Rafik Hajrya
email: rafik.hajrya@ensam.eu

Nazih Mechbal
email: nazih.mechbal@ensam.eu

Perturbation Analysis for Robust Damage Detection with Application to Multifunctional Aircraft Structures

Keywords: Structural health monitoring, robust damage detection, decision-making, analytical threshold, matrix perturbation theory, range subspaces, independent component analysis, piezoelectric ceramic material, composite structures, conformal load-bearing antenna structure, impact damage

The most widely known form of multifunctional aircraft structure is smart structures for structural health monitoring (SHM). The aim is to provide automated systems whose purposes are to identify and to characterize possible damage within structures by using a network of actuators and sensors. Unfortunately, environmental and operational variability render many of the proposed damage detection methods difficult to successfully be applied. In this paper, an original robust damage detection approach using output-only vibration data is proposed. It is based on independent component analysis and matrix perturbation analysis, where an analytical threshold is proposed to get rid of statistical assumptions usually performed in damage detection approach. The effectiveness of the proposed SHM method is demonstrated numerically using finite element simulations and experimentally through a conformal load-bearing antenna structure and composite plates instrumented with piezoelectric ceramic materials.

Introduction

Ongoing research and development programs on advanced smart structures, particularly for aircraft industries, have come up with the concept of multifunctional aircraft structure (MAS). The principle is to take the advantage of new materials to integrate airframe structure with functional systems. The structure has the ability to respond to changes due to environmental conditions and to perform a number of tasks such as transmit/receive function, structural enhancement and repair [START_REF] Wang | A review on structural enhancement and repair using piezoelectric materials and shape memory alloys[END_REF], conformal load-bearing antenna structure (CLAS) [START_REF] Lockyer | Conformal load-bearing antenna structures (CLAS): Initiative for Multiple Military and Commercial Applications[END_REF] and structural health monitoring (SHM) [START_REF] Mahzan | Experimental studies on impact damage location in composite aerospace structures using genetic algorithms and neural networks[END_REF]). On MAS, SHM is the most form of smartness that is studied. It is a broad field encompassing many synergetic technologies that provide together automated systems whose purposes are to identify and characterize possible damage within structures. The SHM problem has occupied many scientific communities in the last considers only second-order statistics to obtain uncorrelated sources, ICA exploits the higher-order statistics embedded in the measurements to extract independent sources.

The present work falls within the SMSE project (Smart Materials and Structures for Electromagnetics), [START_REF] Smse | Research Report-SMSE project: smart materials and structures for electromagnetics[END_REF], where the objective is to evaluate the concept of new materials that enable the realization of compact and reconfigurable antenna composite structures. This adaptability assumes that these structures are equipped with sensors/actuators able to perform SHM, as well as active control (shape control and vibration rejection) tasks [START_REF] Preumont | Vibration control of active structures-An introduction[END_REF]. This requirement leads us to use the Lead Zirconate Titanate piezoelectric ceramics (noted in what follow PZT) as actuators and sensors. Indeed, PZTs have good broadband sensing/actuation properties that make them extensively used for a wide range of frequency, including ultrasonic applications. It is also to be noticed that the SHM proposed approach is not limited to any frequency range, but within the project, the dynamic response of the monitored structures is generated at low frequency range to avoid interference with communication systems.

The proposed damage detection is an iterative one, and it relies on instantaneous knowledge of the structure. Before performing a health monitoring system, the structure is assumed to be in a healthy state. Typically, baseline measurements are recorded when the structure is pristine, and they are stored for comparison to future tested data for damage detection. When no longer damage is detected, the tested data become the new baseline database. The proposed approach is first presented through finite element (FE) simulations, where a composite plate bonded with PZTs is considered, and environmental variability's (temperature and noise changes) are introduced. Then, the method is applied to monitor two test benches: composite plates and a CLAS, subject respectively to impact damage and a delamination of the antenna array. For this last structure, interaction between the PZTs and antenna array has also been investigated in an anechoic chamber.

