Laurent Maurin
email: laurent.maurin@cea.fr

Stéphane Rougeault

Véronique Dewynter-Marty

Jocelyn Périsse

Dominique Villani

Jean-Reynald Macé

Pierre Ferdinand

OFDR DISTRIBUTED TEMPERATURE AND STRAIN MEASUREMENTS WITH OPTICAL FIBRE SENSING CABLES: APPLICATION TO DRAIN PIPELINE MONITORING IN A NUCLEAR POWER PLANT

Keywords: drain pipeline, nuclear power plant, optical fibre, sensing cable, OFDR

This study deals with the testing of innovative Optical Fibre Sensing (OFS) cables deployed on ducts, with the aim to perform distributed temperature and strain measurements. Such cables contain several optical fibres devoted to be interrogated by Optical Frequency Domain Reflectometry (OFDR). The methodology has first been developed and qualified in laboratory. Then, real tests have been performed on a Nuclear Power Plant (NPP) drain system to demonstrate the industrial feasibility of such technology. To do so, two small diameter sensing cables, compatible with distributed temperature and strain measurements, have been qualified and afterwards installed along a sodium drain line at Superphénix NPP (liquid sodium coolant fast breeder reactor in current dismantling). Measurements have been performed during the preheating operation. Recorded data were post-processed according to a semi-empirical model taking into account temperature dependence and thermo-mechanical sensing cable behaviour. Optical fibre distributed temperature measurements were then successfully compared to thermocouple reference measurements, whereas optical sensing cable data were processed to provide distributed strain, then distributed curvature radius, which will enable, after numerical integration, to compute distributed displacement data. The goal is to assess the use of OFS for monitoring both temperature and mechanical strain distribution along a pipe under heat stress.

INTRODUCTION

Optical technologies are now widely used in instrumentation, in laboratory as well as in industry. Optical Fibre Sensors (OFS) are more recent applications of laser and telecom developments. Multiplexed Fibre Bragg Grating (FBG) are used in many industrial applications to monitor both strain and temperature, but their ability to provide distributed measurements is still limited. Here is studied a more recent technology of OFS based on the Rayleigh backscattering analysed in the frequency domain along the optical fibre: this new measurement technique, namely Rayleigh OFDR, is also sensitive to both temperature and strain, but it now enables high-resolution distributed measurements, thus leading to high measurement capacity along a single optical fibre.

SCOPE AND MOTIVATION

In a liquid metal coolant reactor, all the circuits have to be controlled in temperature to both guarantee fluid circulation (sodium is solid below 98°C) and that saturation temperature of oxide is respected. For these reasons, lots of heating cables and thermocouples (TC) are implemented in the plant to perform these basic functional requirements. Other TC sensors are also used to monitor specific areas or circuits like pipes, vessels, sumps, where temperature fluctuations or gradients induce periodic thermo-mechanical loadings which must be avoided for durability reasons. Other issue is the pipes or lines displacements induced by thermal expansion and thermo-mechanical loadings from room temperature up to 550°C in power operation. In particular, pipe monitoring is important for safety to control their durability and to verify design criteria consistency.

Superphénix NPP is being dismantled for 10 years now, and lots of innovating operations and realistic in-field testing conditions are still possible without constraints in comparison with an operating power plant, especially in terms of durability requirements of the equipments to be installed. Such conditions were fulfilled at Superphénix NPP. New OFS cables were implemented on a sodium drain line to monitor distributed temperature, strain and displacement. Important issues like the fixation method of the sensing cables, their routing procedure along the pipe drain line and the interfaces with heating cables have been advantageously evaluated on the field. The experimental feedback and expertise acquired here will be useful for future OFS instrumentation projects in NPP.

LABORATORY VALIDATION TESTS -TEMPERATURE AND STRAINS MEASUREMENTS

Experiments have first started by feasibility laboratory tests in order to validate temperature, strain, and curvature radius measurements. They rely on Rayleigh-based Optical Frequency Domain Reflectometry (OFDR), which determines the distributed State Of Polarisation (SOP) all along the fibre under test (Luna™ OBR-4600 instrument). These data are then post-processed to provide the Rayleigh frequency shift along the optical fibre with typically centimetre spatial resolution [START_REF] Froggatt | High-Spatial-Resolution Distributed Strain Measurement in Optical Fiber with Rayleigh Scatter[END_REF].

This technique now enables the development and qualification of new sensors for distributed measurements with resolutions close to 1 µm/m in terms of strain, and 0.1°C in terms of temperature.

However, since OFDR frequency shift Δν depends on both temperature and strain, it is necessary to proceed, at least, to additional measurements to compensate for the temperature influence. The solution proposed here uses a single optical fibre, free from stress, calibrated in temperature ( §2.1). It has the main advantage to be simple and easy to deploy on-site along a pipe.

Experiments concerning the design of the two sensing cables and the procedure to attach them have also been validated thanks to several tests performed in laboratory.

Temperature measurements: the flexible loose tube solution

The solution adopted relies on a single temperature-resistant optical fibre placed into a flexible loose tube. One key point is to let the optical fibre to move freely without any friction. This is important for both transportation and installation issues (the fibre must not be broken at any time), but also for subsequent measurements: a friction strain Δε friction equivalent to 10 µm/m has a crosstalk effect on temperature ΔT friction close to 1°C (the expected strains range from zero up to few hundreds of µm/m).

Temperature calibration results exhibit a quadratic behaviour [START_REF] Flockhart | Departure from linearity of fibre Bragg grating temperature coefficients[END_REF], and the deviation from the model does not exceed 1°C at the highest calibration temperature. The greatest deviation appears at the lowest temperature (close to 9°C), mainly due to temperature regulation issues, but it will have no impact since the field temperature will range from room temperature up to 220°C (Figure 1).

Strain and curvature radius measurements: the sensing cable

A single optical fibre glued to the pipe is sufficient for average longitudinal strains measurements, provided that temperature compensation means are available. However, additional data are required to perform displacement measurements.

The solution relies on a specific sensing cable made of three optical fibres measuring complementary strain contributions, respectively Δε 1 , Δε 2 and Δε 3 . This additional information enables curvature radius measurements according to Equation (1) [START_REF] Magne | Système de mesure distribuée des courbures d'une structure[END_REF][START_REF] Dewynter | Underground tunnelling monitoring based on sensitive optical fibre cable and Brillouin reflectometry[END_REF][START_REF] Dewynter | Tunnel Structural Health Monitoring with Brillouin Optical Fiber Distributed Sensing[END_REF]. in pipe flexural plane:

√ ∆ ∆ ∆ ∆ ∆ ∆ (1)
The sensitivity of this measurement mainly depends on the distance between each optical fibre, and is characterised by a sensing diameter ! , and the initial curvature radius " (Figure 2). This cable has been tested on a specific set-up designed to minimise friction effects in order to measure pure bending. In this configuration, experimental results exhibit a good correlation with expected data for strains not greater than 3000 µm/m (Figure 3).

Pipe strain and curvature radius measurements

Then, strain and curvature radius measurements have been validated on a mock-up of the same drain pipe as used in Superphénix NPP (1½" stainless steel pipe). The sensing cable has been glued to the pipe to maximise strain transductions between the pipe and the cable.

