3. Operands#

3.1. Keyword factor MODELE_CALCUL#

This keyword factor groups together the characteristics of the numerical model on which we want to extrapolate the measurement. It should only appear once.

3.1.1. Operand MODELE#

♦ MODELE = mocalc

The name of the numerical model on which the expansion base is built.

3.1.2. Operand BASE#

♦ BASE = base

Name of the expansion base. This database is of the mode_meca type. This concept was possibly enriched, via the CALC_CHAMP command, by the deformation and/or modal stress fields calculated at the nodes.

3.2. Keyword factor MODELE_MESURE#

This keyword factor groups together the information on the measured (observed) field that we want to extrapolate to the numerical model. It should only appear once.

3.2.1. Operand MODELE#

♦ MODELE = mostru

The name of the model associated with the observation.

3.2.2. Operand MESURE#

♦ MESURE = measure

The name of the measured field.

This keyword determines the type of concept produced by the PROJ_MESU_MODAL operator. If measure is of the dyna_trans type, the product concept is of the tran_gene type. If measure is of the dyna_harmo type, the product concept is of the harm_gene type. If measure is of the mode_meca type, or mode_meca_c, the product concept is of the mode_gene type.

3.2.3. Operand NOM_CHAM#

◊ CHAM_NAME = | 'DEPL' [DEFAULT]

| 'FAST'

| 'ACCESS'

| 'SIEF_NOEU'

| 'EPSI_NODE'

This keyword allows you to choose the field (s) to be read and extrapolated. The components of the field considered are those that have been measured (observed) and read in measurement. For the time being, a weighting coefficient is not assigned to the various components of the field: each component has the same weight during the inversion.

3.3. Operand NOM_PARA#

◊ NOM_PARA = for

List of the symbolic names of the parameters of the measured data that we want to transmit to the generalized model.

3.4. Keyword factor CORR_MANU#

This keyword factor allows the user to manually define (override) the correspondence between the observation node and the analog node of the digital model. This keyword factor is optional, but it can appear as many times as needed. On the other hand, the operands under this keyword factor go in pairs: a NOEU_MESURE must have its associated NOEU_CALCUL.

If this keyword factor is absent, the spatial association between the measurement points and the nodes of the digital mesh is performed automatically by using the shape function of the numerical model element to determine the value of the field on the measurement point.

3.4.1. Operand NOEU_MESURE#

♦ NOEU_MESURE = no1

This keyword provides the name of the observation node that one wishes to associate with the node of the numerical model no2. In some cases, the mesh file associated with the measurement is in a universal format (Ideas format), so it is not possible to know at first glance the name Aster associated with the node. It is therefore necessary, in this case, to read the mesh from PRE_IDEAS, by LIRE_MAILLAGE in order to be able to assign the name of the node.

3.4.2. Operand NOEU_CALCUL#

♦ NOEU_CALCUL = no2

This keyword provides the name of the numerical model node that you want to associate with observation node no1.

3.5. Keyword factor RESOLUTION#

The resolution method to be used and the parameters associated with this method are defined here.

3.5.1. Operand METHODE#

◊ METHODE =/'READ'

/”SVD”

The LU method (Lower-Upper LU decomposition) and the SVD method (singular value decomposition) are proposed for the calculation of the inverse matrix. For method SVD, the number of singular values to take into account depends on the value of eps that the user enters under the EPS operand. By default, the LU method is adopted.

3.5.2. Operand EPS#

This keyword is used if the SVD method is chosen.

◊ EPS =/0.

/eps

This keyword gives the value at which a singular value is considered zero. It thus determines the number of singular values to be used during the resolution. An eps equal to zero means that all singular values are to be taken into account. eps equal to 1 means that only the largest singular value is considered. By default, we choose EPS = 0.

3.5.3. Operand REGUL#

◊ REGUL =/'NON'

/'NORME_MIN'

/”TIK_RELA”

REGUL allows you to specify the regularization method you want to use. By default, no regularization is added (no additional constraint on the solution: REGUL = “NON”).

Currently, two types of regularization are available (minimum standard: REGUL = “NORM_MIN” or Tikhonov of order 0 and Tikhonov « relative »: REGUL = “TIK_RELA”).

The aim is to minimize, for each order number of the field measured, the following functional with respect to \(\eta\):

\({\mid {q}_{\mathrm{exp}}-{\stackrel{ˉ}{\Phi }}_{\mathrm{num}}\eta \mid }^{2}+{\alpha \mid \eta -{\eta }_{\mathrm{priori}}\mid }^{2}\)

with:

  • \(\eta\): generalized coordinates relating to the \({\stackrel{ˉ}{\Phi }}_{\mathrm{num}}\) expansion base.

  • \({q}_{\mathrm{exp}}\): field measured according to the degrees of freedom of observation.

  • \({\stackrel{ˉ}{\Phi }}_{\mathrm{num}}\): expansion base restricted to degrees of freedom of observation.

  • \(\alpha\): weighting coefficients allowing to specify the weight assigned to the information a prima facie on the solution.

Depending on the method used, the parameters of the preceding functional are divided as follows:

Without regularization: \(\alpha =0\)

Minimum standard (NORM_MIN): \({\eta }_{\mathrm{priori}}=0\)

Tikhonov « relative » (TIK_RELA): \({\eta }_{\mathrm{priori}}\): solution found to the previous order number

It is not recommended to use this keyword when the measured field (measure) is of the mode_meca type.

3.5.4. Operands COEF_PONDER and COEF_PONDER_F#

This keyword corresponds to the weight assigned to the information a prima facie, \(\alpha\). It is used if regularization is applied to solution \(\eta\).

◊/COEF_PONDER = key

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

/COEF_PONDER_F = coef_f

List of weighting functions on the a priory solution (Tikhonov regularization method). The variables of these functions are the same as those of the measured field (measure). If the given number of coefficients or weighting functions is less than the number of base vectors used in the expansion base, the coefficients or weighting functions of the additional vectors are taken to be equal to the last coefficient or to the last function in the list.