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A multi-stage data-fusion procedure for damage detection of linear systems based on modal strain energy

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Abstract

The use of damage indicators based on changes of the systems’ dynamic properties before and after the occurrence of damage, generally represents a good tool in detecting the presence, the position and also the severity of the damage itself. However, signal noises, difficulties to excite systems for identifying the significant modes of vibrations, particularly the ones more sensible to the damage scenarios and also the presence of multiple damage locations can particularly affect the efficiency of these indicators. In recent years, new algorithms and innovative techniques devoted to improve the efficiency of the classical damage indicators have been carried out in many studies. In this context, the paper presents an approach for damage identification of linear systems developed by combining the use of classical damage indicators based on the modal strain energy (MSE) with a multi-stage data-fusion procedure. In particular, modal strain energy change ratios (MSECR) are evaluated by accounting different sets of modes of vibration. Then, the obtained MSECRs are converted in local decisions and involved in a multi-stage data-fusion process which provides indices able to detect the damage location and its extent. The approach provides a significant improvement of the efficiency of the damage indicators particularly in the presence of noises and multiple damages as shown by the numerical applications reported in the paper.

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Abbreviations

\({\varvec{\Phi}}\) :

Matrix containing the identified modes of vibration of the undamaged system

\({\varvec{\Phi}}^{\text{d}}\) :

Matrix containing the identified modes of vibration of the damaged system

\(\overline{{\varvec{\Phi}}}\) :

Matrix containing the undamaged/damaged couples of sets of modes

\(\varvec{K}_{j}\) :

Elemental stiffness matrix of the jth member composing the undamaged system

\(\varvec{K}\) :

Stiffness matrix of the undamaged system

\(\Delta \varvec{K}\) :

Perturbation of the stiffness matrix of the undamaged system due to the presence of damage

\(\alpha_{p}\) :

Coefficient defining a fractional reduction in the pth elemental stiffness matrix

\(\beta_{jp}\) :

Sensitivity coefficients of the MSEC to damage

NE:

Number of suspected damaged elements

N :

Number of members composing the system

n :

Number of identified modes

J :

Number of members accounted for computing MSEC

\(\lambda_{r}\) :

Frequencies of the system in the undamaged state corresponding to the rth mode

\({\text{MSE}}_{ij}\) :

Elemental MSE of the jth member at the ith mode of vibration for the undamaged system

\({\text{MSE}}_{ij}^{\text{d}}\) :

Elemental MSE of the jth member at the ith mode of vibration for the damaged system

\({\text{MSECR}}_{ij}\) :

Elemental MSE change ratio for the jth member and the ith mode

\({\text{MSECR}}_{j}\) :

Damage indicator based on the MSE and referring to the jth member of the system

\(S_{i}\) :

ith primary source

\(\overline{S}_{i}\) :

ith secondary source

\(m_{i} (S_{i} )\) :

BPA corresponding to the ith primary source

\(m_{i} (\overline{S}_{i} )\) :

BPA corresponding to the ith secondary source

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Authors and Affiliations

  1. Department of Civil and Mechanical Engineering DICeM, University of Cassino and Southern Lazio, via G. Di Biasio 43, 03043, Cassino, FR, Italy

    Ernesto Grande & Maura Imbimbo

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  1. Ernesto Grande
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  2. Maura Imbimbo
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Correspondence to Ernesto Grande.

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Grande, E., Imbimbo, M. A multi-stage data-fusion procedure for damage detection of linear systems based on modal strain energy. J Civil Struct Health Monit 4, 107–118 (2014). https://doi.org/10.1007/s13349-013-0070-3

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  • DOI: https://doi.org/10.1007/s13349-013-0070-3

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