Tommaso Di Ianni

Alessandro Perelli

Luca De Marchi

Alessandro Marzani

COMPRESSIVE SENSING FOR FULL WAVEFIELD IMAGE RECOVERY IN STRUCTURAL MONITORING APPLICATIONS

Keywords: Compressive Sensing, Lamb waves, Laser vibrometry imaging

In this paper, a random sampling scheme based on Compressive Sensing (CS) is used in order to reduce the acquisition time of wavefield signals by means of a scanning laser Doppler vibrometer (SLDV) for Structural Health Monitoring (SHM) applications. The sampling process is indeed quite time consuming, because of noise sources and reduced amplitude of acquired signals. By virtue of the sparse characteristic of the wavefield signal representation in terms of sparsity-promoting dictionaries, e.g. Fourier, Curvelet and Wave Atom transforms, the signal can be however recovered through a limited number of measurements. The implemented CS-based procedure has been validated with experimental signals sub-sampled in a pattern of random distributed points, demonstrating the effectiveness of the approach to limit the acquisition time with extremely low information losses.

INTRODUCTION

Guided Waves (GWs) have turned out in recent years to be a suitable tool for Structural Health Monitoring (SHM) applications. In particular, defect detection in plate-like structures through Lamb waves propagation analysis received great attention because of the ability of such waves to propagate long distances with reduced loss in energy [START_REF] Rose | A baseline and vision of ultrasonic guided wave inspection potential[END_REF].

Many Lamb waves applications are based on the inspection of the full wavefield data acquired by means of a scanning laser Doppler vibrometer (SLDV) [START_REF] Staszewski | Structural health monitoring using scanning vibrometry: I. lamb wave sensing[END_REF] over the surface of the structure under investigation. In fact, the visualization of the full wavefield propagating into the material provides a wealth of information about the interaction of the wavefronts with structural geometrical features, in particular emphasizing the presence of unexpected discontinuities, e.g. defects. In order to achieve a proper spatial resolution, the field should be sampled in a very fine grid of points. Moreover, because of noise sources and reduced amplitude of acquired signals, multiple temporal measurements are needed at each location to suppress noise content, hence the sampling process requires a huge amount of time.

The Compressive Sensing (CS) [START_REF] Candès | An introduction to compressive sampling[END_REF] theory asserts that if a signal can be expressed in a sparse manner, i.e. its information content can be well-approximated by a linear superimposition of few atomic functions of a proper basis, then such signal can be exhaustively recovered from a limited number of random distributed measurements into a L1 norm minimization procedure. Therefore, the reconstruction performance for each application is mostly influenced by the choice of a proper decomposition basis. Furthermore, the introduction of any constraint in the randomness of the sampling-point distribution provides better reconstruction results, allowing to control the maximum distance between neighbor points, i.e. spatial gap.

In this paper, a CS-based framework is used with the goal of minimize the amount of waveforms collected on the acquisition domain, effectively decreasing the time needed for the sampling stage while preserving the informative content of the wavefield data. At a first stage, two sampling-point distribution approaches, both providing random scan-point locations while allowing to control the spatial gap, are tested: Jittered and Farthest Point samplings.

Further, the recovery of the sub-sampled wavefield signal by virtue of several sparsity-promoting dictionaries, namely 2-and 3D Fourier transforms, 2-and 3D Curvelet [START_REF] Ma | The curvelet transform[END_REF] and Wave Atom [START_REF] Demanet | Wave atoms and sparsity of oscillatory patterns[END_REF], is performed in order to estimate the best tradeoff between Signal to Noise Ratio and computational time of the recovery stage. The procedure is tested with a wavefield data obtained experimentally with a scanning laser Doppler vibrometer (SLDV) dataset acquired from a 1.5 mm thick Aluminum plate.

SPARSITY-PROMOTING DICTIONARIES 1.1 Fourier transform

The application of multidimensional FTs provides a sparse representation of the wavefield signal [START_REF] Michaels | Frequency-wavenumber domain analysis of guided wavefields[END_REF]. In the frequency-wavenumber domain most components of the acoustic field are indeed concentrated near the surface obtained from the revolution of the dispersion curve.

Many methods were presented before exploiting such sparse characteristic with the goal of improving the visualization of unexpected faults in the structure. In particular, in [START_REF] Ruzzene | Frequency-wavenumber domain filtering for improved damage visualization[END_REF] the FT is used as a valuable tool to separate the incident component, i.e. the exciting wave pulsed by the transducer, by the scattered components introduced by the presence of a defect in the material. The defect is indeed a source of secondary waves exit from its location, which could be completely hidden by the incident wavefront because of their negligible amplitude. Nonetheless, in the frequency-wavenumber domain the incident component can be easily filtered out, allowing a more effective visualization of the residual wave scattered by the defect.

By means of Fast Fourier transforms (FFTs), the decomposition of a discrete N-point signal in the Fourier domain needs O(N log 2 N) operations.

Curvelet transform

The Curvelet transform (CT) [START_REF] Candès | Fast discrete curvelet transforms[END_REF] decomposes a given signal in a linear superimposition of "needleshaped" functions localized in both spatio-temporal and frequency-wavenumber domains. Identified as curvelets, such functions are equipped with a peculiar selectivity in orientation whereby they are particularly suitable yielding a sparse representation of signals with singularities along curves.

For a 2D signal, the curvelet decomposition is based on a tiling of the frequency-wavenumber domain performed by a couple of smooth, nonnegative and real-valued classes of bandpass functions. Let ξ = (ξ 1 , ξ 2 ) be the Fourier domain variables associated with the spatio-temporal coordinates x = (x 1 , x 2 ). The product of concentric square Wν (ξ ) and angular V ν, (ξ ) windows defines the Cartesian windows Ũν,

(ξ ) = Wν (ξ ) •V ν, (ξ ), (1)
where ν and are two parameters indexing the scale and direction, respectively. In the Fourier domain, each function in (1) isolates frequencies near the wedge located at the scale 2 -ν and oriented in agreement to a set of equispaced directions θ = • 2 ν/2 , with = -2 ν/2 , . . . , 2 ν/2 -1. Conversely, in the spatio-temporal domain, a curvelet function is compactly supported in a rectangle centered in x = (x 1 , x 2 ) with major axis orthogonal to the direction θ and obeying the parabolic scaling relation:

length ≈ 2 -ν/2 , width ≈ 2 -ν ⇒ width ≈ length 2 .
For a 3D signal the theory is essentially the same, except that in this case the curvelets are supported in a little plate rather than a rectangle. 3D curvelets are suitable representing objects with singularities along smooth curves.

The computational cost of the CT is O(N log 2 N), and the Curvelab package, which contains the code that computes the Curvelet transform used in this work is available at http://www.curvelet.org.

Wave Atom transform

Under the assumption that the parabolic scaling is essential to yield good sparsity results, the Wave Atom transform (WA) [START_REF] Demanet | Wave atoms and sparsity of oscillatory patterns[END_REF] provides an alternative multiscale strategy for the sparse representation of the full wavefield signal. Following an approach similar to Curvelet transform, the WA performs a dyadic tiling of the frequency-wavenumber domain, decomposing a given signal in a linear superimposition of oscillating functions whose support is approximately a square obeying the parabolic scaling relation:

wavelength ≈ (width/length) 2 .

The main feature of the wave atoms is their isotropic aspect ratio ∼ 2 -ν/2 × 2 -ν/2 in spatio-temporal domain, with oscillations of wavelength ∼ 2 -ν , as can be noticed in Figure 1. The computational cost of the WA transform is O(N log 2 N). Finally, the code performing the WA transform used in this study is available at http://www.waveatom.org.

COMPRESSIVE SENSING

The full wavefield signal can be organized as a 3D data array u(x 1 , x 2 ,t), and the wavefield image at a given time instant t j is produced taking the 2D slice u j = u(x 1 , x 2 ,t j ). As stated before, a good visualization of the defect into the plate refers to a proper spatial resolution of the image u j that hardly involves the time consumption of the sampling process. In the CS approach, the full wavefield signal can be recovered from far fewer measurements than the Shannon/Nyquist theorem suggests.

