An approach to enhance the structural operational deflection shape under random ambient excitation through mode shape expansion / Muhamad Azhan Anuar

Over the years, numerous system identification techniques for vibration analyses have
been evolved, proposed and successfully tested, and implemented for a wide range of
vibrating structures application. Although these techniques have been established,
performed, and tested successfully by many researchers, they fell short of addressing
crucial issues explicitly related to large structures with huge numbers of Degrees of
Freedom (DOFs). In practice, measured responses will display better results using large
numbers of measurement points. Consequently, this requires a complicated procedure
to obtain a better response and accuracy of results with the increasing number of points
on the structure. However, practically this is not possible since it needs a more robust
data/signal processing equipment system with many transducers to be placed at all
DOFs of a structure, especially on a large complex structure. For this reason, the main
objective of this study is to predict the response at unmeasured locations and
subsequently enhance the deflection of the structures at more DOFs using a limited
number of sensors. This study utilizes a modified Local Correspondence Principal
(LCP) to smooth and expand the mode shapes data and obtain much better and greater
information from measured responses. The implementation of this study involves
systematic methodology; (i) Operational Modal Analysis (OMA) as an experimental
method – The experimental data were collected and processed in order to decompose
the signal into modal components using different algorithms to obtain reliable
experimental modal data (ii) Finite Element (FE) as numerical technique – FE model
was developed, and normal modes results were obtained. (iii) An expansion approach
was applied by a linear combination of both OMA and FE mode shapes data using the
modified LCP method (iv) A new algorithm that includes the selection matrix and
rotation matrix were used to obtain the estimated experimental mode shape at higher
DOFs. Using these results, the structural Operational Deflection Shape (ODS) was
enhanced as 'full-blown animation'. A test case for a crack aluminium beam was
considered since it comprises both visible and invisible disturbances. This case study is
important to show the modified LCP method's applicability in improving the results,
although it was modelled without the presence of the crack in the FE. Modal data from
both OMA and FE results show a good correlation since the MAC values for all modes
are approximately equal to 1. Excellent quality of smoothed and expansion mode shapes
was obtained as shown by the optimum number of FE modes with better MAC values.
The results and findings show that the enhanced ODS from measured data were
completely estimated and developed. It shows the ability to predict the response of the
whole structure without being restricted by the number of points of measurements taken.
This new approach has the benefit over traditional methods by reducing equipment cost
and measurement time with less complexity in the procedure while maintaining the
accuracy. It provides the fundamental platform for theoretical expression and algorithm
to smooth and expand the experimental modes and subsequently enhance the ODS to
higher DOFs.