Luca De Marchi
email: l.demarchi@unibo.it

Jochen Moll

Alessandro Marzani

A SPARSITY PROMOTING ALGORITHM FOR TIME OF FLIGHT ESTIMATION IN GUIDED WAVES -BASED SHM

Keywords: Guided wave inspections, Dispersion compensation, Scanning Laser Doppler Vibrometer

Ultrasonic Guided Waves (GW) are employed by many Structural Health Monitoring (SHM) systems. In plate-like components, GW based defect detection and localization is typically achieved through multiple piezoelectric transducers arranged in different array configurations. In active methods, one or more actuators are used to generate GWs and the sensors work as wave detectors. Defects can be detected and localized from the wave scattering that they generate. To increase the precision of localization approaches, it is important to minimize the uncertainty in the estimation of the time of flight (ToF) of the waves scattered by the defect. Such task is complicated by the dispersive and multimodal nature of ultrasonic GW propagation. In this work, we analyse two algorithms to extract the ToF from waveforms acquired with a Scanning Laser Doppler Vibrometer (SLDV). The algorithms outputs are used to feed beamforming procedures to image cracks with various orientations.

INTRODUCTION

The use of Guided Waves (GW) for Structural Health Monitoring (SHM) has interested several researches in the last decades. Detection and localization of defects in plate-like structures by means of Lamb waves has received particular attention [START_REF] Hurlebaus | Automated methodology to locate notches with Lamb waves[END_REF][START_REF] Raghavan | Guided-wave signal processing using chirplet matching pursuits and mode correlation for structural health monitoring[END_REF]. GW are excited and sensed through multiple piezoelectric transducers arranged in different array configurations. In active methods, one or more actuators are used to generate GWs and the sensors work as wave detectors. Defects can be localized from the wave scattering that they generate by adopting classical triangulation procedures. Such procedures are based on the conversion of the waves time-of-flight (ToF) information into distances between sensors and waves reflectors such as plate edges and defects.

To increase the precision of such localization approaches, it is important to minimize the uncertainty in the estimation of the ToF of the wave scattered by the defect. Such task is complicated by the dispersive and multimodal nature of ultrasonic GW propagation. In this work, we analyse two algorithms (A1 and A2) that exploit the concept of frequency warping to extract the ToF.

The first algorithm (A1) for ToF extraction is based on a dispersion compensation procedure [START_REF] Wilcox | A rapid signal processing technique to remove the effect of dispersion from guided wave signals[END_REF][START_REF] Sicard | A numerical dispersion compensation technique for time recompression of lamb wave signals[END_REF]. Dispersion compensation is achieved with a nonlinear rescaling of the frequency axis (frequency warping). Then, the processed signal envelope is extracted as the absolute value of its Hilbert Transform. Maxima of such envelope are taken as the ToF of waves. The second algorithm (A2) is a sparsity promoting algorithm which minimizes the L1-norm of the acquired signal in a suitable representation basis. In particular, the transducer output can be efficiently represented in Warped Frequency (WF) bases [START_REF] De Marchi | Warped basis pursuit for damage detection using lamb waves[END_REF], allowing for a very sparse codification of the informative content associated with the acquired waveform. In the new representation, ToF can be extracted from the highest value coefficients. To design the Warped Frequency tools, adopted by both algorithms, the group velocity curves of the propagating wave modes have to be known. In this work, they were estimated with a semi-analytical finite element (SAFE) formulation [START_REF] Bocchini | Graphical user interface for guided acoustic waves[END_REF].

PREPROCESSING ALGORITHMS 1.1 Dispersion compensation -A1

As well known, the propagation within certain waveguides such as plates, shells or pipes may be dispersive. That is, the wave group velocity changes with frequencies. This results in a non-linear relation among angular frequency and wavenumber that generates pulse spreading over distance of propagation, complicating thus the estimation of waves ToF. This effect should be somehow compensated to accurately estimate the wave distance of propagation, as typically happens in defect localization procedures. Classical dispersion compensation algorithms are based on a non-linear rescaling (warping) of the frequency axis. The application of such warping procedure to the frequency axis acts so that a linear relation among angular frequency and wavenumber is obtained in the transformed domain (see Figure 1). The warping operators have been studied since the early seventies (Warped Frequency Transforms -WFT [START_REF] Oppenheim | Discrete representation of signals[END_REF]) and can be computed with fast algorithms based on Fast Fourier Transforms and interpolation procedures. The inverse warping function is defined as the reciprocal of the group velocity c g ( f ) of the wave mode whose dispersive effect has to be compensated.

K dw -1 ( f ) d f = 1 c g ( f ) (1)
where K is a normalization constant [START_REF] De Marchi | Warped basis pursuit for damage detection using lamb waves[END_REF]. An undamped guided wave S( f , D) at a traveled distance D from the actuator can be modeled in the frequency domain as dispersive system whose response is given by this formula, which can be rewritten highlighting the relation with inverse warping map:

S( f , D) = S 0 ( f , 0) • e -j2π ∫ D/c g ( f )d f = S 0 ( f , 0) • e -j2πw -1 ( f )KD (2)
EWSHM 2014 -Nantes, France

where S 0 ( f , 0) is the frequency spectrum of the signal at the actuator (zero distance). The distortion results from the nonlinear phase term w -1 ( f )KD. The warping of the frequency axis (

f ′ = w( f ))
produces a new waveform whose frequency transform is given by this formula:

S(w( f ), D) = S 0 (w( f ), 0) • e -j2π f ′ KD (3)
It is worth noting that the dispersive effect of the distance is converted in a warped time-delay KD proportional to the distance itself, with a linear dependence of the phase term on the warped frequency f ′ .