To better understand how CS works, let us consider a 1D signal s ∈ R N , sparse in a proper basis Ψ ∈ R N×N , i.e. s Ψ • α k with α k a vector in which all but k N entry are negligible. We are now interested in recovering s from a small set of linear measurements

y i = s, ϕ i , i = 1, . . . , M (2)
with M N: the problem is in general ill-posed and admits many solutions. The samples y i can be then organized as a vector y ∈ R M , such that the sampling process can be expressed in a matrix form as

y = Φ • s + z ΦΨ • α k + z, (3)
where Φ ∈ R M×N is the matrix obtained organizing column-wise the sampling functions ϕ i and z is an unknown error term related to both noise and non-idealities. The CS theory [START_REF] Donoho | Compressed sensing[END_REF] asserts that if Ψ and Φ are sufficiently incoherent, then the signal s can be recovered by solving the basis pursuit denoise (BPDN) problem: where ε bounds the amount of the error term in (3). It can be proven that random waveforms ϕ i with independent identically distributed (i.i.d.) entries are rather incoherent with any given dictionary Ψ.

min α 1 subject to ΦΨ • α -y 2 ≤ ε, (4)
In our approach, a unique pattern of sampling-points random distributed in the acquisition domain is considered for the entire temporal evolution of wavefield propagation. This corresponds to consider M = 1 measurements in (2), extending the theory to a 2D case. On the other hand, the temporal waveforms are acquired according to Nyquist rate.

Sampling-point distribution strategies

In order to deal with the requirement of a spatial gap control, a possible solution is given by Jittered sampling (JS) [START_REF] Hennefent | Simply denoise: wavefield reconstruction via jittered under-sampling[END_REF]. The basic idea is to first decimate the starting grid, then randomly perturb the sampling-point positions around the center of each cell of the coarse grid. This way, a uniform probability distribution is considered in each cell at a time rather than on the whole finest grid all at once.

Conversely, Farthest Point sampling (FPS) [START_REF] Shahidi | Application of randomized sampling schemes to curvelet-based sparsity-promoting seismic data recovery[END_REF] places in turn the sampling points on the finest grid, progressively selecting the next sample to be the farthest point from all previously selected ones, starting from an initial set of a few random distributed points. FPS leads to a more uniform distribution than JS scheme.

EXPERIMENTAL RESULTS

The results of the CS reconstruction of a wavefield signal acquired on a 1.5 mm thick 6061 aluminum plate (638 mm × 558 mm wide) were compared here in order to assess the proposed approach. The presence of a defect was emulated by a 12 mm diameter cylindrical mass bonded on the surface of the plate. A 20 mm diameter PZT transducer was used to excite the guided field in the structure, while the plate response was recorded through a Polytec PSV400M2 SLDV over a rectangular area of 150 mm × 155 mm, in a grid of 141 × 151 equispaced points.

The procedure was implemented in Matlab using the SPGL1 toolbox [START_REF] Van Den | Probing the pareto frontier for basis pursuit solutions[END_REF] for the solution of the BPDN problem, with the support of the suite Sparco [START_REF] Van Den | Sparco: A testing framework for sparse reconstruction[END_REF]. As a general rule, the number of iterations of the solving procedure was fixed to allow each time a comparison of the results obtained through different strategies. The outcomes were compared in terms of both computational time and Signal to Noise Ratio, defined as

20 • log 10 u(x 1 , x 2 ,t) u r (x 1 , x 2 ,t) -u(x 1 , x 2 ,t) ,
where u r is the recovered wavefield signal.

In Table 1 the results of the reconstruction in the Fourier domain with 30 iterations of the wavefield signal sub-sampled in 15% locations respect to the original grid, by means of 1-and 2D Jittered distribution and FPS are shown. Even though the Farthest Point strategy produces a more uniform distribution, JS yields a better recovery in terms of SNR.

On the other hand, the Fourier transforms prove to be the best choice as regards the reconstruction dictionary. The recovery in both 2-and 3D Fourier domain reach indeed the best tradeoff between In order to supply a visual assessment of the approach, in Figure 2(a) the wavefield image at a given instant of time t j relative to the full wavefield signal used as a reference is shown along with the recovered ones by the proposed procedure (Fig. 2(b)-(d)). The recovery was performed starting from less than 34% measurements respect to the original grid. It is worth notice the substantial accuracy of all the recovered signals to the acquired one, which de facto prove the effectiveness of the procedure. Furthermore, the current results are by no means achievable directly interpolating the sub-sampled signal.

CONCLUSIONS

In this paper, a CS framework to minimize the number of scan-point locations over the surface of the structure under investigation is presented. Both sampling-point distribution strategies and sparsitypromoting dictionaries were investigated in order to produce the best recovery for a sub-sampled wavefield signal obtained with a scanning laser Doppler vibrometer from a 1.5 mm thick aluminum plate.

The decomposition of the signal in the Fourier domain has turned out to be the more effective solution, leading to a very accurate recovery starting from less than 34% of measurements respect to the original sampling grid within the smallest computational time. The result can be ascribed to the small complexity of the Fourier transform both with the highest incoherence of such dictionary with the examined sampling schemes, and demonstrates the great potential of the CS approach.

Among the future research needs, an adaptive sampling-point distribution strategy could be developed taking advantage of the progressiveness of the FPS scheme. It is possible indeed to introduce case-specific metrics in order to place each new sampling-point in the position that minimize the recovery error, further improving the tradeoff between the amount of sampled data needed to achieve a suitable resolution and the computational cost in wavefield analysis purposes.

Figure 1 :

 1 Figure 1: Basis function of the Fourier domain (a); curvelet function (b); and wave atom (c).

Figure 2 :

 2 Figure 2: Wavefield image at a given instant of time t j of the acquired full wavefield signal (a); and relative to the signal recovered in the 3D Fourier domain (b); 2D Curvelet domain (c); and Wave Atom domain (d) by less than 34% measurements respect to the original sampling grid.

Table 1 :

 1 CS reconstruction in the Fourier domain with 30 iterations of the wavefield signal 15% subsampled through different sampling-point distribution strategies.

	Sampling Scheme	SNR [dB]
	Jittered 1D	20.64
	Jittered 2D	20.67
	FPS	19.55

Table 2 .

 2 In such a case, the solver yet converges with 30 iterations within a few minutes computational time. Conversely, in both Curvelet and Wave Atom 2D domains, the results are mainly similar in terms of SNR, but within several hours computational times. Finally, the recovery in the 3D Curvelet domain produces unsatisfactory results at all.

Table 2 :

 2 Signal to Noise Ratio and Computational Time of the CS recovery obtained from a full wavefield signal random subsampled in less than 34% locations respect to the original grid distributed with 2D Jittered approach.

	Dictionary	Iterations Computational Time [min] SNR [dB]
	3D FFT	30	2.42	28.38
		90	12.31	28.16
		150	24.37	28.13
	2D FFT	30	2.65	26.29
		90	8.99	26.14
		150	14.84	26.11
	3D CT	30	29.24	11.41
		90	81.00	18.62
		150	137.85	19.29
	2D CT	30	34.95	18.30
		90	101.56	24.22
		150	173.35	24.45
	WA	30	94.33	25.93
		90	283.38	29.24
		150	491.90	29.11

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENTS

The research leading to these results has received funding from the SARISTU project (Grant Agreement no. 284562).


Nicolas Stoffels
email: stoffels@esigelec.fr

Vincent Sircoulomb
email: sircoulomb@esigelec.fr

Guillaume Hermand
email: guillaume.hermand@andra.fr

Ghaleb Hoblos
email: hoblos@esigelec.fr

Principal Component Analysis for Fault Detection and Structure Health Monitoring

Keywords: PCA, sliding windows, fault detection, structure health monitoring. 1 This laboratory, located in Bure

The aim of this paper is to propose an algorithm for detecting faults such as cracks in an underground structure to ensure its health monitoring. The proposed approach is based on the PCA algorithm. Once PCA components are computed, we can see easily the impact of a crack on their norms. The impact represents a good indication to detect abrupt change.

