F Morin

H Courtecuisse

I Reinertsen

F Le Lann

O Palombi

Y Payan

M Chabanas

Intraoperative brain-shift compensation using MR/US elastic registration by means of a constraint-based biomechanical simulation

come

Introduction

During brain tumor procedure, accurate localization of the target is essential. However, the intraoperative deformation of soft tissues, called "brain-shift", is a major source of error. Even if this topic has been widely studied, few of the brain-shift correction methods are usable in a clinical practice [1,2,3], namely easily integrable in the surgical workflow, relevant in terms of execution times and user interactions and validated on actual surgical cases. In this abstract, we present a constraintbased biomechanical finite element (FE) simulation method that fulfills these requirements.

Materials and methods

Preoperatively, brain soft tissues and blood vessels are respectively extracted from MRI and MR Angiography. The tetrahedral FE mesh, only accounting for the hemisphere affected by the tumor, is then mechanically coupled with the vascular tree skeleton. Intraoperatively, navigated US images are acquired in contact with the brain [1]. Power Doppler and B-mode information are recorded simultaneously, respectively allowing to extract the blood vessels and probe footprint. A biomechanical simulation, relying on a linear constitutive law solved with a co-rotational approach, is used to compensate for brain-shift, accounting for the following Lagrangian Multipliers constraints:

I the brain model is prohibited to exit the cavity formed by the dura mater and slides in contact with the falx cerebri and the tentorium cerebelli I the cortical surface is situated under the probe footprint but both are not necessarily in contact I the pre-and intraoperative vessels skeletons are registered After resolution, preoperative MR images are updated with the FE model deformations.

Results

Our method was validated over retrospective data of five patients using landmarks set on vessels and anatomical structures delineated by a clinician. On average 72% of the deformation occurring at the opening of the dura is corrected with our method, with mean error under 1.5 mm for each patient, against 54% with [1]. US images were also available during resection for four of these patients. For tumor close to the cortical surface, our method still shows an improvement over [1] (65% against 56%). However, for deep tumors that necessitate a chimney for the surgical approach, our method fails to correct the deformation, showing the importance of a specific treatment.

  Intraoperative brain-shift compensation using MR/US elastic registration by means of a constraint-based biomechanical simulation F. Morin, H Courtecuisse, I Reinertsen, F Le Lann, Olivier Palombi, Yohan Payan, M Chabanas To cite this version: F. Morin, H Courtecuisse, I Reinertsen, F Le Lann, Olivier Palombi, et al.. Intraoperative brain-shift compensation using MR/US elastic registration by means of a constraint-based biomechanical simulation. EUROMECH Colloquium 595: Biomechanics and computer assisted surgery meets medical reality, 2017, Lilles, France. hal-01935285


Stéphanie Bonnet
email: stephanie.bonnet@univ-nantes.fr

Franck Schoefs

Manuela Salta

Sources of uncertainties for total chloride profile measurements in concrete: quantization and impact on probability assessment of corrosion initiation

Keywords: error modelling, laboratory tests, probabilistic modelling, chloride profiles, statistical analysis, probability of corrosion detection, reliability analysis

come

Introduction

During the past three decades, reliability methods have provided efficient rational aid-tools for the safety assessment of new designed concrete structures (Marquez et al. 2012). They have gradually been extended to include the structural reliability assessment of existing structures. Civil engineering offers key challenges in this field because of the cost and difficulty of on-site measurements to evaluate precisely the material degradation. These methods require to identify the uncertainty sources, then to quantify and model them, generally on the basis of statistical studies. The measurements, achieved through Destructive and Non Destructive Testing (NDT) or Structural Health Monitoring (SHM) sensor, are then assumed perfect [START_REF] Oslakovic | Evaluation of service life design models on concrete structures exposed to marine environment[END_REF][START_REF] Yang | Design and optimization of maintenance strategies for a long life-span port project[END_REF]) except for some works where studies are mainly theoretical [START_REF] Faber | Indicators for inspection and maintenance planning of concrete structures[END_REF][START_REF] Rouhan | Probabilistic modelling of inspection results for offshore structures[END_REF][START_REF] Sheils | Development of a two stage inspection process for the assessment of deteriorating bridge structures[END_REF]2012;[START_REF] Bastidas-Arteaga | Stochastic improvement of inspection and maintenance of corroding reinforced concrete structures[END_REF]. However, most of the time, measurement error modelling assessment is not based on real data because no experimental database is currently available. The aim of this paper is to present the findings of the study conducted to identify sources of uncertainties for the measurement of total chloride profiles in concrete. With this aim in view, uncertainties are then modelled using an appropriate probability density function.

In a marine environment, indeed, the main cause of reinforced concrete structure degradation is the corrosion of steel rebars because of the presence of chloride ions due to concrete porosity. When the chloride ion concentration reaches a critical value, called C crit , the steel bars are not protected anymore and corrosion is initiated. Tuuti proposes a conceptual model dividing the service life of reinforced concrete (RC) structures into two distinct phases: the initiation phase and the propagation phase (Tuuti 1986). The present paper focuses only on the initiation phase through a comparison of the chloride content with the critical chloride level, from which the passivation of steel surfaces becomes unstable. The adoption of corrosion initiation as the limit state to define service life of RC structures has already been challenged by researchers for both saturated and unsaturated concrete [START_REF] Kong | Reliability analysis of chloride penetration in saturated concrete[END_REF][START_REF] Val | Probabilistic evaluation of initiation time of chlorideinduced corrosion[END_REF]. In this, the most accurate determination of chloride profiles with depth is one of the main issues of structure service life prediction.

Non destructive techniques are currently under development in order to detect and quantify corrosion rate and chloride content with good accuracy [START_REF] Ahmad | Reinforcement corrosion in concrete structures, its monitoring and service life predictiona review[END_REF][START_REF] Balayssac | Non destructive evaluation of concrete contamination by chloride[END_REF][START_REF] Montemor | Chloride-induced corrosion on reinforcing steel: from the fundamentals to the monitoring techniques[END_REF][START_REF] Straub | Non-destructive methods for measuring chloride ingress into concrete: State-of-the-art and future challenges[END_REF], Lecieux 2015). These techniques give good results for free chloride content as regards experiments conducted in the laboratory but, as the sensors are affected by many parameters (water content, porosity, cracks, etc.), in situ chloride content measurements are still unreliable [START_REF] Montemor | Multiprobe chloride sensor for in situ monitoring of reinforced concrete structures[END_REF][START_REF] Atkings | Sources of error in using silver/silver chloride electrodes to monitor chloride activity in concrete[END_REF]. Other techniques are under development to achieve chloride profiles without breaking the concrete specimen [START_REF] Silva | Application of LA-ICP-MS for meso-scale chloride profiling in concrete[END_REF]Wall et al. 2008). Unfortunately, these techniques are costly when the key factors for the choice of the method are precisely cost and time.

For these reasons, the present study focuses only on the total chloride profiles determined using a semi-destructive method because both bound and free chlorides are involved in the corrosion process [START_REF] Reddy | On the corrosion risk presented by chloride bound in concrete[END_REF]. As regards the problem of distinguishing experimentally between free and bound chloride, some authors consider that the critical chloride content must be compared to the total chloride content (Tuuti 1982(Tuuti , standard 2006)).