Basis Pursuit in warped domains -A2

A sparse and high-resolution guided wave signal representation can obtained through a linear decomposition of the acquired signal into a dictionary of basis functions ϕ γ .

s(t) = ∑ γ∈Γ α γ ϕ γ (4)
where α γ are real coefficients. In our approach, basis functions are designed to match the spectrotemporal structures of the different propagating GWs by means of the Warped Frequency Transform, and the decomposition method is based on convex optimization (i.e. Basis Pursuit [START_REF] Chen | Atomic Decomposition by Basis Pursuit[END_REF]), which globally minimizes the L1 norm of the coefficients, thus favouring sparse representations.

Examples of the processing results of the A1 and A2 algorithms are represented in Figure 2. The acquired signal (Fig. 2 (a)) is related to a Lamb wave propagating in an Aluminum plate 1.5mm thick. The effect of WFT processing (A1) is represented in Fig. 2 (b), in this representation the horizontal axis can be directly related to the propagating distance of the wave components. Such processing can be combined to time-gating procedure (Fig. 2 (c)) to isolate the contribution due to defect scattering from the one due to the incident wave or to edge reflected waves, under the assumption that the propagation distance is long enough and the incident wave can be separated in time from the reflections coming from the defect and those from structural elements.

The last plot of this figure (Fig. 2 (d)) represents the signal obtained from the Warped Basis Pursuit (WBP) procedure (A2). Once the values of coefficients α γ have been found, they are associated to a propagating distance, and re-ordered accordingly [START_REF] De Marchi | Warped basis pursuit for damage detection using lamb waves[END_REF]. As can be seen, the obtained signal is very sparse and the largest coefficients are concentrated at abscissa values which correspond to the actual distances traveled by the Lamb waves.

BEAMFORMING METHODS

Visual inspection of a structural defect requires an image formation procedure that generates twodimensional maps from the receiver measurements. A conventional method is to use (weighted) beamforming techniques to estimate the position of one or multiple defects. A complimentary technique is given by a model-based approach proposed in [START_REF] Levine | Model-based imaging of damage with lamb waves via sparse reconstruction[END_REF][START_REF] Kexel | Compressed sensing for three-dimensional microwave breast cancer imaging[END_REF] where the position of the scatterer results from the solution of a linear system of equations under a sparsity assumption. In this paper, we will consider three different beamforming techniques and feed them with the output of A1 and A2 related to Lamb wave signals actuated with a single PZT and detected by means of scanning Laser Doppler Vibrometer (SLDV). Since only one actuator is used the method suffers from limited aspect angles leading to a circular smearing in the image reconstructions.

Delay-and-sum beamforming (DAS)

The basic Delay-and-Sum (DAS) algorithm used e.g. in [START_REF] Michaels | Imaging algorithms for locating damage via in situ ultrasonic sensors[END_REF] uniformly superimposes the images of each actuator-sensor-combination to form a two-dimensional intensity map. The index of the actuator is given here by i . . . N A and that of the receiver by j . . . N S . The DAS-method can be expressed as:

I(⃗ x) = N A ∑ i=1 N S ∑ j=1 w i j (⃗ x) • s i j (t -τ i j ) (5)
where the weighting of each channel is equally w DAS i j (⃗ x) = 1. The receiver signal is given by s i j (•) and the time-delay by τ i j . Similar to all other beamforming techniques, the DAS-method requires the group velocity c g to transform the time-traces linearly from time to range-domain. This transformation is realized in this paper by a pre-processing step using either method A1 or A2.

Weighted beamforming using the coherence factor method (CF)

The coherence factor method enables data-adaptive focusing through a spatial coherence quality of the measured signals: the better the signals of all sensor-pairs coherently sum up at a given voxel⃗ x the more this voxel is weighted [START_REF] Klemm | Microwave radarbased breast cancer detection: Imaging in inhomogeneous breast phantoms[END_REF]. The image formation given by Equation ( 5) uses a weighting called the coherence factor w CF i j (⃗ x):

w CF i j (⃗ x) = ∑ N A i=1 ∑ N S j=1 s i j (t -τ i j ) 2 N A • N S • ( ∑ N A i=1 ∑ N S j=1 s i j (t -τ i j ) 2 ) (6)
By definition the weighting factor lies between 0 and 1.

Channel-ranked beamforming technique (RANK)

Another modified DAS-algorithm presented in [START_REF] O'halloran | Channel-ranked beamformer for the early detection of breast cancer[END_REF] is called channel-ranked beamforming technique. For a given focal voxel and a particular actuator-sensor pair, a propagation distance r i j (⃗ x) is mapped to each signal. Longer propagation distances are generally more affected to distortions than shorter ones. Therefore, this method weights channels with shorter propagation distances stronger for each voxel:

w RANK i j (⃗ x) = rank i j (⃗ x) N • (N + 1)/2 (7)
where rank i j (⃗ x) is a linear ordering from 1, 2, 3, . . . , N with 1 assigned to the longest propagation distance.