INTRODUCTION

In industrial systems, Fault Detection and Isolation (FDI) take a primordial place [START_REF] Patton | Issues of fault diagnosis for dynamic systems[END_REF]. Such a problematic can be found in civil engineering structures as well as aerospace [START_REF] Goupil | Airbus efforts toward advanced fault diagnosis for flight control system actuators[END_REF], aeronautics [START_REF] Marzat | Model based fault diagnosis for aerospace systems: A survey[END_REF], industrial production [START_REF] Benkaci | Leaks detection in Diesel air path using Levenberg-Marquardt neural networks[END_REF] or energy production [START_REF] Bennouna | Real-time diagnosis and fault detection for the monitoring of the wind turbine[END_REF]. However, this detection must be ensured promptly and precisely [START_REF] Bennouna | Real-time diagnosis and fault detection for the monitoring of the wind turbine[END_REF]. FDI is also important in SHM (Structure Health Monitoring) because of aging structures, in particular deteriorations and mechanical stress. Such problems, if not repaired, could have disastrous outcomes. In civil engineering, the systems are generally quite large and complex, that is why an approach without model is preferable. In this state of mind, a first approach is to use ultrasonic waves on the concrete surface are used on SHM [START_REF] Garnier | Caractérisation non destructive des bétons par propagation d'ondes ultrasonores[END_REF]; however, this technic can only be used in punctual manner. To ensure proper monitoring of the system, another approach is to implement sensors into the concrete structure, such as Vibrating-Wire Gauges (VWG). This type of sensor has already been used in civil engineering structures such as hydroelectric dams, nuclear power plants or grouted anchor [START_REF] Benmokrane | Monitoring behavior of grouted anchors using vibrating-wire gauges[END_REF][START_REF] Thomas | The design, construction and performance of a vibrating-wire earh pressure cell[END_REF]. On top of that, as these sensors are inserted into the concrete structure, they allow a permanent monitoring [START_REF] Delay | Making of the underground scientific experimental programme at the Meuse/Haute-Marne underground research laboratory, North Eastern France[END_REF]. In this work, the monitoring of concrete liner in underground galleries is studied. Indeed, an underground laboratory 1 was built in order to study the project CIGEO (the Deep Geological Disposal Concept of Andra 2 ). It aims at proposing a safe long-term solution for radioactive intermediate-level long-lived waste and high-level waste at a depth of 500 meters. It will be designed to permanently accommodate radioactive wastes. In these circumstances, the SHM must be ensured thanks to a dedicated instrumentation and processing techniques. In this paper, an approach based on Principal Component Analysis (PCA) calculated on a sliding window is investigated to detect abrupt changes. The PCA is an algorithm used to find correlations between multiple data. It has been used for example in biologic science [START_REF] Adebola | Principal component analysis of variation pattern among Cola nitida, Cola acuminata (Sterculiaceae) and their interspecific hybrids[END_REF][START_REF] Jalkanen | Multivariate data analysis of aerosols collected on the Gulf of Finland[END_REF] or physics [START_REF] Douzal-Chouakria | Principal component analysis for intervalvalued observations[END_REF][START_REF] Denis-Karafistan | Application of principal component analysis to radio properties of Quasars[END_REF] but a very few in civil engineering. In our case, we will use the PCA algorithm to detect faults on a system presenting characteristics to be unsteady, heavily instrumented and without model. In our case, the PCA is used because of the wide number of data and sensors. The main interest here is to reduce the size of our problem to process it easier. This paper is organized as follows. First, in section I the proposed approach is described and the interest for fault detection is justified. Section II shows the obtained results by applying this approach on VWG sensors in the presented underground gallery. Finally, concluding remarks and prospects are given.

PROPOSED APPROACH

The PCA algorithm is a multivariate technique used to analyse data tables [START_REF] Abdi | Principal component analysis[END_REF]. It is used to generate correlation circles which are studied in term of components norms and angles between components.

PCA algorithm

The PCA algorithm is a multivariate technique used to analyze data tables [START_REF] Abdi | Principal component analysis[END_REF]. It is used to generate correlation circles in which components norms and angles between components are studied.

Consider a matrix Y

[n×m] whose coefficient Y ij represents the i th sample (1 ≤ i ≤ n) of the j th variable (1 ≤ j ≤ m).
The first step of the PCA algorithm is to obtain the standardized Matrix Z whose coefficient Z ij is computed by:

j j ij ij Y Y Z    , m j n i     1 1 (1)
where j Y is the mean over time of the j th variable:

   n i ij j Y n Y 1 1 , m j   1 (2)
and σ j is the standard deviation of the coefficients {Y 1j , …, Y nj }:

      n i j ij j Y Y n 1 2 1  , m j   1 (3)
Thus, the correlation matrix R can be defined: At present, let us look for the principal components to reduce the problem size, which could be particularly interesting in the case where m is large. If the problem is reduced to a two-dimension subspace, the principal components are associated to the two largest eigenvalues of R. We will subsequently denote these two eigenvalues by λ a and λ b , 1 ≤ a ≤ m, 1 ≤ b≤ m. Such an assumption about the number of principal components can be considered as satisfied by computing the inertia I j of each component:

Z Z n R T 1  , ( 4
   n i ij j Z I 1 2 , m j   1 (6)
Indeed, if the sum of the two inertias I a and I b represents at least about 80% of the total inertia, then, the number of principal components can be considered as satisfied. In the opposite case, a more important number of principal components must be considered.

Finally, for the j th variable (1 ≤ j ≤ m), the two principal components are the two coefficients C aj and C bj . For the sake of clarity, we will subsequently denote:

  T bj aj j C C X  , m j   1 (7)
Plotting the vectors X j for j = 1, …, m into the same figure leads to a correlation circle as depicted in Fig. 1, where F 1 and F 2 are the two axes corresponding to the two principal components. In the above example, vectors pointing in the same direction indicate that they are correlated (here, X 1 and X 5 ). Vectors in opposite way correspond to anti-correlated measurements and orthogonal vectors to uncorrelated measurements (here X 1 -X 2 and X 5 -X 2 ).

The baseline PCA algorithm is an offline method. To use it in a real time setting, one has to consider a sliding window of size h. In other words, at discrete time , the PCA algorithm is applied to the measurements included between times k -h + 1 and k. Thereby, at each time k, a correlation circle as illustrated in Fig. 1 is computed. This circle, and more especially the norms of the vectors X j , can notably vary with time in the case of faults.

Exploration of PCA component for fault detection

As stated in the introduction, the PCA algorithm can be used for fault detection and diagnosis. For example, by following the evolution of the reduced parameters obtained in a steady system [START_REF] Dunia | Subspace approach to multidimensional fault identification and reconstruction[END_REF], or coupled with another algorithm to identify signature of a fault when a model is available [START_REF] Dunia | Identification of faulty sensors using principal component analysis[END_REF]. An overview of use of the PCA algorithm in fault detection can be found in [START_REF] Chiang | fault detection and diagnosis in industrial systems[END_REF]. Here, the system under consideration is unsteady and no model is known, that's why we are interested in investigating another way to use the PCA algorithm to detect fault.

We assume the healthy case is known. Thus, we have at our disposal the time evolution of each vector norms ||X i || with 1≤ i ≤ m in the correlation circle. In absence of fault, the healthy reference and real-time computed norms are very close (but they are not perfectly identical notably because of measurement noise). In presence of fault(s), these two values are different relative to each other for i  [1; m]. We are then able to detect one or several faults. As long as the healthy case and the studied case are close, variation between the two correlation circles in term of norm are negligible or inexistent.

The difference between the two norms can be used to plot a residual that will be used for fault detection procedure. The advantage of this method is to process a wide number of data and sensors easier than if we process them with a conventional method.

APPLICATION

The underground laboratory of Bure is installed implemented in clay rock. Galleries are located at 500 meters deep; one of them, the GCR3 gallery (figure 2) is the gallery considered in this section. This concrete liner used to take charge of the ground.

The ORS 4 section is implemented in this GCR gallery. This section is used to monitoring the behaviors on the clay, the concrete and to observe the evolution of the coating and the retaining. To do this, some sensors technologies are used like optical fibers, TDR (Time Domain Reflectometry) sensors or VWG. All sensors presented here are implemented in-situ.

VWG sensors are particularly used in this paper. The aim of these sensors is to observe deformation of a concrete structure. This kind of sensors delivers a discrete time signal {y k } where k is the discrete time and . An abnormal change of the deformation reported can be interpreted as a system fault. Applying the PCA algorithm regarding the method given in 1.2 allow to trace correlation circles of sensors measurements. This circle for … is shown in fig. 5. Now, a fault is introduced on these measurements. The fault is added between k=1000 and k=1200, these 200 points correspond to two days. The size of the fault is 70Hz. The new correlation circle is plotted in fig. 7. We can clearly see a difference with the nominal correlation circle in fig. 5. Then, a change in the norm of some vectors occurs, allowing the detection of the fault. This is confirmed in fig. 8 and9 where the blue lines correspond to the time-evolution of the vector norm and the red ones to the faulty case. Two cases can be distinguished if a sensor is directly affected by a fault or not: -In the first case: the evolution of norm curves, for faulty and nominal measurements, is almost the same (fig. 8), -But, in the second case: the norm curves are spaced relative to each other (fig. 9).

