·Table of Contents ·Materials Characterization and testing | Damage Detection by Laser Vibration MeasurementP.Castellini, G.M.RevelUniversita degli Studi di Ancona - Dipartimento di Meccanica via Brecce Bianche - 60131 Ancona - Italy Contact |
Fig 1: The case study: a panel of fiberglass-epoxy. |
Fig 2: Comparison between the Frequency Response Functions (FRFs) measured over the superficial and the deep defects and the average FRF for the whole structure. |
Fig 3: Representation of the defect in the FE model. |
The data obtained both from the FE model (and later from the experimental tests) were processed using Matlab routines, in order to extract synthetic information about the presence and the characteristics of the defects.
The first step of the process is the organisation of data. In fact, in order to transfer the large amount of data (Spectral response or FRF in each point of the grid) produced by a Scanning Laser Doppler Vibrometer (SLDV), the Universal File Format was used. On the other hand, also data from numerical codes have to be re-arranged. In fact, the FE model produces vibration information in each node of the mesh, which in this case presents a different density across the structure (a fine mesh on the defect, a coarse mesh elsewhere). For such reason the statistical weight of defected and non-defected points is artificially different, and it is difficult a comparison with experimental data obtained, generally, in a regular matrix. For these reason FE spectra have to be interpolated in a regular grid.
The second step is the normalisation of the spectra. The a -trimmed average (a =5%) is calculated, frequency by frequency, for all the points of the structure and the obtained spectrum is used as norm in order to obtain a dimensionless spectrum, as shown in (1):
(1) |
where i=1, 2, ..., 290 denotes the index relative to the node (or to the measurement point for the experimental data).
The FRF_{(i)norm} oscillates usually around a unitary value, if relative to a non-defected point in the structure. If no defects were on the panel, a variation with respect to the unitary level could be due only to different factors of modal participation between different FRFs or to noise in the single measurements.
The a
-trimmed average is employed to have a FRF_{average} similar for defected or non-defected panels, according to the hypothesis of small damages. In fact, this kind of average allows reducing the effects of "extreme" data (i.e. of data significantly dispersed with respect to the average value), and thus of defects, even if some residual effect is present. Because of this reason, theoretically, the FRF_{(i)norm} presents a reduced dependence also by resonance or anti-resonance peaks, and therefore a elevated value should correspond to a high dynamic behaviour, i.e. to a defect.
In Figure 4 examples of normalised spectra of a non-defected point, of a superficial defect and of a deep one are shown. The spectra are computed from experimental simulations.
Fig 4: Comparison among spectra of a non-defected point, of a superficial defect and of a deep defect (experimental data). |
In order to simplify the processing procedure and reduce the amount of data without losses of information, the RMS values in a limited number of frequency bands are calculated, according to (2):
(2) |
Fig 5: RMSFRF_{(i)}(B_{k}) maps computed at different frequency bands by processing FE results (adimensional scale). |
where k is the considered band and D
w
is the integration range. In practice, it is equivalent to reduce the number of spectral lines. In Figure 5 some examples of maps obtained from numerical data at some frequency bands are reported.
It is clear that such RMS values represent a good index of the presence of the defect. In addition, also the depth of the delamination can be extracted: in the maps achieved at lower frequencies the superficial defect is more evident, while at higher frequencies the deeper defect seem to have a higher degree of mobility.
The choice of a wide integration band allows to reduce the effect of the noise, but it may reduce excessively the resolution in the depth assessment. For such purpose, it is possible to state that a bandwidth of 10 kHz represents a good compromise between noise rejection and resolution.
However, this technique, even if allows a nice characterisation of the panel, seems to be not very easy to use, being the discrimination capability related to the analysis of several maps, in each of that only a small part of the information is present. Furthermore, also the nodes positioned close to the driving point are seen as defects.
For such reason a procedure for the detection and characterisation of defects was implemented, based on the observation of just 3 maps, the first representing the damage position, the second one the damage depth, the third one the damage danger.
The RMSFRF_{(i)}(B_{k}) function, defined in (2) can be simply interpolated by a linear fitting using a least square algorithm, obtaining a line representing the general trend of the amplitude values in each band.
As shown in Figure 6, the linear fit represents a valid synthesis of the general trend of the spectrum RMSFRF_{(i)}(B_{k}), concerning both the average amplitude level (i.e. the "mobility energy", which in turn is proportional to the RMS value in the whole frequency band) and the spectral distribution (more energy at higher or lower frequencies, which influences the slope of the line).
Fig 6: The features extraction procedure based on linear fitting (light) of the RMSFRF_{(i)}(B_{k}) functions (dark). |
Fig 7: Example of linear fit results on FE data. |
(3) |
where m
_{(i)} represents the average level for each measurement point, as previously defined.
The joint information from such three maps can be used to spatially locate the delamination (Standard Deviation map) and to characterise its depth (slope map), with a low sensitivity to "noise" induced by the measurement procedure and to large amplitudes in the driving point area (recognised in the average level map). As shown in Figure 8, the results of processing the FE data is very satisfactory. The area where the force is applied is clearly identified by comparing the Standard Deviation and the average level maps: the Standard Deviation is, in fact, not increased in the driving point, as the increment in the amplitude values is constant with frequency.
Fig 8: Maps of Standard Deviation D_{(i) } a), adimensional scale), average value m_{(i)} b), adimensional scale) and slope S_{(i)} c), scale in [1/Hz]) of the linear fit of the results from the FE model. |
Fig 9: Measurement grid: the considered points in the high resolution analysis. | Fig 10: Linear fit of the RMSFRF_{(i)}(B_{k}) functions experimentally measured on each point on the defect (adimensional scale). |
Fig 11a: | Fig 11b: |
Average level m_{(i)} a), adimensional scale) and slope S_{(i)} b), scale in [1/Hz]) of points on the defect surface (numerical data). |
Fig 12: Maps of standard deviation (a, adimensional scale), average level (b, adimensional scale) and slope (c, scale in [1/Hz]) obtained from processing of experimental data. |
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