RESULTS

The experiment is conducted on a 1.5 mm thick aluminum plate whose dimensions are 540 mm x 540 mm. A 10 mm diameter PZT transducer was bonded at the center of the plate and 4 through cracks each 30 mm long were introduced. The cracks have different orientation with respect to the actuator position and hence to the incident wavefield. The acoustic wavefield was generated by exciting a short sinusoidal burst with a PZT transducer, and recorded by a Scanning Laser Doppler Vibrometer (SLDV) over the whole plate area. In Fig. 3, a snapshot of the SLDV imaging is plotted. It is worth noting how the incident wave is scattered by the different cracks. A subset of the acquired waveforms was then selected (200 signals), to mimic the behavior of an array of piezoelectric sensors. Such waveforms were processed with A1 and A2, and then with the beamforming techniques mentioned in the previous section. The results can be qualitatively evaluated by looking at Fig. 4, 5, 6 and 7. In these figures, the circles correspond to the selected recording points within the scan area. It is worth noticing that all the considered imaging procedures are baseline free, that is we didn't exploit information about the pristine structure to highlight the presence of defects. Hence, there is no temperature compensation technique required as demonstrated e.g. in [START_REF] Moll | Guided Waves for Autonomous Online Identification of Structural Defects under Ambient Temperature Variations[END_REF]. It is worth noticing that this approach is valid for isotropic structures, but may generate a systematic error for fiber reinforced media (as shown e.g. in [START_REF] Moll | Multi-site damage localization in anisotropic plate-like structures using an active guided wave structural health monitoring system[END_REF]), where the group velocity is directional according to the orientation of the fibers. As further developments, we plan to extend the considered processing to such anisotropic structures.

CONCLUSION

Among the two algorithms evaluated for ToF estimation, the one based on the sparsity promoting representations minimizes the ToF estimation uncertainty and produces a highly resolved defect imaging. Despite this, it was not possible to image the defect oriented at 90 o w.r.t. to the incident wave front since the scattered energy is too weak compared to the incident one. Optimized and adaptive selection of the receiver array shape, size, and weights is under investigation to further improve accuracy of the investigated approach, and to extend its applicability to anisotropic structures.

Figure 1 :

 1 Figure 1 : Dispersion compensation based on the rescaling of the frequency axis

  of actuator-defect-receiver path length of actuator-receiver (direct) path

Figure 2 :

 2 Figure 2 : Processing results of algorithms A1 and A2: (a) Acquired waveform, (b) dispersion compensated signal after the application of A1 to the acquired waveform, (c) dispersion compensated signal after time-gating (the dashed line represents the applied time-window), (d) output of A2

Figure 3 :Figure 4 :

 34 Figure 3 : A snapshot of the acquired wavefield.

Figure 5 :

 5 Figure 5 : Defect imaging obtained by processing the dispersion compensated signals (A1 algorithm) with RANK beamforming.

Figure 6 :Figure 7 :

 67 Figure 6 : Defect imaging obtained by processing the dispersion compensated signals (A1 algorithm) with CF beamforming.

July 8-11, 2014. La Cité, Nantes, France Copyright © Inria (2014)

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENTS

The authors thank Prof. Fritzen (University of Siegen, Germany) for providing the SLDV. The research leading to these results has received funding from the SARISTU project (Grant Agreement no. 284562).


Simonetta Baraccani
email: simonetta.baraccani2@unibo.it

Tomaso Trombetti

Michele Palermo

Giada Gasparini

Stefano Silvestri

Antoine Dib

A METHODOLOGY OF ANALYSIS FOR A CRITIQUE INTERPRETATION OF THE DATA ACQUIRED FROM MONITORING SYSTEM OF HISTORICAL BUILDINGS

Keywords: structural health monitoring, data analysis, reference quantities, historic buildings

Preserving historical buildings is essential in the safeguard of the cultural heritage of any country. The need to carry out structural analysis with non-destructive methods gave structural monitoring a widespread fame in the world of diagnosis and control of historical buildings. The aim of this study is to introduce a standardized approach for the analysis of the data acquired from a monitoring system of an historical building, through the definition of specific reference quantities (extrapolated from the recorded time series) able to characterize the main features of the structural response and the preliminary identification of the order of magnitudes of these quantities. It is assumed that the recorded time series may be decomposed into two fundamental components: the first one related with the natural actions and characterized, in absence of extreme events, by a substantial periodic behavior, the second one related to the other factors such as the evolution of the state of the structure due to material degradation, soil settlements and others. Exploiting the properties of periodic functions, one may identify these reference quantities, which are based on the year and the day variability and allow to monitor the evolution of the phenomena under observation. These reference quantities may be collected in a database and may become fundamental for comparing the response of similar buildings. This methodology has been applied to the data obtained from the monitoring system of the Cathedral of Modena.

INTRODUCTION

In the last recent years, structural monitoring has acquired an increasing importance in the diagnosis and control of buildings, in particular for historical buildings. The main target of a monitoring system is the evaluation of the building "structural health". The engineering discipline dealing with this topic is called "Structural Health Monitoring" (SHM) [START_REF] Sohn | A Review of Structural Health Monitoring Literature: 1996-2001[END_REF]. An SHM strategy requires that the building should be monitored in a determined span of time, during which measurements are taken in order to infer the presence of potential structural criticalities and/or incoming damages. Therefore, structural monitoring allows to get a diagnosis of the building through a non-destructive assessment. The SHM involves the installation of several devices that permit to monitor the time evolution of parameters concerning the structural behavior of buildings -like the strain and stress state of structural elements, the development of specific existing cracks, the inclination at specific critical points of the structure …. The obtained data need to be analyzed in order to gather some useful information on the condition of the building under observation. Analyses carried out on these data can have multiple purposes.