Then, a pulling force has been applied on a specific part of the pipe to create constant flexural strains. The measurements on this section exhibit the expected behaviour with constant strain levels provided by each fibre of the sensing cable. Applied to curvature radius (Equation ( 1)), it also demonstrates the sensitivity of such measurements to strain fluctuations, especially on a straight pipe section (Figure 4).

Pipe temperature calibration measurements

Finally, it is also necessary to calibrate the sensing cable attached to the pipe since the thermal behaviour of the whole set defined by the sensing cable and the pipe has to be taken into account.

To do so, we have used a two-metre long fully instrumented pipe, including the optical fibre temperature sensor in its loose tube. Reference temperature measurements are provided by several TC sensors in contact with the pipe.

The frequency shift of the sensing cable ∆# $%& vs. fibre used for temperature compensation ∆# $%& then clearly exhibits a non-linear dependence in temperature. This non linearity will be taken into account into a semi-empirical model ( §4.2) to get more accurate strain measurements (Figure 5).

ON-SITE INSTALLATION AT SUPERPHÉNIX NUCLEAR POWER PLANT AND MEASUREMENTS

On-site optical fibre sensing line installation

Prior to installation, the optical fibre sensing line has been delivered in a dedicated shipping box to NNS based at Superphénix NPP. Installation issues have been taken into account to facilitate the sensing cable integration on the drain line to avoid any optical fibre break (Figure 6). The sensing cable was deployed over 14 m between the two sodium tanks. A specific care was taken to keep the measurement cable in the flexural plane for maximum strain sensitivity (Figure 7). For temperature reference, several thermocouples were placed at some representative areas along the pipe. An additional sensor was also installed to evaluate the pipe displacement. All the drain line pipe is heated (T>98°C) with electrical heating cables in contact with the pipe to keep sodium in liquid state (Figure 8).

Field measurements during the preheating operation

The measurement stations were located away from the heated pipe, behind a protective wall. The total optical fibre length to the instrument did not exceed the 70 m range to operate in standard mode.

The Luna™ instrument was controlled over a LAN network from a remote computer which sent the appropriate instructions to record the binary SOP data for post-processing purposes (Figure 9). A heating power station was specifically installed and tested by NNS before the measurements, enabling to tune independently each heating cable. In some sections, heating and sensing optical fibre cables overlapped.

The first day was dedicated to a first heating test at max. 100°C to validate the measurement loop and for thermo-mechanical relaxations, and the two other days to higher temperature measurements (Figure 10). Both optical fibre and thermocouples measurements were continuously recorded during three days of experiments, without any loss of data. The resulting binary SOP data volume exceeded 67 GB.

DATA ANALYSIS AND RESULTS

Temperature measurements

The optical measurements were processed according to calibration to get temperature profiles, first for comparisons with thermocouple measurements. Thereby, optical fibre temperature measurements, in comparison with thermocouple reference sensors, appear to be relevant, with limited discrepancies and similar evolutions vs. time. Moreover, optical measurements outside their calibration range are still consistent with thermocouple data (Figure 11). On their side, the distributed measurements underscore, especially during the first day in limited heating power conditions, a non-homogeneous temperature profile with significant gradients. It is also interesting to notice that pipe mechanical attachments are inducing heat leaks, with up to 50°C discrepancies at their position in different heating conditions. Thermal peaks are observed when heating cables are very close to the optical fibre temperature sensor (hot spots) (Figure 12).

Strain measurements

Pipe mechanical strain +, -. / / can now be calculated according to next equations: f, g i and K i are respectively calibration functions for: i) the reference temperature fibre ' 0 1 , ii) the mechanical strains +, -. for each fibre i in the sensing cable, iii) the sensing cable relative sensitivity to temperature ∆# $%& ∆# $%& 234 5 for each fibre i once glued to the pipe (see Figure 5).

+, -. / / 6 ∑ +, -. 6 8 8

+ :; 1 <0 -; > > ? × ' 0 1 6 -' " 0 1 6

+, -. 6 A B, -. " 6 , +# $% & 6 -+# $%& 0 1 6 × D E' " 6 , +# $%& 0 1 6 FG

' 0 1 6 4 E' " 0 1 6 , +# $%& 0 1 6 F (4)

Rayleigh frequency shift measurements are given by HI $J& KLM for the reference temperature section, and by HI $J N& O for each optical fibre i in the sensing cable. The relevant parameters are then calculated taking into account initial reference states in terms of mechanical strains N PLQ R O and temperatures J R O and J R KLM . Parameter α stands for the thermal expansion coefficient (Figure 13). Strain measurements are then processed to get curvature measurements according to Equation [START_REF] Froggatt | High-Spatial-Resolution Distributed Strain Measurement in Optical Fiber with Rayleigh Scatter[END_REF]. The four bends are clearly identified: their curvatures remain quasi unchanged during the heating process. However, on the straight sections, curvature changes are important: this is mainly due to the measurement sensitivity to strain error measurements (see Equation (1) and Figure 4). These data can now be numerically integrated to finally provide distributed displacement measurements [START_REF] Magne | Système de mesure distribuée des courbures d'une structure[END_REF][START_REF] Dewynter | Underground tunnelling monitoring based on sensitive optical fibre cable and Brillouin reflectometry[END_REF][START_REF] Dewynter | Tunnel Structural Health Monitoring with Brillouin Optical Fiber Distributed Sensing[END_REF]. However, this work could not have been achieved in the project timeframe.

Comparison with strain calculations performed earlier to validate the design of the drain lines shows some discrepancies with the measurements (generalised strain ,̅ T ,̅ U :

V V " , W ?XW Y Y with ,̅ U Z ∑ ,U [ ,[
is delivered by numerical simulations, whereas average uniaxial strain 〈, ]] 〉 is measured by the sensing cable along its z axis). However, distributed strain and curvature profiles are consistent with the calculated pipe displacements.

CONCLUSION AND PERSPECTIVES

As a conclusion, a theoretical study and laboratory tests have first been completed on a pipe mockup to qualify prototype sensing cables and estimate both strain and temperature sensitivities. On-site measurements have been performed at Superphénix NPP, in Creys-Malville (France), to validate the feasibility. Installation issues have been taken into account, and cables deployed and connected to the remote OFDR sensing system controlled for continuous measurements during several days. Temperature measurements have first been carried out, and later on, compared with data from thermocouples located at several points all along the pipe, demonstrating the essential contribution of this technique to provide relevant and distributed information in terms of temperature sensing. In the same time, a specific optical sensing cable manufactured for this purpose, enabled distributed strain measurements along the pipe during the sodium drain operation A theoretical model, based on the strain measurements provided by three optical fibres, compensated from temperature crosstalk effects, has been applied to these measurements. It demonstrates the relevance of such measurements, leading first to some consistent strain measurements, and therefore, to distributed curvature radius measurements along the pipe, and finally to subsequent distributed displacements.

Figure 1 :

 1 Figure 1: Temperature calibration results -Optical fibre in loose tube, free from friction effects

Figure 2 :

 2 Figure 2: Strain sensing cable manufactured by Acome™, devoted to curvature radius & strain measurements

Figure 3 :

 3 Figure 3: Curvature radius (centre) and strain measurements (right) with experimental set-up (left)

.

