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6.6  Finite element model updating

While the upcom interface now provides a flexible environment that is designed for finite element updating problems, integrated methodologies for model updating are not stabilized. As a result, the SDT currently only intends to provide an efficient platform for developing model updating methodologies. This platform has been successfully used, by SDTools and others, for updating industrial models, but the details of parameter selection and optimization strategies are currently only provided through consulting services.

Figure 6.5: FE updating process.

The objective of finite element updating is to estimate certain design parameters (physical properties of the model) based on comparisons of test and analysis results. All the criteria discussed in section 3.2 can be used for updating.

The correlation tools provided by fe_sens and fe_exp are among the best existing on the market and major correlation criteria can easily be implemented. With SDT you can thus easily implement most of the existing error localization algorithms. No mechanism is however implemented to automatically translate the results of this localization into a set of parameters to be updated. Furthermore, the updating algorithms provided are very basic.

6.6.1  Error localization/parameter selection

The choice of design parameters to be updated is central to FE update problems. Update parameters should be chosen based on the knowledge that they have not been determined accurately from initial component tests. Whenever possible, the actual values of parameters should be determined using refined measurements of the component properties as the identifiability of the parameters is then clear. If such refined characterizations are not possible, the comparison of measured and predicted responses of the overall system provide a way to assess the probable value of a restricted set of parameters.

Discrepancies are always expected between the model and test results. Parameter updates made based on experimentally measured quantities should thus be limited to parameters that have an impact on the model that is large enough to be clearly distinguished from the expected residual error. Such parameters typically are associated to connections and localized masses.

In practice with industrial models, the FE model is initially divided into zones with one mass/stiffness parameter associated with each zone. The feutil FindElt commands can greatly help zone definition.

Visualizing the strain/kinetic energy distribution of modeshapes is a typical way to analyze zones where modifications will significantly affect the response. The gartup demo shows how the strain energy of modeshapes and displacement residuals can be used in different phases of the error localization process.

6.6.2  Update based on frequencies

As illustrated in demo_fe, once a set of update parameters chosen, you should verify that the proper range is set (see min and max values in section 6.5.4), make sure that Up.copt options are appropriately set to allow the computation of modes and sensitivities (see upcom copt commands), and define a sensor configuration matrix sens using fe_sens.

With test results typically stored in poles IIpo and residues IIres (see section 2.2), the update based on frequencies is then simply obtained by a call of the form

 i2=1:8;  % indices of poles used for the update
 [coef,md1,f1] = up_freq('basic',IIpo(i2,:),IIres(i2,:).',sens);

The result is obtained by a sensitivity method with automated matching of test and analysis modes using the MAC criterion. A non-linear optimization based solution can be found using up_ifreq but computational costs tend to prevent actual use of this approach. Using reduced order models (see section 6.5.5 and start use with upcom('opt model 1')) can alleviate some of the difficulties but the sensitivity based method (up_freq) is clearly better.

6.6.3  Update based on FRF

An update algorithm based on a non-linear optimization of the Log-Least-Squares cost comparing FRFs is also provided with up_ixf. The call to up_ixf takes the form

 coef = up_ixf('basic',b,c,IIw,IIxf,indw)

Using up_min for the optimization you will have messages such as

Step size: 1.953e-03
     Cost       Parameter jumps ...
  3.9341e-01  -9.83e+00   4.05e+00

which indicate reductions in the step size (Up.copt(1,7)) and values of the cost and update parameters at different stages of the optimization. With Up.copt(1,2) set to 11 you can follow the evolution of predictions of the first FRF in the considered set. The final result here is shown in the figure where the improvement linked to the update is clear.

Figure 6.6: Updated FRF.

This algorithm is not very good and you are encouraged to use it as a basis for further study.

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