Mode result ellipse derived from simulations, experiments and schematic representations of the stochastic model updating
AirMod laboratory structure, the degrees of freedom for measurements, and finite element model
The expansion of structural dynamic methods to consider uncertainties in experimental modal data is a key area of work. As a basis for this, a working environment has been established, which enables the analysis and quantification of uncertainties in modal test data. As a basis for this, the functionality of the DLR Correlation Tool was expanded accordingly. The expansion to the stochastic analysis of modal data is based on the assumption that mode shapes during ground vibration tests are identified when the phase separation methods are applied on several occasions, for example, from data obtained from various excitation configurations. Using the correlation of data from modal analysis derived from various excitation configurations, so called mode families can be created. This is a collection of almost identical natural vibration modes, which have been identified from different data sets, and as such, possess slightly different numerical values for the natural frequency, damping ratio and generalised mass. Given that many different excitation configurations may be used in large aircraft, this gives rise to mode families with a strong population and, therefore, statistical analyses of these mode families can be carried out.
As a result, the modal data of a structure does not have a fixed value, but instead can be treated as statistical parametric properties. As such, the result of the statistical analysis of the experimental modal data can generate result ellipses for, the natural frequency for example, as shown on the right hand side of the upper figure.
Expanding the DLR Correlation Tool to include the analysis of uncertainties in experimental modal data was a requirement for further research in the field of Uncertainty Management. A significant contribution for this is the expansion of known model updating methods, in order to take statistical uncertainties in experimental modal data into account. The aim of these ‘stochastic model updating’ approaches is the inverse projection of the uncertainties related to the stiffness and mass parameters of an FE model, as detected in modal test data. It is also necessary that certain parameters of the FE model are no longer only defined by fixed numerical values, but rather, much more as statistical variables with means and standard deviation. In addition, correlation coefficients represent the statistical correlation of the parameters. Using the Monte Carlo methods, results can be produced for eigenfrequencies, for example. The results from numerical simulations and tests do not generally coincide. The aim of the stochastic model updating method is to adapt the statistical parameters of an FE model in order to compare the numerical output and test data from the real structure, thus improving the ability to make predictions about the FE model. The method was successfully tested using real experimental modal data from the laboratory structure AirMod.
The uncertain eigenfrequencies and mode shapes were determined in an experimental modal test campaign where the laboratory structure was tested repeatedly while it was assembled and disassembled 130 times in between each experimental modal analysis. The stochastic modal data set obtained in this way was also made available to other scientific work groups (e.g. University of Liverpool), and could be established in the field of stochastic model updating as a benchmark for real test data.
A further contribution in the area of uncertainty management is interval finite element analysis of wing flutter, which determines relevant uncertainties in flutter-critical flight speeds based initially on uncertain experimental modal data.