The first structure to be studied is a simplified aircraft composite skin panel made of carbon fibre reinforced plastic. The structure is depicted in Figure 7.35(a). The overall size of the plate is 500mm×500mm×1.9mm and its weight is about 1.125kg. The stringers are 36mm high and 2.5mm thick. The properties of the unidirectional (UD) material are given in Table 7.10. The fibre volume is equal toVFiber= 60%. The plate and the stringers
consist of 9 plies. Four piezoelectric transducers PIC-151 from PI Ceramics are attached to the surface of the structure with equidistant spacing. The piezoelectric transducers have a diameter of 10mm and a thickness of 0.5mm.
Localized Mass Problem Firstly, damage on the multilayered composite plate is sim- ulated by placing magnets with the same mass at random orientations on both surfaces of the structure as artificial damage as it is depicted in Figure 7.35(b). The magnets have a disk shape and their diameter, height and mass are 12mm, 5.26mm and 0.004kg, respectively. The reason for using this approach for damage simulation is that local stiff- ness reductions will reduce the natural frequencies and an alternative way of reducing the frequencies might be to locally increase mass [Worden and Manson 2007]. Additionally, the contact area of the magnets and the structure surface will help for energy leakage of the interacted guided wave. For the case of this study, the aim of this form of artificial damage was to introduce reversible changes in the structure along the wave propagation
(a) (b) 0.5 0 0 0.5 ym [] x m[ ] P1 P2 P3 P4 ± 0.5 0 0 0.5 ym [] x m[ ] P1 P2 P3 P4 D1 D2 D3 D6 D4 D5
Figure 7.35. Simplified aircraft composite skin panel: (a) Setup and (b) Damage Positions.
paths without destroying the structure.
The excitation voltage signal is a 12V Hanning windowed cosine train signal with 5 cycles; 150 experiments were recorded per sensor-actuator configuration. To determine the car- rier central frequency for the actuation signal in the structure, a frequency sweep was performed and the spectral content of each signal was analysed. The optimal carrier fre- quency was found to be 50kHz for the structure. The carrier frequency was chosen to maximize the propagation efficiency. This type of excitation generates a dominant A0 mode that is propagated along the structure allowing a better interaction of the guided wave with the simulated damage. In order to evaluate the identification capabilities of the SOM with regard to the input feature vectors generated by the proposed methodology, seven different states of the structures were tested, i.e. the undamaged structure and six localized and independent damages. Table 7.11 outlines the coordinates for the simulated damages on the composite skin panel.
As it was introduced in Section 5, auto-associative neural networks (h-NLPCA) are trained independently using the calculated DWT approximation coefficients extracted from the healthy system in order to build the models. The details coefficients are not taken into account in this study since they are going to be discussed in the next subsection in detail. For the current example, a level eight decomposition was accomplished as the optimal decomposition level. However, before training the network, the data gathered in each
Table 7.11. Damage locations in the simplified aircraft composite skin panel.
Damage Number x position (mm) y position (mm)
1 208.25 400 2 291.55 400 3 374.55 250 4 291.55 100 5 208.25 100 6 124.95 250
actuation step were fused following unfolding procedures.
As a first step, an outlier analysis is performed using standard PCA and h-NLPCA as it is explained in Section 5.6.3. A review of the variances retained in the components was performed in order to define the optimal number of components required for building the models from the pristine structural condition. For this purpose, standard PCA was performed first. It was found that the first three components included around 80% of the total variance into the reduced model. This previous analysis is important in order to ensure that enough variance is retained in the model that allows performing an optimal reduction. A similar analysis was performed for each actuation step and finally, three components were selected as a good representation of the input data for the h-NLPCA. This a reasonable option since it is expected that h-NLPCA will describe the data with greater accuracy and/or by fewer factors than standard PCA. The optimal number of units for the mapping and de-mapping layers was calculated using Eq.(2.38). For the experiments depicted here, 32 neurons were used for both layers.
In this work, the threshold is calculated from the baseline data. As it was explained in Section 5.6.3, the threshold is adjusted to μ + ςσ, where μ is the mean value, σ is the standard deviation value of the novelty index over the baseline, i.e. the undamaged structure, and the factorς controls the degree of confidence. The confidence level is defined to be 99.99% in this study. For the experiments presented here, not all the baseline data were used for building the models. The models were built with 35% of the total data and the remaining percentage was used for validation purposes. The results of applying PCA and outlier analysis as explained before show that damage can be separated from the pristine state using only the first three linear components for all the actuation steps as it is depicted Figure 7.36(a) to (d).