Figure 4 :

 4 Figure 4: Strain measurements along bended instrumented pipe with experimental set-up on left

Figure 5 :

 5 Figure 5: Temperature calibration measurements (left) and relative sensitivity ∆# $'& ( ∆# $'& ) *

Figure 6 :

 6 Figure 6: Installation to be instrumented (tested section in blue), and the measurement cable delivered to NNS

Figure 7 :

 7 Figure 7: Left: reservoir bottom -Centre: passage through the wall -Right: exit to the measurement station

Figure 8 :

 8 Figure 8: Thermocouple temperature sensor (left) and displacement sensor (right) for reference measurements

Figure 9 :

 9 Figure 9: Remote measurement station to control the OBR-4600 (left) and TC measurement station (right)

Figure 10 :

 10 Figure 10: Typical Rayleigh OFDR measurement profiles (left) and thermocouple measurements (right)

Figure 11 :

 11 Figure 11: OFDR measurements compared with 03WT5 NNS thermocouple (left: 1 st day, right: 2 nd day)

Figure 12 :

 12 Figure 12: Distributed temperature measurements on first day (left) and second day (right)

Figure 13 :

 13 Figure 13: Distributed strain measurements during heating (left) and cooling (right) during the first day

Figure 14 :

 14 Figure 14: Distributed curvature measurements during the first day -initial state on left

Figure 15 :

 15 Figure 15: Distributed -amplified -displacement calculation of the pipe (blue line = pipe at rest, red line = pipe with mechanical and thermal loads)

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

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENTS

This project was made possible with the support and interest of EDF/CIDEN in charge of the Superphénix NPP dismantling. Authors would like to thank O. Cunibil and P. Battini from NNS for their support and contribution during the on-site experimentation phase.


Sara Casciati
email: sara.casciati@msn.com

Fabio Casciati

Lucia Faravelli

Daniele Bortoluzzi

MODELLING THE HUMAN INDUCED VIBRATIONS IN A CABLE-STAYED PEDESTRIAN TIMBER BRIDGE

Keywords: human induced vibration, in situ testing, timber footbridge, timefrequencies analysis

In this paper the data acquired on a pedestrian timber bridge under different "moving" loads configurations are reported and analysed by applying a time-frequency decomposition technique. This approach allows the authors to better identify the dynamic behavior of the bridge under the above loads. A first in situ experimental campaign was carried out on November 7, 2013, with the aim of recording the accelerations induced by people walking and running along the bridge (the so called human induced vibration -HIV). For this purpose, the footbridge was equipped by accelerometers. The pedestrian bridge under investigation is located not far from the town of Belluno, Italy, and connects the two sides of the outlet channel of the "Santa Croce" Lake. To better fit the structure to the surrounding naturalistic area, ecofriendly construction materials with low environmental impact were adopted during the design stage. In particular glued laminated timber (GLT) and steel elements are used, limiting the use of reinforced concrete only for the foundation system.

INTRODUCTION

In recent years the use of timber as construction material has become quite common in all Europe, in particular for the design of pedestrian bridges, but not only. This is in general a preferred choice in all those applications where the structure has to fit well in the surrounding landscape. Thanks to the development of new construction materials, as for example the glued laminated timber (GLT), nowadays the designers are able to conceive footbridges with span longer than 100 m using timber elements [START_REF] Caetano | Dynamic design of slender footbridges[END_REF]. As in the considered case study, the realization of large span footbridges usually requires the adoption of a hybrid solution coupling timber with steel. This coupling, together with the slenderness of the structural skeleton of the footbridge, makes quite complicated foreseeing during the design phase the vibrations induced by people crossing (walking and/or running) the bridge ( [START_REF] Van Nimmen | Characterisation of walking loads from inertial motion tracking[END_REF] and [START_REF] Bortoluzzi | Semi-Active Control for the Mitigation of Vibration on a Footbridge[END_REF]). It is well known that these problems are typically not dangerous in terms of structural/resistant safety, but are related to the comfort of the pedestrians. They are well documented in literature, and different procedures are proposed for the vibrations mitigation ([4]- [START_REF] Van Nimmen | Vibration serviceability of footbridges: Evaluation of the current codes of practice[END_REF], among the others), but an unified solution for "pedestrian-crowd loads" is not coded yet. A numerical procedure based on experimental tests was developed by the authors. The reader is referred to [START_REF] Casciati | Human induced vibrations in a pedestrian timber bridge[END_REF] and [START_REF] Casciati | Pedestrian timber bridges: experimental investigation and modelling[END_REF].

In this paper, the measured structural response of an existing GLT cable-stayed pedestrian bridge is reported, analysed and discussed. The authors are cooperating with the bridge designer and with the timber element producer to test different timber footbridges in order to better understand the dynamic behaviour of this type of structures, and develop a numerical model able to simulate the interaction among the structure and the human induced loads in a realistic manner.

THE CASE STUDY: "TESA" FOOTBRIDGE

The footbridge studied in this paper is located in Farra d'Alpago, an Alpine village close to the town of Belluno (Figure 1 The bridge, built in 2005, connects the two sides of the outlet channel of the "Santa Croce" Lake.

To better harmonize the structure with the surrounding naturalistic area, only eco-friendly materials (i.e. wood and steel) were adopted during the design stage, limiting the use of reinforced concrete to the foundations only. Particular care was paid to the protection of the wood specimens; in particular ad hoc protective treatments against the attack of environmental agents (i.e. rain, snow, fungus, molds, and so forth) were used. As one can see from Figure 1-b, the static scheme of the bridge is the classic cable-stayed solution. In total, sixteen steel cables are adopted; in particular, eight "internal-secondary" cables of diameter 32 mm, and other eight "external-main" cables of diameter 44 mm. From a geometric point of view, the span length is about 110 m subdivided into three segments (each of them made of curved GLT-BS14 and GLT-BS16 beams -as indicated in the DIN1052 code) of length 22.5m, 65m (in the middle) and 22.5 m, respectively; while the free crossing width of the deck is about 3.2 m. The two antennas are 16m high. The deck shows a classical "U-shape" cross section (Figure 2-a). It is realized by linking two main curved GLT beams with transversal U-shape steel tubular elements of high strength S355J0 (according to UNI EN10025 code). These elements are connected by steel braces of circular cross-section that provide the lateral stiffness. Each arcuate GLT beam are also posed over neoprene support on both ends (Figure 2-b). The structural scheme is completed mounting, on the "U-shape" elements, four longitudinal GLT rectangular beams (cross section 10x16. The data acquisition is tailored to standard tri-and uni-axial Kinematics accelerometer, while the data transmission is obtained by wireless transceivers developed by the authors [START_REF] Casciati | Human induced vibrations in a pedestrian timber bridge[END_REF]. These devices are able to cover the entire span length of the bridge [10]- [START_REF] Bortoluzzi | Comparison of accelerometric response records on a timber footbridge[END_REF], without the need for the intermediate storage stations. During the in situ tests, a total of six accelerometers is deployed; namely, two uni-axial accelerometers are anchored to the "internal-main" cables and labelled as WSa5_ch1 and WSa5_ch2, and other four tri-axial devices, with the i-th accelerometers denoted as WSai, i=1,..,4, , are located in ad hoc positions along the deck. Further details about the sensor configuration are provided in Figure 3. Different types of loads are considered during the experimental campaign. A first set of acquisitions is focused on the records of the acceleration due to wind loads (environmental loads). These acquisitions are used for the calibration and verification of the data acquisition-transmission system. The following tests are focused on the records of the dynamic response of the footbridge under the so called "human induced loads" (HIL), such as running and walking. Different configurations are considered and are described in the following.

