Octonion structural response vector and potential structural damage identification method

Abstract

A promising method based on octonion structural response vector is proposed for the identification of structural damages according to the database acquired via long-term structural health monitoring. An octonion structural response vector consists of eight elements: seven for structural responses, including normalized static strains at specific positions and natural frequencies of a structure, and one for null. For a perfect structure the octonion structural response vector is a point in the phase plane, whereas for developing damages in the structure the octonion structural response vector manifests itself as a definite trajectory in the phase plane. Therefore, the development of damages in a structure could be investigated by analyzing the trajectory of octonion structural response vector obtained from the data of a long-term structural health monitoring or scheduled routine structural examinations. To demonstrate the implementation of this octonion structural response vector-based method, a two-dimensional numerical model of a simply-supported beam was built with crack-like damages of given location and depth. The octonion structural response vector of the beam corresponding to each state of damages was calculated to draw the trajectory related to the developing damages in the phase plane. The results show that the trajectories are significantly different for different devolvement of damages, even when the damages are in good symmetry. It indicates that the octonion structural response vector-based method recommended in the article could be effective to identify damages of structures using data of structures from long-term structural health monitoring or routine scheduled examinations.

Keywords

Structural damage identification octonion structural response vector structural health monitoring numerical model simply-supported beam

Get full access to this article

View all access options for this article.

References

Abdel Wahab

de Roeck

(1999) Damage detection in bridges using modal curvatures: application to a real damage scenario. Journal of Sound and Vibration 226(2): 217–235.

Baez

(2002) The octonions. Bulletin American Mathematical Society 39: 145–205.

Bagchi

Humar

(2010) Model-based damage identification in a continuous bridge using vibration data. Journal of Performance of Constructed Facilities, ASCE 24(2): 148–158.

Barai

Pandey

(1995) Vibration signature analysis using artificial neural networks. Journal of Computing in Civil Engineering 9(4): 259–265.

Baruch

(1978) Optimization procedure to correct stiffness and flexibility matrices using vibration tests. AIAA Journal 16(11): 1208–1210.

Berman

Nagy

(1983) Improvement of large analytical model using test data. AIAA Journal 21(8): 1168–1173.

Carden

Fanning

(2004) Vibration based condition monitoring: a review. Structural Health Monitoring 3: 355–377.

Cawley

Adams

(1979) The location of defects in structures from measurements of natural frequencies. Journal of Strain Analysis 14(2): 47–47.

Chen

Yang

JCS

(1995) Neural network for structure dynamic model identification. Journal of Engineering Mechanics 121(12): 1377–1381.

10.

Chen

Garba

(1980) Analytical model improvement using modal test results. AIAA Journal 18(6): 684–690.

11.

Chen

Swamidas

ASJ

(1994) Dynamic characteristics and modal parameters of a plate with a small growing surface crack. Proceedings of the 12th International Modal Analysis Conference, Honolulu, HI; USA. 1994. 1155–1161.

12.

Doebling SW, Farrar CR, Prime MB, et al. (1996). Damage identification and health monitoring of structural and mechanical systems from changes in their vibration characteristics: a literature review. Los Alamos National Laboratory Report, LA-13070-MS.

13.

Doebling

Farrar

Prime

(1998) A summary review of vibration-based damage identification methods. The Shock and Vibration Digest 3: 92–105.

14.

Dyke

Koh

(2007) Structural health monitoring for flexible bridge structures using correlation and sensitivity of modal data. Computers and Structures 85: 117–130.

15.

Elkordy

Chang

Lee

(1993) Neural networks trained by analytically simulated damage states. Journal of Computing in Civil Engineering 7(2): 130–145.

16.

Engl

Hanke

Neubauer

(1996) Regularization of Inverse Problems. Dordrecht: Kluwer.

17.

Fabrizio

Danilo

(2000) Damage detection in beam structures based on frequency measurements. Journal of Engineering Mechanics 126(7): 761–768.

18.

Fan

Qiao

(2011) Vibration-based damage identification methods: a review and comparative study. Structural Health Monitoring 10(1): 83–111.

19.

Farrar

Doebling

Nix

(2001) Vibration-based structural damage identification. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 359: 131–149.

20.

Friswell

Mottershead

(1999) Finite Element Model Updating in Structural Dynamics. London: Kluwer Academic Publishers, pp. 63–71.

21.

Gulal

Erdogan

Aykut

(2011) The use of SISO ARX models in the determination of the damage to dams. International Journal of Damage Mechanics 20(7): 979–1001.

22.

Haug

Choi

(1984) Structural design sensitivity analysis with generalized global stiffness and mass matrices. AIAA Journal 22(9): 1299–1303.

23.

Hearn

Testa

(1991) Modal analysis for damage detection in structures. Journal of Structural Engineering ASCE 117(10): 3042–3063.

24.

Hemez FM (1993). Theoretical and experimental correlation between finite element models and modal tests in the context of large flexible space structures. Ph D Dissertation, Department of Aerospace Engineering Sciences, University of Colorado, Boulder, CO.

25.

Wang

Fukunaga

(2001) Damage assessment of structures using modal test data. International Journal of Solids and Structures 38(18): 3111–3126.

26.

Kwatra

Aggarwal

(2007) Damage detection for framed RCC buildings using ANN modeling. International Journal of Damage Mechanics 16: 457–472.

27.

