In structural health monitoring (SHM), using only the existing noise has long been an attractive goal. The advances in understanding cross-correlations in ambient noise in the past decade, as well as new understanding in damage indication and other advanced signal processing methods, have continued to drive new research into passive SHM systems. Because passive systems take advantage of the existing noise mechanisms in a structure, offshore wind turbines are a particularly attractive application due to the noise created from the various aerodynamic and wave loading conditions. Two damage detection methods using a passively reconstructed impulse response function, or Green's function, are presented. Damage detection is first studied using the reciprocity of the impulse response functions, where damage introduces new nonlinearities that break down the similarity in the causal and anticausal wave components. Damage detection and localization are then studied using a matched-field processing technique that aims to spatially locate sources that identify a change in the structure. Results from experiments conducted on an aluminium plate and wind turbine blade with simulated damage are also presented.
Offshore wind turbines generating renewable electricity have been used extensively in European countries and have recently begun to be used in the USA. Since the typical design life of an offshore wind turbine structure is 20 years , it is an ideal candidate for implementing a structural health monitoring (SHM) system . There are many factors and components that can cause a wind turbine to be ‘turned off’, referred to as downtime. The component of interest in this perspective on offshore wind energy is the rotor blade since it is one of the primary components contributing to downtime in wind turbines, based on a recent study by Sandia National Laboratory . One of the driving challenges for offshore wind energy is decreasing the operation and maintenance costs, increasing reliability and increasing performance by expanding the rotor blade size .
Proposed methods for SHM in wind turbine blades include operational modal analysis, acoustic emissions and impedance-based models [2,5,6]. This paper looks into the known approach of using ambient noise for SHM [7,8]. Using operational sources for SHM purposes is a very attractive field because it has the potential for a monitoring system design without the need of an active excitation. However, there are various challenges to passive systems, such as having a high signal-to-noise ratio (SNR), changing excitation sources and discriminating the data acquired, such as in a statistical framework .
The operational environment in wind turbine blades contains many different noise mechanisms including various environmental and aerodynamic noise sources . These sources can create an excitation source that can be used in the same way as if an active excitation were used to interrogate the structure. This excitation source is a primary component in non-destructive evaluation (NDE), where the most common way to interrogate a structure and detect the presence of damage is by transmitting a known signal through the structure and receiving at another point . The transfer function describing the structure’s response is known as the impulse response function or Green’s function.
The impulse response function can be reconstructed from a known method that uses the cross-correlations of long-time signals in noise . The result is a cross-correlation function which contains the two directional impulse response functions. This paper takes a new approach taking two techniques that have been studied in active NDE systems and applying them using the passive reconstruction of the impulse response function.
The first method discussed studies the reciprocity of the two directional impulse response functions. A similarity feature list is introduced and studied on uniform noise field and non-uniform noise field distributions through a sampling study and a bootstrapping technique in a multivariate feature analysis. The second method studies the use of the reconstructed impulse response function applied to matched-field processing (MFP) techniques , a spatial application of the classic plane-wave beamformer [14,15]. Linear, adaptive and robust nonlinear algorithms were used to locate simulated damage. These methods were studied on an aluminium plate and will be applied to a composite wind turbine blade.
Notable research in advancing the use of ambient noise in passive applications of SHM evolved out of leading research work in ocean acoustic and seismology [16–19]. The advantage to using existing noise sources in the ocean removes the limitations and barriers of active sonar that create concerns for ocean wildlife. In seismology, researchers have ambient vibration data from different seismic stations monitoring throughout regions prone to earthquakes. However, large earthquakes, while they have high SNR, are rare. These works have significantly advanced applied research in using the long-time cross-correlations to reconstruct the impulse response function.
The reconstruction of the impulse response function from the long-time cross-correlations requires the recording of signals in a diffuse field or a spatially and temporally uncorrelated field . A diffuse field can be created in a closed medium through the reverberations of the signals. In an open medium, or attenuating medium, where signals have few or zero reflections, there must be enough noise sources surrounding the sensor locations in order to recreate the diffuse environment. In addition, the derivative of the long-time cross-correlation has been shown to closely match forward and backwards impulse response functions . In the correlation function derivative, the causal and anticausal portions correspond to the forwards and backwards impulse response functions 2.1 where Cij is the long-time cross-correlation between sensor i and sensor j, 〈〉 denotes ensemble average, and Gij(t) and Gij(−t) are the causal and anticausal portions of the positive and negative time function, respectively.
