Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
Author (S):
H. ANDRIAMBOLOLONA, Key S. AUDEBERT
:
U4.73.01-D1 Page:
1/10

Organization (S): EDF/R & D/AMA
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
Document: U4.73.01
Operator PROJ_MESU_MODAL

1 Goal

To extrapolate experimental measurements on a digital model in dynamics.

The experimental data can be displacements, speeds, accelerations,
deformations or of the constraints. They are defined as a function of time or the frequency,
or in the form of list.

It is a question of identifying the generalized co-ordinates of measurement relating to a base of projection
defined on the digital model. This base of projection (deformed, forced or deformations)
is calculated as a preliminary according to a concept of the mode_meca type or base_modale. Vectors of
base are then restricted with the measured degrees of freedom. Space association enters the points of
measure and the nodes of the numerical grid can be carried out manually or/and automatically.
The identification of the generalized co-ordinates is carried out by resolution of a problem of
minimization of the least type squares, possibly regularized according to the method of Tikhonov.

Is applicable to any type of model (1D, 2D and 3D).

Product a structure of data of the tran_gene type, harm_gene or mode_gene.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
Author (S):
H. ANDRIAMBOLOLONA, Key S. AUDEBERT
:
U4.73.01-D1 Page:
2/10

2 Syntax

repgene [* _gene] = PROJ_MESU_MODAL

(MODELE_CALCUL
=
_F (
BASE =
base
/
[base_modale]
/
[mode_meca]






MODELE
=
mocalc
[model]






),
MODELE_MESURE =
_F (
MESURE
=
measure
/
[dyna_trans]
/
[dyna_harmo]
/
[base_modale]






MODELE
=
mostru
[model]

NOM_CHAM
=
/
“DEPL”
[DEFAUT]
/
“VITE”
/
“ACCE”
/
“SIEF_NOEU”
/
“EPSI_NOEU_DEPL”






),


CORR_MANU
=
_F (
NOEU_MESURE
=
no1
[node]


NOEU_CALCUL
=
no2
[node]
),


RESOLUTION =
_F (
METHODE =
/
“LU” [DEFECT]
/
“SVD”
If METHODE = “SVD” then:
EPS
=
/
0.
[DEFAUT]
/
eps
[R]





REGUL
=
/
“NON”
[DEFAUT]
/
“NORM_MIN”
/
“TIK_RELA”
If REGUL!= “NON” then:
/COEF_PONDER =/0. [DEFAUT]
/
W
[l_R]
/
COEF_PONDER_F
= w_f
[l_fonction]






),

)


If measurement = [dyna_trans]
then repgene = [tran_gene]
If measurement = [dyna_harmo]
then repgene = [harm_gene]
If measurement = [mode_meca]

then repgene = [mode_gene]
If measurement = [base_modale]
then repgene = [mode_gene]

Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
Author (S):
H. ANDRIAMBOLOLONA, Key S. AUDEBERT
:
U4.73.01-D1 Page:
3/10

3 Operands

3.1 Key word
factor
MODELE_CALCUL

This key word factor gathers the characteristics of the digital model on which one wants to extrapolate
measure. It should appear only only once.

3.1.1 Operand
MODELE

MODELE = mocalc

Name of the digital model on which the base of projection is built.

3.1.2 Operand
BASE

BASE = bases

Name of the base of projection. This base of projection is of mode_meca type or
base_modale. This concept was possibly enriched, via command CALC_ELEM followed of
CALC_NO, by the fields of strains and/or modal stresses calculated with the nodes.

3.2 Key word
factor
MODELE_MESURE

This key word factor gathers information on the measured field (observed) that one wishes
to extrapolate on the digital model. It should appear only only once.

3.2.1 Operand
MODELE

MODELE = mostru

Name of the model associated with the observation.

3.2.2 Operand
MESURE

MESURE = measurement

Name of the measured field.

