Damage in structures may be identified and quantified by using measured frequency
response functions (FRFs) or identified modal properties as a basis for updating. The
main shortcoming of these methods is that if they are used individually the methods using
modal properties do not necessarily predict the measured FRFs and vice versa.
A Multiple Criterion Method (MCM) which uses the measured FRFs and identified
modes simultaneously in an optimisation fashion, is developed in this study. The
Euclidean norm of the error vector resulting from the integration of the mass and stiffness
matrices from the Finite Element Model (FEM) and the measured FRFs in the equation of
motion is minimised. The same procedure is performed using identified modal
properties. The modulus of elasticity of each element in the FEM of the structure is used
as design variables.
The new procedure is tested on a simple beam, a complex beam (with drilled holes that
are hard to model) and an irregular H-shaped structure. The effectiveness of MCM was
compared to other methods that use FRFs and modal properties individually. The
comparison was made by using methods such as Modal Assurance Criterion (MAC), Coordinate
Modal Assurance Criterion (COMAC) and the Frequency Response Functions
Assurance Criterion (FRF AC), which is a new procedure developed specifically as part
this work. It was found that the method is capable of obtaining an updated model which assimilates
the two sets of data from the FRFs and modal properties. It was also discovered that the
method is more successful in determining the presence of damage on the structure; its
location; and its the extent of damage.
Afrikaans: Skade in strukture kan geYdentifiseer en gekwantifiseer word deur die meting van
frekwensieresponsiefunksies (FRFs) of deur die identifikasie van modale parameters as 'n
basis vir opdatering. Die belangrikste tekortkoming van hierdie metodes is dat as hulle
individueel gebruik word, die metodes wat modale parameters gebruik nie noodwendig die
gemete FRFs voorspel nie, en omgekeerd.
'n Multi-kriterium metode wat die gemete FRFs en die geYdentifiseerde modusse gelyktydig
in 'n optimeringsmodus gebruik, word in hierdie studie ontwikkel. Die Euklidiese norm
van die foutvektor wat resulteer uit die integrasie van die massa- en styfheidsmatrikse van
die eindige-elementmodel en die gemete FRFs, in die bewegingsvergelyking word
geminimecr. Diesclfdc prosedure word dcurgcvoer met gebruik van die gei'dcntifisecrde
modale eienskappe. Die elastisiteitsmodulus van elke element in die eindige-elementmodel
word as ontwerpveranderlikes gebruik.
Die nuwe prosedure word getoets op 'n eenvoudige balk, 'n komplekse balk (met geboorde
gate wat moeilik is om te modelleer) en 'n onreelmatige H-vormige struktuur. Die
effektiwiteit van die multi-kriterium metode is vergelyk met ander metodes wat FRFs en
modale parameters afsonderlik gebruik. Die vergelyking is gedoen deur gebruik te maak
van metodes soos die modale korrelasiekriterium, die koordinaat modale
korrelasiekriterium en die frekwensieresponsiefunksie korrelasiekriterium, 'n nuwe
prosedure wat spesiaal ontwikkel is as deel van hierdie werk. Daar is gevind dat hierdie metode in staat is om 'n opgedateerde model te vind wat die twee
stelle data uit die FRFs en die modale parameters assimileer. Daar is verder gevind dat die
metode meer suksesvol is in die bepaling van die teenwoordigeheid van skade in strukture,
die posisie en omvang van die skade.