It is important to note that, due to several factors, the correlation function does not contain the exact impulse response function. One of the more influential disturbances is the frequency-dependent attenuation, where the correlation function result is essentially coloured by the true impulse response functions . The distribution of the noise field is also important. If the measured field is not perfectly diffuse, then the function will not match as closely. For example, if the noise sources are on only one side of the sensors, then the correlation function will be one-sided if there are no other reflections . Additionally, the longer the amount of time used in the correlation the more the coherent signals are recovered.
The recovery of the impulse response function is the primary motivation in this paper. With the addition of using the passively recovered impulse response function, the detectability of damage is studied using similar variations of reciprocity and beamforming techniques in NDE [21–25] with the addition of signal processing techniques well studied in ocean acoustics [19,26,27].
Reciprocity states that the response of linear structure is the same regardless of the direction the energy travels. In other words, an impulse created at one point and received at the other is equal to the vice versa. In vibrations, this is referred to as the Betti theorem.
The long-time cross-correlation function contains both causal and anticausal portions which correspond to the two directional impulse response functions. The use of reciprocity has been previously studied for damage detection in an active/passive methodology [21,22]. It is believed that damage introduces nonlinearities in the wave propagation that break down the reciprocity of the impulse response function. The break in reciprocity occurs because when a wave travels through a nonlinear feature it can experience modulation and attenuation that is different depending on the direction the wave travels. A crack, for example, would have an opening and closing response that would cause varying contact forces .
The reciprocity is examined through the passive reconstruction of the impulse response function. Comparisons between the forwards and backwards impulse response functions were created for a multi-feature analysis. These features are listed in table 1. The feature list allows the use of statistical methods, such as principal component analysis (PCA). PCA has been commonly used in machine learning for dimensionality reduction and visualization, by projecting data into a lower dimensional space through a linear transformation . In the field of SHM in the past decade, researchers have applied PCA to the various feature spaces in order to visualize the data of different structural states or de-couple the structural damage effect from the environmental effect(s) [31–33]. With N samples of data in p dimensions, PCA projects the feature vectors into a new p-dimensional vector space.
(b) Matched-field processing
The reconstruction of the impulse response function is also well suited for MFP, which has been extensively used in underwater acoustics, seismology [19,26,27], and in an initial application of structural vibrations  and damage detection in homogeneous and inhomogeneous plates [23,24]. In MFP, the response in a sparse array is matched to a model, or replica, containing the known solution to the response in a particular spatial ‘look direction’. This is of similar form to the conventional beamformer isolating azimuth directions of plane waves. The MFP procedure can use the reconstructed impulse response as a replacement for the actively generated signal, but matched to an actively generated replica field. The replica can be a synthetic field created from a numerical computation or an experimentally derived model. In the results discussed later, the replica model is obtained experimentally.
The spectral form of the conventional beamforming equation takes the form of the cross-correlation between the look direction and the response data: 2.2 where * denotes the complex conjugate, w( f,a) is the replica vector for source position a, with length equal to the number of sensors at one frequency bin and a spatial position, and d( f) is the response vector, with same length and also at one frequency bin. It is more convenient to use the cross-spectral density matrix (CSDM), which is the Hermitian inner product of the response vector written in the following equation: 2.3 where d*( f) is the Hermitian transpose of d( f), 〈〉 denotes an ensemble average, and U, S, V * are the outputs to a singular value decomposition which will be used later. An ensemble average of the CSDM from several time domain snapshots constructs a full rank matrix. The most common MFP output, referred to as the Bartlett processor, is the power of the conventional beamforming equation in equation (2.2) . Written in terms of the CSDM and summed over a frequency range, the output takes the form 2.4
In the Bartlett processor, the replica vector is ω( f,a) in the pristine structure at frequency f and spatial location a. When the response matches the replica field of location a, or the steering direction, the result is an in-phase sum of the vector components. Additionally, the replica vector is typically normalized at each frequency to decrease unusual contributions from the noise spectrum. To improve the resolution of the spectral output, the processor is averaged for a set of frequencies because, since all arrays used are finite, there will be energy present in the other look directions that result in sidelobes in the other directions. The averaging constructively sums the signal of interest while destructively summing the incoherent noise.