The total chloride profile measurements are commonly used for service life predictions of structures to:

-update the chloride diffusion coefficient used in corrosion prediction models; -calibrate NDT tools [START_REF] Kirkpatrick | Probabilistic model for the chlorideinduced corrosion service life of bridge decks[END_REF][START_REF] Liang | Reliability analysis for the existing reinforced concrete pile corrosion of bridge structure[END_REF]. This study has been conducted within the context of the European Interreg III B project, called Medachs (http://www.medachs.u-bordeaux1.fr). This research project concerns the durability and maintenance of coastal concrete structures. Specifically, the structure studied at the GeM laboratory is a quayside of the Nantes-Saint-Nazaire harbour (France) built in 1971 and located in the estuary of the Loire River on the Atlantic coast of France. Some profiles of concrete cores extracted from the quay have been analyzed using a probabilistic study, which pinpointed problems relating to the lack of measurement uncertainty model [START_REF] Rosquoët | Chloride propagation in concrete harbour structure[END_REF]. The total chloride profiles obtained on field are difficult to analyze with regards to their uncertainty measurement and to the many parameters they are depending on: cement type, environmental parameters and concrete quality and damaging [START_REF] Fraj | New approach for coupled chloride/moisture transport in non-saturated concrete with and without slag[END_REF][START_REF] Castro | Interpretation of chloride profiles from concrete exposed to tropical marine environments[END_REF][START_REF] Costa | Chloride penetration into concrete in marine environment -Part I: Main parameters affecting chloride penetration[END_REF][START_REF] Djerbi | Influence of traversing crack on chloride diffusion into concrete[END_REF][START_REF] Lindvall | Chloride ingress data from field and laboratory exposure -Influence of salinity and temperature[END_REF][START_REF] Sosdean | Experimental and numerical determination of the chloride penetration in cracked mortar specimens[END_REF]. The determination of the chloride profiles, indeed, is a manual procedure [START_REF] Chaussadent | AFREM test procedures concerning chlorides in concrete: extraction and titration methods[END_REF]RILEM 2002;[START_REF] Vennesland | Recommendation of RILEM TC 178-TMC : Testing and modelling chloride penetration in concrete. Methods for obtaining dust samples by means of grinding concrete in order to determine the chloride concentration profile[END_REF], in which the experimenter plays a key role. The profile analysis, therefore, implies that the confidence in the measured values is discussed and quantified to be implemented in a rational decision process for maintenance or inspection planning.

The aim of this

It is important to note that chloride transport mechanisms affect the quantity of chlorides with depth but not the assessment procedure and the error on measurement.

Moreover, the error is assumed to be independent from the chloride content. This is a common assumption when semi-destructive techniques or NDT without any change in the settings of the NDT tool are used.

This paper initially begins with key issues about uncertainty modelling and about their applications for modelling uncertainty of measurement. A probabilistic modelling of errors (human and protocol) is then presented. How it affects reliability assessment is finally discussed.

In order to quantify the uncertainty of measurement, some repetitive tests have to be carried out on laboratory specimens with a process distinguishing between human and other factors influencing the measurement. Section 3 presents the experimental programme, which leads to error measurements. In Section 4, the modelling of the uncertainty in total chloride content measurements is examined. Finally, the statistical analysis, the probabilistic modelling and the effect of uncertainty in measurements for reliability and life-cycle assessment are discussed.

Our main objective is the better understanding of the estimated probabilities that corrosion initiation is detected from on site destructive testing.

Uncertainty of measurement: from identification to modelling 2.1 Sources of uncertainties

Even though the hierarchy of sources of uncertainties in engineering remains an open and controversial question (Der Kiureghian and Ditlevsen 2009), the classification published by [START_REF] Ang | Probability: Basic Principles v. 1: Concepts in Engineering, Planning and Design[END_REF], however, provides a satisfactory framework. This list is divided into two categories of sources of uncertainties: aleatoric and epistemic.

Sources of uncertainties are considered as 'aleatoric' when they come from natural or industrial hazard.

'Epistemic uncertainties' are due to the limitation of human knowledge and modelling of complex reality and are assumed to diminish in the future with the progress of scientific knowledge, the accuracy of protocols and the development of technology. They gather various sources like uncertainty of measurement, error due to lack of experience when using a tool and uncertainty of modelling. [START_REF] Deby | Toward a probabilistic design of reinforced concrete durability: application to a marine environment[END_REF] consider the modelling error of the diffusion coefficient by comparing calculated and experimental coefficients: the model must be selected and the error will vary depending on the model. Henceforth, a special focus is placed on the quality of chloride content assessment itself. The objective of this research is to investigate the sources of uncertainties when the total chloride content is measured and to present the results as regards identification, measurement and modelling. The protocol describing the process is discussed in Section 3.

Effect on structural reliability and probability of defect assessment

Measurement errors affect both the computing of structural reliability and the decision through the probability of assessment of the measured property. Let denotes the measured material property (typically a Resistance parameter) and R the real value of the property measured with a perfect tool:

= R + e t (1)
where e t is the total measurement error.

When measurement data are directly used for reliability assessment without using a structural model and a complex limit state, the reliability can be assessed simply by estimating the probability of failure, P f as, defined as:

P f = P ( > R crit ) (2)
where R crit is the critical value, also called acceptable or limit threshold in Load and

Resistance Factor Design (LRFD) method.

Let us consider a non-perfect measurement of R. A survey of the literature on the concepts of probability of detection and probability of false alarm reveals that a considerable amount of effort has been devoted to this subject for characterizing the performance of Non Destructive

Testing tools [START_REF] Faber | Indicators for inspection and maintenance planning of concrete structures[END_REF][START_REF] Rouhan | Probabilistic modelling of inspection results for offshore structures[END_REF][START_REF] Sheils | Development of a two stage inspection process for the assessment of deteriorating bridge structures[END_REF]. The probability for good assessment, called PGA, is a quantity very useful for decision planning on structural maintenance [START_REF] Sheils | Development of a two stage inspection process for the assessment of deteriorating bridge structures[END_REF]. It is defined by the conditional probability:

PGA = P( > R crit | R > R crit ) (3) R R R R

Experimental programme

This section describes the experimental program applied to assess the total error of measurement, e t (1), in the case of total chloride determination in concrete.

Concrete mixture and specimen preparation

The concrete material used for the repetitive tests is made of ordinary Portland cement and limestone filler. The cement type CEM I 52.5N comes from the Saint-Pierre Lacour's plant (France). The chemical composition, provided by the manufacturer, is detailed in Table 1. The density is 3150 kg/m 3 and the specific surface area is 365 m²/kg.

The limestone filler consisting of 96.8% of CaCO 3 is produced at the Erbray's facility (France). The density and specific surface area are 2696 kg/m 3 and 419 m²/kg, respectively.

The 0/4-mm sand is siliceous river sand with a density of 2580 kg/m 3 and a water absorption coefficient of 0.9% (in mass). The aggregate are 10/14-mm siliceous gravels with a density of 2592 kg/m 3 and a water absorption coefficient of 0.5% (in mass). Concrete composition is described in Table 2. The Water to Binder ratio W/B is O.47.

Five concrete cylinders with a length of 22 cm and a diameter of 11 cm are prepared from a single batch. The concrete is cast in steel moulds and compacted using a mechanical vibrator.

After casting, the cylindrical moulds are stored in a humid chamber maintained at 20°C with a relative humidity (RH) of about 85% for 24 hours before demoulding. Then the cylindrical concrete specimens are stored together in the same humid chamber to be well-hydrated. After 28 days, three cylinders are tested under axial compressive loading conditions to obtain the compressive strength. The mean value obtained is 36 MPa.

The two other cylinders are kept in the humid chamber during six months then cut into cylinders with a length of 2.5 cm and a diameter of 11 cm using the water jet cutting technology. Four specimens, called S1, S2, S3 and S4, are sampled in the middle part of the two cylinders: S1 and S2 from the first cylinder and S3 and S4 from the second one.

All the four specimens are oven-dried at 60°C to constant weight. This drying stage lasts five months. Then, the discs are cooled for 48h in a desiccator at 20°C before being tested. The concrete sample preparation, like cutting or drying for instance, may affect the microstructure of concrete. However, this damaging risk is equally shared by all the concrete samples.

