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Titrate:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
1/12
Organization (S): EDF-R & D/AMA
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
Document: U4.73.02
Macro-command MACR_RECAL
1 Goal
To readjust computation results on experimental results or other computation results.
Let us consider on the one hand one or more test results and on the other hand one or more Aster calculations
modelling these tests. MACR_RECAL makes it possible to determine the parameters of these calculations (which
can be parameters of law of behavior, loading, etc…) describing them as well as possible
tests.
For more precise details on the algorithmy implemented, to refer to [R4.03.06].
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:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
2/12
2 Syntax
Lr
=
MACR_RECAL [listr8]
(UNITE_ESCL
= plain
[I]
RESU_EXP
=
resu_exp
[ESA]
POIDS
=
weight
[ESA]
RESU_CALC
=
resu_calc
[ESA]
LIST_PARA
=
will list_para
[ESA]
UNITE_RESU =/91
[defect]
·uni_r
ITER_MAXI
=
/10
[defect]
·it
RESI_GLOB_RELA =/1.E-3
[defect]
/
resi
PARA_DIFF_FINI =/1.E-3
[defect]
/
coeff
GRAPHIQUE
UNITE
=
/
90 [defect]
/
uni_g
INTERACTIVE =/“NOT”
[defect]
/
“OUI”
FORMAT =/“XMGRACE”
[defect]
/
“GNUPLOT”
);
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
HT-62/06/004/A
Code_Aster ®
Version
8.2
Titrate:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
3/12
3 Presentation
general
3.1
Principle of retiming
Let us consider the model problem of identification of the elastoplastic characteristics E, y, AND
(respectively Young modulus, elastic limit and module of work hardening) of a material on one
uniaxial tensile test.
One has on the one hand the experimental traction diagram giving the evolution of the constraint according to
time and which is a data:
T
There is in addition a function of the 3 parameters which for each value of the triplet E, y, AND returns
a calculated traction diagram:
(E, y, AND)
T
The objective of retiming is then to answer the question:
Which are the values of (E, y, AND) describing my experiment as well as possible?
3.2
Organization of retiming
To conclude a retiming, it is necessary to have the whole of information
following:
·
the NR experimental curves (with each one of these curves can be allotted a weight
arbitrary),
·
the P parameters to readjust like, for each one, an estimate of its initial value, its
minimal value and its maximum value,
·
the command file modelling the NR tests which one wants to readjust,
·
names of the NR sizes to be extracted from the command file above and which will be
readjusted on the NR experimental curves. These sizes must be contained in one
count resulting from POST_RELEVE_T.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
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Code_Aster ®
Version
8.2
Titrate:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
4/12
The setting in data of this information requires the following organization then:
·
a command file says main containing the NR experimental curves, the P
parameters, names of the sizes to be readjusted as well as other information suitable for
retiming, the whole indicated in MACR_RECAL. The various formats used are specified
in what follows,
·
a command file says slave modelling the experimental tests.
Indeed, retiming is an iterative process: the master file carries out the file slave, it recovers
the NR curves calculated with the current prices of the P parameters, it compares the values of
curves calculated with those of the experimental curves, it deduces some from new values for P
parameters and revival the file slave. This process continues until obtaining convergence.
NR experimental curves
Master file
MACR_RECAL
(file .comm of the profile
of study)
P parameters
Loops of retiming
NR calculated curves
File slave
In the following part the operands of MACR_RECAL are described. One refers there to some
notions of the Python language. It is however by no means necessary to know Python to use
this macro command. The part “Exemple of use” is there to light the user.
The structure of data produced is a list of real containing the values of the parameters with
convergence in the event of convergence or with the last iteration in the contrary case.
Handbook of Utilization
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Code_Aster ®
Version
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Titrate:
Macro-command MACR_RECAL
Date:
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:
U4.73.02-C1 Page:
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4 Operands
4.1 Operand
UNITE_ESCL
UNITE_ESCL
Logical number of unit of the file slave, allotted in interface ASTK (column UL).
The extension of this file can be unspecified.
4.2 Operand
RESU_EXP
RESU_EXP
Name of the Python list of NR tables Numeric Python containing the NR experimental curves.
The list is beforehand defined in the form:
resu_exp= [Numeric.array ([
[X, y],
0
0
[X, y],
1
1
…
[X, y]]),
N
N
.....