The present paper is aimed to introduce a standardized approach for the SHM data analysis with a specific reference to historical buildings. The approach is applied to one important Italian monument: the Cathedral of Modena.

APPROACH FOR THE DATA ANALYSIS

From theoretical point of view, it should be straightforward, once the structure is idealized by a mathematical model, to determine the response of a structure under a given, or known, set of actions. However, in most cases, and in particular with reference to historical buildings, the structural behavior, and therefore its idealization (the structural model), may be quite uncertain. In these cases, SHM may provide information on the evolution of the structural response. A simplified standardized approach is presented hereafter for the interpretation of the monitored data. This approach is aimed to:(i) introduce reference quantities based on the identification of the main physical components characterizing the recorded data, (ii) provide order of magnitudes of these physical quantities.

The main components of the recorded data

SHM systems return discrete time series which can be generally referred to as x(ti), where x represents the monitored parameter (e.g. displacement, strain stress, angle inclination, crack width, temperature, …) and ti represents a specific instant of time t. Each parameter time series can be seen as a function of two main factors:

[ ] ( ) ( ), ( ) x t f F t S t = (1)
F(t) are the (time-dependent) forces acting on the structure, and S(t) represent the time evolution of the "state" of the structure, i.e. the condition of the structure due to its geometrical configuration, the materials mechanical properties, its boundary conditions, etc.

The state of the structure can be stationary or variable with time. The variation of the state may due to different factors such as material degradation, incoming coactive states, soil-structure interaction, etc.

The actions occurred on the building, F(t), can be classified into three main groups: • Dead loads D(t): the permanent forces acting on a structure such as the self-weight of the structure. • Live loads L(t): the non-permanent forces acting on the structure. In detail, these loads encompass the forces that depend on the weather effects, which are herein referred to as natural forces, N(t), such as wind, temperature, precipitations, etc. • Accidental loads A(t): the forces depending on rare events, such as earthquakes, hurricanes, explosions, etc. Thus:

( ) ( ) ( ) ( ) F t D t L t A t = + + (2)
The state of the structure may be seen as:

0 0 0 0 S( ) ( ) ( , t) ( , ) t S t S t S S t t = + ∆ = + ∆ (3)
where:

• S0 is the state of the structure at time t0, which is assumed as a known value.

• ΔS(t0,t) represents the variation of the state over the time. If ΔS(t0,t)=0 and S(t)=S(t0), then the state is stationary. On the contrary, if ΔS(t0,t) differs from zero, then it clearly indicates a variation in the state.

The assumptions

If the dead and live loads are within their usual ranges, it is expected that the state of the structure will not substantially change and that the recorded data may be characterized by predominant periodical components due to seasonal and daily temperature excursions.

In the absence of rare events inducing accidental actions, A(t) = 0, and assuming that the live loads are predominately due to the natural forces L(t) = N(t), F(t) can be expressed as the sum of the two components D(t) and N(t). Moreover, assuming that the dead loads may be taken as constant, ( ) D t D = , Eq. ( 2) can be specified as follows:

F( ) (t) t D N = + (4)
Substituting Eqs. ( 2), ( 3) and (4) in Eq. ( 1) leads to:

0 0 x( ) , ( ), , ( , ) t f D N t S S t t   = ∆   (5)
The natural forces are assumed to be periodic functions with two fundamental contributions:

( ) ( )

1 1 2 2 N( ) , , t N T t N T t = + (6)
A contribution N1 with period T1 equal to 365 days (due to the revolution of the earth around the sun) leading to the annual oscillations and a contribution N2 with a period T2 equal to 1 day (relative to the earth rotation around its axis) leading to the daily oscillations. The actions on the structure due to the earth motion of revolution are considered periodic functions with constant amplitude. The actions on the structure due to the Earth rotation are considered periodic functions with variable amplitude depending on the season. Based on the above considerations, it is assumed that the time series x(t) are formed from two components:

( ) ( ) 1 2
x( )

t

Analysis of the data

Based on the assumed functional form of the recorded time series x(ti), the data analysis is conducted introducing the quantities summarized in Table 1.

With reference to the jth generic day, the quantities of interest are the daily amplitude and the mean daily value. With reference to the jth year, the quantities of interest are the annual amplitude and mean annual value. We are also interested in computing the daily residuals at the jth day of the amplitude (rδday,i(k-l)) and of the mean value between two consecutive years k and l (rμday,,j(k-l)). These quantities are useful to obtain information on the evolution of the state S(t). Also, the annual residual of the amplitude ( rδyear,i(k-l)) and of the mean value ( rμyear,i(k-l)) contribute to the knowledge of the evolution of the state S(t).