Nevertheless, it can also be observed that when the different simulated damages are pro- jected into the baseline and the discordance index is calculated, these damages cannot be clearly distinguished. Additionally, one can notice how the first two actuation steps, i.e. the actuation for transducer one and two, provide a more compact representation of the novelty index in which this value is concentrated in a well-defined cloud around the value of one. This is not case for the last two actuation steps, i.e. the actuation for transducer three and four, where a clear higher deviation of the novelty index around the value of one is present. The explanation for this effect is not clear and require further study. However, theoretically, one would expect to obtain a similar behaviour in all the actuation steps due to the geometrical symmetry of the structure.
Following the outlier analysis with the help of h-NLPCA, the results are similar to the ones obtained by applying PCA. In this case again, damage can be separated from the pristine state using only the first three non-linear components for all the actuation steps. Results are depicted in Figure 7.37. In comparison to the previous case, the distribution of the novelty index value seems to be relatively better concentrated around the value
(a) (b) (c) (d) 0 200 400 600 800 1000 10-1 100 101 102 103 Testing Data
Log Novelty Index
Pristine Training Pristine Testing Damage 1 Damage 2 Damage 3 Damage 4 Damage 5 Damage 6 Threshold=3.891 0 200 400 600 800 1000 10-1 100 101 102 103 104 Testing Data
Log Novelty Index
0 200 400 600 800 1000 10-1 100 101 102 103 Testing Data
Log Novelty Index
0 200 400 600 800 1000 10-1 100 101 102 103 Testing Data
Log Novelty Index
Figure 7.36. Outlier analysis by means of PCA: (a) Actuator 1, (b) Actuator 2, (c) Actuator
3 and (d) Actuator 4.
of one in almost all of the actuation steps. Nevertheless, there seems to be almost no considerable differences between both algorithms for the outlier analysis results.
One disadvantage of using the outlier analysis is that, even when unfolding procedures are taken and the sensor data are fused, the information from all the actuation steps (models) must be analysed independently. This is not the case for the methodology proposed in this thesis. The advantage of the proposed methodology is the ability to fuse all the information contained in the different actuation steps for the analysis rather than just analysing each actuation step one by one. The results obtained applying the proposed methodology with help of PCA, SPE measures and SOM are presented in Figure 7.38. The SOM training algorithm used here is implemented in a Matlab®-Toolbox created by [Vesanto et al. 2000]. To find the optimal map size, a control run is repeated by changing the map size. In order to accomplish the selection of the optimal map size, the average quantization error (QE) and topographic error (TE) were analysed. As a result, a map size of 30×10 was defined. Nonetheless, for a proper understanding of the figures, some properties of the U-Matrix must be discussed. It is good to bear in mind that the mountain-like surfaces formed on a U-Matrix surface define the cluster boundaries. Valleys
(a) (b) (c) (d) 0 200 400 600 800 1000 10-2 10-1 100 101 102 103 Testing Data
Log Novelty Index
Pristine Training Pristine Testing Damage 1 Damage 2 Damage 3 Damage 4 Damage 5 Damage 6 Threshold=3.891 0 200 400 600 800 1000 10-2 10-1 100 101 102 103 Testing Data
Log Novelty Index
0 200 400 600 800 1000 10-2 10-1 100 101 102 103 Testing Data
Log Novelty Index
0 200 400 600 800 1000 10-2 10-1 100 101 102 103 Testing Data
Log Novelty Index
Figure 7.37. Outlier analysis by means of h-NLPCA: (a) Actuator 1, (b) Actuator 2, (c)
Actuator 3 and (d) Actuator 4.
on a U-Matrix surface point to cluster centres. The cluster maps in Figure 7.38(a) can be used as a tool to show the different data sets grouped with similar characteristics showing the clustering tendency. However, in this specific case, no clear cluster separation between all the damage scenarios can be identified in the corresponding U-Matrix surface as it is shown in Figure 7.38(b). This can be clearly seen since the simulated damage number two, three and six cannot be differentiated in the U-Matrix surface, i.e. mountain-like surfaces were not formed for allowing a separation between all the damage types. Nevertheless, the undamaged state can be separated very well from the other simulated damage states. This result is sufficient if the objective is just to identify if the system departs from normal condition. However, if one wishes to address the problem of damage identification, the obtained results cannot provide much information about the damage type.
In a similar manner as the one discussed before, analysis were carried out by means of h-NLPCA, SPE measures and SOM. Figure 7.39(a) shows the cluster map. In this case, seven clusters seem to have been well identified. This is the case for the U-Matrix surface as well as it is shown in Figure 7.39(b). Additionally, the boundaries are more clearly formed when compared with the previous example. It is also visible that a more compact
(b) (a)
Figure 7.38. Analysis with fused PCA, SPE and SOM: (a) Cluster map and (b) U-Matrix
surface. In-plane axes correspond to the number of neurons.
representation of the clusters with a lesser variance around the cluster centre is present for the undamaged scenario as it can be seen from Figure 7.39(a).