DATA ACQUISITION AND DATA ANALYSIS

Time-Frequency analysis of the signals

The classical approach to the data analysis is based on the use of the "standard" Fast Fourier Transform (FFT), that allows one to decompose the original signal into a series of trigonometric functions. This approach limits the possibility to capture the time-varying behaviour, or in other words as the frequencies evolve over the time. Thus, the classic approach is not enough sophisticated to characterize the signal recorded on field, especially if the dependence over the time is crucial, as in the case of HIL, where the movement of the pedestrians over the deck, and so the corresponding dynamic response of the footbridge, are sensitive to the time variation [START_REF] Kijewski | Wavelet Transforms for System Identification in Civil Engineering[END_REF]. Thus, in order to highlight the interaction between the pedestrians and the structure and to identify when a particular "dynamic mode" is activated by the humans, a time-frequency analysis of the records on field is developed.

Following the time-frequency procedure proposed by Choi-Williams (CW) [START_REF] Choi | Improved Time-Frequency Representation of Multicomponent Signals Using Exponential Kernels[END_REF] and Cohen

( ) 2 2
, ,

s e s θ τ θ τ - Φ = ∈ℜ , (1)
the time-frequency distribution ( , ) P t ω can be written as:

( ) ( ) ,1 2 1 ( , ) , , 4 i t P t W t u e R t dud τϖ ω τ τ π +∞ - -∞ = - ∫∫ (2)
where R t,1 is the autocorrelation function, u and τ replace t and θ replace ω when integrating R t,1 .

HIL tests carried out and data result

The tests carried out on field during the experimental campaign can be summarized in two groups :

• test I -walking loads: in this configuration different cases, regarding a round trip along the bridge, are considered. In particular in this paper the following tests are analysed: a person (test Ia) and six persons (test Ib); • test II-running loads: this configuration consists of a round trip along the bridge of a running person. In order to give a better interpretation of the data, each record is classified into two different sets: crossing from the right to the left side of the footbridge (labelled as RtoL), and from the left to the ride side (labelled as RtoL). All the accelerations are acquired with a sampling frequency of 100 Hz.

-test Ia

As defined above this test consists of collecting records of the accelerations of the footbridge due to a round trip along the deck. The mass of the person is 85 Kg. Further details about this test are summarized in Table 1. Following the procedure proposed in the previous paragraph the time-frequency analysis is performed for the data acquired by WSa2. Along Y axis three main frequencies (average values) appear: 1.35 Hz: constant over the time; 5.00 Hz: it activates only during the time period from 30 to 70 sec for the RtoL, and from 80 to 120 sec for the LtoR. This means that this particular frequency is detected when the pedestrian is located about 15-20 m before the position of the sensor WSa2; 5.80 Hz: it activates only during the time period from 10 to 32 sec for the RtoL. Several vertical lines (mostly located between 35 and 60 sec), that represent the shifts in terms of frequencies, appear during the RtoL crossing, while they disappear during the LtoR crossing. These shifts can be related to noise into the signal due to the overlapping of the waves associated to the movement of the pedestrian from the sides towards the mid-span. Along Z axis two main frequencies (average values) appear: 2.00 Hz: it activates during the time periods from 35 to 70 sec for the RtoL, and from 105 to 150 sec for the LtoR. This means that this particular frequency is detected while the pedestrian is located about 10 m before the position the sensor WSa2 and about 40 m after it; 6.00 Hz: it activates only during the time period from 30 to 70 sec for the RtoL. Once again, this means that this particular frequency is detected while the pedestrian is located about 10 m before the position the sensor WSa2, and about 40 m after it. During the LtoR crossing, this frequency almost disappear. One can observe that, also for the results along the Z axis, the time-frequency plot for the LtoR crossing is more "clear/clean" with respect to the RtoL crossing. Moreover, the time-frequency plots along the Z axis show, in general, a clear trend compared with the ones along the transversal Y axis.

-test Ib

In this test, the records of a round trip along the deck of six persons is considered. The average mass is 80 Kg. The pedestrians proceed in pairs by keeping a distance of 1 m between each other in the longitudinal direction of the footbridge, and a distance of about 0.5-0.7 from the closest lateral edge of the footbridge. Further details about this test are summarized in Table 2.

-test II

During this test, the footbridge response under a running person along the deck (round trip) is recorded. The average mass is 85 Kg. Further details about this test are summarized in Table 3.

NUMERICAL MODEL OF PEDESTRIAN(S) LOAD(S)

A numerical model of the pedestrian(s) load(s) is developed and implemented within a finite element model of the footbridge built within MARC Mentat2010 environment [16]. Given the distribution of the nodes of the mesh and the configuration of the pedestrian(s) , the force-time trend can be easily defined following simple kinematics considerations. In particular, in this paper the numerical implementation of the previously described test Ib is considered as an example. The following hypotheses are introduced when developing this model:

• • •
• Each person is considered as a point load on the node of the mesh. The mass is assumed to be 80 Kg/person (that is 785 N/person). The transversal (along Y axis) component of the load is assumed to be 10% of the component along the gravity (Z) axis; • • • • The distance between each pair of the mesh nodes is assumed to be 62.5 cm, which is comparable with a human average footstep during a "normal" walk; • • • • "Mass" and "load" are moving along the deck as described by assigning the above defined force-time trend to each node of the mesh; • • • • The velocity of the pedestrian crossing the footbridge is held constant along the simulation of a uniform linear motion, and is assumed, for the example herein reported, to be 1.35 m/s; • • • • The spatial configuration of the pedestrians is assumed the same along the simulation. In other words, the distance between two consecutive pedestrian in both the longitudinal and transversal directions of the deck is fixed. This implies that, during the walk, each following pedestrian takes the place of his/her predecessor. Further details of the pedestrians loads model are summarized in Figure 6-a. Once the model has been implemented in the finite elements software, a dynamic transient analysis is performed. The above described time-frequency analysis approach is applied to the acceleration time histories obtained from the numerical simulation. In Figure 6 As one can see from the above plots, the results achieved by the proposed model fit well the on field measurements (the reader is referred to Figure 4-b for a comparison). Some discrepancies can be related basically to two aspects: first, the average value of the velocity is assumed constant for the proposed model and could be not exactly the same as during the test on field (in other words, during the test probably the pedestrian walked with a non-uniform linear motion); second, the assumption of an equal distribution of the mass/load among the persons could be too restrictive.

CONCLUSIONS

In this paper the dynamic response data under HIL were carried out on field during experimental tests. The results are analysed and compared in order to identify the behaviour of the structure. Numerical model of the pedestrian(s) load(s) is implemented. It is worth noting that this is a preliminary approach in order to introduce a numerical procedure that reproduces the pedestrian(s) load(s), and it represents a "deterministic" strategy to identify the HIL. A more sophisticate model (based on a stochastic simulations approach ) is in process of elaboration and definition by the authors.