Numeric.array ([
[U, v],
0
0
[U, v],
1
1
…
[U, v]])
N
N
]
4.3 Operand
POIDS
POIDS
Name of table Numeric Python containing the NR weight to be assigned to the NR experimental curves.
So nonwell informed, then the table is made up of 1. The list is beforehand defined under
form:
POIDS= Numeric.array (p0, p1,…)
4.4 Operand
RESU_CALC
RESU_CALC
Name of the Python list of NR Python lists containing the definition of the numerical answers
corresponding to experimental measurements on which one will carry out retiming.
4.5 Operand
LIST_PARA
LIST_PARA
Name of the Python list of P Python lists containing the names of the variables, their values
initial, their minimal values and their maximum values. This list is beforehand defined
in the form:
List_para= [[“PARA1__”, INI_1, MIN_1, MAX_1],
[“PARA2__”, INI_2, MIN_2, MAX_2],
….
[“PARAP__”, INI_P, MIN_P, MAX_P]]
Caution:
It is asked that the names of the variables end in two white underlined (by
example: YOUN__).
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:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
6/12
4.6 Operand
ITER_MAXI
ITER_MAXI
Iteration count maximum of retiming.
4.7 Operand
RESI_GLOB_RELA
RESI_GLOB_RELA
Relative total residue of retiming.
This value is disjoined of that well informed for nonlinear solveurs STAT_NON_LINE and
DYNA_NON_LINE.
4.8 Operand
UNITE_RESU
UNITE_RESU
Logical number of unit of the file of result of retiming (evolution of the parameters during
iterations, criteria of convergence).
4.9 Operand
PARA_DIFF_FINIES
PARA_DIFF_FINI
Retiming requires the calculation of derived from the answers compared to the parameters. This calculation
is realized by finished differences. PARA_DIFF_FINIES corresponds to in the following formula:
F
F (X + X) - F (X
)
X
X
4.10 Operand
GRAPHIQUE
UNITE
Logical number of unit of the graphs produced during retiming. With each iteration,
MACR_RECAL produce NR graphic POSTSCRIPT representing the NR experimental curves and
calculated.
INTERACTIF
Display of the graphs in an interactive way.
Caution:
This is not possible that when retiming turns in interactive and not in batch.
FORMAT
Choice of the software of display in interactive mode: xmgrace or gnuplot.
Handbook of Utilization
U4.7- booklet: Operations on the results and the fields
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Code_Aster ®
Version
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Titrate:
Macro-command MACR_RECAL
Date:
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O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
7/12
5 Precautions
of employment
Here a whole of consultings essential to correct use of retiming.
·
The experimental curves are defined like tables with two columns: for
X-coordinates and for the ordinates.
·
The experimental curves must be functions: to a X-coordinate does not have to correspond
that an ordinate.
PROHIBITED AUTHORIZES
·
One must readjust NR curves calculated on NR experimental curves.
·
The first calculated curve will be readjusted on the first experimental curve, the second
calculated curve will be readjusted on the second experimental curve, and so on in
the command indicated for operands RESU_EXP and RESU_CALC.
·
The sizes calculated well informed under operand RESU_CALC must result from
POST_RELEVE_T.
·
The parameters of retiming must be declared in block at the beginning of the command file
slave. For example:
DEBUT ();
DSDE__ = 200.;
YOUN__ = 8.E4;
SIGY__ = 10.;
......
·
The initial values of the parameters of retiming are those well informed for the operand
LIST_PARA and not those present in the file slave of the user.
·
With each iteration of retiming, the calculations defined in the file slave must converge.
Within the framework of retiming of nonlinear calculations, it is thus strongly recommended
to use the automatic cutting of the step of time.
·
Within the framework of retiming of nonlinear calculations with automatic cutting of the step of
time, it is essential to define a list of filing under operand LIST_ARCH.
·
Retiming is a powerful means to obtain values of parameters with started from tests. It
is however not miraculous: the experimental curves must contain sufficiently
information to identify the parameters. It is for example impossible to identify
elastoplastic parameters with a test remaining in the elastic range. Tests
experimental must thus excite the parameters to be identified.
·
In same logic, it is desirable that the experimental curves contain
points in a number sufficient for describing the action of the parameters well to be identified.
·
Lastly, in the case of the use of several experimental curves, the fact that they have it
an even many points balance the information which they bring.