In this case, the proposed methodology and algorithms seem to outperform the results obtained with the previous methodology based on standard principal component ana- lysis. The main advantage of using the processing approach presented here is to provide robustness in the analysis by the use of data fusion using the projections obtained by each model together with the square prediction errors measurements as inputs to a self- organizing map.
Localised Increasing Mass Problem As it was previously discussed, it has been shown that the proposed methodology was able to detect damage and the different damage cases. Nevertheless, since the type of damages which were simulated in the previous example are not very realistic with respect to a growing damage process, a second series of experiments
(b) (a)
Figure 7.39. Analysis with fused h-NLPCA, SPE and SOM: (a) Cluster map and (b) U-Matrix
surface. In-plane axes correspond to the number of neurons.
were undertaken. In these experiments damage is simulated again by a localised mass, but the difference resides in that damage increase is simulated by locally increasing the mass at the same damage location by steps so that damage states could be realistically simulated. The magnets employed have a disk shape and their diameter, height and mass of the magnets are 25mm, 10mm and 0.012kg, respectively. The magnets were placed on both sides of the structure. A combination of magnets was used to get different mass values. Four damage evolution steps were simulated using the following mass increase:
1. Damage state one corresponds to a localized mass of 0.024kg. 2. Damage state two corresponds to a localized mass of 0.048kg. 3. Damage state three corresponds to a localized mass of 0.072kg. 4. Damage state four corresponds to a localized mass of 0.096kg.
(b) (a)
Figure 7.40. Analysis with fused h-NLPCA, SPE and SOM for the localised increasing mass
problem: (a) Cluster map and (b) U-Matrix surface. In-plane axes correspond to the number of neurons.
The damages were located in the middle position between P1 and P2. For the current example, a level eight decomposition was accomplished as the optimal decomposition level as with the previous example. The size of the mapping and demapping layer are kept the same as well as the map parameters and number of retained components. For comparison reasons, analyses are carried out by means of h-NLPCA, SPE measures and SOM as presented before. Figure 7.40(a) shows the cluster map. In this case, four clusters seem to have been identified. Nevertheless, the distance in the map between the clusters associated to damage three and four is not significant. As it is shown in Figure 7.40(b), this effect is also reflected in the U-Matrix surface as well. One can observed that for the first two damage states the boundaries are very well-defined. However, the boundaries separating the clusters for damage states three and four have very low values making an separation between the states not so visibly clear and straight-forward to be identified.
It seems from that from Figure 7.40 one could relate the damage severity with respect to the distance between the cluster centres to the undamaged case. Nevertheless, as it is going to the shown in the following subsections, where real damage is introduced to a structure, this principle does not seem to always hold.
Temperature Influence on Damage Assessment Capabilities In order to conclude the analyses with this structure, a final experiment was performed. As it was done previously done, all the controlling parameters are kept the same for comparison purposes, i.e. DWT decomposition levels, number of retained components, etc. The idea behind the exper- iments carried out here is to depict the influence of changing environmental conditions, i.e. temperature changes, in the assessment capabilities of the method. For this purpose, baseline measurements are taken at different temperature levels. Temperature is varied fromT = 25°C to T = 75°C in increments of 10°C. The temperature was measured by two
PT100 sensors mounted on opposite corners of the aircraft composite skin panel. Results are depicted in Figure 7.41.
These results are obtained by projecting the new measurements recorded at different temperatures into the baseline models at T = 25°C, similarly to all the previous cases.
Figure 7.41(a) clearly shows how the recorded data are properly clustered according to the temperature of measurement. It can be observed how the baseline measurements at T = 25°C fall into a single and compact cluster around a neuron. The other clusters
appear to have a larger deviation around their cluster centres, even though, they are well separated. This can be explained by the fact that during the temperature measurements there was a temperature variation of ±3.5°C around the desired reference temperature. Figure 7.41(b) shows that at higher temperatures, that is to say at T = 55°C, 65°C and
75°C, the boundary values between the clusters formed at these temperature levels are very high. Even when it is not visually evident at first sight, the separation of the measurements between the baseline model atT = 25°C and the measurements at T = 35°C and T = 45°C
have also well defined boundaries. As it was depicted before, special measures must be taken into account in order to avoid false-positive indication of damage. As a result, it is very important to collect training datasets over a wide range of environmental conditions of the system so that the minimization of false indications of damage are accomplished and in order to develop a robust monitoring system.