  ) Now, let and respectively be the eigenvalues of R and their associated eigenvector coordinates in an original basis B o . Then, using the Gram-Schmidt orthogonalization process, we can obtain EWSHM 2014 -Nantes, France from B o an orthonormal basis B n . The corresponding change of basis matrix is denoted P. Thus, the eigenvector coordinates C in the orthonormal basis B n are:

Figure 1 :

 1 Figure 1 : Example of a correlation circle for m = 5

F 1 F 2

 12

Figure 2 :

 2 Figure 2 : View of the ORS section

Figure 3 :

 3 Figure 3: A vibrating wire gauge

Figure 4 :

 4 Figure 4: VWG measurements in the nominal case.

Figure 5 :

 5 Figure 5 : Correlation circle in nominal case for time k = 1

Figure 6 :

 6 Figure 6: VWG measurements in the faulty case.

Figure 7 :

 7 Figure 7: Correlation circle at time k = 1 in the nominal case

Figure 8 :

 8 Figure 8: Comparison between healthy case and faulty one (not directly affected by the fault)

Figure 9 :

 9 Figure 9: Comparison between healthy case and faulty one (directly affected by the fault)

Rigid Conception Gallery.

observation of the coating and retaining

In this work, the results have been obtained in the case of a unique sensor fault. It permit to obtain a good detection indicator.

CONCLUSION AND PERSPECTIVE

In this paper, a PCA based algorithm has been proposed for sensor fault detection. It consists in comparison between the norm curves for faulty and nominal cases. The case of a unique sensor fault has been considered. The detection of the fault is feasible by using, for example, residual. As outlook of this work, on the one hand, it is very important to resolve the fault isolation problem in the case of a unique sensor fault. On the other hand, the case of multiple faults is very interesting to be considered.

Then, all of these results can be easily extended for micro-crack detection in the concrete.

REFERENCE


Jean-Michel Simonin
email: jean-michel.simonin@ifsttar.fr

Pierre Hornych

MONITORING OF ARTIFICIAL DEFECTS WITHIN A PAVEMENT STRUCTURE WITH A NDT METHOD BASED ON A MECHANICAL IMPACT

Keywords: Pavement monitoring, Interface defects, Non Destructive Technique, Fatigue testing, Frequency Response Function

). Rectangular debonded areas of different size (of longitudinal or transversal direction) have been created artificially, using different techniques (sand, textile, absence of tack coat). The construction has been carried out by a road construction company, using standard road works equipment. Then, the pavement fatigue testing facility has been used to apply traffic loading on this pavement, to study the effect of such sliding interfaces on the mechanical behaviour of the pavement, and the evolution of the defects with traffic.

INTRODUCTION

This paper presents a non-destructive testing method (NDT) used to monitor a pavement structure which contains artificial defects. The method is based on the variation of the Frequency Response Function which is sensitive to the presence of damage. A prototype has been developed to easily apply the method on roadways. A methodology has been adjusted to transform the FRF into a normalized damage matrix. The method has been used to survey an experimental pavement during a full scale fatigue test, and follow the evolution of the artificial defects with traffic.

PRESENTATION OF THE TEST SITE

A 25 m long pavement section has been built on the full scale accelerated pavement testing facility of IFSTTAR in Nantes. The structure is made of two bituminous layers (8 cm thick base layer, and 6 cm thick wearing course), over a granular subbase. Several types of defects have been included at the interface between the two asphalt layers (figure 1). Rectangular debonded areas of different size (of longitudinal or transversal direction) have been created artificially, using different techniques (sand, textile, absence of tack coat). The construction has been carried out by a road construction company, using standard road works equipment. Then, the pavement fatigue testing facility has been used to apply traffic loading on this pavement, to study the effect of such sliding interfaces on the mechanical behaviour of the pavement, and the evolution of the defects with traffic.

Principle of the test method

Road pavements constitute continuous structures on which the complex FRF can be measured. For a healthy structure, the shock generates vibrations of the whole pavement. The presence of damage, such as interface defects or vertical cracks, reduces the stiffness of the structure and thus reduces the first Eigen frequency. This low frequency vibration mode corresponds to the vibration of a part of the structure (above the interface defect or close to the crack). Thus it is a good indicator of the presence of a discontinuity in the structure (presence of a debonded interface, or of a crack). The FRF modulus estimated for the damaged structure is thus higher than the one of the healthy structure. It increases at each of the eigen frequencies. Thus, a difference of FRF modulus can be observed in a sensitive frequency band. This band and particularly the lowest frequency, depends on the characteristics of the defect (extension, depth, nature).

Application to pavement

Application of this analysis method to a pavement [START_REF] Simonin | Structural roadway assessment with frequency response function Bearing Capacity of Roads and Airfiels[END_REF] consists in collecting the FRF all along a pavement section. Then, the FRF modulus measured at each measurement point is compared with the "reference" FRF modulus representative of the healthy structure (measured at a point where the structure presents no damage). The objective is to identify the points where the FRF is significantly different from this "reference". It has to be noted that the "reference" function is related to the investigated pavement section. So, we suppose that all measurements are recorded on a homogeneous structure (with identical materials and layer thicknesses). The variations observed are then representative of the presence of damage, which leads to a "softer" structure. On this homogeneous zone, data is processed in 2 steps:

 Definition of a reference function representative of the healthy structure;  Calculation of a normalized damage.

To define the reference function modulus, it is assumed that a part of the tests was carried out on a healthy zone. This could be done voluntarily by investigating an un-trafficked zone such as an emergency lane. In practice we usually consider the set of FRF moduli, ( ) measured at a fixed frequency, , on the points of the section. The reference value at this frequency, ( ) , is defined as a percentile of this selected population. The percentile 20 % is usually adopted which allows obtaining a low value representative of the healthy structure and eliminating abnormal measurements. The set of reference values at different frequencies constitutes the reference transfer function representative of the healthy structure and is used to normalize the FRF modulus measured at each point, at each frequency. Thus, a damage value

) , ( i f D k is calculated
for each frequency, according to equation [START_REF] Ewins | Modal testing: theory, practice and application[END_REF]. This value varies between 0 and 1. The matrix D represents the damage of the road section, for the different frequencies. It can be presented as a "damage mapping" where:

 The X-coordinate is the abscissa along the road section;  The Y-coordinate is the frequency band;

 Colors represent the level of damage (between 0 and 1)

          ,i) FRF(f ) (f FRF ) (f FRF ,i) FRF(f i f D k k réf k réf k k 1 if 0 ) , (
Figure 2 shows such mapping obtained over different artificial defects.

APPLICATION ON THE TEST SITE

Comparison between different defects

The method was used to monitor longitudinal profiles of the experimental pavement, at the radius of 16 m, above the different debonded areas. Above the larger defects (I11, I12 and I13), measurements were made at points spaced at a distance of 0.05 m close to the limits between debonded and bonded areas and at a distance of 0.20 m far from these limits. Figure 2 compares maps obtained with this method. Each map presents the damage level, as a function of distance (X) and frequency (Y). The colors represent the damage level from 0 (blue) to 1 (red). On each map, the debonded area is located between distances 0.5 and 2m. The method locates accurately the areas with defects, however the interface without tack coat is more difficult to locate (lower map). The method is very sensitive to the textile and sand interfaces, on a wide range of frequencies. It is less sensitive to the interface without tack-coat which represents a low level of interface damage.

Monitoring of the evolution of defects with loading

One objective of the experiment was to follow the evolution of the defects during loading, and to evaluate their effect on pavement performance. This will be helpful in optimizing pavement monitoring with different NDT methods.

The experiment consisted in applying to the pavement 300 000 loads, with dual wheel axles, loaded at 65 kN. Investigations have been done at different stages of the experiment :

•

At the beginning of the experiment to characterize the initial state of the pavement; • After 10000 loads when the structure is consolidated; • After 50 000, 100 000, 150 000, 200 000 and 300 000 loads to survey the structure.

The method was used to monitor longitudinal profiles at the 16 m radius above the debonded areas I1, I2, I3 I11, I12 and I13. It was also used to survey transverse profiles above the defect I10.