This key word determines the type of concept produced by operator PROJ_MESU_MODAL. If measurement
is of type dyna_trans, the produced concept is of tran_gene type. If measurement is of type
dyna_harmo, the produced concept is of harm_gene type. If measurement is of mode_meca type or
base_modale, the produced concept is of mode_gene type.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
Author (S):
H. ANDRIAMBOLOLONA, Key S. AUDEBERT
:
U4.73.01-D1 Page:
4/10

3.2.3 Operand
NOM_CHAM

NOM_CHAM =
/“DEPL”
/“VITE”
/“ACCE”
/“SIEF_NOEU”
/“EPSI_NOEU_DEPL”

This key word makes it possible to choose the name of the field measured to extrapolate in a list of names
symbolic systems predefined. Only one field is authorized. Components of the field considered
are those which were measured (observed) and were read in measurement.

3.3 Key word
factor
CORR_MANU

This key word factor makes it possible the user to manually define (to overload) the correspondence enters
the node of observation and the similar node of the digital model. This key word factor is optional,
but it can as many appear time as necessary. On the other hand, operands under this key word
factor go per pair: a NOEU_MESURE must have its corresponding NOEU_CALCUL.
If this key word factor misses, space association between the points of measurement and the nodes of
numerical grid is carried out automatically by using the function of form of the element of
digital model to determine the value of the field on the point of measurement.

3.3.1 Operand
NOEU_MESURE

NOEU_MESURE = no1

This key word informs the name of the node of observation which one wishes to associate the node
digital model no2. In certain cases, the file of grid associated with measurement is with
universal format (Ideas format), one cannot thus know the name Aster associated a priori with
node. It is thus necessary, in this case, of reading the grid resulting from PRE_IDEAS, by
LIRE_MAILLAGE in order to be able to name of the node.
3.3.2 Operand
NOEU_CALCUL

NOEU_CALCUL = no2

This key word informs the name of the node of the digital model which one wishes to associate the node
of observation no1.

3.4 Key word
factor
RESOLUTION

One defines here the method of resolution to be used and the parameters associated with this method.

3.4.1 Operand
METHODE

METHOD =/“LU”
/
“SVD”

One proposes the method LU (decomposition out of LU Lower-Upper) and method SVD
(decomposition in singular values) for the calculation of the opposite matrix. For method SVD,
the number of singular values to take into account depends on the value of eps that the user
inform under operand EPS. By defect, one adopts the method LU.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
Author (S):
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:
U4.73.01-D1 Page:
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3.4.2 Operand
EPS


This key word is used if method SVD is chosen.

EPS
=/
0.
/
eps

This key word gives the value from which a singular value is regarded as null.
It determines the number of singular values thus to exploit at the time of the resolution. A eps equal to
zero mean that all the singular values are to be taken into account. eps equal to 1 means
that one considers only the greatest singular value. By defect, one chooses EPS = 0.

3.4.3 Operand
REGUL

REGUL =/
“NON”
/“NORME_MIN”
/
“TIK_RELA”

REGUL makes it possible to specify the method of regularization which one wants to use. By defect, one
do not add a regularization (not additional constraint on the solution: REGUL =
“NON”).
Currently, two types of regularization are available (minimal standard: REGUL =
“NORM_MIN” or Tikhonov of command 0 and “relative” Tikhonov: REGUL = “TIK_RELA”).
One seeks to minimize, for each sequence number of the measured field, the functional calculus
following compared to:

2
2
Q
- + -

exp
num
priori

with:

·
: generalized co-ordinates relating to the base of projection.
num
·
Q: measured field following the degrees of freedom of observation.
exp
·
: base projection restricted with the degrees of freedom of observation.
num
·
: coefficients weighting making it possible to specify the affected weight with information has
priori on the solution.