As illustrative example, a time series x(t) simulating generic data from a SHM system has been generated and displayed in Figure 1. For the sake of clearness, Figure 2 illustrates some reference quantities: daily amplitude (σ), mean daily value (m), annual amplitude (Σ) and mean annual value (M). From the graph of the residual, it is possible to evaluate the trend through linear regression of the data and the histogram of the annual cumulative values curve to extrapolate: (i) linear regression of rσ and rm (trend of the residuals), (ii) cumulative of the residuals (stability of the measured event). In addition to the above described quantities, sudden drops (Δ) may also be present in the recorded time series x(t). These sudden drops may be related either to an instrument malfunctioning, to external factors or to accidental events (earthquakes, hurricanes, …).

The introduction of the reference quantities summarized in Table 1 can be useful in order to collect data in a systematic way and to compare them with those of similar structural buildings. In the following sections, some selected data from SHM related to two important Italian monuments systems are analyzed and preliminary reference values are obtained for the defined quantities.

THE CATHEDRAL OF MODENA

The Cathedral of Modena, whose construction began in 1099 through the instrument of architect Lanfranco and finished in 1184, is one of the most important examples of the Romanesque art in Italy (Figure 3). In 1997, it has been declared "UNESCO Cultural Heritage" site. The Cathedral has a basilica plan with three naves culminating in three apses. The cathedral is connected to the contiguous Ghirlandina Tower (a tower of about 86 meters height) through two masonry arches. During the centuries, the monument experienced various interventions and transformations [START_REF] Armandi | II Duomo di Modena[END_REF][START_REF] Sandonni | Cronaca dei restauri del Duomo di Modena[END_REF]. Recently, a conservation project, which is currently under development, has been planned with the purpose of strengthening the main walls, the vaults and of providing the structure with a box behavior. In the context of this retrofit project, a SHM system was also installed.

The Monitoring System

The monitoring system allows monitoring the main cracks across the walls and vaults, the relative displacements between the cathedral and the tower, the inclination of the external longitudinal walls, the foundation settlements, the water table level and the temperature. Most of the instruments were installed in 2003, while others (such as the inclinometers) were installed in 2010. Data are acquired at time intervals of 30 minutes. Figure 4 shows the location of the sensors. The symbols indicate: D: deformometer, E: extensimeter, MGB: biaxial joint meter, MGT: triaxial joint meter, FP: inclinometer, T: thermometer.

The data obtained from the SHM

A summary of the reference quantities defined in section 1 is reported in Table 2. Each value refers to a single specific device except for the biaxial joint meter whose value is obtained computing the average of all instruments of that type. As illustrative example, a more detailed data analysis following the approach introduced in the previous section is conducted with reference to the biaxial joint meter MGB1 placed on a crack on the south longitudinal wall (Figures 5 to 8). Figure 5a displays the complete time series over years 2004-2012. With the exception of few spikes, this series clearly shows the daily and annual periodicity with an almost constant average value, thus not showing a significant evolution of the state S(t). A more in depth inspection of the time series is provided by the Figure 5b which provides the two main components of the signal x1 and x2. For this specific case, the periodic contribution is essentially given by the harmonic with period T1 = 365 days, whilst the amplitude of the harmonic T2 = 1 day is order of magnitudes lower. In addition, the signal component x2 is characterized by a significant periodicity whose fundamental harmonic has a period T of 300 days.

Figure 6a displays the daily amplitude (σ about 1/100 mm) and the mean daily value related to a generic day. Figure 6b represents the annual amplitude (Σ about 1/10 mm) and the mean annual value related to year 2006. Note that the ratio σ/Σ seems to be equal to 1/10. Figure 7a plots the daily amplitude (σ) and the daily mean value (m) over the entire observation period (9 years). It can be noted that m oscillates around an almost constant value, indicating a stable behavior of the monitored crack (no evolution in time), whilst σ is small and bounded within 0.02 mm, despite isolated spikes. Figure 7b plots the daily residual of the mean daily value rm. These graphs further confirm that no significant evolution of the state S(t) is observed: the trend regression line is practically horizontal.

CONCLUSIONS

This paper presents a simple approach for a standardized analysis of the data recorded by a Structural Health Monitoring system installed in an historical building. The main objective is to introduce significant reference quantities from the recorded data in order to detect possible anomalies from the usual structural behavior. This information may be collected in a database and adopted as reference quantities (order of magnitudes) for the analyses of data of similar buildings in order to have reference values leading to a more sound interpretation of the SMH data.

As illustrative example, with reference to masonry displacements, the values of the daily amplitude σ (about 1÷1,3 /100 mm) and the values of the annual amplitude Σ (about 2÷2,2/10 mm) which were detected in the Cathedral of Modena gave us the ratio σ/Σ, which is roughly equal to 1/10.

Figure 1 :

 1 Figure 1:Time series x(t).

Figure 3 :

 3 Figure 3: The Cathedral of Modena.

Figure 4 :

 4 Figure 4: Location of the sensors.

Figure 5 Figure 6 Figure 7 Figure 8

 5678 Figure6adisplays the daily amplitude (σ about 1/100 mm) and the mean daily value related to a generic day. Figure6brepresents the annual amplitude (Σ about 1/10 mm) and the mean annual value related to year 2006. Note that the ratio σ/Σ seems to be equal to 1/10. Figure7aplots the daily amplitude (σ) and the daily mean value (m) over the entire observation period (9 years). It can be noted that m oscillates around an almost constant value, indicating a stable behavior of the monitored crack (no evolution in time), whilst σ is small and bounded within 0.02 mm, despite isolated spikes. Figure7bplots the daily residual of the mean daily value rm. These graphs further confirm that no significant evolution of the state S(t) is observed: the trend regression line is practically horizontal. Figures8a and brepresents the histograms of the annual residuals RΣ and RM, and their cumulative curves. The cumulative curves indicate a quite stable behavior, with compensations along the years (except for year 2012 in RΣ).