Measurements were made at points spaced at a distance of 0.02m all along the transverse profile centred on the radius 16m. Figure 3 compares maps obtained with the FRF method along the transverse profile located at the middle of the defect I10. Each map presents the damage level, as a function of distance (X) and frequency (Y). The colours represent the damage level from 0 (blue) to 1 (red).

The debonded area clearly extends with traffic. It must be noted that the defect is located at a positive abscissa at the beginning of the experiment, and that it extends to a negative abscissa with traffic. Therefore, the width of the defect has increased laterally, covering the whole width of the wheel-path at the end of the experiment. This confirms that the evolution of the debonded area is due to traffic. Measurements on a second transverse profile above I10 show a similar evolution even if the lateral extension is more reduced. On the contrary, no longitudinal extension of the debonded area has been detected from the survey of longitudinal profiles. Figure 3. Mapping above a transverse profile of defect I10, illustrating the lateral extension of the defect in the wheel-path.

CONCLUSION

An experiment has been performed on the IFSTTAR APT facility on a bituminous pavement including different artificial debonded interfaces, between the two bituminous layers. A nondestructive testing method, based on mechanical wave propagation, and determination of the FRF function, has been used to calculate an indicator of damage and to survey their evolution under traffic. The method presents a good sensitivity to debonded areas. It has been clearly able to distinguish the different types of artificial interfaces (sand, textile, absence of tack-coat), which simulate different levels of damage. After 300 000 loads, visual survey didn't detect any damage at the surface of the road. Results of the NDT method indicate an increase of the level of damage using the damage indicator, but no extension of the damage along the longitudinal profile. However a significant extension of the damage along the transversal profile has been observed.

As no damage has been observed yet at the surface of the pavement, it is planned to continue the experiment, in conjunction other APT programs, up to at least 500 000 loads. NDT tests will continue to be performed on the pavement at regular intervals. Research will also be carried out to optimize data processing and to develop numerical response models, to improve the interpretation of the results.

The new Colibri apparatus, an automated system, is able to apply the FRF method at a high rate (1 measurement per second). It can be used to investigate several hundred meter long pavement sections, to provide the road engineer with a picture of the internal damage of the road base and wearing course.

Figure 1 .

 1 Figure 1. Interface defects before wearing course construction (left); Map of the different sliding areas (right)

Table 1 .

 1 Characteristics of the different defects introduced in the pavement Defect

Figure 2 .

 2 Figure 2. Map of damage level recorded above the 3 sliding interfaces

EWSHM 2014 -Nantes, France


Xavier Chapeleau
email: xavier.chapeleau@ifsttar.fr

Juliette Blanc
email: juliette.blanc@ifsttar.fr

Pierre Hornych
email: pierre.hornych@ifsttar.fr

Jean-Luc Gautier

Jean Carroget

USE OF DISTRIBUTED FIBER OPTIC SENSORS TO DETECT DAMAGE IN A PAVEMENT

Keywords: Distributed fiber optic sensor, asphalt concrete pavement, cracks, nondestructive inspection

This paper presents the feasibility of damage detection in the asphalt pavements by embedded fiber optics as a new non-destructive inspection technique. The distributed fiber optic sensing technology called "Rayleigh technique" was used in this study. The main advantage of this technique is that it allows to measure strains over long length of fiber optic with a high spatial resolution, less than 1 cm. By comparing strain profiles measured at different time, an attempt was made to link strain changes with the appearance of damage (cracking) in the pavement. This non-destructive method was evaluated on the IFSTTAR accelerated pavement testing facility, in a bituminous pavement. In our experimentation, the optical fibers were placed near the bottom of the asphalt layer. The application of 728 000 heavy vehicle loads (65 KN dual wheel loads) was simulated in the experiment. Optical fiber measurements were made at regular intervals and surface cracking of the pavement was surveyed. After some traffic, a significant increase of strains was detected by the optical fibers at different points in the pavement structure, before any damage was visible. Later, cracking developed in the zones where the strain profiles were modified, thus indicating a clear relationship between the increased strains and crack initiation. These first tests demonstrate that distributed fiber optic sensor based on Rayleigh sensing technique can be used to detect crack initiation and propagation in pavements, by monitoring strain profiles in the bituminous layers.

INTRODUCTION

The fiber optic sensor technologies offer interesting benefits when compared with traditional sensors. The main advantages are small size, electrically passive operation, electromagnetic immunity, flexibility, corrosion resistance, etc. Moreover, the technologies of fiber optic sensors become more and more efficient and reliable. Fiber optic sensors can be used to perform local or distributed measurements with precision in a wide range of strain and temperature. Several of them have already been used for structural health monitoring and surveillance with positive results. The most promising technology is the distributed sensing technique, which can be used to make practically continuous measurements over long lengths of fiber.

FIBER OPTIC SENSOR SELECTED FOR THE STUDY

The "Rayleigh sensing technique" is one of the distributed fiber optic sensing techniques having the highest spatial resolution (less than 1cm). It is sensitive to both strain and temperature. This distributed sensing technique is based on the measurement of the backscattering of light by random fluctuations of the refractive index profile along the length of the optical fiber. A strain (or temperature) profile can be obtained from two successive measurements of the Rayleigh signal, one acquired at an initial state and the second one measured at time t. The typical accuracy of the Rayleigh sensing technique is better than ±1°C in temperature and ± 1µm in strain with a centimeter spatial resolution.

The idea, in this study, is to use the strain profile to detect cracks in pavements. If a crack occurs transversely to the fiber optic sensor, the strain transfer from the host material to the fiber optic will be modified locally. By comparing strain profiles measured at different times to detect strain changes along the fiber optic, internal damage (cracks) in the pavement should be detectable. This paper presents a first evaluation of this non-destructive damage detection method on the IFSTTAR accelerated pavement testing facility.

DESCRIPTION OF THE EXPERIMENTATION

Accelerated pavement testing facility

The pavement fatigue carrousel of IFSTTAR (Figure 1) is a large scale circular outdoor facility, unique in Europe by its size (120 m length, 6 m width) and loading capabilities [START_REF] Autret | The circular test track of the laboratoire central des ponts et chaussées (LCPC) Nantes -First Results[END_REF]:

 maximum loading speed 100 km/h,  loading rate 1 million cycles per month,  4 arms which can be equipped with different wheel configurations,  lateral wandering of the loads to reproduce real traffic.

Fiber optic sensors and measurement system

The Rayleigh sensing technique can be applied to standard fiber optic cables used for telecommunication systems. However, for engineering structures monitoring like pavements, special fiber optic cables designed for sensing measurement should be used. They must have high enough mechanical resistance for easy handling and to withstand the stresses experienced during the pavement construction process. For this experimentation, an optical fiber cable containing 6 fibers (only one fiber optic was used), protected by an epoxy overcoat and a hytrel jacket was selected.

This cable is robust enough to be embedded in asphalt layers, while keeping a small diameter (2mm).

The measurements were made using a commercial device called "Optical Backscatter Reflectometer" (Luna's OBR). Strain or temperature profiles can be obtained from two measurements of Rayleigh signal. The measurement range is approximately 70m with a measurement time less than 10s. This sensing technique has already been tested successfully for damage detection in composites laminates [START_REF] Güemes | Optical Fiber Distributed Sensing -Physical Principles and Applications[END_REF], for crack detection in concrete [START_REF] Chapeleau | Study of ballastless track structure monitoring by distributed optical fiber sensors on a real-scale mockup in laboratory[END_REF][START_REF] Henault | Qualification of a truly distributed fiber optic technique for strain and temperature measurements in concrete structures[END_REF] and for structural tests of wind turbine blade [START_REF] Kaplan | Distributed optical fiber sensing for wind blade strain monitoring and defect detection[END_REF]. Its main limitation is the measurement time, which allows making measurements only under static loads.

Experimental pavement structure

The fiber optic measurement technique was evaluated on a typical French low traffic pavement [START_REF] Corte | Design of pavement structures: the French technical guide[END_REF] consisting of 80 mm of high modulus asphalt, over a granular sub-base (300 mm thick, 300 MPa of modulus), and a sandy subgrade soil.