Figure 1 :

 1 Figure 1 : Footbridge under study. a) location (red line indicates the bridge); b) lateral view

Figure 2 : 1 . 1

 211 Figure 2: Structural scheme of the deck. a) view from the bottom ; b) detail of the neoprene support 1.1 First experimental campaign On November 7, 2013 the first experimental campaign was performed. The aim of this first set of measurements was the acquisition of the dynamic response (in detail, the acceleration components of relevant points along the footbridge deck were measured) under different loading conditions.The data acquisition is tailored to standard tri-and uni-axial Kinematics accelerometer, while the data transmission is obtained by wireless transceivers developed by the authors[START_REF] Casciati | Human induced vibrations in a pedestrian timber bridge[END_REF]. These devices are able to cover the entire span length of the bridge [10]-[START_REF] Bortoluzzi | Comparison of accelerometric response records on a timber footbridge[END_REF], without the need for the

Figure 3 .

 3 Figure 3. Sensors equipment configuration employed during the first tests in situ

[ 13 ]

 13 , let t denote the time and ω the pulsation; by introducing the Fourier Transform W(t-u) for the kernel function ( ) , θ τ Φ of CW, which is given by

Figure 4 ,Figure 4 .

 44 Figure 4. Time-frequency plots from the data recorded by sensor WSa2 during test Ib. a) RtoL data along Y transversal axis; b) RtoL data along Z gravity axis

) 4 .Figure 5 .

 45 Figure 5. Time-frequency plots from the data recorded by sensor WSa2 during test II. a) RtoL data along Y transversal axis; b) RtoL data along Z gravity axis

Figure 6 .

 6 Figure 6. Pedestrians model implemented for test Ib. a) Scheme of the loads induced by pedestrians; b) Timefrequency plots of the acceleration response simulated at node ID647 (WSa2) for the RtoL crossing along Z gravity axis

Table 1 :

 1 Walking (round trip) of one person.

	Type	ID
	Day/Time	November 7,2013 / 2.48 pm
	Test type	walking (round trip)
	Air temperature	15°C
	Pedestrian(s) num.	1 person
	Total Pedestrian(s) mass	85 Kg
	Total time duration	≈2:30 min
	RtoL time duration	≈1:15 min
	LtoR time duration	≈1:15 min
	Average velocity of the pedestrian(s)	1.45 m/s

Table 2 :

 2 Walking (round trip) of six persons.

	Type	ID
	Day/Time	November 7,2013 / 3.00 pm
	Test type	walking (round trip)
	Air temperature	15°C
	Pedestrian(s) num.	6 persons
	Total Pedestrian(s) mass	480 Kg
	Total time duration	≈2:42 min
	RtoL time duration	≈1:21 min
	LtoR time duration	≈1:21 min
	Average velocity of the pedestrian(s)	1.35 m/s
	As an example in

Table 3 :

 3 Running (round trip) of one person.

	Type	ID
	Day/Time	November 7,2013 / 3.15 pm
	Test type	running (round trip)
	Air temperature	15°C
	Pedestrian(s) num.	1 person
	Total Pedestrian(s) mass	85 Kg
	Total time duration	≈0:46 min
	RtoL time duration	≈0:23 min
	LtoR time duration	≈0:23 min
	Average velocity of the pedestrian(s

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

EWSHM 2014 -Nantes, France

ACKNOWLEDGMENTS

The authors acknowledge the cooperation of the designers Dr. Arch. Lio Parcianello and Dr. Ing. Stefano Boranga and, for the timber elements produced by Rubner Holzbau S.p.A. of Bolzano (ITA). They are also in debt with the Municipality of Farra d'Alpago and the owner of the bridge (Comunità Montana dell'Alpago), for providing them access to the structure and to the technical documents. Moreover, the authors acknowledge the cooperation of Erjon Prenga and Marco Archinti who developed the data analyses as partial fulfilment of their duties toward the Master Degree in Civil Engineering at the University of Pavia.


Marian Ralbovsky
email: marian.ralbovsky@ait.ac.at

João Pedro Santos

Maciej Kwapisz

Sonja Dallinger

Jose Manuel Catarino

Jose Manuel

Catarino Damage

José Manuel Catarino

Damage Detection Based on Structural Response to Temperature Changes and Model Updating

Keywords: damage, detection, temperature, model updating, sensitivity

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

INTRODUCTION

Successful damage detection on bridges highly depends on extracting suitable indicators from monitoring data. These indicators should fulfil the requirement of being highly correlated with damage phenomena. One of the first indicators used for damage detection were dynamic properties: eigenfrequencies, mode shapes and later also damping. Model updating based on data from vibration monitoring was a topic of many scientific contributions. A summary of vibration-based damage detection techniques was given by Doebling [START_REF] Doebling | A Summary Review of Vibration-Based Damage Identification Methods[END_REF]. The research headed later towards combination of different indicators, example of which is the contribution of Shih [START_REF] Shih | Vibration Based Structural Damage Detection in Flexural Members Using Multi-criteria Approach[END_REF], where a multi-criteria approach using vibration-based indicators was proposed. The combination of different indicators was extended to the use of static measurements. Application of such approach on a long-span suspension bridge was shown by Wang [START_REF] Wang | Progressive Finite Element Model Calibration of a Long-span Suspension Bridge based on Ambient Vibration and Static Measurements[END_REF]. The necessity of engineering judgement in the process of model updating was described by Schlune [START_REF] Schlune | Improved Bridge Evaluation through Finite Element Model Updating using Static and Dynamic Measurements[END_REF], who emphasized the need of manual model adjustments prior to model updating. The effect of temperature on damage detection results was detected early. Eigenfrequency changes caused by temperature effects on different structures were described in the works of Peeters&DeRoeck [START_REF] Peeters | One-year Monitoring of the Z24-Bridge: Environmental Effects versus Damage Events[END_REF], Farrar [START_REF] Farrar | Variability of Modal Parameters Measured on the Alamosa Canyon Bridge[END_REF] or Ralbovsky [START_REF] Ralbovsky | Frequency Changes in Frequency-based Damage Identification[END_REF]. The effect of temperature was considered as an obstacle for damage detection. Various methods for removing this effect were proposed, for example in the works of DeRoeck [START_REF] Deroeck | Dynamic Monitoring of Civil Engineering Structures[END_REF], Hu [START_REF] Hu | Continuous Dynamic Monitoring of a Lively Footbridge for Serviceability Assessment and Damage Detection[END_REF] and many other scientists. The present paper aims not at supressing the temperature effect, but rather the opposite: its use for damage detection purposes. The methodology is explained in chapter 1, following by presentation of simple demonstrative numerical examples in chapter 2. The method is applied on two bridges described in chapter 3. Results of simulated damage scenarios are shown in chapter 4.

METHODOLOGY

Temperature load represents a static load case. Structural response to a given temperature loading is determined by structural stiffness matrix K, thermal expansion properties and the boundary conditions. For the success of damage detection using the proposed method it is vital that the damage to be identified affects the stiffness matrix. Typical examples of damage cases affecting the stiffness are development of cracks in concrete and change of boundary condition's stiffness. Furthermore, bridge deformation can also influence the stiffness matrix due to second-order effects. If the vector of structural response X (which includes displacements, strains and inclinations) to a given temperature loading T is dependent on structural parameters influencing the stiffness matrix K, then identification of structural parameters based on measured structural response X is possible. The identification can be accomplished by model updating, which is defined by solving an optimization problem. The procedure implies evaluation of an objective function J that quantifies the discrepancy between measured and calculated responses. Mathematical optimization procedures are then used to adjust structural parameters p in such way as to minimize the objective function J. In the proposed method, the objective function is defined as:

                            i i m i c i m T X T p X T X p J , , , 1  (1) with   T p X i c   ,
and T X i m   , being the calculated structural sensitivity of quantity i (displacement, strain or inclination at a given point on a structure) to temperature change and the mean of its measured counterpart, respectively. The difference between the calculated and measured sensitivities is then divided by standard deviation  of the measured sensitivity, which ensures normalization of different quantities, as well as their weighting by measurement uncertainty.

