sti ening stringers of angle section run along the length of the sheet. The tests used ... Damage was simulated by a Saw Cut in the outside stringer 125mm from.
EXPERIMENTAL VALIDATION OF TWO STRUCTURAL HEALTH MONITORING METHODS Keith Worden, Graeme Manson, Robin Wardle & Wieslaw Staszewski Dynamics Research Group Department of Mechanical Engineering University of Sheeld UK
David Allman
Aero-Structures Department Mechanical Sciences Sector DERA Farnborough UK
SUMMARY The object of this study is to experimentally validate two approaches to structural health monitoring using a stiened panel which simulates an aircraft wingbox. The rst analysis uses Novelty Detection based on transmissibility FRFs. The FRFs from normal condition are used to construct a novelty detector and the damage threshold for unambiguous detection is established. The second experiment involves a top surface modal analysis for each stage of damage. The natural frequencies and modeshapes are extracted for each level of damage and modal damage indicators are computed at each stage of damage in order to detect and locate.
DAMAGE IDENTIFICATION: THE FOUR LEVELS The problem of damage detection can be regarded as a hierarchical structure (Rytter,Cempel):
Level 1. (DETECTION) The method gives a qualitative indication that damage might be present in the structure. Level 2. (LOCALISATION) The method gives information about the probable position of the damage. Level 3. (ASSESSMENT) The method gives an estimate of the extent of the damage. Level 4. (PREDICTION) The method oers information about the safety of the structure e.g. estimates a residual life.
NOVELTY DETECTION In terms of the detection problem (level 1), recent work has looked at novelty or anomaly detection. The philosophy of the approach is to establish a description of normality using features representing the undamaged condition of the structure and then test for abnormality or novelty when new data becomes available. There are numerous dierent methods of novelty detection. These include: Simple distance measures, outlier analysis (Basseville,Worden) Probability density estimation (Gaussian mixture models and Parzen windows) (Bishop, Tarassenko) Articial Neural Networks (Roberts, Pomerleau, Worden) Wavelet analysis (Staszewski)
The method used here will be outlier analysis.
OUTLIER ANALYSIS I A discordant outlier in a data set is an observation that is surprisingly dierent from the rest of the data and therefore is believed to be generated by an alternate mechanism to the other data. For damage detection purposes, the reference data are simply the normal condition patterns of the structure. The case of outlier detection in univariate data is relatively straightforward The discordancy measure is based on deviation statistics and given by, (1) z = jx s; xj where x is the potential outlier and x and s the mean and standard
deviation of the sample respectively. The measure can be inclusive or exclusive. The discordancy is compared to a threshold value and the observation declared, or not, to be an outlier or novel.
OUTLIER ANALYSIS II A multivariate data set consisting of n observations in p variables may be represented as n points in p-dimensional object space. Detection of outliers in multivariate data is more dicult. The multivariate equivalent of equation (1) is the Mahalanobis squared distance measure, (2) D = (x ; x) S 1(x ; x) where x is the potential outlier, x is the mean of the sample observations 0
;
and S the sample covariance matrix.
The mean and covariance may be inclusive or exclusive measures. In the case of on-line damage detection, the potential outlier is always known beforehand - it is the most recent sampled point - so exclusive measures are used to avoid 'contamination' of the normal condition data. Determination of the rejection threshold is critical. This value is dependent on both the number of observations and the number of dimensions of the problem being studied. A Monte Carlo method was used here.
THE EXPERIMENTAL PANEL The upper surface of the panel is 750 500 3mm Aluminium sheet. This is stiened by two ribs of C -channel riveted to the short edges. Two stiening stringers of angle section run along the length of the sheet. The tests used free-free boundary conditions for the panel. 100mm
Top sheet 3mm thick Aluminium Ribs and stringers 1/8’’ thick Aluminium
200mm
125mm 750mm
200mm
Damage Location
1’’ 1’’ 2’’
Ribs - C channel Secured with rivets at 30mm centres
1’’
Stringers - angle Secured with bolts at 30mm centres
Damage was simulated by a Saw Cut in the outside stringer 125mm from the edge of the panel. Nine levels of damage were investigated from 10% depth to 90%. As the stringer is one inch in extent, each level corresponds to 2.5mm of damage.
