Closed-loop load vectors for structural damage localization

Martin Dalgaard Ulriksen*, Martin Jepsen, Dionisio Bernal

*Corresponding author for this work

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review


The null vectors of a rank-deficient transfer matrix perturbation contain information on the spatial distribution of the perturbation. This property constitutes the basis of the well-established Dynamic Damage-Locating Vector (DDLV) method, which facilitates localization of stiffness-related damage in dynamical systems. The DDLV method operates by applying the null vectors of the transfer matrix perturbation – now referred to as DDLVs – as loads to the considered system, whereby damage will be confined to the subdomain exhibiting rigid-body motion in steady state. In real systems, where disturbances will render the transfer matrix perturbation non-singular, the DDLVs must be extracted from a quasi-null space, and this will impair the contrast between undamaged and damaged subdomains. The present paper proposes a closed-loop formulation of the DDLV method to enhance the localization robustness by improving the conditioning of the linear map that infers the damage location. The closed-loop formulation, which is feasible for minimum-phase systems where open-loop input–output data can be collected prior and posterior to damage formation, is implemented virtually and does not, therefore, impose any practical overhead on the original DDLV method. Numerical examples demonstrate how the proposed closed-loop formulation can lead to significant damage localization improvement compared to the original method.

Original languageEnglish
Article number110321
JournalMechanical Systems and Signal Processing
Number of pages11
Publication statusPublished - Aug 2023


  • Damage localization
  • Structural health monitoring
  • Virtual output feedback


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