An additional technique for enhancing the resolution is an adaptive beamforming method known as the minimum variance distortionless response (MVDR). It has the potential to improve the results over the Bartlett processor by constructing a look direction that focuses in the direction of interest . The MVDR look direction of the form in equation (2.2) is solved by minimizing the function 2.5 where γ is the Lagrange multiplier. After solving the minimization function , the solution for wMV( f,a) is 2.6 where K−1( f) is the inverse of the ensemble average of K. Substituting the solution in place of w( f,a) in equation (2.4), the nonlinear MVDR output simplifies to 2.7
While this aims to reduce the sidelobes seen in the linear beamformer, it is also more sensitive to low SNR and variations in the replica vector. When a replica field in the MVDR is not exact, the signal of interest might be seen as interference and suppressed since the output is unconstrained except in the look direction .
To increase signal detection with a non-exact replica field, an inequality constraint against white noise gain is included in the minimization function. Cox et al.  showed the signal mismatch was equivalent to the reciprocal of the white noise gain. The inequality constraint on the white noise gain is included to form the optimization 2.8 where δ2 is in the inverse of the white noise gain. The solution is similar to the solution for MVDR look direction in equation (2.6) but with added noise to the inverse of the CSDM 2.9 where has white noise added to K−1, which can be simply done by adding noise, ϵ, through the reconstruction from the eigenvalues and eigenvectors of K : 2.10
When the maximum amount of white noise is added, the results of the beamforming equation will equal the output of the linear Bartlett processor. When zero noise is added, the output is equal to the MVDR. Thus, the white noise gain constraint (WNGC) aims to increase the MFP sum, or maximize the detection of a source.
(c) Projection operator
MFP is straightforward when the source wave is strong, or loud, as is the case when the source is essentially the same source used to create the mode (one would expect a perfect match). However, when a weak source exists, such as a defect that would cause a scattering in the wave field, the source of interest is buried in the dominant MFP output. There are techniques used to localize weak sources by the use of an orthogonal projection that uses the orthogonal eigenvector space of K( f), equation (2.3) [19,39].
To obtain a new dataset z(w) without the dominant source, the projection is created by subtracting the dominant signal space, which is often the first or first few eigenvectors. This is achieved by pre-multiplying the original data by the projection operator defined by the subtraction of the Hermitian product of the dominant set of m eigenvectors from an identity matrix I: 2.11 and 2.12
It is important to note that the new dataset will be rank deficient, so a subset of the data will need to be used in order to build a new full-rank CSDM that can be used in the beamforming equations, particularly for the MVDR and WNGC processors that use a matrix inverse. The weaker sources can then be localized using the same MFP techniques. Additionally, these techniques can be applied in the active or passive conditions, where the active response is the passively reconstructed impulse response in equation (2.1).
3. Plate and wind turbine blade experiments
The passive damage detection techniques discussed above were tested on a homogeneous aluminium plate and an inhomogeneous composite wind turbine blade. The aluminium plate shown in figure 1a–c measures 1.6 mm thick by 1220 mm wide by 1220 mm long. The wind turbine blade, shown in figure 2a–c, is a version of the CX-100 experimental blade developed at Sandia National Laboratory [40,41].
In both experiments, six high-frequency PCB 352B accelerometers were used to create 15 unique wave paths between sensors in the first approach and a spare array in the second approach. In the aluminium plate, a hexagon-like pattern in the centre of the plate, as shown in figure 1a. In the blade, a section of the blade skin on the trailing side of the internal shear web was used as the test area, outlined in figure 2a. The sensor array on the blade, marked in figure 2b, consisted of two columns of three sensors placed along the chord direction.
An active excitation was created by holding an electrodynamic shaker to the tested structure. The shaker has an operating upper frequency of 10 kHz. The first flexural Lamb-wave mode of the plate has a wavelength of approximately 10 cm at 1 kHz and 2.5 cm at 10 kHz. The wavelengths in the blade were slightly larger. In all cases, the responses in the accelerometers were recorded at a sampling rate of 100 kHz for a long period (1–5 s) while a random white noise signal was sent to the shaker. The plate was supported by foam blocks along the edges, essentially creating a free–free boundary condition. The wind turbine blade was fixed to a support wall in the UCSD Powell Laboratories.