Kaouk

Zimmerman

(1993) Evaluation of the minimum rank updating in damage detection: an experimental study. Proceedings of the 11th International Modal Analysis Conference, Kissimmee, FL; USA. 1061–1067.

28.

Kaouk

Zimmerman

(1994) Structural damage assessment using a generalized minimum rank updating theory. AIAA Journal 32(4): 836–842.

29.

Kirkegaard

Rytter

(1994) Use of neural for damage assessment in a steel mast. Proceedings of the 12th International Modal Analysis Conference, Honolulu, HI; USA. 1128–1134.

30.

Kiran

Bogdan

(2008) Multiple augmentations of nonlinear systems and generalized minimum rank perturbations for damage detection. Journal of Sound and Vibration 316: 101–121.

31.

Kabe

(1985) Stiffness matrix adjustment using mode data. AIAA Journal 23(9): 1431–1436.

32.

Lam

Wong

(1998) Localization of damaged structural connections based on experimental modal and sensitivity analysis. Journal of Sound and Vibration 210(1): 91–115.

33.

Leath

Zimmerman

(1993) Analysis of neural network supervised training with application to structural damage detection: damage and control of large structures. Proceedings of the 9th VPI & SU Symposium, Blacksburg, Virginia; USA. 583–594.

34.

Messina

Williams

Contursi

(1998) Structural damage detection by a sensitivity and statistical-based method. Journal of Sound and Vibration 216(5): 791–808.

35.

Norris

Meirovitch

(1989) On the problem of modeling for parameter identification in distributed structures. International Journal for Numerical Methods in Engineering 28: 2451–2463.

36.

Parloo

Guillaume

Van

(2003) Damage assessment using mode shape sensitivities. Mechanical Systems and Signal Processing 17(3): 499–518.

37.

Pandey

Biswas

(1991) Damage detection from changes in curvature mode shapes. Journal of Sound and Vibration 145(2): 321–332.

38.

Rezos

Aspragathos

Dimarogonas

(1990) Identification of crack location an magnitude in a cantilever beam from the vibration modes. Journal of Sound and Vibration 138(3): 381–388.

39.

Rytter A (1993). Vibrational based inspection of civil engineering structures. PhD Dissertation, Department of Building Technology and Structural Engineering, Alborg University, Denmark.

40.

Qiao

Lestari

(2007) Curvature mode shape-based damage detection in composite laminated plates. Composite Structures 80(3): 409–428.

41.

Sahin

Shenoi

(2003) Quantification and location of damage in beam like structures by using artificial neural networks with experimental validation. Engineering Structures 25: 1785–1802.

42.

Salawu

(1997) Detection of structural damage through changes in frequency: a review. Engineering Structure 19(9): 718–723.

43.

Shi

Law

Zhang

(2000) Damage localization by directly using incomplete mode shapes. Journal of Engineering Mechanics ASCE 126(6): 656–660.

44.

Soheil S (2003). Structure health monitoring and detection of progressive and existing damage using artificial neural networks based system identification. PhD Dissertation, North Carolina State University.

45.

Sohn HS, Farrar CR, Hemez FM, et al. (2003). A review of structural health monitoring literature: 1996–2001. Los Alamos National Laboratory Report, LA-13976-MS.

46.

Song

Zhang

(1986) The application of the time domain method in strain modal analysis. Proceedings of the 4th International Modal Analysis Conference. Union College, USA. 1986. 31–37.

47.

Szewczyk

Hajela

(1994) Damage detection in structures based on feature-sensitive neural networks. ASCE Journal of Computing in Civil Engineering 8(2): 163–178.

48.

Tang

Luo

Liu

(2010) Structural response vector——A possible new method for structure damage identification. International Symposium on Reliability Engineering and Risk Management, Shanghai; China. 486–491.

49.

Trujillo

(1987) Application of dynamic programming to the general inverse problem. International Journal on Numerical Methods in Engineering 23: 613–624.

50.

Tsang

(1990) Use of dynamic strain measurements for the modeling of structures. Proceedings of the 8th International Modal Analysis Conference 2. Union College & SEM, USA, 1246–1251.

51.

Venkatasubramanian

Chan

(1989) A neural network methodology for process fault diagnosis. Journal of AICHE 35(12): 1993–2002.

52.

Wang

Fukunaga

(2001) Structural damage identification using static test data and changes in frequencies. Engineering Structures 23(6): 610–621.

53.

West

(1984) Illustration of the use of modal assurance criterion to detect structural changes in an orbiter test specimen. Proceedings of the Air Force Conference on Aircraft Structural Integrity, California; USA. 1–6.

54.

Ghaboussi

Garrett

(1992) Use of neural networks in detection of structural damage. Computers &Structures 42(2): 649–659.

55.

Xia

Hao

(2003) Statistical damage identification of structures with frequency. Journal of Sound and Vibration 263(4): 853–870.

56.

Miles

(1995) Nondestructive evaluation of the structural damage based on the strain distribution information. Proceedings of Smart Structures and Materials 1995. USA, SPIE, 216–226.

57.

Yan

Cheng

(2007) Development in vibration-based structural damage detection technique. Mechanical Systems and Signal Processing 21(5): 2198–2211.

58.

Zhang QW (1999). Model updating and damage identification of bridge. PhD Dissertation, Tongji University, Shanghai.

59.

Zimmerman

Kaouk

(1994) Structural damage detection using a minimum rank updating theory. Journal of Vibration and Acoustics 116: 222–231.