Uncertainty analysis of strain modal parameters by Bayesian method using frequency response function

  • Xu Li  (徐丽)Email author
  • Yi Weijian  (易伟建)
  • Zhihua Yi  (易志华)


Structural strain modes are able to detect changes in local structural performance, but errors are inevitably intermixed in the measured data. In this paper, strain modal parameters are considered as random variables, and their uncertainty is analyzed by a Bayesian method based on the structural frequency response function (FRF). The estimates of strain modal parameters with maximal posterior probability are determined. Several independent measurements of the FRF of a four-story reinforced concrete frame structural model were performed in the laboratory. The ability to identify the stiffness change in a concrete column using the strain mode was verified. It is shown that the uncertainty of the natural frequency is very small. Compared with the displacement mode shape, the variations of strain mode shapes at each point are quite different. The damping ratios are more affected by the types of test systems. Except for the case where a high order strain mode does not identify local damage, the first order strain mode can provide an exact indication of the damage location.


frequency response function uncertainty strain mode Bayesian method local damage damage detection concrete frame 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Beck JL and Au Siu-Kui (2002), “Bayesian Updating of Structural Models and Reliability Using Markov Chain Monte Carlo Simulation,” Journal of Engineering Mechanics, 128(4):380–391.CrossRefGoogle Scholar
  2. Beck JL and Katafygiotis LS (1998), “Updating Models and Their Uncertainties I: Bayesian Statistical Framework,” Journal of Engineering Mechanics, 24(4): 455–461.Google Scholar
  3. Ching Jiany and Beck JL (2004), “New Bayesian Model Updating Algorithm Applied to a Structural Health Monitoring Benchmark,” Structural Health Monitoring, 3(4):313–332.CrossRefGoogle Scholar
  4. Doebling SW and Farrar CR (2000), “Estimation of Statistical Distributions For Modal Parameters Identified From Averaged Frequency Response Function Data,” Los Alamos National Laboratory, Scholar
  5. Doebling SW, Farrar CR and Goodman RS (1997), “Effects of Measurement Statistics on the Detection of Damage in the Alamosa Canyon Bridge,” Los Alamos National Laboratory, Scholar
  6. Dong Cong (2001), The Theory and Application of Present-day Structure System Reliability, Science Press, Beijing, China. (in Chinese)Google Scholar
  7. Edwin Reynders, Guido De Roeck, Pelin Gundes Bakir, et al. (2007), “Damage Identification on the Tilff Bridge by Vibration Monitoring Using Optical Fiber Strain Sensors,” Journal of Engineering Mechanics, 133(2): 185–193.CrossRefGoogle Scholar
  8. Elkordy MF, Chang KC and Lee GC (1994), “Application of Neural Networks in Vibrational Signature Analysis,” Journal of Engineering Mechanics, 120(2): 252–265.CrossRefGoogle Scholar
  9. Fu Zhifang and Hua Hongxing (2000), Modal Analysis Theory and Practice, Shanghai Jiao Tong University Press, Shanghai, China. (in Chinese)Google Scholar
  10. Herlufser H (1984), Dual Channel FFT Analysis (Part II), Technical Review No.2. Denmark: Brüel & Kjær.Google Scholar
  11. Katafygiotis LS and Yuen Ka-Veng (2001), “Bayesian Spectral Density Approach for Modal Updating Using Ambient Data,” Earthquake Engineering and Structural Dynamics, 30:1103–1123.CrossRefGoogle Scholar
  12. Paez TL and Hunter NF (1998). “Statistical Series: Part-5: Fundamental-concepts of the Bootstrap for Statistical Analysis of Mechanical Systems,” Experimental Techniques, 22(3):35–38.Google Scholar
  13. Papadimitriou C, Beck JL and Katafygiotis LS (1997), “Asymptotic Expansions for Reliability and Moments of Uncertain Systems,” Journal of Engineering Mechanics, 123(12): 1219–1229.CrossRefGoogle Scholar
  14. Vanik MW, Beck JL and Au SK (2000), “Bayesian Probabilistic Approach to Structural Health Monitoring,” Journal of Engineering Mechanics, 126(7):738–745.CrossRefGoogle Scholar
  15. Wang Baisheng, Ni YQ and Ko JM (2001), “Numerical Study of Damage Localization for TSING MA Bridge Deck,” China Civil Engineering Journal, 34(3): 67–73. (in Chinese)Google Scholar
  16. Yao GC, Chang KC and Lee GC (1992), “Damage Diagnosis of Steel Frames Using Vibrational Signature Analysis,” Journal of Engineering Mechanics, ASCE, 118(9):1949–1961.Google Scholar
  17. Yi Weijian, Wu Gaolie and Xu Li (2006), “A Study on the Uncertainty of Model Parameters by Bayesian Method,” Chinese Journal of Computational Mechanics, 23(6): 700–705. (in Chinese)Google Scholar
  18. Yuen Ka-Veng and Katafygiotis LS (2001), “Bayesian Time-domain Approach for Modal Updating Using Ambient Data,” Probabilistic Engineering Mechanics, 16: 219–231.CrossRefGoogle Scholar
  19. Yuen Ka-Veng and Katafygiotis LS (2002), “Bayesian Modal Updating using Complete Input and Incomplete Response Noisy Measurements,” Journal of Engineering Mechanics, 128(3):340–350.CrossRefGoogle Scholar
  20. Zhou Xianyan and Shen Pusheng (1997), “Study of Damage Assessment of Concrete Structures by Strain Model Method,” Journal of Hunan University (Natural Science), 24(5): 69–74. (in Chinese)Google Scholar

Copyright information

© Institute of Engineering Mechanics, China Earthquake Administration 2007

Authors and Affiliations

  • Xu Li  (徐丽)
    • 1
    • 2
    Email author
  • Yi Weijian  (易伟建)
    • 3
  • Zhihua Yi  (易志华)
    • 4
  1. 1.Beijing University of TechnologyBeijingChina
  2. 2.Guangzhou UniversityGuangzhouChina
  3. 3.Hunan UniversityChangshaChina
  4. 4.City College of New YorkUSA

Personalised recommendations