A collection random excitations at several locations simulated the diffuse field. In the aluminium plate experiment, excitations were created in all 576 (24×24) locations in the 50.8×50.8 mm grid drawn on the plate shown in figure 1a. The hand-held shaker was placed close to the centre in each grid box. Arranging the excitations in the grid facilitated the study of different distributions of noise sources. In the blade experiment, 107 randomly placed excitations were created on the outside of both sides of the vertical arrays. The locations of these noise sources were not tracked as in the aluminium plate experiment, because they were not used in the replica field.
The damage was simulated using either modelling clay (figures 1b and 2c) or a heavy steel cylinder (figure 1c). The clay acts as both a scatterer and source of nonlinearity through contact nonlinearity or the hyperelastic behaviour of the material. The experimental results using the reciprocity feature list in table 1 will be described first, followed by the results from the MFP.
(a) Damage detection by principal component analysis of reciprocity features
(i) Aluminium plate
In this experiment demonstrating the PCA of the features comparing reciprocity, damage in the plate was simulated from the one 50 mm wide piece of modelling clay at the location shown in figure 1b between sensors one and five. The data recorded by the six sensors from two sets of experiments (‘pristine’ and ‘damaged’) at the 576 locations consisted each of 3456 time signals with length of 500 000 (5 s at 100 kHz sampling rate). For each signal, the waveform was divided into 25 segments with no overlap. This provided the sample pool in which to randomly select cross correlation functions for the ensemble average.
Two signals of the same time segment from the specific sensor pair were analysed and stored for the ensemble average, creating the impulse response functions from randomly sampling and averaging the cross-correlations from 343 000 samples out of 14 400 sample pool. For each sensor pair, this bootstrapping procedure was conducted multiple times in order to build up the sample population, resulting in 100 unique estimations. To evaluate the reciprocity in both cases, the reciprocity-based statistics features from table 1 were computed.
A feature analysis was first conducted to demonstrate the differences between ‘pristine’ and ‘damaged’ cases. The separability of the features were examined for each wave path through the histograms. Consider two wave paths, 1-5 and 3-5, and four features, 2, 12, 22, 23, shown in figure 3. The sensor pair containing the clay in the direct path, 1-5, was considered to be the ‘damaged’ case while the sensor pair 3-5 was considered to be the ‘pristine’ case. In the histograms shown, 2, 12 and 23 identify with the ‘damaged’ and ‘pristine’ assumption, while feature 22 shows a false positive. While only four features and two wave paths are shown, this is a representative set of cases encountered. The overall criterion followed for the selection of the features in the PCA was an observable separation of feature histograms (true positives) for those cases with clay along the direct wave path and alternatively an overlap in histograms (true negatives) when no clay is present in the direct wave path. The final number of features for the PCA was further minimized by an iterative analysis targeting the most effective clustering between ‘damaged’ and ‘pristine’ cases. The features used in the PCA were 2, 12, 13, 14, a total of 4 in all. The histograms for all wave path and feature combinations have been uploaded as part of the electronic supplementary material.
The results of the PCA conducted on the reduced feature space are visualized in figure 4a–h with a projection of all data samples from the pristine and damaged cases. The projection space was formed from the eigenvectors of a training set created using 50 feature vectors from the pristine condition. An eigenvalue analysis reports that over 90% of the full data variance has been encapsulated in the first two principal components. The results illustrate the existence of separable clusters of the pristine and damaged cases on some of the sensor pairs which are expected to be affected by the presence of clay. Two of these wave paths, 1-5 and 2-6, are shown in figure 4a,b. However, in figure 4c,d,g,h, the two datasets are separable when these wave paths were considered to be undisturbed. In this analysis, undisturbed wave paths should follow the results from wave paths 3-5 and 4-5 shown in figure 4e,f, where the datasets are not separable. This study indicates the wave paths are affected by the clay even if the wave path is not in the direct field (multi-mode scattering).