The layout of this paper is as follows: a description of the technique used to extract the feature using ICA is provided in section 2. In Section 3, the damage index is established. In Section 4, MPT is addressed to drive the SHM decision-making. The damage detection methodology is applied on a finite element model of an active composite plate, and it is presented in section 5. Section 6 explores the proposed approach on the two test benches. A discussion regarding the proposed damage detection methodology is presented in section 7. Concluding remarks and future perspectives are drawn in Section 8.

Brief overview of ICA theory

The BSS model considered in this paper is a linear simultaneous mixture formulated as [START_REF] Comon | Handbook of Blind Source Separation[END_REF]:

𝒚(𝑘) = 𝐓𝒔(𝑘) + 𝝐(𝑘) (1)
where 𝒚(𝑘) = [𝑦 1 (𝑘) … 𝑦 𝑛 𝑦 (𝑘)] 𝑇 is a zero mean measurement vector from 𝑛 𝑦 sensors at time index 𝑘, 𝐓 is the mixing matrix, 𝒔(𝑘) = [𝑠 1 (𝑘) … 𝑠 𝑛 𝑦 (𝑘)] 𝑇 is the sources vector and 𝝐(𝑘) = [𝜖 1 (𝑘) … 𝜖 𝑛 𝑦 (𝑘)] 𝑇 represents all the uncertainties and disturbances effects.

In the present study, the unnoisy model is conducted. Uncertainties and perturbation's effects will be incorporated through the proposed threshold:

𝒚(𝑘) = 𝐓𝒔(𝑘) (2)
BSS is an estimation problem, that is accomplished by finding only from the observed data 𝒚(𝑘) an estimated sources vector and a separating matrix noted respectively 𝒓(𝑘) ∈ ℝ 𝑛 𝑦 ×1 and 𝐖 ∈ ℝ 𝑛 𝑦 ×𝑛 𝑦 :

𝒓(𝑘) = 𝐖𝒚(𝑘) (3)
In this paper, the sources are assumed to be temporally identically and independently distributed and non-Gaussian, which leads to the ICA method.

One way to solve the separation problem using ICA is to use the mutual information. Indeed, it is a measure of independence between variables of a random vector. It is always non-negative and zero, if and only if, the variables are statistically independent [START_REF] Cover | Elements of Information Theory[END_REF]. Using the concept of negentropy introduced by [START_REF] Donoho | On Minimum entropy deconvolution[END_REF], the mutual information (noted 𝐼(𝒓)) between the components 𝑟 𝑖 of a random vector 𝒓 is given by:

𝐼(𝒓) = 𝐼(𝒓 𝑔 ) + 𝐽(𝒓) -∑ 𝐽(𝑟 𝑖 ) 𝑛 𝑦 𝑖=1 (4)
where 𝐼(𝒓 𝑔 ), 𝐽(𝒓), 𝐽(𝑟 i ), 𝐻(𝒓) and 𝐻(𝑟 𝑖 ) represent respectively the mutual information of a Gaussian random vector, the joint negentropy, the marginal negentropy, the joint differential entropy and the marginal differential entropy. These quantities are defined by the following relations [START_REF] Cover | Elements of Information Theory[END_REF]:

𝐼(𝒓 𝑔 ) = 1 2 𝑙𝑛 ∏ 𝜎 𝑟 𝑔𝑖 2 𝑛 𝑦 𝑖=1 𝑑𝑒𝑡(𝚺 𝒓 𝑔 ) (5) 𝐽(𝒓) = 𝐻(𝒓 𝒈 ) -𝐻(𝒓), 𝐽(𝑟 𝑖 ) = 𝐻(𝑟 𝑔𝑖 ) -𝐻(𝑟 𝑖 ) (6) 𝐻(𝒓) = -∫ 𝑝 𝒓 (𝝃) ℝ 𝑛 𝑦 𝑙𝑛 𝑝 𝒓 (𝝃)𝑑𝝃, 𝐻(𝒓 𝑔 ) = 1 2 𝑙𝑛{(2𝜋𝑒) 𝑛 𝑦 𝑑𝑒𝑡(𝚺 𝒓 𝑔 )} (7) 𝐻(𝑟 𝑖 ) = -∫ 𝑝 𝑟 𝑖 (𝜉 𝑖 ) ℝ 𝑙𝑛 𝑝 𝑟 𝑖 (𝜉 𝑖 )𝑑𝜉 𝑖 , 𝐻(𝑟 𝑔𝑖 ) = 1 2 𝑙𝑛{2𝜋𝑒𝜎 𝑟 𝑔𝑖 2 } (8)
𝑝 𝒓 , 𝑝 𝑟 𝑖 are respectively the joint and marginal probability density functions, 𝚺 𝒓 𝑔 and 𝜎 𝑟 𝑔𝑖 2 are respectively the covariance matrix of the Gaussian random vector 𝒓 𝑔 and the variance of its components 𝑟 𝑔𝑖 .