Chloride contamination in concrete

The objective is to obtain the homogeneous chloride content in the concrete specimens for conducting repetitive tests. Consequently, the chloride content with depth should be the same for all the specimens. The specimens must be in equilibrium with the salted solution.

Three dried samples (S1, S2 and S3) are fully submerged in a container filled with a sodium chloride solution, which is renewed regularly to maintain the desired chloride content in the surrounding solution. This solution combines a 30g/l NaCl solution closed to the level of NaCl in the Atlantic Ocean and a concentrated solution of KOH (0.083 mol/l) and NaOH (0.025 mol/l) to obtain a pH closed to that of the interstitial pore solution to avoid leaching of concrete. The samples are weighed weekly to constant mass. The immersion stage lasted four months.

The fourth sample (S4) is submerged four months too in another container filled with demineralised water loaded with KOH (0.083 mol/l) and NaOH (0.025 mol/l) only. S4 is used as a control sample to measure chloride content without chloride contamination.

Procedure for obtaining total chloride content

The well-known procedure recommended by the RILEM 178-TMC Technical Committee is used here. After exposure, the cylindrical cores are taken from the immersion tank to be ground in several steps of 4-mm each, perpendicular to the top faces of the cylinders using a grinding instrument. A 4-mm increment is chosen to obtain enough concrete powder for analysis by three operators. The powder is collected and stored in sealed plastic bags. This procedure recommended by [START_REF] Vennesland | Recommendation of RILEM TC 178-TMC : Testing and modelling chloride penetration in concrete. Methods for obtaining dust samples by means of grinding concrete in order to determine the chloride concentration profile[END_REF] does not use water. The grinding areas are larger than 40 cm² (an 8-cm diameter hole) to avoid excessive contribution from large aggregates.

The procedure described below is used to determine the total chloride content from concrete powder [START_REF] Chaussadent | AFREM test procedures concerning chlorides in concrete: extraction and titration methods[END_REF]Arliguie 1999, RILEM TC 178-TMC 2002). Approximately 5g of concrete powder is taken from each layer and placed in a beaker. HNO 3 and deionised water are added and the mixture is stirred and heated to 80°C for 30 min. The solution is then filtered into a 250-cm 3 volumetric flask. The chloride concentration of the filtered solutions is determined by potentiometric titration using an automatic titrator with 0.01-M silver nitrate (AgNO 3 ).

All concrete specimens are ground in the same laboratory and by the same operator (called O2) while the others steps (filtration and titration) are conducted by different operators in two different laboratories for samples S1, S2 and S3. Four operators and two laboratories are then involved in the experimental program: O1 and O2 belonging to the same laboratory and O3 and O4 to the second laboratory. S2 and S3 samples are analysed twice by operator O2

(profiles indicated with brackets in Figure 1). These repetitive tests are carried out to quantify the error (cf. S96+ection 4). The different experimental steps and the corresponding operators are summarized in Table 3.

Total chloride profiles

Figure 1 presents nine total chloride profiles, which are supposed to be identical, and one total chloride profile for the specimen not contaminated with chloride (S4). Three profiles are provided for each sample immersed in chloride solution (S1, S2 and S3) to assess test errors on chloride determination. The nine profiles should be identical since the samples are made of the same concrete and contaminated with the same solution. They should also be horizontal (same content with depth) as the equilibrium is reached using the same sodium chloride solution. However, it is not. Therefore, the error is quantified in Section 4 using the information about this unexpected scattering.

With a cylinder length of 2.5 cm, six points are expected for each profile. Yet since the concrete samples broke when the grinding instrument reached a depth of approximately 2 cm, only five points have been obtained for samples S2 and S3 and four points only for sample S1. The error, therefore, will be calculated on 42 points.

The non-contaminated specimen S4 presents a profile with a non-zero concentration. The experimental mean content for S4, calculated using the five points obtained as a function of depth, is 2.61 10 -4 kg/kg of concrete. It is related to the initial chloride content of the different concrete compounds: cement, filler, aggregates and water.

The chloride from the concrete components is calculated by considering the initial chloride content of each component given by the manufacturers (Table 4). The 10/14 aggregate material does not appear here because its initial chloride content is null. The apparent concrete density used to calculate the chloride content in kg of chloride by kg of concrete is 2293 kg/m 3 . The value obtained is 2.52 10 -4 kg/kg of concrete with the primary source of chloride, coming from sand. Indeed, the sand used here is extracted from sand mines in the Loire estuary. This value is close to the experimental value obtained with the profile (2.61 10 -4 kg/kg of concrete). The error e s is due to the variability of the samples, which are assumed to be identical.

Error modelling

Samples S1, S2 and S3 being saturated with the same solution and the chloride penetrating all the surfaces, the total chloride content should be the same and uniform for all the samples.

However, this has not been experimentally verified and the profiles, which appear in Figure 1 show variability. This can be accounted for by the concrete heterogeneity even though the specimens are laboratory samples. In the case of concrete used for bridges in a marine environment, sampling under the same conditions provides some significantly different assessments of chloride ingress and service life predictions. These differences are probably due to concrete variations in areas assumed to be homogeneous [START_REF] Goltermann | Variation of chloride profiles in homogeneous areas[END_REF]). This error is assessed by conducting a test of porosity measurement, for which all other uncertainties (protocol and human errors) are negligible. Porosity can be considered as the key-factor affecting chloride penetration into concrete. If porosities are similar, the specimens can be considered as homogeneous. The porosities studied here are assessed using the water saturation method (Table 5). The scattering of the porosity being weak, we can consider that the samples are similar. The scattering of the measurements between the samples is quantified below in order to analyse its impact in comparison with other uncertainties. 6 and presented by profiles in Figure 1.

The three sources of uncertainties are considered to be independent and added up to obtain the total error: e t = e p + e s + e h (4)

The human error can lead, for instance, to the underestimation of the chloride content in a given sample in the case of a badly rinsed filter. In case of structure maintenance, an underestimation may mislead the manager and prompt a 'do nothing' decision although repair or protection is necessary. More generally, human errors do not lead systematically to the under or overestimation of the chloride content. Protocol error, however, leads to either over or underestimation. An overestimation leads to 'False Alarms' in terms of decision theory [START_REF] Straub | Non-destructive methods for measuring chloride ingress into concrete: State-of-the-art and future challenges[END_REF][START_REF] Rouhan | Probabilistic modelling of inspection results for offshore structures[END_REF]. Repair works are then planned when they are not fully needed, thus giving rise to additional costs.

Data available for quantization of error

The experimental campaign includes three samples (S1, S2 and S3) and four operators (O1, O2, O3 and O4) (Tables 3 and6). Forty-two measurements have been performed with five points for each profile (Figure 1). According to the confidence interval of sampling theory, the statistical uncertainty due to a limited amount of data is quantified. If a conclusion can be drawn, then the available data are sufficient. Subsequently, we therefore show that the samples are adequate in quantity to demonstrate the main statistical properties and to quantify probability distribution statistical estimates. The chloride content as a function of the distance to the surface of the samples, which have a maximum length of 2.5 cm, is presented in Figure 1. It can be recalled that all the surfaces of the cylindrical samples are in contact with the salt solution and that the specimens broke during the grinding step, thus reducing the profiles by 2 cm. No significant trend between the samples is visible along the depth axis. This observation confirms that the samples are homogeneous (no depth effect) and that each measurement carried out on a sample at different depths can be considered as a repetitively test, i.,e., a test with the same concrete in the same conditions. Operators O1, O2, on the one hand and O3, O4, on the other hand, have worked in their respective laboratory and used the same devices and products.

