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Structural damage can be detected using frequency response function (FRF) measured by an impact and the corresponding responses. The change in the mechanical properties of dynamic system for damage detection can seldom be estimated using FRF data extracted from a very limited frequency range. Proper orthogonal modes (POMs) from the FRFs extracted in given frequency ranges and their modified forms can be utilized as damage indices to detect damage. The POM-based damage detection methods must be sensitive to the selected FRFs. This work compares the effectiveness of the damage detection approaches taking the POMs estimated by the FRFs within five different frequency ranges including resonance frequency and antiresonance frequency. It is shown from a numerical example that the POMs extracted from the FRFs within antiresonance frequency ranges provide more explicit information on the damage locations than the ones within resonance frequency ranges.

Structural damage is detected based on the variation in dynamic responses due to the local change of physical properties at damage region. There have been many attempts to provide the accurate damage detection methods related to structural health monitoring. Many indices like mode shapes, mode shape curvature, frequency response function (FRF) curvature, modal strain energy, and so forth to evaluate the structural performance have been utilized [

One of the measurement data types is FRF data set. The FRF can be estimated by impact hammer test and the energy is propagated from the impact point. The FRF data measured from experimental work are utilized to estimate the characteristics of dynamic system. It indicates that the measured FRF data set can be used as an index to detect damage. Phani and Woodhouse [

Proper orthogonal decomposition (POD) analysis captures most of the kinetic energy in the least number of modes possible. Its application is similar to that of Fourier analysis, except that it normally requires far less modes to represent the system within a desired level. POMs extracted from the FRF data in a prescribed frequency range are utilized as an index to recognize the existence of damage. The POD method has been widely applied in various fields of engineering and science. Ramanamurthy et al. [

The parameter matrices as well as damage region of dynamic systems can be predicted using FRF data sets within a specific frequency range rather than at a specific frequency. The FRF data sets are transformed to the POM to represent the principal axes of inertia formed by the distribution of data on the modal coordinate curve. The POM can be changed depending on the FRF data sets extracted from full sets of FRFs. Beginning with the FRFs measured from the dynamic finite element model, this work investigates the sensitivity of the damage detection method using the POMs to be estimated from the FRFs corresponding to five different frequency ranges including resonance frequency and antiresonance frequency. A numerical example compares the sensitivity of the damage detection method depending on the extracted FRFs.

The dynamic behavior of a structure, which is assumed to be linear and approximately discretized for

Frequency response function

For the case of a displacement response at station

The FRF data,

The measured FRFs can be reduced by the POD and are transformed to the POD to extract extremal data set. The POD technique is effective method because basis elements are formed in an optimal way. The POD basis collects snapshots. The FRFs of a system are generated by forcing the system.

Let the

The POMs may be used as a basis for the decomposition of

The slope of the POM data corresponding to two adjacent nodes from Figure

Slope of POM.

Damage introduced into the flexural beam to be modeled as finite elements also leads to local changes in the shape of POM curvature obtained by POMs. The curvature at each location

A numerical experiment was performed in detecting the damage in a finite element model of a three-span continuous beam shown in Figure

A three-span continuous beam structure model.

The damage leads to the local stiffness deterioration and the variation of the natural frequencies. Its existence can be recognized through the comparison with the natural frequencies at the undamaged state. The first three natural frequencies of the damaged dynamic system exist at 24.67 Hz, 40.89 Hz, and 69.69 Hz, respectively. Figure

Dynamic characteristics of the system: (a) mode shapes and (b) FRF curve.

This numerical study investigates the sensitivity of the damage detection depending on the FRFs extracted in the neighborhood of two resonance frequency ranges at points (B) and (D) in Figure

Frequency ranges of the extracted FRFs.

Location | (A) | (B) | (C) | (D) | (E) |
---|---|---|---|---|---|

Selected frequencies | 10 Hz |
24.67 Hz |
34.25 Hz |
40.89 Hz |
50.93 Hz |

Less than first resonance | Resonance | Antiresonance | Resonance | Antiresonance |

Figure

POM curves using noise-free FRFs within the five different frequency ranges: (a) beam 1, (b) beam 2, and (c) beam 3.

Figure

POM curvature curves using noise-free FRFs: (a) beam 1, (b) beam 2, and (c) beam 3.

Figures

POM curvature curves using FRFs in the region (A) containing 1% external noise: (a) beam 1, (b) beam 2, and (c) beam 3.

POM curvature curves using FRFs in the region (B) containing 1% external noise: (a) beam 1, (b) beam 2, and (c) beam 3.

POM curvature curves using FRFs in the region (C) containing 1% external noise: (a) beam 1, (b) beam 2, and (c) beam 3.

POM curvature curves using FRFs in the region (D) containing 1% external noise: (a) beam 1, (b) beam 2, (c) beam 3.

POM curvature curves using FRFs in the region (E) containing 1% external noise: (a) beam 1, (b) beam 2, and (c) beam 3.

Figure

Figure

Figure

This work compared the damage detection methods utilizing three different damage indices depending on the extracted FRFs within five different frequency ranges including resonance frequency and antiresonance frequency. It is shown from a numerical example that the damage detection method can be explicitly and widely carried out by the three damage indices of the POM corresponding to the first POV to extract the FRFs in the first and third antiresonance frequencies despite the external noise. The POM-based approaches using the FRFs extracted in the other ranges should be sensitive to the external noise and can be utilized by close examination of the POM curve.

The authors declare that they have no conflicts of interest.

This research is supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (NRF-2016R1D1A1A09918011).