To accelerate damage, artificial cracks were initiated in the pavement by inserting steel bars with different shapes (triangle, T shaped and flat) in the layer of asphalt. These bars were placed at the bottom of the asphalt layer, in the transverse direction, to initiate bottom-up cracking (Figure 2). The objective was to initiate cracks at an early stage, which would propagate transversely to the wheel path axis between the two bars of the same shape, placed 40 cm apart. The distributed fiber optic sensor was placed in the wheel path axis of the pavement, over a length of 8m, in the zone containing the steel bars. The optical cable was put in place in three steps. First, a thin layer of asphalt (about 10 mm thick) was placed manually on the UGM foundation and compacted. The optical cable was put on this layer of asphalt (photo in the right corner of Figure 2) and covered manually by a thin layer of asphalt to maintain it in place. Finally, a paver and compactor were used to place an asphalt layer of 80 mm. By this process, the optical cable was integrated in the pavement at 70 mm depth, near the bottom of the asphalt layer.

EXPERIMENTAL PROTOCOL

Applied loads

In this experimentation, the four arms of the pavement fatigue carrousel have been equipped with standard dual wheels, loaded at 65 kN (standard French equivalent axle load). The tires used are Dunlop 1200 R20 SP321, inflated at 850 kPa and the loading speed was 6 rounds per minute (43 km/h). At the beginning of the experimentation (until 308 000 load cycles) the dual wheels were loaded at 65 kN. Afterward, the loads on each arm were increased to 75 kN, to accelerate pavement damage.

For testing schedule reasons and maintenance operations of the pavement fatigue carrousel, the experimentation was conducted in several phases:

 between August 2012 and September 2012, until 308 000 load cycles,  between December 2012 and January 2013, until 525 000 load cycles,  between September 2013 and December 2013, until 728 000 load cycles.

Fiber optic measurements

The fiber optic measurements were performed every 50 000 load cycles and surface cracking of the pavement was surveyed at the same time. All the measurements were obtained using the same protocol:

1. A "reference" measurement of the Rayleigh signal was performed with no load applied on the area of the fiber optic embedded in the pavement. 2. Then, one of the four dual wheels (65kN or 75 kN) of the pavement fatigue carrousel was placed at different positions above the fiber optic sensor (positions "P", "C", "T" and "S" on Figure 2), and a second measurement was made.

To minimize the influence of the viscoelastic asphalt material behavior (leading to creep of the material under static load), the same time interval was always kept between the application of the load and the Rayleigh signal measurement (one minute). In addition, the measurements at the different positions were performed, for each sequence, in less than 20 minutes, to avoid temperature variations.

A fiber optic measurement consists in recording the Rayleigh backscattered signal along the optical fiber. The distributed strains can be obtained from two measurements where one is used as reference. So there are different ways (based on the choice on the reference scan) to post-treat the Rayleigh signal measurements which were performed according to the protocol described previously:

 Method 1: This method consisted in comparing the measurements made at the same number of load cycles, under the application of a static wheel load, and with no load. The strain profiles obtained with this method represent the relative strain change between the "loaded" and "unloaded" state.  Method 2: In this method, no load was applied, and the measurements made after a certain number of load cycles were compared with the "reference" measurement performed at the beginning of the experimentation (at zero load cycles). With this second method, the strain profiles obtained represent the evolution of strains along the optical fiber throughout the duration of the experiment.

RESULTS AND DISCUSSION

First of all, it is worth to underline that all the fiber optic cables were embedded successfully in the asphalt layer without any damage. The conditions of construction of the pavement fatigue carrousel were close to road or highway construction. The fiber optic cable has withstood the high temperature of the asphalt mix (about 170 °C) and the compaction of the pavement layer.

Nevertheless, we recognize that the level of compaction was slightly lower that in real pavement construction to avoid to damage irremediably the fiber optic cable. Note that in this experiment, we chose to test a low-cost fiber optic cable which was not specially designed to support compression. It would have been possible to find more resistant optic cable, but at a price per meter 3-5 times higher. The first results presented in Figure 3 were obtained according to method 1 described previously. This figure shows the strain profiles measured at different numbers of load cycles, with a static load applied at the position "P", where the flat steel bars were placed to initiate cracking. As can be seen, all the strain profiles from the beginning of the experimentation to 300 000 load cycles have the same shape. No significant change of width and maximum of the peak can be observed. The only difference is that the abscissa of the peaks is slightly shifted. It is due to the fact that the tire (the load) was not placed exactly at the same position for the different measurements. In addition to fiber optic measurements, regular visual inspections (Figure 4-a) did not permit to detect any cracks on the experimental pavement. So it seems logical to detect no change in the strain profile measurements.

The first cracks were detected on the surface of the pavement after 350 000 load cycles. They appeared, as expected, at the ends of the steel bars placed in the pavement to initiate early cracks (Figure 4-b). At the same time, between 300 000 and 350 000 load cycles, the strain profile curves measured by the optical fibers started to change, the peak becoming wider and more flat in comparison with the previous measurements..

After 400 000 and 450 000 loads cycles, the maximum of the peak of the strain profile curves continued to increase and simultaneously, the surface crack propagated over the whole width of the pavement section. However, at the beginning, the crack remained very thin and difficult to detect by human eye. Then, at 525 000 load cycles, the crack observed on the surface split in two cracks, (Figure 4-c) and at the same time, a second peak appeared on the strain profile. This result shows unequivocally the ability of the optic fiber to detect the initiation of cracks in the pavement. It is probable that the two peaks on the strain profile can be distinguished because the distance separating the two cracks is sufficient (about 20 cm). The stress transfer from the crack to the sensor seems to occur over a length of approximately 20 centimeters.

After 500 000 load cycles, the cracks still continued to grow, and news cracks appeared in the same area. At the end of the experimentation (728 000 load cycles), the pavement was severely damaged. As shown in figure Figure 4-d, at the end, the cracks were interconnected, creating a pattern called " alligator cracking". It is worth to note that the fiber optic cable continued to respond well despite the severe cracking of the pavement structure. However, the multiple cracks cannot be clearly distinguished, because the distance between them is less than the length of the stress transfer mechanism.

Similar results were obtained at the positions "C" and "T", where steel bars were also inserted in the pavement. The evolution of strain profiles at these positions was very similar to that obtained at position "P". These measurements were again consistent with observations of cracks at the surface of the pavement. All these results clearly demonstrate that distributed fiber optic sensors based on Rayleigh sensing technique can detect crack initiation and propagation by monitoring the shape of the strain profiles measured near the bottom of the pavement layer, at different times. However, the method of post-treatment of the Rayleigh signal measurements which was used to obtain the strain profiles presented above is not suitable for monitoring of long road sections. Indeed, this method requires applying a static load on the pavement which is very time consuming. For this reason, we have also tested another measurement method, which requires no load. With this method, The reference measurement (no load applied on the area of the fiber optic embedded in the pavement) used in the post-treatment of the fiber optic measurements was the reference measurement performed at the beginning of the experimentation (zero load cycles). The other measurements performed at different load cycles were then compared to this reference. With this procedure, it was possible to survey the evolution of strains along the optical fiber from the beginning to the end of the experimentation.

Figure 5 shows the strain profile curves obtained with the method described above. The first thing to underline is the very good repeatability of the strain profiles between 100 000 and 300 000 load cycles. The connections and disconnections of the fiber optic sensor to the interrogator imposed by the measurements at different days did not deteriorate the signal/noise ratio of the strain measurements. Moreover, the good repeatability of the strain profiles can be related to the fact that no cracks appeared until 300 000 load cycles. At 350 000 cycles (green curve), first significant changes can be observed on the strain profile. The positions where these changes occur (x=8m and x=9,5m) correspond well to the positions of the first cracks on the pavement, which were detected several thousand cycles later. At 400 000 cycles, two strain peaks appear at position "P" (x=8m) corresponding to the two cracks observed close to this point. At 525 000 load cycles, the entire strain profile located between x=7m and x =12m is strongly modified. This corresponds to the appearance and the growth of various cracks in this area (see figure 6). For the portion of the fiber optic located between x=12m and x=15m, however, the change of the strain profile curves is less significant. This is in accordance with the fact that no cracks were detected by visual inspection for x > 12 m, until the end of the experimentation (see figure 6). So, these results show that the second measurement method, where no load is applied on the pavement, can also successfully detect the initiation of cracks or damage within the pavement, without requiring the application of a static load on the pavement. This second approach seems to be more appropriate to monitor long lengths of pavements.

