Damage assessment through changes in mode shapes due to non-proportional damping

Iezzi, Fabrizio; Spina, Daniele; Valente, C.

doi:10.1088/1742-6596/628/1/012019

Cited by 12 publications

(9 citation statements)

References 12 publications

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“…To this aim, the amount of complexity of mode shapes is evaluated via a non‐negative scalar function (a sort of norm) allowing to follow the damage evolution path. Resorting to the results in Iezzi et al, 28 for discrete n degrees‐of‐freedom systems the following complexity indexes I h , h = 1, 2, … , 5 are eligible and effective for localised damage (| • | and ‖ • ‖ stand for absolute value and Euclidean norm, respectively): modal polygons 38

I_{1} = true \sum_{i = 1}^{n} \frac{A_{i}}{n A_{m a x}}, A_{m a x} = n \cos ((), \frac{π}{n}) \sin ((), \frac{π}{n}),

where A i is the area enclosed by the polygon representing the modal components of U i , L in the complex plane, whereas A max is the maximum potential area of modal polygons; phase differences 38

I_{2} = true \sum_{i = 1}^{n} \frac{φ_{i, m a x} - φ_{i, m i n}}{n π}

with φ i the phase angles of the displacement normalised i th mode and subscripts denoting maximum and minimum value; the φ i span the first quadrant of Gauss' plane and are the phase angles of the vectors | Re ( U i , L ) | + ı | Im ( U i , L )|; modal collinearity 32

I_{3} = true \sum_{i = 1}^{n} \frac{1}{n} \frac{false| R e {false({boldU}_{i, L} false)}^{T} I m false({boldU}_{i, L} false) false|}{\sqrt{false[R e {false({boldU}_{i, L} false)}^{T}}}

…”

Section: Governing Equationsmentioning

confidence: 90%

“…To this aim, the amount of complexity of mode shapes is evaluated via a non-negative scalar function (a sort of norm) allowing to follow the damage evolution path. Resorting to the results in Iezzi et al, 28 for discrete n degrees-of-freedom systems the following complexity indexes I h , h = 1, 2, … , 5 are eligible and effective for localised damage (j • j and ‖ • ‖ stand for absolute value and Euclidean norm, respectively):…”

Section: Modal Complexity For Damage Detectionmentioning

confidence: 99%

“…Nevertheless, dissipative properties are rarely adopted to identify the presence of damage or for structural health monitoring purposes. On this topic, Kawiecki 27 can be considered a pioneering work; another recently published proposal exploring this basic principle is by Iezzi et al 28 Anyway, these works are mainly focused on detecting the presence of damages. Some attempts dedicated to non‐proportional damping identification, although not specifically related to damages, are reported in Link et al, 29 where a method based on model updating is applied to a finite element scheme.…”

Section: Introductionmentioning

confidence: 99%

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Dynamic damage identification using complex mode shapes

Lofrano

Paolone

Ruta

2020

Struct Control Health Monit

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Damage, be it a material or a geometric degradation, modifies some features of the response foreseen by the original structural design. These variations, once the dependence on the damage causing them is established, can be used for identification purposes. In the literature, vibration-based approaches usually compare some responses of linear elastic structures with dissipative properties that are assumed proportional to the mass and stiffness measures. However, such an assumption is reasonable for new, undamaged structures, but can be unreliable in existing, potentially damaged structures, particularly for damages localised in narrow areas. The eigenmodes of a proportionally damped system can be reduced to the real ones of the relevant ideal undamped system. On the other hand, non-proportional damping exhibits complex eigenmodes that cannot be reduced to those of the ideal, or of the proportionally damped, structure. Thus, we may assume the complexity of the eigenmodes as a measure of nonproportional damping, hence of damage. On this basis, some contributions in the literature verified the relationship among presence of damage and amount of complexity. Here, we propose a perturbation approach and an objective function able to identify presence, location and amplitude of localised damages, intended as sources of non-proportionality in viscously damped linear systems. A prototype naturally discrete structure with four degrees-of-freedom is chosen to test and show capability and accuracy of the proposed method.