PRESENTATION OF SIMPLE EXAMPLES

The use of changes in structural sensitivity to temperature loading is presented in this chapter using simple numerical examples. Structural damage, which produces stiffness reduction, changes structural response to temperature loading, as it is shown in the example of continuous girder below. On structures that have pronounced second-order effects, the structural response changes with deformation state, which is shown below using an example of single span girder. The examples presented in this chapter are solely results of numerical calculations.

Effect of damage on structural response to uniform temperature

The following example is a three-span continuous girder, on which stiffness reductions were introduced and their effects analysed. The girder has span lengths of 6 m, 8 m and 6 m. Its crosssection comprises 30 x 60 cm and the utilised material has elasticity modulus of 30 GPa. Beam elements were used for the model. Introduced damages are listed in Table 1. The damage extent was varied between 0% (no stiffness reduction) and 100%, which represents damage extents as listed in Table 1.

Effect of permanent deformation on structural response to uniform temperature

This example of single-span girder is presented to illustrate second-order effects on structural sensitivity to temperature loading. A simple single span girder with 9 m span was modelled using the same cross-section and material as in previous example. Amplitude of permanent deformation was varied (0 -34 cm), as well as stiffness of horizontal springs (8 -8192 MN/m). In these differrent configurations, sensitivity of strain and deflection in midspan to uniform temperature change of T=+1 K was calculated. It was found that both strain and deflection sensitivity (Figure 2) exhibit distinct changes at higher values of horizontal stiffness of boundary condition. The value pairs of strain and deflection sensitivity can be uniquely linked to value pairs of permanent deformation and spring stiffness. Thus, measurements of strain and deflection sensitivity can be used for identification of permanent deformation and horizontal spring stiffness. However, at low values of horizontal spring stiffness, the sensitivity is radically reduced, which would render identification of permanent deformation unfeasible.

BRIDGE MONITORING SYSTEMS

Two bridges with running monitoring installations were analysed as case studies. The bridge structures and monitoring installations are in this chapter, while simulated damage scenarios and evaluated identification capabilities are shown in chapter 4.

Prestressed concrete box-girder bridge with tie bars

The prestressed concrete box-girder "Teufenbach" Bridge, located in Austria, was erected in 1959. In 2010 an autonomous online SHM system was installed with the aim of carrying out early damage detection, thus contributing to increase of safety and to reduction of maintenance costs. Sensor positioning was based on the principle that any damage in the bridge would produce dead load redistribution and change in cable forces. Consequently, displacement and rotation changes close to cable anchorages were chosen as sensitive quantities that should be measured (Santos [START_REF] Santos | Multivariate statistical analysis for early damage detection[END_REF]).

Hydrostatic pressure cells (NL) and magnetostrictive transducers (DH) were used for measuring deck and joint displacements, respectively. Bi-axial inclinometers (CL) were installed on the top of the pylons. Differential displacements and rotations are also monitored using the same type of inclinometers (CL), installed in each foundation and abutment (Figure

Finite-Element Models

The Finite-Element models that were used in model updating (Figure 5) were constructed using commercial software packages. Soil behind the abutments of Teufenbach Bridge was modelled using horizontal and vertical springs, the stiffness of which was adjusted in model updating process.

SIMULATED DAMAGES AND MODEL UPDATING

Structural identification performed on these two bridges aimed at identification of the current state and evaluation of damage detection capability in particular simulated damage cases. Identification of current deformation state was performed on the Teufenbach Bridge that has a structural type suitable for such application. Relevant damage scenarios were simulated on both bridges.

Identification of deformation state and boundary stiffness

The Teufenbach Bridge is of a structural type sensitive to second order effects. The vertical deformation has a distinct effect on bridge response to temperature. Also the soil behind abutments affects significantly the structural response. Model updating using the two model parameters: boundary condition stiffness and permanent deflection at midspan was carried out. Model optimization was performed with the target of fitting to measured values of deflection sensitivity at midspan (0.82 mm/K), and strain sensitivity in the midspan at girder bottom (11.0 µm/m/K). Figure 6 shows objective function values for different combinations of boundary stiffness k and midspan deflection w. The optimal solution was reached for parameter value pair of k=15000 MN/m and midspan deflection of w=23 cm. The updating results were verified by measurement of bridge geometry using precision total station. By comparison of measured bridge geometry with construction plans, a deformation of 23 cm at midspan could be determined. The displacement measured by total station matched exactly the value calculated by model updating.

Damage scenarios on Teufenbach Bridge

In order to investigate the capability of damage detection, several damage scenarios were simulated. Six types of damages were simulated (Table 2) and each was introduced using different extents. Damage types 3 and 4 produced change of bridge stiffness, whereas damage types 1,2,5,6 were assumed without change of structural stiffness.

Damage scenarios on the Guadiana River Bridge

FE-model of the cable stayed bridge was changed in 37 damage types and each damage type was simulated with different extents. Beside reduction of cable stay stiffness, damages in bridge deck and pylon were simulated. In this chapter, the scenarios with cable stay stiffness reductions are presented. In each scenario, the stiffness of one single cable was reduced starting from 0% up to 90% of its original stiffness. Figure 7 shows the structural response in terms of dead load effect (left) and temperature effect (right). Each line represents the effect of stiffness reduction of one particular cable stay. Considering the fact that deflection sensitivities of more than 0.01 mm/K are considered to be detectable, whereas the detectability limit of change in absolute displacement is 0.2 mm, it can be observed that using deflection sensitivities to temperature gives no advantage over using absolute displacement values in this case. The advantage would be present in the cases where no measurements of healthy state would be available. In such cases, the changes of absolute displacement would not be available, whereas the deflection sensitivity can still be determined.

CONCLUSION

The damage detection method presented in this paper shows the applicability of using structural response to temperature as indicator of structural changes and its use in the objective function of model updating algorithm. It was shown in the examples that the method was successful in identifying structural deformation state on a bridge that is sensitive to second order effects, where the calculated deformation value was also verified by measurements of bridge geometry. Furthermore, it was concluded that measured absolute change of structural deformation (displacement, strain, inclination) in different damage cases can be considered as a more sensitive indicator than change of sensitivity to temperature. However, in cases where measurements before occurrence of damage are not present, such data on change of deformation is not available. The sensitivity of structural response to temperature can still be measured, thus the presented method can still offer a possibility to identify the structural state. It was shown in the presented calculations that deformation sensitivity to temperature varies between structural types and simulated damage cases. Therefore, performance of the method should be evaluated for each particular application. If available, it is recommended to use this identification procedure in addition to other detection methods, for example methods based on dead load redistribution, to achieve higher reliability and robustness of results.