The BSS problem comes down to estimate a source's vector 𝒓 = [𝑟 1 ⋯ 𝑟 𝑛 𝑦 ] 𝑇 which follow a non-Gaussian distribution and whose components are statistically independent. The first step is the pre-whitening, which is the process of removing the correlation between the components of a data vector. It is accomplished by applying a linear transformation to the measured data vector 𝒚 to produce a vector whose elements are mutually uncorrelated, and all have unit variance (in this case 𝐼(𝒓 𝑔 ) = 0). Then, the separating matrix 𝐖 is obtained by minimizing 𝐼(𝒓):

min 𝐖 𝐼(𝒓) = min 𝐖 {𝐽(𝒓) -∑ 𝐽(𝑟 𝑖 ) 𝑛 𝑦 𝑖=1 } (9)
Based on approximate form of the negentropy quantities 𝐽(𝒓) and 𝐽(𝑟 𝑖 ), [START_REF] Gävert | The FastICA Matlab package[END_REF] have developed an efficient fixed-point toolbox for ICA (named FastICA). This algorithm calculates the separating matrix noted in what follow 𝐖 ICA , and allows then identification of the independent component vector (sources vector).

Vibration analysis using ICA

The dynamic response of a linear mechanical system with 𝑛 𝐷𝑂𝐹 degrees of freedom is described by the flowing equation:

𝐌𝒙̈(𝑡) + 𝐂𝒙̇(𝑡) + 𝐊𝒙(𝑡) = 𝒇(𝑡) (10)
where 𝐌, 𝐂 and 𝐊 ∈ ℝ 𝑛 𝐷𝑂𝐹 ×𝑛 𝐷𝑂𝐹 are respectively the mass, damping and stiffness matrices, 𝒙(𝑡) ∈ ℝ 𝑛 𝐷𝑂𝐹 ×1 and 𝒇(𝑡) ∈ ℝ 𝑛 𝐷𝑂𝐹 ×1 are the time varying displacement response and the applied force.

The free vibration response (𝒇 = 𝟎) of a lightly damped structure can be described through the modal expansion form:

𝒙(𝑡) = ∑ 𝜳 𝑖 𝑛 𝐷𝑂𝐹 𝑖=1 𝑎 𝑖 𝑒𝑥𝑝(𝜉 𝑖 ) 𝑐𝑜𝑠(𝜔 𝑖 𝑡 + 𝜑 𝑖 ) (11)
𝜉 𝑖 , 𝜔 𝑖 , 𝜑 𝑖 represent respectively the damping ratio, natural frequency and phase angle of the mode shape 𝜳 𝑖 , 𝑎 𝑖 is a constant.

In discrete-time and matrix form, Eq. ( 11) is rewritten as:

𝒙(𝑘) = 𝚿𝒒(𝑘) ( 12
)
where 𝑘 is discrete-time index, 𝚿 ∈ ℝ 𝑛 𝐷𝑂𝐹 ×𝑛 𝐷𝑂𝐹 is the mode shape matrix, 𝒒(𝑘) ∈ ℝ 𝑛 𝐷𝑂𝐹 ×1 is a vector containing the modal coordinates.