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I_{1} = true \sum_{i = 1}^{n} \frac{A_{i}}{n A_{m a x}}, A_{m a x} = n \cos ((), \frac{π}{n}) \sin ((), \frac{π}{n}),

where A i is the area enclosed by the polygon representing the modal components of U i , L in the complex plane, whereas A max is the maximum potential area of modal polygons; phase differences 38

I_{2} = true \sum_{i = 1}^{n} \frac{φ_{i, m a x} - φ_{i, m i n}}{n π}

I_{3} = true \sum_{i = 1}^{n} \frac{1}{n} \frac{false| R e {false({boldU}_{i, L} false)}^{T} I m false({boldU}_{i, L} false) false|}{\sqrt{false[R e {false({boldU}_{i, L} false)}^{T}}}

…”

Section: Governing Equationsmentioning

confidence: 90%

Section: Modal Complexity For Damage Detectionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Dynamic damage identification using complex mode shapes

Lofrano

Paolone

Ruta

2020

Struct Control Health Monit

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show abstract

“…As specified in [12][13][14][15][16] it is known that the local damage occurring between two lumped mass elements causes a discontinuity in the difference between the damaged and undamaged eigenvectors. The relation between the damage index vector { , } and the normalized ′th mode shown in Eq.…”

Section: The Cases Of Unit Pulse and White Noise Input Excitationsmentioning

confidence: 99%

The inner product vector as an output-only cross-correlation-based feature to structural damage assessment

Morgantini¹,

Betti²

2020

J. vibroeng.

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This paper presents a structural damage assessment method that relies on a crosscorrelation-based damage sensitive feature known as Inner Product Vector (IPV). Such a feature is extracted from the dynamic response measured at different locations within a structure. Previous investigations on the use of the IPV in a damage detection framework were conducted through laboratory tests by manipulating the excitation source in an input-output approach. In this paper, a new output-only approach has been developed to extract the Inner Product Vector only from the structural response time histories without knowledge of the input excitation. This is a more realistic scenario in structural health monitoring applications where it is difficult (in some cases, impossible) to monitor the external forces. The new estimation of the IPV is accomplished by taking the cross-correlations between filtered contributions to the overall structural response. It is shown how the elements of the IPV are affected by changes of the structural properties induced by damage and how effective the proposed approach is in the presence of external disturbances. The proposed approach has been proven to be very effective in dealing with dense sensor networks requiring large computational efforts. Numerical and experimental tests have been performed to address the reliability of the proposed damage index as a damage sensitive feature in an output-only framework.

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“…Based on these considerations, over the last decades several contributions have spread in the literature trying to verify the relationship between damage and modal complexity in order to exploit this information for structural health monitoring of existing artefacts. Worth of mention are the pioneering work of Kawiecki [18], who tried to use the modal damping characteristics of a tested structure for damage detection; the investigations carried out by Iezzi et al [22], [23], [24], who applied and validated the effectiveness of a measurable complexity index to detect the presence of damage in framed structures having a typical "shear-type" behaviour; the study of Masciotta et al [14], who embarked on the analysis of the real and imaginary components of complex eigenvectors for damage localization; and the very recent study of Lofrano et al [21], who proposed a numerical approach based on a perturbation method to detect, locate and quantify the damage in framed structures by exploiting state-of-the-art complexity indices. Despite the scientific robustness of the developed approaches and the consensus reached on the pivotal role that complex eigenmodes can play as a measure of structural damage, the applicative counterparts have shown some limitations.…”

Section: Introductionmentioning

confidence: 99%

Tracking the variation of complex mode shapes for damage quantification and localization in structural systems

Masciotta

Pellegrini

2022

Mechanical Systems and Signal Processing

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Real structures' mode shapes estimated by modal analysis techniques have a common feature: in most cases they are complex, and this complexity can derive from nonproportional damping, nonlinearities, mass loading effects, high modal density and localized damage, among others.Starting from the contributions available in the literature, the present paper investigates, from a numerical and experimental point of view, the correlation existing between localized damage and variation of global modal complexity indices conventionally employed to quantify the nonproportionality of damping in structural systems. Finally, driven by the inferences made through numerical and experimental test cases by tracking the variation of complex modes over multiple and progressive damage scenarios, a new index for damage localization and quantification is formulated and validated against real data.

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Damage assessment through changes in mode shapes due to non-proportional damping

Cited by 12 publications

References 12 publications

Dynamic damage identification using complex mode shapes

Dynamic damage identification using complex mode shapes

The inner product vector as an output-only cross-correlation-based feature to structural damage assessment

Tracking the variation of complex mode shapes for damage quantification and localization in structural systems

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