When considering the three previous errors, the data are used as follows:

-protocol error: The tests performed on the control sample S4 can be used to quantify part of the protocol error. The measurements carried out by O2, twice on S2 and S3 can also be used to quantify the protocol error because a single operator followed the same protocol.

-sample error: The data from operator O2 are used to quantify the effect of the heterogeneity of samples because that same operator did all the measurements on S1, S2 and S3.

-human error: The operator influence is analysed by comparing the results obtained with Sample 1 because three different operators O2, O3 and O4 carried out measurements on S1.

Results

Probabilistic modelling

A probabilistic method is used to model uncertainties. The error is modelled using some random variables obtained from forty-two values. If insufficient information is available, other methods can be applied: interval theory and fuzzy logic (Möller and Beer 2008). A probabilistic 3-D space is considered based on the assumption that e p , e s and e h are independent random variables. From a theoretical point of view, this assumption is acceptable because the nature of the errors is different. From a statistical point of view, the limited amount of data cannot be used to investigate deeper this property using a factorial analysis (this may require further dedicated examination). Moreover, due to the under or overestimations of the chloride content (cf. Section 4.1), the total error is modelled by adding a bias b and a zero mean variable , as:

e t = b +  (5)
The bias is defined by: b = -C r (6) with C r : the reference chloride content value (assumed to be the real value);

: the mean error, which is the average of the measured value .

We note that C r is:

-very close to 0 in the reference sample S4;

-calculated for samples S1, S2 and S3 using the concrete porosities and the supposed chloride binding capacity. When the equilibrium is reached, the concrete solution within porosity is supposed to be concentrated in chloride to a volume of 30g/l. This allows for the calculation of the free chloride content in kg/kg of concrete for each sample by taking porosity values displays in Table 5 into account. The chloride binding capacity used here has been found in the literature [START_REF] Francy | Measuring chloride diffusion coefficients from non steady-steady state diffusion test[END_REF] on mortars casted using the same cement. This information permits the evaluation of the supposedly bound chloride content. Free, bound and total chloride contents are summarized in Table 7. The discrepancy observed between the maximum (S1) and the minimum (S3) values is only 0.08 10 -3 kg/kg of concrete.

The fact that C r is subjected to the condition 'C r ≥ 0', we obtain the condition: b + ≥ 0.

Assessment of bias b:

Each component of e t, starting with the protocol error, is now examined. Table 8 shows the values of C, and b for S4. Although sample S4 is assumed to be free of chlorides, detection is made. This part of the protocol error is modelled using a deterministic bias, called b p. The bias is calculated as the mean value of the five chloride measurements carried out on sample S4. We obtain: b p = 0.26 10 -3 (kg/kg of concrete) (7) Sample S1, for which the bias includes the bias due both to operator and protocol is now considered. The results of all the operators are used. However, because only four measurements are available for each operator, it is not sufficient to highlight a significant difference between operators. Moreover, the results show a weak scatter of the standard e e e e deviation between 0.12 10 -3 for O2 and O3, and 0.19 10 -3 for O4 but, since the 95% confidence interval around a theoretical value of 0.15 10 -3 for four measurements is [0.08510 - 3 , 0.56 10 -3 ], the scatter is considered negligible. Therefore, no significant correlation between the standard deviation and the operator experience or laboratory is found. They are considered as independent events of the same variable. Consequently, all the data obtained by the operators are gathered. Then, the global standard deviation of  is 0.14 10 -3 and the coefficient of variation is approximately 9%. The bias b 1 (notation of bias for S1) is the sum of the protocol plus human factor biases and is obtained from Equation ( 6). The result (-0.4 10 -3

(kg/kg of concrete)) is reported in Table 8, where sign '-', for b, denotes an overestimation of the total chloride content.

Assuming that protocol gives a bias b p of 0.26 10 -3 (kg/kg of concrete), the bias b h due to the operator reaches -0.66 10 -3 as:

b h = b 1 -b p = (b h + b p ) -b p = (-0.4 10 -3 ) -(0.26 10 -3 ) = -0.66 10 -3 (kg/kg of concrete) (8)
The other samples, whose results increase the size of the database (Table 6: 12 to 15 tests) are finally considered. The accuracy of the bias assessment is improved. Knowing the theoretical value of C r for each sample, the values obtained with the three samples for b i and e i (i denotes the sample number) are computed and presented in Table 9. The discrepancies among the three biases are very small and stand within the range -0.4 10 -3 and -0.3 10 -3 . The statistical assessment error from twelve measurements, on the other hand, provides a 95% confidence interval of [-0.42 10 -3 ; -0.31 10 -3 ]. The bias mean value is selected and considered subsequently as the average value: -0.37 10 -3 .

We thus obtain: b = -0.37 10 -3 (kg/kg concrete); b p = 0.26 10 -3 (kg/kg of concrete); b h = -0.66 10 -3 (kg/kg of concrete)

Assessment of the zero mean error :

The measurement error  is now assessed. As underlined, the gathering of the results obtained by different operators makes it possible to analyze the effect of the material heterogeneity using a larger number of tests (Table 6: 12 to 15 tests). For each sample, scattering includes errors due both to operator and protocol. On the basis of the value of b (Table 9), the sample of  is obtained from Equation 5. The standard deviation of  is 0.14 10 -3 for samples S1 and S2 and 0.07 10 -3 for sample S3, respectively. The coefficients of variation are 9%, 8% and 4%

for samples S1, S2 and S3, respectively.

This discrepancy is small considering the small amount of data available (12 or 15) because the width of the 95% confidence intervals for the standard variation ranges between 0.06 10 -3 and 0.12 10 -3 . The 95% confidence intervals are [0.1 10 -3 ; 0.24 10 -3 ], [0.09 10 -3 ; 0.21 10 -3 ] and [0.047 10 -3 ; 0.1 10 -3 ] for S1, S2, S3, respectively. This result confirms the findings in Section 4.1 about e s : the heterogeneity of this test is not a key factor in interpreting both bias and scatter. The error modelling is then obtained by gathering the forty-two tests. The standard deviation is then 0.12 10 -3 with a higher confidence whereas the 95% confidence interval is reduced to [0.1 10 -3 ; 0.16 10 -3 ]. We note that a different reference value is considered for each sample by using the bias in Table 8 and when computing zero mean error.

The  distribution is given in Figure 2 from forty-two values. The zero-mean distribution is not symmetrical. The classical assumptions on error distributions, normal or uniform [START_REF] Sheils | Investigation of the Effect of the Quality of Inspection Techniques on the Optimal Inspection Interval for Structures[END_REF] are not suitable here. Using the maximum likelihood estimates (MLE) of parameters [START_REF] Jöreskog | Some Contributions to Maximum Likelihood Analysis[END_REF] for fitting the error distribution using a probability density function (pdf), a comparison between three pdf is carried out. Generalized Extreme Value (GEV), Student and Normal. The GEV is selected because of its non-symmetrical shape whereas Student and Normal are usually considered for modelling error of measurements.