TRANSMISSIBILITIES The rst stage of analysis was novelty detection based on transmissibility FRFs. These features were chosen as they have the potential for use in on-line systems. At each stage of damage, FRFs were taken from the panel. Two transmissibility paths were identied: AB and DC . AB is along the line of the damaged stringer, while DC is oset by 100mm. A
B
D
C
Stringer
TRANSMISSIBILITIES II The frequency range over which the transmissibilities were taken was 0 to 250 Hz, 2048 spectral lines were taken. In order to have clean data to identify which modes were sensitive to the damage, an averaged transmissibility was taken for each path. 128 averages were taken in each case. In order to accumulate a normal condition set, 128 transmissibilities (not averaged) were taken for each path. This was in order to validate the damage detection methods without resorting to assumptions regarding the measurement noise. For each of the damage cases, an average over 128 transmissibilities was taken as well as 10 unaveraged patterns to form the test set.
NOVELTY DETECTION RESULTS I The rst results given here are based on the transmissibility data for the path AB , directly along the stringer.
Transmissibility Magnitude
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It was decided to use the raw transmissibility functions for the basic patterns. The functions only proved sensitive to the damage in the immediate vicinity of the modes. The next step singled out individual modes to examine which ones showed highest sensitivity to the damage. The fourth mode showed the most signicant and systematic variations with damage state. Spectral lines 1886 to 1935 were selected to form a 50-dimensional feature vector.
NOVELTY DETECTION RESULTS II In order to allow a fast on-line diagnostic, it was decided to use unaveraged data to train and test the novelty detectors. The gure shows three examples of unaveraged patterns from mode 4 of the transmissibility, the level of noise is substantial in the region of the resonance. 7.0
Transmissibility Magnitude
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In order to train the various novelty detectors, 118 of the raw patterns were used to form the training set. The remaining 10 patterns were taken, with each of the 10 patterns from the nine damage levels, to form the testing set. The training set was used to estimate a mean vector and covariance matrix for the patterns. Equation (2) was then used to obtain the Mahalanobis distances for all points in the training and testing sets.
250.0 225.0
Mahalanobis Distance
200.0 175.0 150.0 125.0 100.0 75.0 50.0 25.0 0.0
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50 75 Training Patterns
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log Mahalanobis Distance
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10 20 30 40 50 60 70 80 90 100 Testing Patterns
NOVELTY DETECTION RESULTS II A further stage in the analysis concerned the o-stringer transmissibility i.e. that along line CD. The same mode as for transmissibility AB was selected data from the same 50-point window was used. The results for outlier analysis on the CD transmissibilities were broadly similar to those for path CD - the analysis detected damage consistently when the level was above 20%. The conclusion from the analysis of dierent transmissibility paths is that the damage detection capability does not seem to be overly sensitive to the transmissibility path within the restricted range considered here.
DAMAGE LOCATION The second experimental phase was to carry out a complete top surface modal analysis using 19 measurement points for each stage of damage (location 1 is the shaker attachment point, points 2 to 20 are the accelerometer positions). The natural frequencies and modeshapes were extracted for each level of damage and the modal damage indicators dened by Stubbs were computed at each stage of damage in order to detect and locate. 1
Stringer 2
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THE STRAIN ENERGY METHOD The approach here was developed by Stubbs and Kim and is based on modal strain energy. It has been applied in a number of experimental studies, including an analysis of a full scale bridge structure. Until recently, the method has only been applied to beam-like or 1dimensional structures. As the objective here is to identify and localise damage along the stringer, this is sucient. Consider a beam-like structure discretised into a number of elements labelled by j = 1 : : : Ne, and suppose that measured modal data (x) is available for Nm modes. The diagnostic uses a smeared version of the modal curvature namely, for the undamaged beam,
fij =
2 !2 R aj aj;1 dx ddx2i 2 2 RL d i 0
dx
(3)
dx2
with a similar denition for the damaged quantity (fij evaluated in terms of the modeshapes of the damaged structure i ).
