Abstract
In this paper, a damage detection method based on modal parameters, which deals with incomplete measurement, is presented. Intact and damaged structures are modeled using the finite-element method. Damage in structure is assumed as a reduction in elastic modulus. This study utilizes an approximate stiffness matrix of damaged structure to improve the data expansion methods, which is used to complete the incomplete modal parameters of damaged structures. Verification of proposed method is done using a 2D truss and a 2D frame. This method is able to expand the measured data and to solve the sensitivity equation, which depends on complete mode shapes and frequencies of intact and damaged structure, and to detect the damage in the presence of noises, such as measurement and modeling errors. Results show that damage detection using improved data expansion is more accurate and reliable than damage detection using common data expansion.
Similar content being viewed by others
References
Abdo MA-B, Hori M (2002) A numerical study of structural damage detection using changes in the rotation of mode shapes. Sound Vib 251(2):227–239
Araujo dos Santos JV, Mota Soares CM, Mota Soares CA, Pina HLG (2000) A damage identification numerical model based on the sensitivity of orthogonality conditions and least squares techniques. Comput Struct 78(1–3):283–291
Araujo dos Santos JV, Mota Soares CM, Mota Soares CA, Maia NMM (2003) Structural damage identification: influence of model incompleteness and errors. Compos Struct 62(3–4):303–313
Chen HP, Bicanic N (2000) Assessment of damage in continuum structures based on incomplete modal information. Comput Struct 74(5):559–570
Chen HP (2010) Mode shape expansion using perturbed force approach. Sound Vib 329(8):1177–1190
Esfandiari A, Sanayei M, Bakhtiari-Nejad F, Rahai A (2010) Finite element model updating using frequency response function of incomplete strain data. AIAA J 48(7):1420–1433
Farhat C, Hemez FM (1993) Updating finite element dynamic models using an element-by-element sensitivity methodology. Am Inst Aeronaut Astronaut 31(9):1702–1711
Flanigan CC, Freymiller JE (1994) In: Using dynamic expansion to improve test-analysis correlation, 12th international modal analysis conference, Honolulu, Hawaii, Jan 31–Feb 3 1994
Fushun L (2011) Direct mode-shape expansion of a spatially incomplete measured mode by a hybrid-vector modification. Sound Vib 330(18–19):4633–4645
Fushun L, Wenwen Ch, Weiying W (2014) An expansion method dealing with spatial incompleteness of measured mode shapes of beam structures. Appl Math Inf Sci 8(2):651–656
Ghodrati Amiri G, Seyed Razzaghi SA, Bagheri A (2011) Damage detection in plates based on pattern search and genetic algorithms. Smart Struct Syst 7(2):117–132
Guyan RJ (1965) Reduction of stiffness and mass matrices. Am Inst Aeronaut Astronaut 3(2):380
He RS, Hwang SF (2007) Damage detection by a hybrid real-parameter genetic algorithm under the assistance of grey relation analysis. Eng Appl Artif Intell 20(7):980–992
Huang Q, Gardoni P, Hurlebaus S (2012) A probabilistic damage detection approach using vibration-based nondestructive testing. Struct Saf 38:11–21
Khoshnoudian F, Esfandiari A (2011) Structural damage diagnosis using modal data. Sci Iran 18(4):853–860
Kim JT, Stubbs N (1995) Model-uncertainty impact and damage-detection accuracy in plate girder. Struct Eng 121(10):1409–1417
Kim JT, Ryu YS, Cho HM, Stubbs N (2003) Damage identification in beam-type structures: frequency-based method vs mode-shape-based method. Eng Struct 25(1):57–67
Law SS, Chan THT, Wu D (2001) Efficient numerical model for the damage detection of large scale structure. Eng Struct 23(5):436–451
Lim TW (1990) Submatrix approach to stiffness matrix correction using modal test data. Am Inst Aeronaut Astronaut 28(6):1123–1130
Lin RM, Lim MK, Ong JH (1993) Improving finite element models in the higher frequency range using modified frequency response function sensitivity method. Finite Elem Anal Des 15:157–175
Peterson LD, Doebling SW, Alvin KF (2008) Experimental determination of local structural stiffness by disassembly of measured flexibility matrices. J Vib Acoust 120(4):949–957
Petryna YS, Kratzig WB, Stangenberg F (2002) Structural damage: simulation and assessment. In: Computational Structures Technology pp 351–377
Rahai A, Bakhtiari-Nejad F, Esfandiari A (2007) Damage assesment of structure using incomplete measured mode shapes. Struct Control Health Monit 14(5):808–829
Ren W, Roeck G (2002) Structural damage identification using modal data. I: simulation verification. J Struct Eng 128(1):87–95
Ren W, Roeck G (2002) Structural damage identification using modal data. II: test verification. J Struct Eng 128(1):96–104
Ricles JM, Kosmatka JB (1992) Damage detection in elastic structures using vibratory residual forces and weighted sensitivity. Am Inst Aeronaut Astronaut 30(9):2310–2316
Salawu OS (1997) Detection of structural damage through changes in frequency: a review. Eng Struct 19(9):718–723
To WM, Ewins DJ (1991) Non-linear sensitivity analysis of mechanical structures using modal data. Mech Eng Sci 205(13):67–75
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hosseini, M., Khoshnoudian, F. & Esfandiari, A. Improved data expansion method used in damage detection method. J Civil Struct Health Monit 7, 15–27 (2017). https://doi.org/10.1007/s13349-016-0205-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13349-016-0205-4