Maximum likelihood estimation results (log likelihood) are given in Table 10. The maximum value of MLE is obtained for GEV pdf whose expression is given in Equation ( 9). As shown in Figure 2, good fit to the distribution of experimental data and compliance with the asymmetry is provided. This pdf, therefore, proves to be the best choice. Its parameters (scale, shape and location parameters, respectively) are: [K=0.016; =9.3 10 -5 ; =-8.4 10 -5 ]. Here, K>0 and GEV is called type II, or Frechet, extreme value distribution [START_REF] Kotz | Quantification and uncertainty analysis of a structural monitoring device: detection of chloride in concrete using DC electrical resistivity measurement[END_REF]. We obtain:

(9) with Analysis results are compared using a probabilistic model. The error directly calculated from the statistical results is obtained as the difference between the measured value and the reference value as:

e t = -C r (10) ) ) 1 ( exp( ) 1 ( 1 ) ( ) / 1 ( ) / 1 1 ( K K z K z K x f             x z C Ĉ ˆ
The experimental distribution is plotted (with bars) and fitted with an extreme value (EV) pdf (in dashed line) in Figure 3. Modelling, on the other hand, assumes that the error e t is the addition of the bias (0.37 10 -3 ) and the zero mean error  according to a GEV with the above parameters. We find: e t =  -0.37 10 -3 (kg/kg of concrete) (

A comparison of this model with the real distribution of error is carried out by adding the distribution curve obtained from the model in Figure 3 (full line). The model results appear to be consistent with the experimental data. This is the first time that the bias is identified and quantified and that the error is modelled with a non-symmetrical (GEV) pdf. This contribution will help to introduce a real model for maintenance updating and semidestructive testing optimization and to quantify the benefit over Non Destructive Testing.

Effect on the probability of chloride detection

When considering the corrosion of steel bars, two different probabilistic approaches are possible. The first one considers the corrosion as a stochastic process and aims to assess the probability of corrosion time [START_REF] Mori | Reliability-based service life assessment of aging concrete structures[END_REF][START_REF] Sheils | Investigation of the Effect of the Quality of Inspection Techniques on the Optimal Inspection Interval for Structures[END_REF]. The second approach is considered here. Its objective is to assess the probability of failure (Equation 2).

In reliability analysis of reinforced concrete, it is generally computed as the probability that the residual steel area A r,s can be lower than a critical area A crit at time t. The critical area is either the percentage of acceptable loss of steel or the minimum area required to fulfill service or else the ultimate limit state of a structural component. The probability of failure is therefore expressed as:

P(A r,s (t)< A crit ) = P(A r,s (t)< A crit |C>C crit ) . P(C>C crit ) (12)
The probability of systematic failure is called instantaneous probability of failure. Assume C crit is a deterministic critical chloride content, called detection threshold in the literature, that we want to detect. In this paper, it is considered as deterministic to avoid the introduction of an additional random variable and to focus on the analysis of the effect of the uncertainty of measurement. NF EN 206-1 standard suggests that the limit content of chloride ions by weight of cement be taken as 0.4% (NF-EN 206-1 2000), which represents 0.0005 kg/kg of concrete when considering the cement content. This value is the same than that used by [START_REF] Goltermann | Variation of chloride profiles in homogeneous areas[END_REF]. We then define PGA-CI (Probability of Good Assessment of Corrosion Initiation-see ( 3)) as:

PGA-CI = P(C + e t > C crit | C > C crit ) (13)
where e t is defined in (5) and C is the real value. This concept proves very useful for the riskbased maintenance of existing structures (Breysse et al. 2009). Then, Equation ( 13 4. We can conclude that the result is highly dependent on the value of the critical chloride content, which is a deterministic value here. This value is deeply dependant on the type of concrete and could be used as a probabilistic value in the future.

Conclusions and future

In marine or de-icing salt environments, chloride concentration is the main input factor considered by concrete structure operators in the decision chain. The chloride concentration value is currently the only rational decision aid-tool for repair strategies and planning of future control campaigns. However, the reliability of the measured values must be discussed and quantified to provide a truly rational decision aid-tool for repair or inspection planning. In order to address this problem, the determination of measurement errors on chloride concentration is the key factor. Errors depend mainly on the different steps of the protocol:

grinding, preparation of powder, acid attack, dilution, concentration measurements.

The paper addresses the problem by examining chloride concentration measurements in saturated samples carried out by four operators from two different laboratories. The three samples being saturated with the same solution and the chloride penetrating all the surfaces, the total chloride content should be the same and uniform with depth.

f e (x)dx C-C crit ; C-C crit >0 +¥ ò
The forty-two chloride content measurements are analysed in order to assess the total measurement error by considering three main errors (protocol error ep, sample error es and human error eh). The total measurement error is modelled using a bias and a zero mean error, well fitted by the Generalized Extreme Value probability density function. A value of the bias is also provided. Finally, the model results satisfactorily agree with the experimental results showing an unusual model: bias and non-symmetrical probability density function.

The probability of detection of corrosion initiation is then assessed as a function of the margin between the critical concentration and the real concentration. We observe that if this margin does not exceed 0.0001 (by weight of concrete), the probability of detection is less than 86%.

This lack of information will affect the decision of action by

  paper is to quantify the measurement reliability in providing a rational decision aid-tool for inspection or work planning. With this aim in view, error measurement of total chloride profiles is essential. To our knowledge, no previous experimental works was carried out until now to assess and model the several sources of measurement uncertainties.

4. 1

 1 Modelling of measurement uncertaintyGenerally, measurement uncertainties are due to three main errors: protocol error e p , sample error e s and human error e h . The term "error" is purposely used in here because experimental results are compared with theoretical values.The protocol error e p comes from all the uncertainties in devices and materials used throughout the experimental process (cf. Section 3.3). As regards the accuracy of the devices used for the measurements, the key factors are: the quality of the sample preparation (built in the laboratory or extracted on site), the quality of the testing devices. As regards measurement, it is a matter of quality of the post-treatment algorithm providing the output useful indicator. So, key factors involved here are: powder quality (powder fineness and heterogeneity), quality of the demineralised water and procedure for chloride extraction from concrete powder.

  The error e h, called human factor, is caused by the operator. It mainly occurs in the course of the different non-automated sample preparation steps or when using the testing and measurement devices within predefined and normalized quality requirements (NF in France or EN in Europe). The error e h due to the operator usually occurs during solution filtration steps or when pipetting for titration dosing, which must be carried out very thoroughly. The human factor can be assessed after selecting the variability sources. Both, training (laboratory) and experience appear to be key-factors. Thus, four operators with different experience in two different laboratories have been selected. The tests have been carried out three times in the same laboratory using samples S2 and S3: twice by operator O2 and once by operator O1 who is an expert on this experimental procedure. Sample S1 has been analysed only once by operator O2 in order to save extra powder for the tests in the other laboratory (LNEC). These tests have been carried out by Operators O3 and O4. Test results are displayed in Table

  Figure4presents the evolution of PGA-CI with C crit -C. The probability of detection of a chloride content of 0.0006 reaches 87%. C-C crit =0.0001 is represented by the coordinate point (0.0001, 0.8667) in Figure4. We can conclude that the result is highly dependent on the value

Figure 1 .Figure 2 .Figure 3 .Figure 4 .

 1234 Figure 1. Total chloride profiles

Figure 1 .Figure 2 .Figure 3 .

 123 Figure 1. Total chloride profiles

Table 9 .

 9 Values of bias in case of heterogeneous samples (sample error)

Table 1 .

 1 Chemical composition of cement

Table 2 .

 2 Ordinary Portland Concrete composition

Table 3 .

 3 Operator experimental steps

Table 4 .

 4 Initial chloride content provided by concrete components

Table 5 .

 5 Open porosities measured by water saturation

Table 6 .

 6 Available data (S: sample ; O: Operator)

Table 7 .

 7 Free, bound and total chloride contents for samples S1, S2 and S3

Table 8 .

 8 Values of bias due to bothhuman and protocol errors

Table 9 .

 9 Values of bias in case of heterogeneous samples (sample error)

Table 10 .

 10 Maximum likehood estimates (MLE) for three candidates

Table 1 .

 1 Chemical composition of cement

	Compounds

Table 2 .

 2 Ordinary Portland Concrete composition

	Compounds	Mix
		ingredients
		(kg/m 3 )
	Aggregate 10-14 mm	887,1
	Sand (Loire) 0-4 mm	852,8
	Cement CEM I 52.5	215,7
	Calcareous Filler	161,4
	Total water	176
	Water to binder ratio (W/B)	0,47

Table 7 .