According to the method used, the parameters of the preceding functional calculus are declined like
follows:
Without regularization: = 0
Minimal standard (NORM_MIN): prior = 0
“Relative” Tikhonov (TIK_RELA): prior: solution found with the preceding sequence number

It is disadvised using this key word when key word NOM_PARA is DEFORMEE.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
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:
U4.73.01-D1 Page:
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3.4.4 Operands
COEF_PONDER and COEF_PONDER_F

This key word corresponds to the affected weight with information a priori, it is used if one is applied
regularization with the solution.

/COEF_PONDER =
coeff

List weighting coefficients on the solution a priori (method of regularization of
Tikhonov) [bib3].

/
COEF_PONDER_F
= coef_f

List weight functions on the solution a priori (method of regularization of
Tikhonov). The variables of these functions depend on key word NOM_PARA. If NOM_PARA is
INST, the variable are time. If NOM_PARA is FREQ, the variable is the frequency. If
NOM_PARA is DEFORMEE, the variable is the sequence number of the deformation.

If the number of coefficients or weight functions given is lower than the number of
basic vectors used in the base of projection, the coefficients or functions of
weighting of the additional vectors are taken equal to the last coefficient or to
last function of the list.

4
Phase of checking and execution

4.1 Calculation of the base of projection restricted with the degrees of freedom
measured

Initially, the grid of measurement is projected on the grid of the digital model. One
determine then the participation of the nodes of the digital model for each node of measurement via
the function of form of the element which contains the node of measurement. Correspondence obtained between
nodes is provided in file MESSAGE of the Aster study.

The second processing consists in calculating the component of the field (projection bases) to the node of
measure according to the measured degrees of freedom.

4.2
Calculation of the generalized co-ordinates

The solution of the equation of minimization is given by:

(
)
- 1
0 = [T
T Q
num
num]
()
0
num exp

(
I) = [T + (I)
T Q
I
I
num
num
] - 1 (
() + ()
num exp
prior)

With:

·
(I): co-ordinates generalized for the sequence number I (Ti or fi),
·
Q (I): measure with the sequence number I,
exp
·
: base projection restricted with the degrees of freedom of measurement,
num
·
(I): coefficients allowing to specify the affected weight with information a priori with the number
of command I. These variables or functions are defined by the user in the operands
COEF_PONDER or COEF_PONDER_F of the key word factor RESOLUTION. They are introduced
in the form of a list of realities or functions and correspond, term in the long term, with each
vector of the base of projection selected.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
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Titrate:
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Date:
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:
U4.73.01-D1 Page:
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According to the method used, the preceding parameters are declined as follows:
Without regularization: = 0
Minimal standard (NORM_MIN): prior = 0
“Relative” Tikhonov (TIK_RELA): prior = i-1

Notice 1:

If a weighting coefficient is negative, the processing stops in fatal error.

Notice 2:

If all the weighting coefficients are null for a given sequence number and that it
a many measurements are strictly lower than the number of basic vectors, a message
of alarm is emitted to prevent risk of singular matrix indeed (, in this case, it does not have there
not unicity of the solution).

At the end of calculation, the identified generalized co-ordinates are derived in order to calculate them
speeds and corresponding accelerations.

The result of the inversion is a concept of the tran_gene type, harm_gene or mode_gene.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
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:
U4.73.01-D1 Page:
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5
Example of use of PROJ_MESU_MODAL

For the examples of use, it is highly advised to refer to the cases tests SDLD104 and
SDLV122.

One presents in this paragraph the various stages for the expansion of measurement on the model
numerical.

·
Reading of the grid made up of the points of measurement:
This operation aims to read the position of the points of measure to a file of the type
grid. The format of this file must be readable by Code_Aster (format GIBI, universal (I-deas)
or soon MED). Meshs connecting the nodes of measurement can have been defined.
They do not have obviously any physical significance but will possibly allow
to display the results at the time of the phase of postprocessing.
In the majority of the cases, the grid results from a code of experimental measurement which provides one
file with the universal format (I-deas format). To transform it into Aster format, one uses
operator PRE_IDEAS.

