Damage Quantification from the Column Space of Flexibility Changes

The deflection of the beam estimated from modal flexibility matrix (MFM) indirectly is used in structural damage detection due to the fact that deflection is less sensitive to experimental noise than the element in MFM. However, the requirement for mass-normalized mode shapes (MMSs) with a high spatial resolution and the difficulty in damage quantification restricts the practicability of MFM-based deflection damage detection. A damage detection method using the deflections estimated from MFM is proposed for beam structures. The MMSs of beams are identified by using a parked vehicle. The MFM is then formulated to estimate the positive-bending-inspection-load (PBIL) caused deflection. The change of deflection curvature (CDC) is defined as a damage index to localize damage. The relationship between the damage severity and the deflection curvatures is further investigated and a damage quantification approach is proposed accordingly. Numerical and experimental examples indicated that the presented approach can detect damages with adequate accuracy at the cost of limited number of sensors. No finite element model (FEM) is required during the whole detection process.

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The Octagonal-Girder Four-Column Space Frame

Transactions of the American Society of Civil Engineers ◽

10.1061/taceat.0007290 ◽

1956 ◽

Vol 121 (1) ◽

pp. 995-1021

Author(s):

Paul C. Disario ◽

John S. Podolan ◽

Nicholas A. Weil

Keyword(s):

Space Frame ◽

Column Space

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Multiscale Modeling of Heterogenous AC and Damage Quantification

Airfield and Highway Pavements 2021 ◽

10.1061/9780784483503.006 ◽

2021 ◽

Author(s):

Zafrul Khan ◽

Rafiqul Tarefder

Keyword(s):

Multiscale Modeling ◽

Damage Quantification

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All about the ⊥ with its applications in the linear statistical models

Open Mathematics ◽

10.1515/math-2015-0005 ◽

2015 ◽

Vol 13 (1) ◽

Cited By ~ 4

Author(s):

Augustyn Markiewicz ◽

Simo Puntanen

Keyword(s):

Statistical Models ◽

Inner Product ◽

Real Matrix ◽

Inner Products ◽

Column Space ◽

The Matrix ◽

Linear Statistical Models ◽

Extensive List

Abstract For an n x m real matrix A the matrix A⊥ is defined as a matrix spanning the orthocomplement of the column space of A, when the orthogonality is defined with respect to the standard inner product ⟨x, y⟩ = x'y. In this paper we collect together various properties of the ⊥ operation and its applications in linear statistical models. Results covering the more general inner products are also considered. We also provide a rather extensive list of references

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