(ii) Wind turbine blade
The same procedure was conducted on the experimental wind turbine blade. In this experiment, responses from noise excitations created outside of the sensor array were recorded in the six accelerometers. The data recorded by the six sensors from two sets of experiments (pristine and damaged) at 107 randomly selected locations outside the sensor array consisted of 642 time signals with length of 500 000 (5 s at 100 kHz sampling rate). The impulse response functions were created by randomly sampling and averaging the cross-correlations from 21 000 samples out of 2675 sample pool.
Similarly, select histograms of four features, 3, 5, 10, 19, for two wave paths, 2-5 and 2-3, representing the ‘damaged’ and ‘pristine’ cases, respectively, are shown in figure 5a–h. Here, the features are all distinguishable, true-positives, for wave path 2-5, while three of the four features are non-distinguishable, true-negatives, for wave path 2-3. The same selection process used for the aluminium plate was used in this study on the blade. This is a representative set of the cases encountered. In all, the features that showed the best performance were 2, 3, 4, 5, 6, 8, 10, 17, 18, 19 and 23. The histograms for all wave path and feature combinations have been uploaded as part of the electronic supplementary material.
The results of the PCA in figure 6a–h are presented with the same manner, with the projection of the datasets onto the projection space created from a set of training data. The results illustrate clear separation of clusters in wave paths 1-6 and 2-5, both with the clay in the direct-field path. While sensor pairs 3-4, 3-5, 1-4 and 4-5 show varying degrees of separation, they are not as distinguishable as wave paths 1-6 and 2-5. Additionally, wave paths 1-3 and 2-3 do not show separation as would be expected for those wave paths. In the application of this method on the wind turbine blade, the direct field appears to play a larger role than in the aluminium plate.
(b) Damage imaging by matched-field processing
(i) Aluminium plate
While the previous set of experiments focused on identifying damage using the direct field, the MFP techniques take advantage of the full-field response. The sparse array was used to produce images localizing a test source by matching measured data with a replica field. The replica field for the aluminium plate was created from the 576 active excitations produced in each grid box. The replica vector for each spatial location was constructed from the first eigenvector of an ensemble averaged CSDM constructed from the 0.1 s long snapshots of recorded data, overlapped by 0.04 s.
Similarly, for the ‘measured’ data, an ensemble averaged CSDM was constructed using the same snapshot length and overlap. The ensemble average CSDM of the measured data was used in the processor equations described previously and matched with the replica vector as described. The final MFP output is an average of the results at each frequency between 114 Hz and 2 kHz at an interval of 1.52 Hz. Note that, in this experiment, all data were low-pass filtered at 10 kHz.
To first demonstrate the performance of the experimentally derived replica field, each sensor on the plate was the location of a noise excitation. The excitation at sensor 4 was localized and the results are shown in figure 7. The three images are from the three different processors, Bartlett, MVDR and WNGC (with a 7 dB down constraint on the white noise gain), respectively. All images were smoothed using interpolation between each grid output.
The Bartlett output shows a 4.5 dB dynamic range over the side lobes, while the MVDR output shows an increased resolution over the side lobes with a 2 dB increase in dynamic range. The WNGC processor enhances the detection by an additional 1.5 dB to a total of 8 dB gain. The detection of the active source illustrates the imaging output improvement in the WNGC over the Bartlett and MVDR. Results identifying the location of an active excitation at the other sensor locations are not shown but are of similar quality.
Locating simulated damage was tested by using a steel cylinder shown in figure 1c. In the new dataset, again, each sensor was modelled as an active source but with the passively reconstructed impulse response functions used in place of a true active source. Additionally, the dominant signal space associated with this active source was removed using the projection operation constructing a new dataset through equation (2.11). The same output images were constructed using the three processors. The six images from each sensor treated as a source are coherently averaged, which reduces the side lobes even further. The resultant sum of the six output plots are shown in figure 8. The location of the cylinder is denoted by the circle icon between row lines 14 and 15. The Bartlett processor output shows a 2 dB gain though resolution is better than the adaptive methods. The gain in the MVDR output actually decreases to 1.4 dB, while the WNGC output gain increases to 3 dB even though the resolution is still not as clear as in the Bartlett processor output.