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:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
8/12
6 Example
of use
6.1 Identification of the parameters of a law of behavior
elastoplastic on a tensile test
This example is treated by test ZZZZ159A [V1.01.159].
6.1.1 Position of the problem
One has the results of a tensile test. It is about the evolution of constraint SIYY to the course
time as well as evolution of the plastic deformation cumulated in the course of time.
Constraint SIYY
Cumulated plastic deformation
One wishes to readjust on these tests the Young modulus, the elastic limit and the slope of work hardening
of an elastoplastic law of behavior to linear isotropic work hardening.
6.1.2 Setting in data
6.1.2.1 Experiment
One starts first of all by defining our test results. They consist of two curves that one
defines as follows.
experience= [Numeric.array ([[0.00000E+00, 0.00000E+00],
[5.00000E-02, 5.00000E+01],
.........
[9.50000E-01, 2.07500E+02],
[1.00000E+00, 2.08000E+02]]),
Numeric.array ([[0.00000E+00, 0.00000E+00],
[5.00000E-02, 0.00000E+00],
.........
[9.50000E-01, 3.71250E-03],
[1.00000E+00, 3.96000E-03]])]
experiment is thus the name of a Python list (definite between hooks) of 2 Numeric tables
Python.
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U4.7- booklet: Operations on the results and the fields
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Code_Aster ®
Version
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Titrate:
Macro-command MACR_RECAL
Date:
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Author (S):
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:
U4.73.02-C1 Page:
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6.1.2.2 Calculation
One writes then the command file Aster slave modelling this tensile test where go
to appear our 3 parameters as well as the two curves to be readjusted.
DEBUT ();
# ASSIGNMENT OF THE VALUES OF THE PARAMETERS TO BE READJUSTED
# THE VALUES INDICATED HERE ARE OF NO IMPORTANCE
# ALONE COUNT THE VALUES INDICATED IN THE MASTER FILE
DSDE__ = 200.;
YOUN__ = 8.E4;
SIGY__ = 1.;
........
ACIER=DEFI_MATERIAU (ECRO_LINE=_F (D_SIGM_EPSI=DSDE__,
SY=SIGY__,),
ELAS=_F (NU=0.3,
E=YOUN__,),);
........
EVOL=STAT_NON_LINE (CHAM_MATER=CHMAT,
MODELE=MO,
ARCHIVAGE=_F (LIST_INST=INSTANTS,
ARCH_ETAT_INIT=' OUI',),
CONVERGENCE=_F (ITER_GLOB_MAXI=10,
RESI_GLOB_RELA=1.E-05,),
COMP_INCR=_F (RELATION=' VMIS_ISOT_LINE',),
INCREMENT=_F (LIST_INST=INSTANTS,
SUBD_PAS=4,
COEF_SUBD_PAS_1=1.0,
SUBD_PAS_MINI=1.E-05,),
NEWTON=_F (REAC_ITER=1,
REAC_INCR=1,),
EXCIT=_F (CHARGE=TRACTION,
FONC_MULT=RAMPE,),);
.......
# EXTRACTION OF ANSWER SIGMAYY (T)
REPONSE1=POST_RELEVE_T (ACTION=_F (OPERATION=' EXTRACTION',
INTITULE=' SIGYY',
RESULTAT =EVOL,
NOM_CHAM = ' SIEF_ELNO_ELGA',
NOM_CMP = “SIYY”,
GROUP_NO = “A”,),);
# EXTRACTION OF ANSWER EPSP (T)
REPONSE2=POST_RELEVE_T (ACTION=_F (OPERATION=' EXTRACTION',
INTITULE=' V1',
RESULTAT =EVOL,
NOM_CHAM = ' VARI_ELNO_ELGA',
NOM_CMP = “V1”,
GROUP_NO = “A”,),);
FIN ();
Handbook of Utilization
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Code_Aster ®
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Titrate:
Macro-command MACR_RECAL
Date:
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:
U4.73.02-C1 Page:
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It is necessary for us now to define in the master file the initial values and the ranges of variations of
our parameters. One wishes:
1.E5
<
Initial Young modulus = 1.E5
< 5.E5
5.
<
Initial elastic limit = 30.
<
500.