 7 Free, bound and total chloride contents for samples S1, S2 and S3

		S1	S2	S3
	Chloride content
	(kg/kg of concrete)
	Free chloride	1.87 10 -3	1.81 10 -3	1.79 10 -3
	Bound chloride	0.19 10 -3	0.19 10 -3	0.19 10 -3
	Total chloride	2.06 10 -3	2 10 -3	1.98 10 -3
	C r

Table 8 .

 8 Values of bias due to both human and protocol errors

	Reference,
	error and bias
	(kg/kg of concrete)

Table 10 .

 10 Maximum likelihood estimates (MLE) for three pdf candidates

	Probability	GEV	Normal	Student
	density function
	MLE	323	319	320

E-mail address: stephanie.bonnet@univ-nantes.fr (S. Bonnet).

Acknowledgements

This study has been conducted within the context of a double research programme: the MEDACHS project (2005)(2006)(2007)(2008) "Marine environment damage to Atlantic coast historical and transport structures and buildings: methods of assessment and repair, maintenance") and the DuratiNet project (2009-2014) "Network durable transport infrastructure in the Atlantic area "). Funds were provided by grants from ERDF for the European Union, program Interreg III B and supplemented by funds provided through the French project MAREO (2007MAREO ( -2012) ) "MAintenance and REpair of concrete coastal structures: risk based Optimization", thanks to which this research has been conducted under better conditions.


Gabriel Vasile
email: gabriel.vasile@grenoble-inp.fr

INDEPENDENT COMPONENT ANALYSIS BASED INCOHERENT TARGET DECOMPOSITIONS FOR POLARIMETRIC SAR DATA -PRACTICAL ASPECTS

Keywords: Independent Component Analysis, Pol-SAR, speckle filtering

The Independent Component Analysis (ICA) has been recently introduced as a reliable alternative to identify canonical scattering mechanisms within PolSAR images. This paper addresses an important practical aspect for applying such methods on real data, namely speckle filtering with ICA. A novel algorithm is introduced by adjusting the Lee's sigma filter to the particular nature of the Touzi's polarimetric decomposition. In its current form, it allows the use of the ICA mixing matrix in the derived speckle filter.

INTRODUCTION

Polarimetric target decomposition is a PolSAR image interpretation technique that relies on the analysis of the interaction between the illuminated area and the transmitted waveform, considering each polarimetric state of the latter. More specifically, it enables the description of an image cell as a sum of canonical scattering mechanisms (also called as target vectors) making it more intuitive to understand the behaviour of the clutter and therefore to analyse it [1].

Polarimetric target decompositions are mainly classified in coherent, if their interest lies on the scattering matrix analysis for each resolution cell, like the ones proposed by Cameron [2], or incoherent, if they are based on a statistical analysis of neighbouring pixels. Incoherent target decomposition (ICTD) theory assumes that the scattering process in most natural media is a combination of coherent speckle noise and random vector scattering effects. Therefore, a stochastic approach is required and the concept of average or dominant scattering mechanisms is associated to each imaging cell [START_REF] Cloude | A review of target decomposition theorems in radar polarimetry[END_REF]. Most methods described in the literature focus on the Hermitian, semidefinite positive coherence or covariance matrix [START_REF] Cloude | A review of target decomposition theorems in radar polarimetry[END_REF]. Nevertheless, the investigation of higher order moments has recently sparked great interest of the SAR community, introducing supplementary information to the clutter analysis Thanks to the French Aerospace Lab for providing the PolSAR data. and consequently leading to new ICTD approaches [START_REF] Besic | Polarimetric incoherent target decomposition by means of independent component analysis[END_REF], [START_REF] Pralon | Evaluation of ICA-based ICTD for PolSAR data analysis using a sliding window approach: convergence rate, gaussian sources, and spatial correlation[END_REF], [START_REF] Pralon | Evaluation of the new information in the H/α feature space provided by ICA in PolSAR data analysis[END_REF].

The combined use of the Eigenvector approach with Cloude and Pottier's parametrisation gave rise to one of the most employed and most traditional classification schemes in PolSAR data analysis, the H/α feature space [START_REF] Cloude | An entropy based classification scheme for land applications of polarimetric SAR[END_REF]. The entropy, H, measures the degree of randomness of the scattering phenomenon, given as a function of the eigenvalues of the coherence matrix. Each eigenvector correspond to a scattering mechanism within the image cell and therefore each one will provide a different α angle. The authors in [START_REF] Cloude | An entropy based classification scheme for land applications of polarimetric SAR[END_REF] state that the best estimate of such parameter to represent the image cell is an weighted average based on the eigenvalues of the coherence matrix.

The parameters H and α are plotted in a plane, originating the so called H/α feature space. Upon the introduction of the aforementioned method, Cloude and Pottier suggested the partitioning of the plane in 9 regions, based on the polarimetric behaviour of known type of natural phenomenons. Therefore, once the H and the average α parameters are extracted from the target polarimetric signature, it is straightforward to classify it as one of the corresponding type of scattering mechanisms. Many works are based on such method, from geophysical parameters inversion algorithms (in varied regions from the globe) to detection and classification algorithms. Having a remarkable correspondence to ground truth, the usage of this unsupervised technique has had very few improvements since its conception. Nevertheless, there is an important remark still uncovered related to this method. The orthogonality constraint of the eigenvectors of the coherence matrix generates unfeasible regions in the plane. It is important to highlight that these regions are mathematically, and not physically, unfeasible.

Within this context, this paper addresses some of the main practical considerations when applying the independent component analysis (ICA) as an ICTD method with respect to both the H/α and the TSVM [1] decompositions.

ICA BASED ICTD

In [START_REF] Besic | Polarimetric incoherent target decomposition by means of independent component analysis[END_REF], a new strategy to polarimetric target decomposition was presented by incorporating the ICA as an alternative to identify the canonical scattering mechanisms within an image cell. The ICA is a blind source separation technique based on higher order statistical moments and cumulants whose utility has already been explored in many different research areas, such as wireless communications, data compression and brain imaging applications. The results presented in [START_REF] Besic | Polarimetric incoherent target decomposition by means of independent component analysis[END_REF] proved it to be a very promising area in polarimetry, mainly when non-Gaussian heterogeneous clutters (inherent to high resolution SAR systems) are under study. The theoretical potential in estimating similar entropy and first component, when compared to traditional eigenvector decomposition, but rather a second most dominant component independent with respect to the first one and unconstrained by the orthogonality introduces an alternative way of physically interpreting a polarimetric SAR image. In [START_REF] Pralon | Evaluation of ICA-based ICTD for PolSAR data analysis using a sliding window approach: convergence rate, gaussian sources, and spatial correlation[END_REF], the ability of ICA to correctly identify clutters composed by non-orthogonal type of scatters is further investigated, as well as its performance under a sliding window approach, enabling a more accurate comparison to the results obtained with the Eigenvector based approach.

In general, the limiting curves on the H/α plane reduce the analysis of high entropy type of targets in a more limiting way than the analysis of low entropy ones. Even though polarimetry is a better suited tool to analyse low entropy type of targets, the ability to correctly estimate the parameters that describe the illuminated scatters is crucial. Once again, it is important to highlight that these regions are mathematically, and not physically, unfeasible [START_REF] Pralon | Evaluation of the new information in the H/α feature space provided by ICA in PolSAR data analysis[END_REF].

Previous results [START_REF] Pralon | Evaluation of ICA-based ICTD for PolSAR data analysis using a sliding window approach: convergence rate, gaussian sources, and spatial correlation[END_REF] demonstrate the 11×11 spatial neighbourhood is well suited for the estimation of the Touzi's TSVM parameters from the ICA mixing matrix (using Sigle Look Complex target vectors). This In the present work, our focus relies on addressing the following practical issue: to apply speckle filtering in ICA-ICTD for better preservation of spatial features.