From the previous relation, the correspondence between the modal expansion (Eq. ( 11)) and the static mixture BSS model (Eq. ( 2)) is straightforward: the modal coordinates act as virtual sources, and the mixing matrix reflects the mode shape matrix [START_REF] Zhou | Blind source separation based vibration mode identification[END_REF]. BSS techniques can be seen as a non-parametric output-only modal identification method. Furthermore, as damages produce changes on the modal coordinates and the mode shape matrix; the virtual sources, the mixing and the separating matrices are also affected. Thereby, ICA can be used as a basis to build damage indices. In the sequel, a specific damage index based on monitoring the range subspaces of the separating matrix is proposed.

Damage index

Let 𝐖 ICA ℎ , 𝐖 ICA 𝑢 ∈ ℝ 𝑛 𝑦 ×𝑛 𝑦 be the separating matrices, obtained respectively from data sensors of the structure in healthy and unknown state. For ease of reading, we abridge the notations:

𝐀 = 𝐖 ICA ℎ , 𝐀 ̅ = 𝐖 ICA 𝑢 (13)
Now, using the singular value decomposition, the matrix 𝐀 is rewritten as follows:

𝐀 = 𝐔𝚪𝐕 = [𝐔 𝟏 𝐔 𝟐 ] [ 𝚪 𝟏 𝟎 𝟎 𝚪 𝟐 ] [𝐕 𝟏 𝐕 𝟐 ] 𝐓 = 𝐀 𝟏 + 𝐀 𝟐 (14)
where:

𝐔 1 = [𝒖 11 ⋯ 𝒖 1𝑛 𝑟 ] ∈ ℝ 𝑛 𝑦 ×𝑛 𝑟 , 𝚪 1 = 𝑑𝑖𝑎𝑔(𝜎 1 ⋯ 𝜎 𝑛 𝑟 ), 𝐕 1 = [𝒗 11 ⋯ 𝒗 1𝑛 𝑟 ] ∈ ℝ 𝑛 𝑦 ×𝑛 𝑟
are respectively the matrix of left singular vectors, the matrix of singular values, the matrix of right singular vectors, associated to the principal subspaces (left and right) of the matrix 𝐀. These matrices are related to the main singular values, for example, concentrating more than 98% of the system total energy. 𝐔 2 = [𝒖 2(𝑛 𝑟 +1) ⋯ 𝒖 2𝑛 𝑦 ] ∈ ℝ 𝑛 𝑦 ×(𝑛 𝑦 -𝑛 𝑟 ) , 𝚪 2 = 𝑑𝑖𝑎𝑔(𝜎 𝑛 𝑟 +1 ⋯ 𝜎 𝑛 𝑦 ) , and

𝐕 2 = [𝒗 2(𝑛 𝑟 +1) ⋯ 𝒗 2𝑛 𝑦 ] ∈ ℝ 𝑛 𝑦 ×(𝑛 𝑦 -𝑛 𝑟 )
are respectively the matrix of left singular vectors, the matrix of singular values, and the matrix of right singular vectors, associated to the residual subspaces of matrix 𝐀.

In the same way, the matrix 𝐀 ̅ is defined as:

𝐀 ̅ = 𝐔𝚪𝐕 = [ 𝐔 1 𝐔 2 ] [ 𝚪 1 𝟎 𝟎 𝚪 2 ] [ 𝐕 1 𝐕 𝟐 ] 𝑇 = 𝐀 ̅ 1 + 𝐀 ̅ 2 (15)
As it was highlighted previously, the presence of damage causes a change in the mode shape matrix, and consequently a change in the separating matrix. Accordingly, the left and right principal subspaces of 𝐀 ̅ are deflected to those of 𝐀 (Fig. 2). The proposed damage index (DI) is based on the calculus of the angle between the range subspaces of the matrix 𝐀 1 and those of 𝐀 ̅ 1 . Let: 𝑅{𝐀 ̅ 1 }, 𝑅 {𝐀 ̅ 1 𝑇 } be the ranges associated respectively to the left and right principal subspaces of matrix 𝐀 ̅ , 𝑅{𝐀 1 }, 𝑅{𝐀 1 𝑇 } be the ranges associated respectively to the left and right principal subspaces of matrix 𝐀 ̅ , 𝐏 𝑅{𝐀 ̅ 1 } , 𝐏 𝑅{𝐀 ̅ 1 𝑇 } , 𝐏 𝑅{𝐀 1 } and 𝐏 𝑅{𝐀 1 𝑇 } be the orthogonal projection on theses ranges, defined as:

𝐏 𝑅{𝐀 ̅ 1 } = 𝐔 1 𝐔 1 𝑇 , 𝐏 𝑅{𝐀 ̅ 1 𝑇 } = 𝐕 1 𝐕 1 𝑇 (16) 𝐏 𝑅{𝐀 1 } = 𝐔 1 𝐔 1 𝑇 , 𝐏 𝑅{𝐀 1 𝑇 } = 𝐕 1 𝐕 1 𝑇 (17)
By introducing the following quantities: ‖sin 𝜽[𝑅{𝐀 ̅ 1 }, 𝑅{𝐀 1 }]‖ UI : the sinus angle between the range 𝑅{𝐀 1 } and 𝑅{𝐀 1 }, ‖sin 𝝋[𝑅 {𝐀 ̅ 1 𝑇 } , 𝑅{𝐀 1 𝑇 }]‖ UI : the sinus angle between the range 𝑅 {𝐀 ̅ 1 𝑇 } and 𝑅{𝐀 1 𝑇 }.

where ‖. ‖ UI denotes a general unitarily invariant norm, and the Euclidean norm ‖. ‖ 2 is used for the calculus.

The sinus angle norm of the aforementioned ranges is defined as [START_REF] Golub | Matrix Computation[END_REF]:

DI ICA 1 = ‖sin 𝜽[𝑅{𝐀 ̅ 1 }, 𝑅{𝐀 1 }]‖ = ‖(𝐈 𝑛 𝑦 -𝐏 𝑅{𝐀 1 } )𝐏 𝑅{𝐀 ̅ 𝟏 } ‖ (18) DI ICA 2 = ‖sin 𝝋[𝑅 {𝐀 1 𝑇 } , 𝑅{𝐀 1 𝑇 }]‖ 2 = ‖(𝐈 𝑛 𝑦 -𝐏 𝑅{𝐀 1 𝑇 } )𝐏 𝑅{𝐀 1 𝑇 } ‖ (19)
From these relations and considering the SHM problem of smart structures, a damage index is stated by the following proposition:

Proposal 1: Damage index Consider a smart structure with 𝑛 𝑦 sensors, damage could be detected by monitoring the following damage index:

DI ICA = √DI ICA 1 DI ICA 2 𝑛 𝑟 (20)
where 𝑛 𝑟 is the number of principal components retained, and DI ICA 1 , DI ICA 2 are defined in Eqs. (18) and ( 19).

Damage index based on the angle between subspaces was first proposed by De Boe and Golinval (2003). In their work, the authors have applied the QR decomposition (𝐘 = 𝐐𝐑) to the measurement matrix of the healthy and unknown states to get the cosines of the principal angles. The physical interpretation that underlies the proposed damage index is the fact that its definition is based on the ICA method, which is a procedure that allows to extract a basis for a modal decomposition [START_REF] Zhou | Blind source separation based vibration mode identification[END_REF]. As modes are known to be sensitive to structural changes, it follows that the subspaces spanned by the ICA feature are deflected to those obtained from the healthy state. Furthermore, in the proposed damage index, we are monitoring the left and right subspaces of the separating matrix, i.e., 𝑅{𝐀 1 } and 𝑅{𝐀 1 𝑇 }, in the case where one of them is more sensitive to the presence of a damage.

Analytical threshold

Now that the damage index is defined, a threshold has to be established. Indeed, as stated previously, a critical issue in SHM is to be able to differentiate the disturbance effects that a healthy monitored structure undergoes from damage. Furthermore, environmental disturbances such as measurement noises, temperature variations could lead to false-positive alarms or missing detection. To overcome this drawback, probabilistic decision making approaches are in general used, which suppose a set of probabilistic models and assumptions. However, these models need in general large database to correctly approximate them.