Table 1 :

 1 The reference quantities for the analysis of the recorded data

	Reference quantity										Definition
	Daily Amplitude		δ	, day j	=	 	( ) i max x t	-	( ) i min x t	  =	σ	ti day j
	Mean Daily Value						μ	, day j	=	n i j = 1 1 n j ∑ x(t ) m i =	ti day j
	Annual Amplitude	δ	year, j	=	 	( ) i max x t	-	( ) i min x t	  = Σ	ti year j
	Mean Annual Value					μ	year,		1 n	n	1	x(t )

Table 2 :

 2 Reference values for each kind of instrument

	Device

EWSHM 2014 -Nantes, France


Camille Flament
email: camille.flament@ec-lyon.fr

Michelle Salvia
email: michelle.salvia@ec-lyon.fr

Bruno Berthel

Gérard Crosland

LOCAL STRAIN AND DAMAGE MEASUREMENTS ON A COMPOSITE WITH DIGITAL IMAGE CORRELATION AND ACOUSTIC EMISSION

Keywords: Digital Image Correlation, Acoustic Emission, Location, Composite Material

Certain material have a non linear stress-strain behaviour under monotonic loading. This non linearity can be caused by continuous damage. To highlight this phenomena simultaneous strain and damage measurements should be taken. When working with inhomogeneous or anisotropic materials, such as continuous fibre composites, local information is essential. On the one hand, full field strain data can be obtained with Digital Image Correlation (DIC). On the other hand Acoustic Emission (AE) recording is a method that can be used for damage monitoring and location if, at least two sensors are placed on the specimen under loading. The aim of this work is to combine these two techniques to correlate strain measurements and damage location on a complex composite material during a monotonic tensile test. This composite is a continuous fibre reinforced friction material used in car clutches. These measures were used to understand the non linearity of the stress-strain curve of the as received material as well as detect volume damage after thermal cycling.

CONTEXT

To predict the behaviour of a structure, a good knowledge of the constitutive relations of each part is essential. To obtain the stress/strain relations strain measurements are conducted on simple mechanical tests. For certain materials, the stress-strain curve may be non linear. Damage is one of the causes of non linearity in the stress/strain curve. To identify such a behaviour strain and damage must be measured simultaneously. To measure strain many techniques can be used (extensometers, strain gauges, ..), however, when working with inhomogeneous or anisotropic materials, such as continuous fibre composites, accurate strain measurements call for full field data. Amongst the different full field measurement techniques, Digital Image Correlation (DIC) is one of the most popular [START_REF] Sutton | Image Correlation for Shape Motion and Deformation Measurements[END_REF]. It is an optic contactless experimental technique to measure full field displacements and strains with sub-pixel accuracy. Failure mechanisms can be identified with different non destructive techniques such as Acoustic Emission (AE) recording which can be used for damage monitoring. In fact elastic waves are emitted as a consequence of crack initiation and propagation. Therefore analysing the acoustic activity gives information on the type of damage that occurs in the material. Furthermore, if at least two sensors are placed on the specimen under loading, and the wave propagation velocity is known, location of each acoustic event is possible. The aim of this work is to combine these two techniques to correlate strain measurements and damage location during a monotonic tensile test and determine if the non-linearity of the stressstrain curve is due to volume damage. In addition, as car clutches are submitted to thermal cycling, volume damage was characterised on thermally cycled specimens by using AE signals emitted during a monotonic tensile test.

MATERIAL AND LOADING

The material studied is the organic clutch facing that transmits the rotary motion between the engine and the wheels. It is an annular shaped continuous fibre composite constituted by a fibre glass yarn fitted with copper strips. The studied clutch facing has external and internal diameters of 240 and 160 mm respectively. The composite matrix is mainly composed of a phenolic thermosetting resin. The steps of the process of fabrication are described in [START_REF] Bezzazi | Experimental characterization of frictional behaviour of clutch facings using Pin-on-disk machine[END_REF]. During the preforming operation, a machine guides the impregnated fibres coupling a uniform rotation with a radial translation. The two movements have different frequencies resulting in a fibre organisation such as presented figure 1. The number of sin wave per 2π phase angle (N) is an important parameter as it defines the fibre orientation [START_REF] Karadeniz | A numerical study on the coefficients of thermal expansion of fiber reinforced composite materials[END_REF]. The preform is put into a heated mould pressed and cured at 250°C. The fibre organisation confers an orthotropic behaviour to the material. The orthotropic axes are the radial and the tangential axes [START_REF] Flament | Digital image correlation applied to thermal expansion of composites[END_REF]. In this paper only mechanical properties in the tangential direction were studied. Rectangular specimens (20x120) were cut into the disc to perform the tensile tests as shown figure 1.