Table 1 :

 1 Damage cases simulated on three-span girder Damage case Location, affected length, max. extent dc1 At support S2, L = 0.7 m, K red,max = 70% dc2 Midspan of central span 2, L = 0.8 m, K red,max = 50% dc3 At support S3, L = 0.7 m, K red,max = 70% dc4 Midspan of right span 3, L = 0.8 m, K red,max = 50% The girder was assumed to have permanent deformation of max. 3 cm (Figure 1(a)). Stiffness of horizontal springs is 512 MN/m. Damages were introduced to the model and it was loaded with uniform temperature change of T=+1 K. Strain response to the temperature load was calculated at the midspan of the left and central span's bottom fiber, in different damage states. Structural strain response to unit temperature loading, referred in the following as strain sensitivity [µm/m/K],exhibited changes dependent on introduced damage. Thus it can be concluded that strain sensitivity could be used in this case as indicator of damage.

Figure 1 :

 1 Figure 1: Three-span girder. (a) Model with permanent deformation, (b) Strain response in midspan of left span, (c) Strain response in midspan of central span.

Figure 2 :

 2 Figure 2: Single-span girder. (a) Deformed model, (b) Deflection response in midspan and (c) Strain response in midspan in 6 cases of horizontal spring stiffness ranging from 8 to 8192 MN/m.

  The main span is 64 m long, with additional cantilevers of 4.8 m on each side. Both of them are connected to the foundation by prestressed concrete tie bars. Visual inspection of these bars' structural condition is not possible, as they are entirely covered with soil. The box-girder crosssection has a variable height ranging from 1.3m to 3.7m, which results in a slenderness of 1/50 in the central mid span. The superstructure is fixed to the concrete abutment. The bridge has a shallow foundation with diameters 3 to 10m, i.e. with no piles. The Structural Health Monitoring (SHM) system consists of the following sensors (Figure3): 2 electronic water level gauges in the mid span, 6 strain gauges, 4 structural temperature sensors inside each wall of the box-girder and 2 acceleration sensors (Reiterer[START_REF] Reiterer | Extension of Bridge Lifetime by use of Structural Health Monitoring[END_REF]).

Figure 3 :

 3 Figure 3: Monitoring system installed on Teufenbach Bridge 3.2 Cable-stayed bridge The International Bridge over River Guadiana is a cable stayed bridge located in the South West of the Iberian Peninsula and was opened to traffic in 1991. The bridge has a central span of 324 m and two lateral and transition spans of 135 m and 36 m, respectively. The deck is a prestressed concrete box girder 18m wide and 2.5m high, suspended by one hundred and twenty-eight stay cables. They are composed by individually sheathed mono strands, varying from 22 to 55, with the length from 48m to 167m, and are spaced every 9.0 m on the deck and every 1.8 m on the pylons. The A-shaped pylons are 95m and 96 m high and consist of concrete hollow sections which, besides anchoring the cables, support the deck at a height of 35 m by means of hollow section transverse beam.In 2010 an autonomous online SHM system was installed with the aim of carrying out early damage detection, thus contributing to increase of safety and to reduction of maintenance costs. Sensor positioning was based on the principle that any damage in the bridge would produce dead load redistribution and change in cable forces. Consequently, displacement and rotation changes close to cable anchorages were chosen as sensitive quantities that should be measured (Santos[START_REF] Santos | Multivariate statistical analysis for early damage detection[END_REF]).

Figure 4 :

 4 Figure 4: Monitoring system installed on Guadiana River bridge

Figure 5 :

 5 Figure 5: Finite-Element models. Left: Teufenbach Bridge, right: Guadiana River Bridge

Figure 6 :

 6 Figure 6: Objective function values during model updating

Figure 7 :

 7 Figure 7: Effect of cable stay stiffness reduction. Left: absolute displacement change [mm], right: Deflection sensitivity to temperature [mm/K]

Table 2 :

 2 Introduced damage types

	Damage type	Description
	1	Failure of prestressing cable in tie bars, without crack formation
	2	Failure of continuous prestressing cable, without crack formation in box-girder
	3	Stiffness reduction of tie bar
	4	Stiffness reduction of box-girder slab
	5	Foundation movement
	6	Failure of short prestressing cable at midspan, without crack formation

Table 3

 3 shows the results of calculated structural response to various damage cases. Within the four columns of results, the first two represent change of deflection-and strain-sensitivity to temperature [%], whereas the last two columns represent the expected change of displacement [mm] and strain [µm/m] absolute values. The cells with values that are considered detectable are highlighted. As expected, the damage types that do not change structural stiffness have little effect on displacementor strain-sensitivity to temperature, whereas damage types 3 and 4 are detectable. On the other hand, changes of absolute values of deflection or strain are sensitive also to damage types that do not change structural stiffness, but produce detectable deformations.

Table 3 :

 3 Structural response to introduced damage scenarios

	Introduced damage	Change of temperature sensitivity	Change due dead load effect
	Type		Extent	(U z /T) [%]	(/T) [%]	 U z [mm]	 [µm/m]
	1	1 2 6	failed cables	-0.01 -0.03 -0.09	0.00 0.00 0.00	0.10 0.18 0.49	0.41 0.71 1.94
	2	1 2	failed cables	-0.17 -0.15	-0.09 -0.09	0.67 0.60	8.27 8.20
		10	[%]	-0.31	-0.09	0.07	0.28
	3	20	stiffness	-0.65	-0.17	0.15	0.58
		50	reduction	-1.93	-0.52	0.45	1.72
		1	[%]	0.75	0.00	0.12	0.04
	4	5	stiffness	3.83	-0.17	0.62	0.22
		10	reduction	7.87	-0.26	1.29	0.46
	5	0.1 0.3	[cm] movement	0.10 0.30	0.00 0.09	-0.56 -1.68	-2.10 -6.30
	6	1 2 6	failed cables	-0.18 -0.37 -1.08	-0.09 -0.17 -0.52	0.68 1.42 4.14	5.32 13.33 40.66

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

EWSHM 2014 -Nantes, France

ACKNOWLEDGEMENTS

The presented work was accomplished within the research project TRIMM (Tomorrow's Road Infrastructure Monitoring and Management), which is part of FP7 research programme funded by the European Commission.


M Mounkaila
email: mounkaila@laas.frcamps@laas.fr

T Camps

S Sassi

Ph Marguerès

Ph Olivier

C Escriba

J Y Fourniols

CURE MONITORING AND SHM OF CARBON FIBER REINFORCED PO LY M ER PART I : IMPEDANCE ANALYSIS AND MULTIPHYSIC SENSITIVITY

Keywords: electrical modelisation, impedance analysis, cure monitoring, SHM

The high-performance composite materials based on carbon fiber are increasingly used in critical security areas (aeronautics, civil engineering). Thus, it is important to know their characteristics during curing process or their use. We present herein a technique of electrical impedance analysis to extract some specific material properties (resistance and capacitance) in order to know its behavior. As the material microstructure contains a conductor part (carbon fiber) and an insulator part (resin), a model of electrical conduction in the material was established by using a network of a resistance R P connected in parallel with a capacitance C P (impedance Z). Spectroscopic impedance analysis of the studied samples informs about the intrinsic properties of material and shows a sensitivity of these electrical parameters (R P , C P ) according to the curing cycle. Then the sensitivity to some physical parameters (temperature, deformations, etc.) will be demonstrated in order to know the health of the material, thus ensure Structural Health Monitoring (SHM).

INTRODUCTION

Carbon Fiber Reinforced Polymers (CFRP) are highly used in aeronautics for high mechanical performances as regards to their low density. They offer many benefits such as mechanical strength, mass and consumption reduction. With the aim of optimizing their use, efforts are employed by using several techniques to monitor their curing cycle or the health of structures during their use.