In this work, since the proposed damage index deals mainly with matrix decomposition and subspace projections, we propose to bind analytically the deviation that appears in the subspaces of the separating matrix, when the structure undergoes a low level environmental variability. Thereby, MPT is addressed to define an analytical threshold and to get rid of statistical assumptions.

MPT considers how matrix functions such as subspaces change when the matrix is subject to perturbations [START_REF] Stewart | Matrix Perturbation Theory[END_REF]:

𝐀 ̃= 𝐀 + δ𝐀 (21) where the matrix 𝛿𝐀 describes the variation that matrix 𝐀 is subjected due to disturbances. Then, the objective is to define a robust average that estimates how much the damage index DI ICA (Eq. ( 20)) is affected.

To drive the proposed analytical bound, the early work of [START_REF] Wedin | Perturbation bounds in connection with singular value decomposition[END_REF] on perturbed matrices was opted. The idea is to estimate ‖δ𝐀‖ by performing several tests or simulations on the healthy structure and by evaluating the gap between specific singular values in order to define an upper bound for the damage index.

Proposal 2: Analytical threshold and detection rate Assume that ∃ 𝜂 ≥ 0, 𝑎𝑛𝑑 𝛿 > 0, an upper threshold noted 𝛽 ICA of the damage index is defined as:

𝛽 ICA = √(𝜀 + 𝜂DI ̃ICA 2 )(𝜀 + 𝜂DI ̃ICA 1 ) (𝜂 + 𝛿)𝑛 𝑟 ( 22
)
where DI ̃ICA 1 and DI ̃ICA 2 are defined in the same way as in Eqs. (18)-( 19) by replacing 𝐀 ̅ 1 by 𝐀 ̃1, 𝜀 quantifies the magnitude of the environmental disturbances and it is defined in Eq.( 31), 𝑛 𝑟 is the number of principal components retained, and the two scalars 𝜂 and 𝛿 are defined as:

𝜂 ≥ 𝜎 max (𝐀 2 ) (23) 𝜂 + 𝛿 ≤ 𝜎 min (𝐀 ̃1) (24)
The DI defined in Eq. ( 20) and its associated threshold of Eq. ( 22) define the following detection rate:

R ICA = DI ICA 𝛽 ICA ( 25
)
if R ICA > 1 then the structure is damaged, otherwise it is healthy.

Derivation:

The proposed analytical threshold is derived following three major steps: First step: Consider the variation 𝛿𝐀 that the separating matrix 𝐀 is subjected due to the environmental disturbances. To describe this variation, a second test/simulation is performed on the healthy state of the structure, ICA algorithm is then applied to determine the new separating matrix noted 𝐀 ̃. This matrix is rewritten as:

𝐀 ̃= 𝐔 ̃𝚪 ̃𝐕 ̃= [𝐔 ̃1 𝐔 ̃2] [ 𝚪 ̃1 𝟎 𝟎 𝚪 ̃2] [𝐕 ̃1 𝐕 ̃2] 𝑇 = 𝐀 ̃1 + 𝐀 ̃2 (
Second step: Assume now, that there exist two scalars: 𝜂 ≥ 0 𝑎𝑛𝑑 𝛿 > 0, such that the relations defined in Eqs. ( 23)-( 24) hold, then using the results demonstrated in [START_REF] Wedin | Perturbation bounds in connection with singular value decomposition[END_REF], the following relations are derived:

DI ̃ICA 1 = ‖sin 𝜽[𝑅{𝐀 ̃1}, 𝑅{𝐀 1 }]‖ 2 ≤ 𝜀 + 𝜂DI ̃ICA 2 𝜂 + 𝛿 (32) DI ̃ICA 2 = ‖sin 𝝋[𝑅{𝐀 ̃1 𝑇 }, 𝑅{𝐀 1 𝑇 }]‖ 2 ≤ 𝜀 + 𝜂DI ̃ICA 1 𝜂 + 𝛿 (33)
Third step:

The damage index defined in Eq. ( 20) is calculated from the separating matrix of the healthy and unknown states 𝐀, 𝐀, while the term DI ̃ICA is calculated from the separating matrices 𝐀, 𝐀 ̃ of the healthy state under disturbances. Consequently, the term DI ̃ICA satisfies:

DI ̃ICA ≤ √(𝜀 + 𝜂DI ̃ICA 2 )(𝜀 + 𝜂DI ̃ICA 1 ) (𝜂 + 𝛿)𝑛 𝑟 (34)
The general framework of the proposed damage monitoring procedure is outlined in Fig. 3. It is to be noticed that the proposed approach is an unsupervised learning method, which implies that the data from a damaged state are not used to build this threshold. Moreover, it is an incremental and iterative procedure. In practice, the design procedure depicted in Fig. 3 is first performed, and then if there is no longer detected damage, the unknown state becomes the baseline, and the design is repeated. The incremental procedure, summarized in Fig. 4 permits to ensure that the healthy baseline structure is always updated.

Simulation results on a composite plate

Composite plate specimen

The test specimen is of a fuselage piece. It is a composite plate of dimension 400 × 300 × 2 𝑚𝑚 3 , and made up of 16 layers carbon epoxy material. The layer sequences are: [0 2 °/ 45 2 °/ -45 2 °/ 90 2 °/ 90 2 °/ -45 2 °/ 45 2 °/ 0 2 °].The mechanical properties of the composite material are illustrated in Table 1. Table 2 depicts the mechanical and electrical properties of the PZT, type PZ29 [START_REF] Ferroperm | Material data based on typical values for piezoceramic[END_REF]. Using the controllability and observability Gramians, an optimal placement of the PZTs with dimension of 30 × 20 × 0.2 mm 3 was proposed by the authors [START_REF] Hajrya | Active damage detection and localization applied to a composite structure using piezoceramic patches[END_REF]) (see Fig. 5(a)).

FE modeling of the active composite plate

In order to outline the environment effects and to test the validity of the proposed damage detection algorithm, a detailed FE model of the active plate has been developed using the Structural Dynamics Toolbox (SDTools). The developed model is devoted to simulate vibratory data.

SDTools is a FE toolbox developed in Matlab environment. It has a specific parameterized FE model of PZT elements with electromechanical coupling, that allows to perform predictive behavior of the active structure [START_REF] Balmes | Modeling structures with piezoelectric materials[END_REF]. For wave propagation, computation of periodic solutions using Fourier/Floquet solutions is proposed in the toolbox. Moreover, following the approach used by [START_REF] Valliappan | Finite element analysis of anisotropic damage mechanics problems[END_REF], a parametrical damage is introduced. The damage is represented by a reduction of material properties in a chosen area (see Fig. 5(a)). To introduce this damage, we used a strategy inspired by the one employed in SDTools for PZT modeling. Indeed, a parameterized damaged patch is generated with a specific mesh, where its dimension and mechanical properties could then be changed and adjusted (Fig. 5(b)). The introduction of this patch before changing its properties does not change the modal properties of the structure in the frequency range of interest (Fig. 5(c)).

The FE model is under free-free boundary and consists of 195 elements; each element has dimension of 15 × 10 mm 2 . This mesh size is compatible with the frequency range of interest ([0 10 kHz ]). The model was calculated with 𝑛 𝑚 = 50 first modes with proportional damping, satisfying Caughey's criteria [START_REF] Adhikari | Damping modeling using generalized proportional damping[END_REF].

In both of simulations and experiments of the composite plate, the signal excitation used is a Schroeder signal, with frequency range of [0 2 kHz]. This signal has a flat power spectral density over its frequency range (Fig. 6). The choice of this frequency range was imposed by the real time acquisition system used in the experiments described in the next section. The simulated actuation was applied through PZT 7, while the other PZTs are used as sensors. The characteristic of the simulated data are: sampling frequency 𝑓 𝑠 = 8 kHz, and 𝑁 = 2 14 time samples.