EXPERIMENTAL TECHNIQUES

Digital Image Correlation

The digital image correlation (DIC) technique provides displacements and strain maps on deformed surfaces. The correlation is possible only if the surface has a random texture, such as a black and white speckle. The surface is often painted with black and white spray paint. A region of interest (ROI) is defined on the specimen surface. The ROI is divided into subsets which are tracked by the algorithm which finds the corresponding location of the reference subsets in the deformed image. To compare the deformed and reference subsets, the DIC algorithm compares the gray level of each pixel in each subset. Once the matching is done, the displacement components of the centre of the reference and deformed subset can be determined. The strain field is then derived from the filtered displacement field. When using one camera, (2D-DIC), the temporal correlation as described above does not take into account out of plane displacements. To determine the position of an object in the three dimensions, two simultaneous images of the same object, with a different camera angle are needed. Digital image stereo correlation (DISC or 3D-DIC) combines temporal and stereoscopic matching (Figure 2). The DISC method makes the difference between strain and out of plain displacements and gives access to 3D profiles. In order to correlate the stereo-images, the correlation algorithm needs information on the orientation and position parameters of the cameras as well as the intrinsic parameters of each camera. These parameters are determined by calibrating the stereo-vision set up which is done by recording images of a calibration target. The system used in our laboratory is Vic 3D developed by Correlated Solutions [START_REF]Correlated Solutions.Inc[END_REF].

Acoustic emission : accuracy of location

Acoustic emission (AE) signals were acquired and processed with the AE acquisition and analysing system AEwin for Mistras of Physical Acoustics Corp. The AE signals during the tests were detected by two piezoelectric sensors (type R15) attached to the sample by a silicon grease and clips. The threshold of the AE system was set to 35dB, any event with a lower amplitude was not detected. To test the accuracy of the AE system when locating events, 100 dB events were generated on a marked specimen. The AE location map was then compared to the known location of the events. Two sources of errors have been identified : the velocity uncertainty and the repeatability of the acquisition system. The wave velocity of our specimens is 2 770 +/-140 m/s . Here, this uncertainty corresponds to a variability in the location of +/-1 mm. The repeatability was also tested and that gave an uncertainty of +/-1.9 mm. These two tests give an overall confidence interval of 5 mm on the location accuracy of our system.

Experimental set up

Specimens were cut into the annular disc in the tangential direction. The dimensions of the loaded area were 20x80 mm. The tensile loading was performed at an imposed displacement rate of 1mm/min until the complete failure of the specimen. During the test the load, the strain field and the acoustic emissions signals were recorded. The two sensors were placed at each end of the specimen, 70mm from each other. The wave velocity was measured for each specimen prior to testing. The outline of the experimental set up is shown Figure 3.

Acoustic emission signals versus load

AE signals are detected very early in the test under 10% of the maximum load. In the first phase (1), up to 60% of the maximum stress, many events of small amplitude and low energy occur (figure 4.a). These events are often related to matrix cracking [START_REF] Ceysson | Caracterisation du comportement en fluage de materiaux compoistes carbone/epoxyde étude de l'endommagement[END_REF]. In this phase the AE emission rate increases drastically (figure 4.b). In the second phase events over 80 dB and high energy are measured. These events are linked to fibre break. Over a load of 60% the AE rate is constant and around 100 events per second. Low amplitude and low to average energy events still occur in this phase. These two aspects combined could indicate friction due to fibre/matrix debonding. This change in damage mechanisms is not visible on the stress curve. The third phase is when failure occurs : multiple high energy and high amplitude events indicate multiple fibre breakage. In the same time, numerous events of lower amplitude are a sign of important matrix cracking. In this phase the material fails. The load was applied in the Y direction. The strain field before failure and the cumulative AE events are shown figure 6. To match the coordinate system of the acoustic emission location and the strain field, the coordinates of the crack were used : the maximum strain was matched with the crack location. The same repositioning was applied to the AE histogram : the maximum number of hits was matched with the crack coordinates. Considering the location accuracy and the repositioning of each coordinate system, the AE events were counted on 5 mm strips, every 5 millimetres (no overlap). On the AE event histogram (top of figure 6) a higher number of events occur around 30-35 mm and 40-50 mm. These two regions correspond to two high strain areas in the strain field. These high strain zones are in fact strips oriented at around 45° from the loading axis. The fibre organisation in the specimen is complex as shown on figure 1. However a previous study [START_REF] Flament | Digital image correlation applied to thermal expansion of composites[END_REF] revealed that the rectangular specimen had meshes in the 45° direction which could explain the aspect of the strain field.

