Damage Localization with SP2E Under Changing Conditions

Wernitz, Stefan; Pache, Dorian; Grießmann, Tanja; Rolfes, Raimund

doi:10.12783/shm2019/32505

Cited by 5 publications

(5 citation statements)

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“…For any controllable and observable LTI system with r deterministic inputs and m outputs, r eigenvalues can be rendered invariant to damage-induced stiffness perturbations of rank m−1 or less. This invariance property is used for damage localization by postulating different stiffness Figure 2: Damage metric statistics for different damage pattern postulates (with pattern 3 enclosing damage) attained with (a) β = v (1) and (a) β = v (2) .…”

Section: Discussionmentioning

confidence: 99%

“…We take a damage pattern as a unit reduction of a single inter-story stiffness and postulate a pattern for each inter-story, hence resulting in six different damage patterns for which rank(δA G ) = 1. The damage localization analysis is, with reference to the discussion on β in Subsection 2.3, conducted in two different settings; one with β = v (1) and one with β = v (2) , where v (i) is the ith right-singular vector of Q. In both settings, the eigenvalue is placed at 0.9κ 1 , where κ 1 is the first open-loop eigenvalue.…”

Section: Numerical Examplementioning

confidence: 99%

“…In particular, the mean and standard deviation of damage metric (29) are provided along with the associated 99% quantile decision threshold. For the first setting, in which β = v (1) , the third inter-story is correctly classified as damaged under H 0 in 95 of the realizations, while the remaining inter-stories are correctly classified as undamaged under H 1 in all 100 realizations. In the second setting, where β = v (2) , inter-stories 1, 2, 5, and 6 are correctly classified as undamaged in all 100 realizations, while the third inter-story is correctly classified as damaged in 99 realizations.…”

Section: Numerical Examplementioning

confidence: 99%

“…A problem in vibration-based damage localization is that the identifiable vibration features carry insufficient information on damage to provide the required level of robustness [1,2]. In the attempt to resolve the robustness problem, different feedback strategies have been adopted from control engineering [3].…”

Section: Introductionmentioning

confidence: 99%

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Perturbation-invariant eigenvalue assignment for statistical damage localization

Ulriksen,

Greś,

Bernal

2024

J. Phys.: Conf. Ser.

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The present paper reviews a recently proposed eigenvalue assignment scheme for structural damage localization. The eigenvalue assignment is, under the assumption of system controllability and observability, formulated with the objective of rendering an eigenspectrum subset invariant to low-rank perturbations in the considered system. Damage localization follows with the perturbations being realized as damage patterns postulated in different subdomains using a model of the system. The damage location can thus be inferred from the damage-induced shifts in the assigned eigenvalues, which, ideally, will be zero when postulating a pattern that entails the physical damage distribution. In real applications, eigenvalue invariance is unattainable due to, among other phenomena, stochastic disturbances, so the localization is conducted by hypothesis testing with the assigned eigenvalues and their uncertainty bounds. The paper reviews the proposed damage localization method and tests its applicability in the context of a numerical example.

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Section: Discussionmentioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

Section: Numerical Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Perturbation-invariant eigenvalue assignment for statistical damage localization

Ulriksen,

Greś,

Bernal

2024

J. Phys.: Conf. Ser.

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“…A commonly encountered challenge in vibration-based damage localization is that the identifiable vibration features carry insufficient information on damage to provide the required level of robustness [1,2]. In the attempt to resolve the robustness problem, different feedback strategies have been adopted from control engineering [3].…”

Section: Introductionmentioning

confidence: 99%

Eigenvector Assignement for Damage Localization With Invariant Eigenvalues

Dahl,

Ulriksen,

Nielsen

2023

10th ECCOMAS Thematic Conference on Smart Structures and Materials

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A recently proposed scheme infers the spatial location of structural damage by interrogating the damage-induced shifts in assigned closed-loop system eigenvalues. The concept is to render the assigned eigenvalues invariant to model-based damage pattern postulates using eigenstructure assignment with left eigenvectors. In an idealized setting, damage is then confined to the pattern for which the damage-induced shifts in the assigned eigenvalues are zero. In practice, invariance is unattainable due to disturbances and the inevitable discrepancy between the physical system and its model representation, thus damage is located when the induced eigenvalue shifts are minimized. This paper explores how the assignment of the associated left eigenvectors affects the methodological robustness and proposes three different eigenvector assignment procedures for promoting it. The first procedure, which constitutes an optimization problem, explicitly maximizes the sensitivity to damage outside the postulated patterns, while the second procedure seeks to maximize the noted sensitivity in a direct setting based on singular value decomposition (SVD). The third procedure, which is also cast as an optimization problem, seeks to promote robustness by minimizing the uncertainties on the assigned eigenvalues. The proposed procedures are tested in a numerical example, and their individual viability, in terms of damage resolution promotion and computational efficiency, is discussed.

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