A multiple criterion updating method for damage detection on structures

Abstract

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.