EFFECT OF THERMAL CYCLING

During the engagement manoeuvre, sliding contact occurs between the clutch facing and the counter The temperature rise can be important in the case of repetitive engagement. The thermal loading is cyclic as the clutch is engaged and disengaged many times during its life cycle. Thermal cycling can cause volume damage and a good knowledge of these phenomena are necessary to guarantee life expandency. To identify and quantify this degradation mechanism, specimens were submitted to 6 thermal cycles, described in figure 7, with a maximum temperature of 200°C or 300°C. The specimens were then tested with the same monotonic tensile test as described in part 3.3. Strain fields and AE signals were measured. Figure 8 shows the stress-strain curves for the as-received and cycled material. The 200°C thermal cycles hardly change the ultimate strength of the material but decreases the maximum strain before failure. The 300°C cycles have a greater impact on the ultimate strength : after 6 cycles the ultimate strength is reduced by 30 %. AE signals for the two cycled specimens are shown figure 9. The phases 1, 2 and 3 have been identified with the same criteria as part 4.1, based on the AE rate and the discontinuities of the stress curve. When cycled at 200°C the specimen has the same ultimate strength but different AE signals. The shift from phase 1 to 2 happens at half the load of the as received one (30 % max stress of the as received material). Furthermore acoustic events of high energy and high amplitude are measured for a very low load, including 100dB events. The same observations can be made for the specimen cycled at 300°C, however the second phase is shorter and the material starts failing earlier in the test, discontinuities appear on the stress curve. Fibres break when 20% of the maximum load of the as received material is reached. The AE signals have shown that damage initiation and propagation in a thermally cycled material is different from the as-received material. This evolution is a sign of damage creation and weakening of the matrix and the fibres caused by thermal cycling. Fibres are more affected by 300°C cycles. These results give an information on the volume degradation which completes previous results on the damage mechanisms occurring on a thermally cycled clutch facing where surface cracking was observed [START_REF] Flament | Effect of thermal cycling on the mechanical properties of a continuous fibre composite used for car clutch facings[END_REF]. Macroscopic cracks were found on the surface of the 300°C cycled specimens, however nothing was visible, at that scale, on the 200°C cycled. The additional information given by AE signals as a damage monitoring technique has highlighted the fact that 200°C cycled specimen are affected by thermal cycling.

Figure 1 :

 1 Figure 1 : Preform and view of the rectangular specimen cut into the disc.

Figure 2 :

 2 Figure 2 : Schematic view of the process of DISC

Figure 3 :

 3 Figure 3 : Outline of the experimental set up (a) and photo (b)

Figure 4 :Figure 5 :Figure 6 :

 456 Figure 4 : (a. left) Amplitude and energy of the AE signals and stress curve. (b. right) AE rate versus stress

Figure 7 Figure 8 :

 78 Figure 7 : Thermal cycles

Figure 9 :

 9 Figure 9 : Amplitude and energy of the AE signals with the stress curve the 200°C and 300°C cycled specimens respectively.

EWSHM 2014 -Nantes, France

CONCLUSIONS

The aim of this work was to have a better understanding of the non-linearity of the stress-strain curve of the composite used in car clutch facings. To answer this question, simultaneous measures of the strain field, using DIC, and damage location, using AE, were done on a rectangular specimen under monotonic tensile loading. Local strain was then compared to local damage. The correlation between strain fields and AE location is possible providing correct use of the coordinate systems. It was found that maxima in the strain field correspond to increased local AE activity. Continuous damage was recorded during the test which could explain the non-linearity of the stress-strain curve. Furthermore AE signals were use to detect volume damage on specimens that were thermally cycled at 200°C or 300°C. After 6 cycles, the specimens were tested under monotonic tensile load with AE sensors detecting AE signals. These measures revealed volume damage of the 200°C cycled specimens that was neither visible on the stress-strain curve nor on the surface of the specimen.


Nicolas C M Marty

Sylvain Grangeon

Fabienne Warmont

Catherine Lerouge

Catherine Lerouge Alteration

Alteration of nanocrystalline Calcium Silicate Hydrate (C-S-H) at pH 9.2 and room temperature

Alteration of nanocrystalline Calcium Silicate Hydrate (C-S-H) at pH 9.2 and room temperature Nicolas C.M. Marty 1 , Sylvain Grangeon 1 , Fabienne Warmont 2 and Catherine Lerouge 1 1. BRGM, 45060 Orléans Cedex 2, France 2. CRMD, FRE 3520-CNRS -Université d'Orléans, 45071 Orléans Cedex 2, France

In the French design of deep underground radioactive waste disposal, cementitious materials will be used to build access structures, galleries, vaults and waste packages for Intermediate Level Long-lived Waste (ILLW). Part of these cementitious materials will be in physical contact with the Callovian-Oxfordian clay host rock formation (COx). The pH of the COx pore water is around 7 and its composition is very different from the cementitious pore water. Due to this chemical contrast, a chemical gradient will develop at the cement/clay interfaces and will induce mineralogical transformations.

Nanocrystalline calcium silicate hydrates (C-S-H) are the main constituents of concretes and are essential for cohesion of cement paste. It is therefore fundamentally important that we be able to reliably estimate C-S-H weathering/dissolution rates if we wish to estimate the durability of various cementitious materials. In order to mimic a clay/concrete interface, C-S-H alteration was studied with flow-through experiments at 25 °C and pH 9.2. Three materials with apparent Ca/Si ratios of 1.47, 1.38 and 0.86 were investigated. Physical (TGA/DTA), mineralogical (XRD) and chemical (EPMA, TEM/EDX) analyses were performed to characterize the reacting minerals. Initial stoichiometric Ca/Si ratios (C/S) were 1.22, 1.22 and 0.85, respectively. The excess of calcium is attributed mainly to the presence of CH intimately mixed in with C-S-H particles. Under our experimental conditions the stoichiometric C/S ratios decreased continuously with time. C-S-H compositions were monitored during flow-through experiments in order to know the mineral stoichiometry. The kinetics were found to be a function of the C/S. A decrease in layer-to-layer distance in the early stage of the alteration process is interpreted as interlayer Ca/Na exchange. A second dissolution step, marked by the stoichiometric release of calcium and silicate, certainly results from layer dissolution.