CONCLUSION

A new non-destructive technique for the detection of cracking in asphalt pavements was tested at real scale on the pavement fatigue carrousel of IFSTTAR. It is based on the use of a fiber optic cable embedded in the pavement layer as distributed sensor. The fiber optic is interrogated by the Rayleigh sensing technique and from the evolution of the strain profiles measured at different time (after different levels of traffic) cracks can be detected.

In our study, we showed that two methods of post-treatment of the fiber optic measurements can be used. With both methods, significant changes of shape of the strain profiles could be directly linked to crack initiation and propagation. However, the method which does not require to apply a load on the pavement is the most promising, since it becomes possible to make measurements over relatively long distances of pavement (70 m with the equipment used in this study, but more with other techniques).

It is planned to continue to evaluate the efficiency of the technique described in this paper. Indeed, the first results need to be confirmed for other pavement structures. Some additional tests will be performed on our pavement fatigue carrousel in the next months. A laboratory study is also planned, to carry out bending tests on pre-cracked asphalt plates, equipped with a continuous optical fiber. These tests, carried out in controlled conditions, should allow a better assessment of the sensitivity of the fiber to the presence of a crack in the asphalt, and of the influence of various parameters (loading time, temperature) on the results.

Figure 1 :

 1 Figure 1: Accelerated pavement testing facility of IFSTTAR

Figure 2 :

 2 Figure 2: Plan of implementation of the steel bars and of the fiber optic cable

  Wheel path (1.2 m) P : flat steel bar (up) C : triangle steel bar (down) T : T shaped steel bar (down) Defects

Figure 3 :

 3 Figure 3: Strains measured at position "P" at different numbers of load cycles

Figure 4 :

 4 Figure 4: Evolution of cracking of the pavement structure at position "P"

Figure 5 :

 5 Figure 5: Strains measured by the fiber optic at different load cycles

Figure 6 :

 6 Figure 6: Photos of cracked pavement section at the end of the experimentation

EWSHM 2014 -Nantes, France


Mathias Kersemans
email: mathias.kersemans@ugent.be

Klaas Allaer

Joris Degrieck

Koen Van Den Abeele

Lincy Pyl

Filip Zastavnik

Hugo Sol

Wim Van Paegem

Ultra- Sonic An

Gauge Strain

Wim Van Paepegem

An Ultrasonic Strain Gauge

Keywords: ultrasound, 3D strain field, DC06 steel, Lankford parameter

niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

A lot of engineering structures, such as large diameter pipelines, are subject to extreme loading conditions during their lifetime, resulting to large (plastic) strains. Assessment of a strain field is crucial in order to ensure the designed functionality of the structure. In practice however, conventional strain measurement techniques are most of the time not applicable in a real industrial environment because of a number of reasons including (i) the need for a reference measurement, (ii) the necessity to physically attach the gauge, (iii) the limited range of measurable strain fields, (iv) the inapplicability for offshore applications and (v) the large sensitivity to small misalignments and external vibrations.

Recently, it has been shown by the present authors that the in-plane parameters of a periodic (sub)surface structure, i.e. periodicities and symmetry orientations, can be ultrasonically characterized in the Bragg scattering regime [1], simply by evaluating the backscattered wave amplitude for a wide range of oblique incidence angles Ψ(φ,θ) [2]. A schematic of the so-called harmonic ultrasonic backscatter polar scan (H-UBPS) method is shown in Figure 1a, in which the ultrasonic transducer is operated as both emitter and receiver. A H-UBPS experiment, recorded at f = 6 MHz, is displayed in Figure 1b for a polycarbonate plate in which a perfect 2D surface corrugation with a depth of 17 μm is ablated by means of a high-quality excimer laser [2]. The angular axis represents the in-plane orientation angle, further called the polar angle φ, the radial axis the angle with the vertical normal, further called the incident angle θ, while the assigned color pigment is a measure for the backscattered amplitude. Both the periodicities and symmetries of the insonified 2D surface structure are encoded in the exact location of the backscatter spikes (spikes 'A', 'B', 'BB', 'A+B' and 'A-B') in the H-UBPS experiment [2]. The reflected signal at normal incidence (spike 'O') is used to compensate for angular misalignment, thus experimental alignment is of minor concern. In this paper, we present an ultrasonic strain gauge which is based on the detection of shifting diffraction peaks in a H-UBPS image for measuring the in-plane strain field components. Additional analysis of the reflected signal at normal incidence on the other hand provides a measure for the out-of-plane strain component. As such, the ultrasonic strain gauge determines a 3D strain field. A limited physical background about the ultrasonic strain gauge is given in the next section. Section 3 provides several results obtained with the here introduced method for DC06 steel sheet at various strain levels. At last, several conclusions are rephrased in section 4.

BACKGROUND OF ULTRASONIC STRAIN GAUGE (USG)

In-plane Strain Field

The necessary condition for the appearance of diffraction spikes in a H-UBPS experiment is obviously the presence of a geometrical surface structure. Instead of manufacturing a specific surface corrugation which introduces residual stress concentrations and thus effectively weakens the material, we directly employ the deterministic surface roughness typically left during the manufacturing process of different materials. For example the skin passing of textured work rolls in case of a cold-rolled steel sheet or the imprint left by the peel-ply during a pressurized autoclave cycle for manufacturing fiber reinforced plastics. Figure 2a displays an optical image (coherence correlation interferometry) of the structured surface roughness (R a = 1.1 μm) of a cold-rolled DC06 steel sample. Figure 2b shows the obtained H-UBPS image at frequency f = 5 MHz. The location of the high amplitude back-diffraction spikes comprises information about the geometry of the local surface structure [1-2]. Appropriate analysis then yields the deterministic surface parameters, i.e. periodicities and orientations. Upon loading the DC06 steel sheet, strain is induced which obviously transforms the surface structure parameters. As a consequence, a positional shift of the diffraction spikes in the H-UBPS image is induced (see Figure 3), reflecting the transformation of the surface parameters. Knowledge of both the original surface parameters and the transformed surface parameters then provides a means for determining the in-plane strain field components ε xx and ε yy at the surface.

Out-of-plane Strain Field

By extending the H-UBPS methodology with the analysis of the reflected ultrasonic broadband pulse at normal incidence (which can be readily identified in the H-UBPS experiment) in temporal frequency domain, the stimulation conditions for a thickness resonance are exposed. This is numerically demonstrated in Figure 4 for the DC06 steel sheet. The considered material parameters for the DC06 steel have been obtained through inversion of ultrasonic data [3]. Figure 4a displays the dispersion curves θ(fd) which put on view the Lamb wave stimulation conditions for plane wave insonification. The curves show the presence of several cut-off frequency-thicknesses fd at normal incidence θ = 0° (indicated by the dashed lines) [4]. Figure 4b shows the computed reflection and transmission coefficient at normal incidence θ = 0° as a function of frequency-thickness fd. At a cutoff frequency-thickness fd, it can be observed that the reflection and the transmission coefficient is characterized by a dip and a peak respectively. Hence, any shift of a cut-off frequency thickness fd has to be linked to a change in thickness d, thus providing a measure for the out-of-plane strain component ε zz . As such, the here presented ultrasonic strain gauge (USG) provides a non-contact and singlesided measurement of a local strain field (both the in-plane and the out-of-plane engineering strain components) without the necessity of difficult alignment procedures. Obviously, the local character of the strain measurement depends on the dimensions of the employed ultrasonic transducer.

EXPERIMENTAL APPROACH AND RESULTS

Results are presented for the widespread cold-rolled DC06 deep drawing steel having a designed thickness of d = 0.8 mm. First, the virgin DC06 steel sheet has been ultrasonically scanned at several arbitrary spots in order to obtain a measure of its original state, i.e. its deterministic surface roughness and its thickness. The employed transducer has a diameter of 13 mm and is operated in both the harmonic regime (in-plane parameters) and the pulsed regime (out-of-plane parameters). These scans indicate the highly uniform nature of the different geometrical parameters of the coldrolled DC06 sheet. This is comfortable as we can take fixed reference values for all DC06 coupons rolled by these work rolls. Secondly, coupons have been cut at a length of 300 mm and a width of 30 mm which were then loaded in the plastic regime on an electromechanical Instron 5800R machine with 50 kN load cell. Plastic strains ranging from 2% up to 35% are considered. During the tensile tests, conventional strain measurement techniques have been applied, including manual micrometer (MM), longitudinal and transverse extensometer (EM) and mono-and stereovision digital image correlation (DIC). A typical stress strain curve obtained by extensometer and DIC is presented in Figure 5a for specimen DC07-07 which was loaded up to a longitudinal plastic strain of ~30%. Figure 5b-c shows the stereovision DIC results (transverse and longitudinal strain component) after unloading of the specimen (see red arrow in Figure 5a), and reveals a small degree of non-uniformity of the strain field. Because of the immobility of the ultrasound setup, the tested samples have to be first unloaded and demounted from the tensile machine before it can be placed in the ultrasound setup to perform a second scan. The immobility of the present ultrasound setup is the main reason why only plastic strain fields are considered in this study. The two ultrasound scans are then used to track down any change in the geometrical parameters of the DC06 specimen, in view of determining both the inplane and the out-of-plane strain field. In the next, we discuss the obtained results for the DC06-07 specimen using the different strain gauge techniques more into detail.

