DEFECT]

One seeks a point of discretization of the function in an interval defined by the position
absolute or relative around a value of the parameter of the X-coordinates for which the function
must be estimated:

·
[inst (1-prec), inst (1+prec)] if CRITERE = “RELATIF”
·
[inst - prec, inst + prec]
if CRITERE = “ABSOLU”

The produced concept is a table whose parameters of access are:

FUNCTION, METHOD, INST_INIT, INST_FIN, RMS.

3.5 Word
key
NOCI_SEISME

/NOCI_SEISME
=

/FONCTION = F,
/SPEC_OSCI = sro,

Name of the function or the tablecloth considered which must be defined in DEFI_FONCTION
[U4.31.02] with NOM_RESU=' ACCE'.

If a tablecloth is considered, only the calculation of spectral radiant intensity is available.
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

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/OPTION =

Allows to choose one or more of the six following indices of harmfulness:

|
“TOUT”


give all six index of harmfulness,

|
“MAXI”

give the maximum of acceleration, speed and displacement
PGA = max {(T)}, PGV = max {v (T)} PGD = max {X (T)}
T [
T,
T [
T,
T [
T,
I T F]
I T F]
I T F]

|
“INTE_ARIAS”
T
give the intensity of Arias I =
2 T
() dt
With
F
T
2g I

|
“POUV_DEST”
I
3

T
give the destroying capacity Pd = A =
v T 2
() dt
C
ft

2g I
0

|
“VITE_ABSO_CUMU”
T
give the cumulated absolute value speed CAV = F T () dt
Ti
|
Lasted “DUREE_PHAS_FORT” of strong phase:

Minimal duration T
- T such as:
sup
inf
T
binf× I
sup 2 T
() dt B
× I
With

sup
With
T
2g inf

|
“INTE_SPEC” spectral radiant intensity
(,)
I = fine S F N
v
df
H
fdeb
F 2
|
“ACCE_SUR_VITE” ratio Amax/Vmax
max {(T)}
T [
T, it F]
ITE
ACCE_SUR_V
=
.
max {v (T)}
T [
T, it F]

According to the option, one must inform certain parameters, if one does not indicate an option, by defect, one
thus calculate all the indices it is necessary all to inform.

The method of integration is the method of the “TRAPEZE”

INST_INIT = tdeb,
INST_FIN = tfin,

Limits lower and higher of the interval of time.
If these values are not indicated, the points of discretization inferior and superior (
relation of command being defined compared to the parameter in X-coordinate) are taken as limits
the interval.
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

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PRECISION =/0.001,
/
prec,

CRITERE =
/“ABSOLU”,
/
“RELATIVE”, [DEFECT]
One seeks a point of discretization of the function in an interval defined by the position
absolute or relative around a value of the parameter of the X-coordinates for which the function must
to be estimated:

·
[inst * (1-prec), inst * (1+prec)] if CRITERE = “RELATIF”
·
[inst - prec, inst + prec]
if CRITERE = “ABSOLU”
·
[freq * (1-prec), freq * (1+prec)] if CRITERE = “RELATIF”
·
[freq - prec, freq + prec]
if CRITERE = “ABSOLU”

COEF = r1

Constant of integration, by defect 0. In option “MAXI”, one calculates speed and it
displacement by two successive integrations of damping, it is thus necessary to inform
COEF if one does not want to take it by defect.

FREQ_INIT = fdeb,
FREQ_FIN = fine,

Frequencies representing the two terminals of integration for the calculation of the spectral radiant intensity.
Those must lie between the extréma base of frequencies defining
tablecloth SRO, if not poses a problem of interpolation. By defect, these two frequencies
0,4Hz and 10Hz are worth.

AMOR_REDUIT = amndt
Reduced damping, for the calculation of the spectral radiant intensity.

FREQ = lfre

fre = (

1,…,
,)

I
. List frequencies.

LIST_FREQ = lfreq

List frequencies provided under a concept listr8.

NORME = r2
The spectrum of oscillator will be normalized with the value r2 (value of pseudo-acceleration).

BORNE_INF = binf,
BORNE_SUP = bsup,

Terminals limiting the share of Arias intensity defining the moments initial and final of the strong phase
(between (binf) % and (bsup) % of (IA) max) of the seism.

3.6 Operand
TITER

TITER = T

Titrate attached to the concept produced by this operator [U4.03.01].

3.7 Operand
INFO

INFO
=

Specify the options of impression on file MESSAGE.

1
no impression
2
impression of the descriptor of the function (default option) and of the list of the 10 first
values of each function in the order ascending of the first 10 parameters.
Handbook of Utilization
U4.3- booklet: Function
HT-62/06/004/A

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4 Examples

4.1
Seek extrema of a function

A5=DEFI_FONCTION (
NOM_RESU=' SIGM',
NOM_PARA=' EPSI',
VALE= (0.002, 400.0,
0.003, 500.0,
0.0045, 550.0,
0.0065, 580.0,
0.008, 590.0,
0.01, 600.0,
0.02, 600.0,
),
PROL_DROITE=' CONSTANT',
PROL_GAUCHE=' LINEAIRE',
)
= INFO_FONCTION (MAX=_F (FONCTION=A5),)

IMPR_TABLE (TABLE=tab)

give on file “RESULTAT”.

#
# ASTER 8.02.00 CONCEPT CALCULE 24/01/2006 A 16:14:04 OF TYPE
# TABLE_SDASTER
STANDARD FUNCTION EPSI SIGM
A5 MINI 2.00000E-03 4.00000E+02
A5 MAXI 1.00000E-02 6.00000E+02
A5 MAXI 2.00000E-02 6.00000E+02

Handbook of Utilization
U4.3- booklet: Function
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Titrate:
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