(ii) Wind turbine blade
A similar procedure was performed on a dataset produced from the array on the wind turbine blade. A 9×10 grid shown in figure 2b is used as a replica field similar to that in the plate. The final MFP output is an average of the results at each frequency between 114 and 762 Hz at an interval of 1.52 Hz. The eigenvalues of the dominant signal space were highest in magnitude at the lower frequency ranges.
In the same manner, image results from when one sensor, in this case sensor 1, is the location of active excitation are shown in figure 9. Here, the active excitation is identified on the boundary of the replica field.
The noise excitations created on either side of the sensor array were used to produce the reconstructed impulse response function to be used as the active source in the MFP process. The projection procedure was performed on the dataset to remove the primary response and to isolate the clay. The six MFP output images were also incoherently averaged. The images identifying the clay source are shown in three MFP output images in figure 10a–c. The Bartlett output, figure 10a, shows the clay is detected but with large side lobes. In the MVDR output, the clay is detected but is actually less than that of other side lobes. In the WNGC, however, the dynamic range at the clay position is the largest at 5 dB and markedly improving the resolution over the Bartlett and MVDR images.
4. Discussion and conclusion
The plate and blade experimental results presented demonstrate two approaches for using ambient noise for damage detection. The first set of results show a promising method that can detect damage by monitoring the reciprocity of the impulse response functions reconstructed passively from diffuse wave fields. The second set of results show a very exciting method that can locate and detect damage using an MFP procedure which uses the passively reconstructed sources from each sensor. Since both methods rely on passive-only sensors and diffuse wave fields created during operation, they lend themselves to the application of SHM in structures subjected to random noise, such as the operational acoustic noise sources in a wind turbine blade. When applied to an SHM system on a wind turbine blade, the expected result would provide the wind turbine operators and maintenance crews with the ability to identify the location of damage by detecting a change in reciprocity in a sensor pair or through the methods of MFP.
There are many challenges in implementing these approaches in wind turbine blades, with further study needed to understand the methods of damage detection. First, the characterization of the noise propagating within a wind turbine blade is not well understood since most interest is related to the radiation to the surrounding areas. A further understanding of the noise critical to the use of the proposed methods would further aid the study of passive damage detection methods in wind turbine blades. Because noise is not a significant issue in offshore wind energy, the perspective of having a noisier wind turbine blade for damage detection is not the conventional thought, but could lend itself well to the deployment of passive damage detection methods. However, the varying conditions of the wind turbine blade will also play a role in the effectiveness the methods. While the random nature of the noise field is ideal, the spatial and temporal distribution of non-uniform noise fields could produce varying Green’s function results.
Another major challenge is the detection ability of the damage of concern in wind turbine blades, such as delaminations in composite materials, cracks in composites and possible gaps in adhesive disbonds, which may not be visible from the exterior. The reciprocity approach discussed has already been studied preliminarily on a wind turbine blade with these types of defects. However, further tests are necessary to validate the approaches presented here to the specific defect types of wind turbine blades.
Additionally, the experimental tests involved damage inside the sensor grid. While the proposed method using the reciprocity of the impulse response function is targeting direct wave paths, it is assumed this method would be limited to damage within the sensor grid. Regarding the issue of damage being detected that is outside the direct wave path between two sensors, it is difficult to quantitatively predict the effect of secondary wave paths. Since the clay outside of the direct wave path may generate refractions that result in secondary wave arrivals at the receiver, it is conceivable that appropriate time gates may be imposed to eliminate such refractions, or alternatively to enhance the effect of the refractions. This aspect should be subject to further study.
However, in the case of the MFP damage detection method, damage outside the sensor array is possible and has been successfully demonstrated in other applications of MFP. More experimental tests need to be performed to verify similar expected performance of localization of the clay outside of the sensor array.
The authors would like to acknowledge the National Science Foundation for funding this work through grant CMMI no. 1028365. Also acknowledged is Prof. William Kuperman of UCSD’s Scripps Institution of Oceanography for his guidance and discussions on the passive reconstruction of the Green’s functions and the MFP methods.
One contribution of 17 to a theme issue ‘New perspectives in offshore wind energy’.
- © 2015 The Author(s) Published by the Royal Society. All rights reserved.