The MM measurements have been obtained at the three different spots S 1 , S 2 and S 3 (see indicators at Figure 5b). For each spot, 10 measurements have been obtained from which an average value and a standard deviation is obtained. Obviously, the MM is limited to the extraction of the transverse and the out-of-plane strain component. The obtained results are listed in the first row of Table 1. The strong inequality of the ε yy and ε zz component indicates the plastic anisotropic nature of the tested DC06 steel sheet. A measure for quantifying the plastic anisotropy is found in the Lankford parameter R, which is the ratio between the transverse plastic strain component and the through-the-thickness plastic strain component [5]. Hence, a material which is plastically isotropic has a Lankford parameter R = 1. For the different spots of the DC06-07 specimen, we obtain a Lankford parameter R 1 = 2.62, R 2 = 2.64 and R 3 = 2.73, indicating its anisotropic plastic nature.

The EM provides only a single measurement of the in-plane strain field components at a single spot. This spot furthermore differs from the three above spots as the EM sensors have to be attached outside the DIC imaging field to avoid overlapping of the DIC speckle pattern. Thus, straightforward comparison with the strain results for spots S 1 , S 2 and S 3 has to be done with caution. In addition, the transverse strain measurement saturated at 8.33% for the DC06-07 specimen because the travel of the transverse extensometer is limited to  2.5 mm. The obtained EM result is listed in the second row of Table 1. To indicate that the longitudinal strain component was extracted at a different spot while the transverse strain component saturated, the row is put in gray.

The mono-and stereovision DIC results extracted at the different spots S 1 , S 2 and S 3 are listed in the third, respectively fourth row of Table 1. The differences between mono-and stereovision data can be attributed to the fact that out-of-plane displacements are present coming from Poisson's contractions and deviations from the ideal planarity. It can be observed that the different DIC values compare well to both the MM data and the EM data.

Finally, the strain field at the three different spots S 1 , S 2 and S 3 has been measured by means of the newly developed ultrasonic strain gauge. Each spot has been scanned four times, from which an average value and a standard deviation is obtained. The results are listed in the fifth column of Table 1. Contrary to the other methods, the USG provides all three strain components. As a matter of fact, the USG also provides the in-plane shear strain component γ xy . Though, for the here considered loading case (tension) this strain component has a negligible value and is therefore not discussed. It can be readily seen that the USG extracted values show good correspondence with the results obtained by means of the other methods, while the determined standard deviations are rather low. Though, the longitudinal strain component ε xx for spot S 1 shows a clear divergence from the other results, which is easily explained on the basis of Figure 5c. Indeed, it can be observed that the longitudinal strain component ε xx around the location of spot S 1 varies significantly. If the ultrasonic measurement at spot S 1 has been accidentally obtained 5 mm upwards, a value of ~32% would have been determined by means of DIC. Similar as done for the MM measurements, one can extract the Lankford ratios for the ultrasonic data at the different spots; R 1 = 2.69, R 2 = 2.70 and R 3 = 2.71 is obtained. Good correspondence with the above determined Lankford parameters is obtained. The consistency of the Lankford parameter is a clear indicator of the robustness and correctness of the determined strain fields. The above analysis is obviously valid for different applied loads and strain levels. For brevity however, we only show the MM and USG extracted Lankford ratios as a function of applied longitudinal strain (see Figure 6a). Note that the MM does not provide information about the longitudinal strain component, therefore the ultrasonic data has been adopted. Except for the data at ε xx = 2%, good agreement is found between both sets of data. The results further indicate a dependency of the Lankford parameter on the applied longitudinal strain. Such a dependency has recently been observed in literature for the DC06 steel [5]. The incompressibility hypothesis, which states that the volume remains constant upon straining a sample, provides another check for the accuracy and validity of the extracted strain field components. It has been found that the incompressibility hypothesis is not violated by more than δ = 1.8% for the ultrasonic data (see Figure 6b). Unfortunately, this deviation cannot be compared with results of the other strain gauge techniques as none of them provide the three needed strain field components ε xx , ε yy and ε zz .

CONCLUSION

A novel strain gauge method has been introduced on the basis of ultrasound waves. The in-plane strain field is measured by exploiting the interaction of oblique incident ultrasonic waves with a deterministic surface roughness, while the out-of-plane component is obtained by tracing the stimulation condition of a thickness resonance. The method has been applied to cold-rolled DC06 steel samples, which were loaded by means of a tensile machine to induce various plastic strain fields. The ultrasonic strain measurements have been validated with conventional strain gauge techniques, such as manual micrometer, mechanical extensometer, and both mono-and stereovision digital image correlation. Good agreement has been obtained with respect to the different methodologies. To demonstrate the capability of the ultrasonic strain gauge, Lankford ratios have been extracted as a function of strain level, revealing the strain dependent plastic anisotropy of the DC06 steel.

Figure 1 :

 1 Figure 1: Schematic of the H-UBPS method (a) and H-UBPS recording (f = 6 MHz) for a 2D corrugated polycarbonate sample (b).

Figure 2 :

 2 Figure 2: Unit cell of the surface structure of a cold-rolled DC06 steel sample (a) and H-UBPS recording at f = 5 MHz for an unstrained DC06 sample (b).

Figure 3 :

 3 Figure 3: H-UBPS recording at f = 5MHz for a strained DC06 sample (a) and extracted diffraction spikes for the unstrained (black) and strained (red) DC06 sample (b).

Figure 4 :

 4 Figure 4: Dispersion curves θ(fd) (a) and reflection and transmission characteristics at θ = 0° (b) for waterimmersed DC06 steel. The thickness resonances are indicated by the dashed lines.

Figure 5 :

 5 Figure 5: Stress-strain curve of specimen DC06-07 (a). Results of stereovision DIC: transverse strain component (b) and longitudinal strain component (c) for specimen DC06-07.

Figure 6 :

 6 Figure 6: Lankford parameter R as a function of applied longitudinal strain ε xx (a) and error δ on the incompressibility hypothesis (b).

Table 1 :

 1 Strain field measurements (average values and standard deviation) for the three different spots of sample DC06-07. MM = micrometer, EM = extensometer, 2D/3D DIC = mono-/stereovision digital image correlation and USG = ultrasonic strain gauge. The EM row is put in gray because the data is obtained at a different spot, while the signal in the y-direction saturated.

			S 1			S 2			S 3
		ε xx (%) ε yy (%) ε zz (%) ε xx (%) ε yy (%) ε zz (%) ε xx (%) ε yy (%) ε zz (%)
	MM	----	-17.022 ± 0.094	-6.501 ± 0.220	----	-16.575 ± 0.057	-6.272 ± 0.135	----	-16.711 ± 0.082	-6.120 ± 0.094
	ME	29.672 --	-8.33 --	----	29.672 --	-8.33 --	----	29.672 --	-8.33 --	----
	2D DIC	30.585 --	-17.491 --	----	29.981 --	-17.274 --	----	29.595 --	-17.101 --	----
	3D DIC	30.158 --	-17.523 --	----	29.740 --	-17.212 --	----	29.352 --	-17.012 --	----
	USG	32.350 ± 0.160	-17.808 ± 0.136	-6.609 ± 0.274	30.320 ± 0.131	-16.800 ± 0.183	-6.221 ± 0.112	30.443 ± 0.137	-17.158 ± 0.234	-6.338 ± 0.194

7th European Workshop on Structural Health Monitoring July 8-11, 2014. La Cité, Nantes, France Copyright © Inria (2014)

EWSHM 2014 -Nantes, France