PRE_IDEAS (UNITE_IDEAS = 19, UNITE_MAILLAGE = 21,)
mailmesu = LIRE_MAILLAGE (UNITE = 21,)

·
Assignment of a mechanical model to the grid:
This operation aims to define the model of the support of the nodes of the grid made up
points of measurement. Two cases can be considered: assignment of a modeling DIS_T
(discrete in translation => 3 degrees of freedom per node: DX, DY and DZ) or assignment of one
modeling DIS_TR (discrete in translation - rotation => 6 degrees of freedom per node: DX, DY,
DZ, DRX, DRY and DRZ) if measurements of rotation are carried out.

modlmesu = AFFE_MODELE (MAILLAGE = mailmesu,
AFFE

=
_F (
GROUP_NO

=
“noeumesu”,
MODELISATION
=
“DIS_T',
PHENOMENE
=
“MECANIQUE”,),
)

·
Reading of measurement:
Measurement can be read via operator LIRE_RESU. This operator allows to read a file with
universal format (dataset 58). He recovers the component of the field observed and assigns it to the model
corresponding.

measure = LIRE_RESU (FORMAT = “IDEAS”,
UNITE = 33,
DATASET_58 = “OUI”,
MAILLAGE = mailmesu,
TYPE_RESU = “DYNA_TRANS”,
NOM_CHAM = “SIEF_NOEU”,)

·
Definition of the base of projection:
The base of projection must be of the mode_meca type or base_modale. This concept can result
MODE_ITER_SIMULT or DEFI_BASE_MODALE.
If one wants to extrapolate a field of strain or stress, the base must be enriched, via
order CALC_ELEM followed by CALC_NO, by the fields of strain or stress
calculated with the nodes.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
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H. ANDRIAMBOLOLONA, Key S. AUDEBERT
:
U4.73.01-D1 Page:
9/10

·
Calculation of the generalized co-ordinates:
The calculation of the generalized co-ordinates relating to the base of projection is ensured by
operator PROJ_MESU_MODAL.

repgene = PROJ_MESU_MODAL (
MODELE_CALCUL
=
_F (
MODELE = modlcalc,
BASE = bases,),
MODELE_MESURE
=
_F (
MODELE = modlmesu,
MESURE = measurement,
NOM_CHAM = “SIEF_NOEU”,),
CORR_MANU
=
_F (
NOEU_MESURE = “no1”,
NOEU_CALCUL = “no2”,),
RESOLUTION =
_F (
METHOD = “SVD”,
EPS = 1.E-4,),
)

·
Expansion on the digital model:
This expansion consists in calculating on all the nodes of the digital model, the field
compatible with the field observed on the measured degrees of freedom. This expansion is
realized by command REST_BASE_PHYS.

answer = REST_BASE_PHYS (RESU_GENE = repgene,
TOUT_CHAM = “YES”,)
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

Code_Aster ®
Version
8.2
Titrate:
Operator PROJ_MESU_MODAL


Date:
31/01/06
Author (S):
H. ANDRIAMBOLOLONA, Key S. AUDEBERT
:
U4.73.01-D1 Page:
10/10

6 Bibliography

[1]
C. VARE: Extrapolation of experimental results of measurement on a digital model
in dynamics ­ Spécification of the developments in Code_Aster. Note EDF/DER
HP-54/98/063/B
[2]
S. AUDEBERT: Comparative evaluation of various methods of inversion. Note EDF/DER
HP-62/93/036
[3]
A. TIKHONOV, V. ARSENINE: Methods of resolution of badly posed problems. ED. Mir
1976
[4]
Mr. BONNET: Digital processing of problems opposite of source in linear accoustics.
Contract EDF ­ Convention P55L08/1E5240
[5]
A. TARANTOLA: Opposite problem theory ­ Methods for dated fitting and model parameter
estimate. Elsevier ­ 1987
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A

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