Beyond existing methods of unique measurement of resistance [START_REF] Gillet | Prediction of electrical properties of an aeronautic composite[END_REF][START_REF] Xia | Modeling of mechanical damage detection in CFRPs via electrical resistance[END_REF] or capacitance [START_REF] Inada | Smart cure monitoring method of carbon/epoxy laminates using electric capacitance change with applied alternating current frequency[END_REF][START_REF] Maistros | Dielectric monitoring of cure in a commercial carbon-fiber composite[END_REF], we present in this paper a method of impedance measurement and analysis that provides both electrical parameters (resistance and capacitance). The conductive and insulating properties of materials are studied by applying an alternating current combined with a voltage measurement using a dedicated instrumentation. Here the studied material is made from carbon T700/epoxy M21 prepregs (used in aerospace).

Firstly, a three-dimensional (3D) model of electrical conduction is considered to describe the anisotropy of the material. This model consists of a resistance and a capacitance connected in parallel (R P , C P ). Then, we will describe the insertion method of thin electrodes (35 μm thick) inside the material and the specific impedance measurement bench developed to make a real-time measurement of R P and C P . The sensitivity of both R P and C P in different stages of the curing cycle will be also studied here. All this aims to provide a cure monitoring and the possibility to real-time control to obtain the desired properties of the produced composite structures. Finally, we will present the measurements on manufactured composite samples to demonstrate the sensitivity of R P and C P according to physical loads (such as deformations and temperature) in order to provide necessary elements to know or predict the material health (for SHM purpose).

MODEL USED FOR THE ELECTRICAL CONDUCTION

Prepregs are plies (256 µm thick) made of M21 epoxy resin and high strength carbon fibers (7 µm diameter). The fibers orientation is unidirectional (UD) inside the ply. This confers anisotropic electrical properties. As the material contains a conductor part (fibers) and an insulator part (resin), we consider a resistive conduction linked to the conduction through fibers or percolation points, and a capacitive conduction through resin or voids (see figure 1). In order to improve the representation of the different mechanisms of this electrical conduction, analyses of the conduction in the fibers plane in mono-ply samples (inside one ply: intra-ply) and multi-plies samples (inside laminates) were undertaken. Intra-ply conduction analysis In order to reduce the interface resistances and to avoid being intrusive, thin and flexible electrodes (flex) are inserted between one prepreg cured on a FR4 substrate (printed circuit board). The flex used in this case is a copper tape (50-µm thick, 6-mm wide and 4-cm long) covered with a polyimide film (35-µm thick) at masking areas. Several flex are placed in the longitudinal and transverse directions to the fibers orientation (see figure 2). The impedance analysis requires a frequency sweep, here from 10 Hz to 1 MHz. The resistive measurements are performed at 10 Hz and the capacitive measurements at 100 kHz.

In the longitudinal direction (intra-fibers), preliminary measurements show that changes in the resistance value depend on the distance between electrodes. This evolution is almost linear (see figure 3. a). We obtained a resistivity value around 15.10 -5 Ω.m; its determination is difficult because of the presence of significant contacts resistances (R C between 1 to 4 Ω) disrupting our measurements. These impose 4-points measurement method. Capacitances are sporadic because of the low resistances values disrupting also their measurements. In the transverse direction (interfibers), the measurements show high resistance values with a resistivity around 1.5 Ω.m (against 15.10 -5 Ω.m in the intra-fibers conduction); but the capacitances are more significant (see figure 3. b). In this case 2-points measurement method is used because contacts resistances effects are negligible. Finally, the intra-fibers electrical conduction is essentially resistive (through fibers and percolation points) and it is modeled as distributed resistances. But the inter-fibers conduction is resistive and capacitive (through percolation points, resin and voids). This later is modeled as a network of resistances in parallel with capacitances (R P , C P ) as shown in the figure 4. The intra-ply conduction in the multi-plies is considered as the same as the one in the mono-ply. The inter-plies conduction is similar to the one in the transverse direction (conduction through percolation points, resin or voids). It is modeled as a resistance in parallel with a capacitance. Finally the 3D electrical model equivalent to a multi-plies composite material can be considered as a cascaded structure of hexapole nodes (see figure 6).

CURE MONITORING

A test bench is developed here for cure monitoring of composite materials (see figure 7). It contains:

• Impedance analyzer : R P (at 10 Hz The real-time measurements are realized during curing (in an oven) on 24 plies UD samples to characterize the inter-plies conduction. The measurement is made between flex 1 and 4 (22 plies). Figure 8 shows the results of R P and C P obtained during curing. As could have been expected, R P decreases versus time from 30 kΩ to few hundred ohms. This is due not only to contacts improvement between the fibers and the electrodes but also to the increasing of the percolation network. The changes in C P during curing show two peaks; the first one corresponds to the point of polymer liquefaction and the second one to the gel point. The work in progress focuses on the the state of the considered material. Thus it could be possible to use this instrument to monitor the curing process and better still to control it. Therefore, it should be possible to establish in real time the appropriate moments for stopping, modulating or correcting the cure cycle. This monitoring can be used to optimize the manufacturing process (energy savings, reduction of curing time etc.) and thus the properties of the manufactured material it-self. Furthermore obtained results show the R P and C P sensitivity to temperature and mechanical deformations. This could enable us to ensure functionalization of the material or monitor its health during the phases of conditioning and service (SHM).

Figure 1 :

 1 Figure 1: Equivalent electrical model in composite material

Figure 2 :Figure 3 :

 23 Figure 2: Intra-ply conduction test sample

Figure 4 :Figure 5 :

 45 Figure 4: Intra-ply conduction modeling

Figure 6 :

 6 Figure 6: 3D electrical conduction model for a multi-plies composite material

  ) and C P (at 100 kHz) measurement with a frequency sweep from 10 Hz to 1 MHz; • Channel selector : measurement on several samples or positions; • Temperature measurement circuit via a K thermocouple; • LabView software : on-line monitoring of the later parameters.

Figure 7 :

 7 Figure 7: Measurement bench

reproducibility and repeatability of these measurements on multi-plies UD and QI (quasi isotropic) samples. The obtained results will be correlated with those of rheological analyses (conducted by our colleagues of the ICA -Institute Clément Ader).

IMPEDANCE ANALYSIS FOR SHM

Keeping the same instrumentation, after-curing measurements enable us to characterize the material behavior to temperature and deformation loading. The studied samples are UD mono-plies. When the temperature of the composite increases the measured resistance (R P ) increases but capacitance (C P ) decreases and vice-versa. The resistance changes up to 4% and capacitance up to 15% in the range from -50°C up to 150°C (figure 9 a). R P and C P measurements are also sensitive to the mechanical deformations; up to 8% and 500% respectively (see figure 9 b). These impedance measurements could enable us to detect defects inside the material such as fibers breakage, cracks or delamination. Furthermore, the material could be used as an actuator (defrost device for aerospace applications, for example).

CONCLUSION AND OUTLOOK

In this study, we developed a simple and robust instrumentation method by using flexible electrodes (flex) and an ad-hoc acquisition system designed to achieve electrical impedance measurement inside a T700/M21composite material.

Considering a simple 3D electrical conduction, the developed instrumentation enables us to monitor the material behavior during curing (here in an oven). This later depends on the changes in