The assumption is that damage will cause a redistribution of strain energy and raise the beam curvature in the vicinity of damage.
THE STRAIN ENERGY METHOD II The quantity of interest is the damage index ik associated with mode i and element k,
ik = ffik ++ 11 ik
(4)
In order to obtain a more robust diagnostic, one can integrate the information across all the measured modes and form,
k =
PNm
i=1fik + 1 PNm i=1fik + 1
(5)
As in the novelty detection methods, it is important to have a threshold. If the index is assumed to have a Gaussian distribution then indices more than two standard deviations above the mean can be associated with possible damage locations. Alternatively, if the normalised index Zk is used, where,
Zk = k; ; 2
then potential damage sites are associated with positive Zk .
(6)
RESULTS FROM STRAIN ENERGY METHOD I In order to use the 1-D formulation of the strain energy method, only the modeshapes along the stringer were used. The frequency interval up to 150 Hz contained 8 distinguishable modes and these were selected for the analysis. A time-domain curve-tting technique was used to extract modal parameters from the measured FRFs, broadband excitation was used. A modal analysis was carried out for the normal condition and for all nine levels of damage. Only modes 6 to 8 showed any signicant systematic variation in their frequencies as the damage increased. Mode 7 showed the most systematic variation with modes 6 and 8 not much dierent. 0.75 Levels 0-50% Level 60% Level 70% Level 80% Level 90%
Modeshape
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5 6 7 8 Transducer Number
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RESULTS FROM STRAIN ENERGY METHOD II The damage indices for all modes were computed using equation (4) and normalised as in (6). There are only nine measurement points per modeshape, following Stubb's practice, a polynomial interpolation was used to estimate the modeshape at 19 regularly-spaced points between the sensors. This gave an array of 161 pseudo-sensor values for the modeshape. The modal damage index for mode 7 clearly signaled damage from the 60% level onwards. More importantly, there were no spurious excursions above threshold. 6.0 Levels 10-50% Level 60% Level 70% Level 80% Level 90%
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Damage Index
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60 80 100 120 140 160 Element Number
RESULTS FROM STRAIN ENERGY METHOD III The peaks in the damage index are consistently over element 139. This is the location of sensor 9 while the damage is in element 134. This amounts to a location error of 21.25mm. Multi-mode damage indices were also computed using equation (5) and modes 6, 7 and 8 and the results were very similar those above. Damage was detected from the 60% level onwards and the location accuracy was much as before. In order to investigate a coarser mesh, a calculation was carried out using sensors 2, 4, 6, 8 and 10. The result using modes 6, 7 and 8 agged damage for level 70% and beyond however, the algorithm located the damage at sensor 8, which is the nearest sensor in the coarse mesh. 4.0 Levels 0-60% Level 70% Level 80% Level 90%
Modeshape
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DISCUSSION AND CONCLUSIONS The rst method considered was a level one diagnostic. The patterns were measured transmissibilities. Outlier analysis succeeded in detecting damage from a 7.5mm saw-cut. The method appeared to be insensitive to the transmissibility path. The second method used the level two strain energy damage index. It was possible to detect a 15mm saw-cut and to locate it with an accuracy of less than 21mm over a 725mm stringer. The analysis raised an issue concerning the use of an interpolation routine to multiply the 'sensor' readings. Outlier analysis detected the damage at a lower level than the damage index - a 7.5mm saw-cut was identied, compared with a 15mm cut. However, the damage index provided the damage location. The data required by the novelty index is simple to acquire, needing only basic spectral analysis. The damage index approach requires a modal analysis to be carried out. In order to locate the damage along the stringer, nine sensors were used as compared with two sensors to extract the transmissibilities for the novelty index. Once the required features have been obtained, post-processing for both methods is extremely fast.