ICA-ICTD SPECKLE FILTERING

One of the most powerful and widely used speckle filters in PolSAR is the Lee's sigma filter, with its recent improvement proposed in [START_REF] Lee | Polarimetric SAR speckle filtering and the extended sigma filter[END_REF]. In this paper, we propose to use the same algorithm for deriving the adaptive MMSE coefficient b from Eq. ( 6) in [START_REF] Lee | Polarimetric SAR speckle filtering and the extended sigma filter[END_REF]. Further on, the following modifications are operated.

Firstly, instead of using each intensity image separately, we propose to use the Polarimetric Whitening Filter for taking into account simultaneously all the PolSAR channels. To do that, one good candidate is the texture parameter τ from [START_REF] Vasile | Optimal parameter estimation in heterogeneous clutter for high resolution polarimetric SAR data[END_REF] computed in each pixel:

τ = k † [ M ] -1 F P k, (1)
where [ M ] -1 F P is the Fixed Point polarimetric covariance matrix estimated over the centred boxcar neighbourhood and k the corresponding target vector.

Secondly, the MMSE filter is modified in each pixel of the PolSAR span image as:

s = (1 -b) σ 0 + b τ , (2)
where

σ 0 = k † [ M ] -1 F P k k † [ T ] -1
SCM k and [ T ] SCM the sample covariance matrix.

Thirdly, the strong deterministic scatterers, previously detected by the 98th percentile as in [START_REF] Lee | Polarimetric SAR speckle filtering and the extended sigma filter[END_REF], are updating the values of the MMSE coefficient b to 1. For each pixel, the values of this coefficient is stored and will be used later for filtering the corresponding TSVM parameters. One can notice that, at this stage, we have available the filtered PolSAR span and the MMSE coefficient images.

When adapting the Lee's sigma filter to the ICA-ICTD, the most important constraint is the non-orthogonality of the ICA derived backscattering mechanisms. In [START_REF] Lee | Polarimetric SAR speckle filtering and the extended sigma filter[END_REF], the MMSE filter from Eq. (2) has been directly applied for the multi-look PolSAR covariance matrix. This holds because two Sample Covariance estimates can be averaged, but this is not true for the ICA derived mixing matrices.

Instead of taking the average of the two covariance matrices, the mixing matrices barycenter could be addressed. The implementation of such approach is not straightforward, since the task of estimating matrix geometric means is a complex subject. The concept of geometric mean for more than two matrices has only been fully defined recently [START_REF] Bhatia | Riemannian geometry and matrix geometric means[END_REF], powered by the association of the geometric mean of two positive definite matrices, [M ] 1 and [M ] 2 , as the midpoint of the geodesic (with respect to a natural Riemannian metric) joining [M ] 1 and [M ] 2 . While the derived theory is valid when addressing positive definite matrices (which is the case of the covariance matrices), it does not hold for the mixing matrices estimated with ICA, which are not necessarily positive definite.

Nevertheless, the solution relies on the rotational invariance of the Touzi's TSVM decomposition. From [1], one can observe that the rotation invariant scattering vector has the following form:

- → v orient-inv = µ   cos α s cos(2τ m ) sin α s e jΦα s -j cos α s sin(2τ m )   , (3)
where the four roll-invariant parameters α s (symmetric scattering type magnitude), Φ αs (symmetric scattering type phase), τ m (helicity), and µ (maximum amplitude return) are necessary for an unambiguous description of the corresponding PolSAR scattering mechanism. As described in [1], -→ v orient-inv is obtained by constructing the Graves power matrix and performing the con-diagonalization from [START_REF] Kostinski | On foundations of radar polarimetry[END_REF] followed by the Huynen desying.

In each pixel, we propose to filter independently each rotation invariant scattering vector -→ v orient-inv i retrieved from the columns of the ICA derived mixing matrix (i = 1, 3 for monostatic PolSAR). The two vector estimates -→ v orient-inv

3×3

and -→ v orient-inv 11×11 correspond to the ICA applied independently on 3 × 3 and respectively 11 × 11 boxcar neighbourhoods:

- → v orient-inv = (1 -b) - → v orient-inv 11×11 + b - → v orient-inv 3×3 . (4)
Finally, the Cloude and Pottier entropy can be evaluated using the maximum amplitude returns µ i , while the Cloude and Pottier α is equivalent to Touzi's α s for symmetric scattering [1].

POLSAR EXPERIMENTAL RESULTS

The PolSAR dataset was acquired by the French Aerospace Lab (ONERA), in 2009, over the French Guiana, in the frame of the ESA campaign TropiSAR.

CONCLUSION

This paper addressed one important practical aspect when computing the ICA-ICTD on real PolSAR data: speckle filtering. By applying the MMSE filter on each of the ICA derived rotation invariant scattering vectors, we demonstrated the spatial resolution can be better preserved with respect to the conventional PolSAR boxcar speckle filter. Further studies will address plugging the ICA-ICTD in a reliable PolSAR segmentation algorithm.

Fig. 1 .Fig. 2 .Fig. 3 .

 123 Fig. 1. Paracou P-band airborne dataset, H/α classification map: (a) PCA and (b) ICA.

Fig. 4 .

 4 Fig. 4. Paracou P-band airborne dataset, TSVM parameters after ICA MMSE speckle filtering: (a) entropy, (b) symmetric scattering type magnitude, (c) helicity and (d) symmetric scattering type phase.

  R. Touzi, "Target scattering decomposition in terms of rollinvariant target parameters," IEEE Transactions on Geoscience and Remote Sensing, vol. 45, no. 1, pp. 73-84, 2007.[2] W. L. Cameron and L. K. Leung, "Feature motivated polarization scattering matrix decomposition," in Proceedings of the IEEE International Radar Conference, Arlington, USA, 1990, pp. 549-557.

Fig. 5 .

 5 Fig. 5. Paracou P-band airborne dataset, Poincaré sphere representation of symmetric targets: (a) PCA with boxcar, (b) MMSE with ICA.


Gabriel Vasile
email: gabriel.vasile@gipsa-lab.grenoble-inp.fr

Teodor Petrut

Eric Guy D'urso
email: guy.durso@edf.fr

De Oliveira
email: eric.de-oliveira@edf.fr

IoT Acoustic Antenna Development for Fish Biomass Long-Term Monitoring

This paper proposes a novel Internet of Things (IoT) hardware framework for detecting and counting operations for fish biomass estimation. Based on a multi-static configuration, the core part of the system is using a single board computer with high capabilities in ADC and DAC and an analog multiplexer with a competitive switching rate.

I. INTRODUCTION

Hydropower plants have important effects on migrating fish species as they can perturb and even block the migration and thus contribute to the decline and even the extinction of species. Allowing hydropower plants and river system biodiversity coexisting is a challenge, which requires sustainable solutions touching economic, social and environmental aspects. The European Commission published proposals for regulation by which passage channels are used to by-pass the fish migration paths and to permit the upstream migration of salmon and trout species [START_REF]Strategic study for development of small hydropower in the European Union[END_REF]. Among the environmental risk mitigation measures, fish passes and downstream bypass are of increasing importance for the restoration of free passage for fish and other aquatic species in rivers.

Bypass channels provide a way to completely circumvent the undesired barrier to fish migration. It is designed to match any side channel of the main river system both in form and function. Bypass channels mainly used to small scale barriers such as low head weirs (< 2 m), where the height difference between up and downstream does not lead to an overly long bypass section. More technical details can be found in [START_REF] Larnier | Pool fishways, pre-barrages and natural bypass channels[END_REF].

