, Volume 51, Issue 11, pp 2861–2871 | Cite as

Steady state shift damage localization

  • D. BernalEmail author
  • A. Kunwar
Nonlinear Dynamics, Identification and Monitoring of Structures


The accuracy of the identified modal model is the weak link in many vibration based damage localization schemes. This paper presents a localization approach that avoids identification by operating with two frequency domain subspaces, one obtained by Fourier transformation of output measurements and the other from a model of the reference state and a postulated damage distribution. The approach differs from a model updating framework in that only the damage distribution, and not the extent, enters the formulation. The method operates on the premise that the loads are time limited, have an invariant distribution in space and requires that the histories be repeatable, or that the excitation be a single history, in which case repeatability is not necessary. The time histories of the excitation are not used in the technique and therefore need not be known. It is shown that multiple damages can be considered without combinatorics if \(e \ge \kappa\) where e is the number of available actuators and \(\kappa\) is the rank of the change in the transfer matrix due to damage. The constraint on the number of measurements, m, is \(m \ge \kappa .\) The method, designated as the steady state shift damage localization (S3DL) is experimentally tested on an aluminum plate where damage is simulated by mass additions and by an edge cut.


Damage localization Frequency domain Steady state response Harmonic excitation Thin plates 


  1. 1.
    Worden K (1997) Structural fault detection using a novelty measure. J Sound Vib 201:85–101ADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    Sohn H, Law KH (1997) Bayesian probabilistic approach for structural damage detection. Earthq Eng Struct Dyn 26:1259–1281CrossRefGoogle Scholar
  3. 3.
    Lim TM, Kashangaki TA (1994) Structural damage detection of space truss using best achievable eigenvectors. AIAA J 32(5):1049–1057ADSCrossRefGoogle Scholar
  4. 4.
    Lim TW (1995) Structural damage detection using a constrained eigenstructure assignment. J Guid Control Dyn 18(3):411–418ADSCrossRefzbMATHGoogle Scholar
  5. 5.
    Choudhury R, He J (1996) Structural damage location using expanded measured frequency response data. In: Proceedings of the 14th modal analysis conference, IMAC-XIV, Society of Experimental Mechanics, Bethel, CT, pp 934–942Google Scholar
  6. 6.
    Bernal D (2002) Load vectors for damage localization. J Eng Mech 128(1):7–14MathSciNetCrossRefGoogle Scholar
  7. 7.
    Bernal D (2007) Damage localization from the null space of changes in the transfer matrix. AIAA J 45:374–381ADSCrossRefGoogle Scholar
  8. 8.
    Bernal D (2006) Flexibility-based damage localization from stochastic realization results. J Eng Mech 132(6):651–658MathSciNetCrossRefGoogle Scholar
  9. 9.
    Bernal D (2010) Load vectors for damage location in systems identified from operational loads. J Eng Mech 136:31–39CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Civil and Environmental Engineering Department, Center for Digital Signal ProcessingNortheastern UniversityBostonUSA
  2. 2.Civil and Environmental Engineering DepartmentNortheastern UniversityBostonUSA

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