1.E3
<
Modulate initial work hardening = 1.E3 < 1.E4
What one writes under the forme=
Parameters
= [[“YOUN__”, 100000., 50000., 500000.], [“DSDE__”, 1000., 500., 10000.],
[“SIGY__”, 30., 5., 500.]]
Finally it remains us to define in the master file the sizes to be extracted from the command file
slave above. We wish on the one hand to extract column INST and column SIYY from the table
REPONSE1 and in addition column INST and the V1 column of table REPONSE2. We write it:
calculation = [[“REPONSE1”, “INST”, “SIYY”], [“REPONSE2”, “INST”, “V1”]]
6.1.2.3 MACR_RECAL
We now inform this information in the body of MACR_RECAL:
RESU=MACR_RECAL (
UNITE_ESCL =3,
RESU_EXP =experience,
LIST_PARA =parametres,
RESU_CALC =calcul,);
6.1.2.4 ASTK
One defines finally the profile of study according to:
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Code_Aster ®
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Titrate:
Macro-command MACR_RECAL
Date:
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:
U4.73.02-C1 Page:
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6.1.3 Results
Once the study carried out, the file of result of ZZZZ159_opti.resu retiming contains information
following:
Calculation of the sensitivity compared to = YOUN__ DSDE__ SIGY__
=======================================================
Iteration 0 =
=> Fonctionnelle = 1.0
=> Résidu = 1.0
=> Paramčtres =
YOUN__ = 100000.0
DSDE__ = 1000.0
SIGY__ = 30.0
=======================================================
Calculation of the sensitivity compared to = YOUN__ DSDE__ SIGY__
=======================================================
Iteration 1 =
=> Fonctionnelle = 0.259742161795
=> Résidu = 0.30865397471
=> Paramčtres =
YOUN__ = 300857.888503
DSDE__ = 9135.12770111
SIGY__ = 152.548047532
=======================================================
Calculation of the sensitivity compared to = YOUN__ DSDE__ SIGY__
=======================================================
Iteration 2 =
=> Fonctionnelle = 0.0757636994765
=> Résidu = 0.473053125246
=> Paramčtres =
YOUN__ = 157723.378846
DSDE__ = 2022.7431335
SIGY__ = 213.155325073
=======================================================
Calculation of the sensitivity compared to = YOUN__ DSDE__ SIGY__
=======================================================
Iteration 3 =
=> Fonctionnelle = 0.00190706595529
=> Résidu = 0.0520849911718
=> Paramčtres =
YOUN__ = 192302.166747
DSDE__ = 895.845518907
SIGY__ = 203.753909707
=======================================================
Calculation of the sensitivity compared to = YOUN__ DSDE__ SIGY__
=======================================================
Iteration 4 =
=> Fonctionnelle = 2.70165453323e-06
=> Résidu = 0.00172172540305
=> Paramčtres =
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:
Macro-command MACR_RECAL
Date:
31/01/06
Author (S):
O. NICOLAS, A. ASSIRE, NR. TARDIEU Key
:
U4.73.02-C1 Page:
12/12
YOUN__ = 199801.572817
DSDE__ = 1928.08902726
SIGY__ = 200.274590793
=======================================================
Calculation of the sensitivity compared to = YOUN__ DSDE__ SIGY__
=======================================================
Iteration 5 =
=> Fonctionnelle = 2.65431115925e-12
=> Résidu = 1.83121468206e-06
=> Paramčtres =
YOUN__ = 199999.975047
DSDE__ = 1999.86955101
SIGY__ = 200.000462987
=======================================================
=======================================================
CONVERGENCE REACHED
=======================================================
Eigenvalues of Hessien:
[7.17223479e+00 3.67264061e-01 6.25194340e-04]
Associated clean vectors:
[[0.98093218 - 0.00549396 - 0.19427266]
[- 0.19418112 - 0.06940835 - 0.97850712]
[0.00810827 - 0.9975732 0.0691517]]
--------
One can deduce from it that:
The following combinations of parameters are dominating for your
calculation:
1) +9.8E-01 * YOUN__ - 1.9E-01 * DSDE__
associated the eigenvalue 7.2E+00
The following combinations of parameters are insensitive for your
calculation:
1) - 1.9E-01 * YOUN__ - 9.8E-01 * DSDE__
associated the eigenvalue 6.3E-04
And file POSTSCRIPT ZZZZ159.ps contains:
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