Fish passes represent a range of in-channel structures designed to facilitate the upstream and downstream movement of fish and other aquatic fauna. Fish passes are applied to watercourses where natural (or human) obstructions such as dams, weirs, or culverts prevent or interfere with fish migration. Such fish passage problems can occur at almost any site where the water level difference between upstream and downstream of the structure is higher than about 0.5 m [START_REF]Environment Agency annual report and accounts 2009 to 2010[END_REF]. An extensive presentation of French fish passes types can be found in [START_REF] Aigoui | Guide Passes poissons -Voies navigables de France[END_REF].

The monitoring of fish passages in a channel could be done using different technologies, like camera filming, infrared systems, passive sonars, active acoustic tagging or RFID tagging [START_REF] Cuchet | Behavioural experiments on the design of downstream fish passage facilities for potamodromous species[END_REF]. In this work, we propose a 500 kHz-acoustic system for counting fishes in passage channels, which operates on the principle of multi-static acoustic antenna [START_REF] Vasile | Reference selection for an active ultrasound wild salmon monitoring system[END_REF], [START_REF] Vasile | Intensitydriven-adaptive-neighborhood technique for POLSAR parameters estimation[END_REF]. The current system was developed in collaboration between the GIPSA-lab and the EDF R&D. It is composed of several acoustic barriers: each fish passage will obstruct the acoustic propagation channel between the emitter and the receiver, which makes possible fish monitoring. Each acoustic barrier can act as an independent conventional immersed wideband ultrasound system in bistatic configuration, also.

In the same time, emerging Internet of Things (IoT) solutions provide nowadays a new perspective both in terms of cost reduction and remote operation capabilities. Because the passage channel is a highly noisy and relatively fast changing environment, our motivation for designing the proposed IoT system is to increase the quality of signals and to simplify the computational load of the processing algorithms for the detection of events.

The paper is structured as follows. Section II illustrates in several points the general hardware architecture proposed for the fish monitoring system, while Section III presents some qualitative and quantitative performance assessment. Section IV concludes the paper.

II. IOT HARDWARE ARCHITECTURE

The main advantages of the proposed acoustic system, as compared to commercial active acoustic systems are: cost effectiveness and minimal preparations for on site installation. The designed configuration schematic is shown in Fig. 1-(a),(b).

As it can be observed, three modules are composing the IoT fish monitoring system:

• the IoT client -an embedded system capable of managing signal acquisition, real time processing (intelligent triggering option) and sending the recorded data to the server ; • the IoT hub -a processing unit for data management, storage and final signal processing ; • Ultrasound transducers and electronic conditioning. In the remaining part of this section, we provide more in depth details on these modules.

A. IoT client embedded system

The proposed system uses one of the most advanced single board computer on the market, Red Pitaya STEMLab 125-14 (RP), which contains a system-on chip (SoC) composed of the Xilinx FPGA, with an ARM Cortex A9 processor, 256 MB RAM and ports for 1 Gb/s Ethernet communication. The board has 2 fast analog inputs and 2 fast analog outputs, which allows analog-to-digital conversion up to 14 bits and 125 MHz sampling frequency. This is more than suitable for using ultrasound frequencies around 500 kHz (or lower). Giving the fact that the board has only 2 analog inputs, we propose to use an analog multiplexer: a Texas Instruments MUX36D04 containing 2:8 (2 input channels to 8 output channels) or 1:4 multiplexing capability (Round Robin or sequential sampling). At its full potential, the multiplexer can switch channels at about 100 ns. In this very first version of the system we use the Red Pitaya's outputs digital pins to command the TI multiplexer. Therefore, by means of analog multiplexing, we are able to set up to 8 physical ultrasound paths, or acoustic barriers across the passage channel. In the next version, both the analog multiplexing and the acquisition are to be driven by an external digital pattern generator (Arduino Due).

B. IoT hub and server processing unit

We have used as IoT data collection hub and real-time signal processing an Intel Next Unit of Computing equipped with i5 7260U processor, 8 GB of RAM and 256 GB of SSD storage. The server is connected to the IoT client via Gigabit Ethernet (by a direct cable or by a wireless USB 2.0 dongle). The communication is established either by direct TCP / IP with fixed IP addresses or via a LAN router.

In a separate paper, we discuss the software architecture and the signal processing algorithms for the fish monitoring in the respective passage channel.

C. Ultrasound transducers and electronic conditioning

Like any other acoustic acquisition and processing system, it comprises the standard stages of a conventional active emission-reception configuration. The system is bi-static, which means we use two emitters (Ultran Group WS-100-1) and 2 receivers (Ultran Group KS-100-1) face-to-face to establish two acoustic barriers across the passage channel. The emitted signal has been amplified by a power amplifier APEX Microtechnology PA107 (gain at 20 dB), whereas the received signal has been conditioned by a low noise amplifier (Texas Instruments VCA 5807).

III. RESULTS AND DISCUSSION

Pilot tests have been already applied on the system in a controlled passage channel with fishes inside. The test and measurement campaign has been realised within the EDF R&D facilities, Chatou, France, in 2018. The setup of the ultrasound transducers is shown in Fig. 2. In order to validate the obtained fish detection results, an underwater camera has been installed, also.

In our 3-day experiment, the IoT client has been programmed to continuously transmit two types of arbitrary waveforms in burst mode: sine-wave with a squared weighting window and linear chirp with Hamming weighting window At the IoT hub level, the demodulation by normalized crosscorrelation (match filtering with the non-linearity corrected reference from [10]) is performed, also: the peak value for each burst is recorded in order to construct the associated time series for fish monitoring. The obtained detection results, which have been validated using the installed underwater camera are illustrated on Fig. 5 for one night of continuous monitoring.

One can observe the monitored fish activity is decreasing dramatically during nighttime. More acoustic detections have been obtained by the lower depth barrier indicating that the weaker signal level has no significant impact on the proposed algorithm.

IV. CONCLUSION

In conclusion, a low power consumption and cost effective IoT acoustic system was designed to achieve monitoring of fish passages in channels near hydropower plants or dams. The system is based on a multi-static configuration of 1 emitter to 4 receivers or 2 emitters to 8 receivers. The core part of the system is using a single board computer with high capabilities in ADC and DAC operations and an analog multiplexer with a competitive switching rate. The IoT system was tested for real-time operations and proved to be very robust with respect to signal acquisition, data transmission to the server and real-time signal processing. The main scope is fish detection and counting, but further applications like classification or localisation could be added. The future tests will also include the multiplexing stage in order to increase the number of acoustic barriers across the passage channels.

Fig. 1 .

 1 Fig. 1. Setup configuration developed for the fish counting application: (a) global set-up and (b) data processing modules.

Fig. 2 .

 2 Fig. 2. Ultrasound transducers installed on Channel 12 at the EDF R&D: (a) global view, (b) trout passage and (c) underwater camera photo.

[ 9 ]Fig. 3 .

 93 Fig. 3. Ultrasound chirp signals received by the IoT client and retrieved via the IoT hub : (a) time domain and (b) frequency domain -normalized amplitude.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Ultrasound sine-wave signals received by the IoT client and retrieved via the IoT hub : (a) time domain and (b) frequency domain-normalized amplitude.

ACKNOWLEDGMENT

This work has been developed in the framework of the ACOUEAU project, supported by the European Union Regional Development Fund, the SCANUS project, supported by the SATT LINKSIUM Grenoble Alpes, and the Scientific Equipment 2017 AO project, supported by the LabEx OSUG@2020. The authors would like to thank to Gelu Ionescu, Steeve Zozor, Amaury Nègre and Pascal Bellemain, form the GIPSA-lab, and to Géry Hachet and Alexandre Girard, from the EDF R&D, for their precious support in hardware and software development.