Baseline using noise and temperature changes

To calculate the novelty analytical threshold, 50 simulations were conducted by considering the healthy plate model under different values of noise and temperature. An inspection of the nature of the experimental noise was first exanimated in the test bench described in section 6. For this purpose, tests on the experimental healthy and damaged composite plates were conducted by recording signal sensors in the case where no excitation is acting on the structure. The idea here is to use the same noise that the one acting on the structure. Using the marginal negentropy defined in Eq. ( 6), the non-Gaussianity of the measured noises was quantified. The results are illustrated in Tables 34, and show that the negentropy of the measured noises are different from zero. These results conclude the fact that the experimental noise is non-Gaussian. Therefore, in the sequel, a non-Gaussian noise will be added to all the finite element simulations to mimic a type of disturbance.

With the inherent anisotropy of composite materials, any attempt to simulate the effect of environmental disturbance like temperature requires relevant experimental data from the structure in an enclosed heated space. These data will feed the FE model to yield reasonably accurate prediction. However, it is expected that the first-order thermal effects in an instrumented composite structure will be associated with the difference between the evolution of constitutive behaviour of the composite matrix, its fibers and the PZT. As a rough approximation, one can consider varying moduli for the composite plate with fixed mechanical properties for the PZT.

Following this modeling manner, the moduli (E 1 , E 2 , G 12 , G 23 ) were varied by a percentage of 𝜃 ∈ [0.04 1.44]%, with a step of 0.0071% and for each of these simulations, different variance of random non-Gaussian noise were added (from 1% to 25.5%). Once the baseline built, step 3 of the framework presented in Fig. 3 was applied, and the novelty analytical threshold was calculated: 𝜇 𝛽,𝐼𝐶𝐴 = 0.0673.

Simulation results of damage scenarios and test of false-positive alarms

In order to test the performances of the proposed method, 54 simulations with different damaged elements and environmental disturbances were conducted. The first 4 simulations (no°51-no°54) concern a reduced stiffness of 4% for damages 𝐷1, . . 𝐷5 (see Fig. 5(a)), and with different temperature change and non-Gaussian noise. The other simulations (no°55-no°104) were performed to test the damage detection methodology regarding false-positive alarms. These simulations were performed by varying the moduli (E 1 , E 2 , G 12 , G 23 ) by a percentage 𝜃 ∈ [0.08 1.48]%, with a step of 0.0071% . It is to be noted that the aforementioned simulations do not belong to those used to build the baseline test. Fig. 7 depicts some of the results associated to these simulations. On one hand, the damaged states are well detected and separated from the analytical threshold. On the other hand, no false-positive alarms were noted: the analytical threshold is robust to the simulated new perturbations.

Experimental applications

Active composite plates

Following the optimal placement results [START_REF] Hajrya | Active damage detection and localization applied to a composite structure using piezoceramic patches[END_REF], PZTs were glued on two composite plates: a healthy (Fig. 8 (a)) and a damaged one (Fig. 8 (b)). The two plates have the same characteristics and dimensions: 400 × 300 × 2 𝑚𝑚 3 , except that in one of them, damage was introduced. This later has undergone an impact damage (diameter of 5 mm) produced by a calibrated impact device. In order to test the proposed approach regarding false-positive alarms, two additive masses were used for boundary condition changes: see Fig. 8 (c). These masses represent 0.5% and 0.2% of the total composite plate weight.

The input excitation and the data acquisition were performed using a voltage amplifier (TREK Model 601C) and charge amplifiers (type 5011B). The actuation and sensor records were done following the same procedure as in the simulation: actuation using the Schroeder signal, frequency range of [0 2 kHz] (Fig. 6), sampling frequency 𝑓 𝑠 = 8 kHz, and 𝑁 = 2 14 time samples. To calculate the analytical threshold, 𝑛 = 40 tests with enough time lags between them were conducted on the healthy plate.

The vibratory data acquired from the sensors of the composite plates (see Figs. 9-10) were transformed into features through the ICA method. From many tests of the healthy and damaged plates, the damage index and the analytical threshold defined respectively in Eqs. ( 20) and ( 22) were calculated. Fig. 11 depicts the obtained results; one can see that the impact damaged tests are well detected and separated from the healthy sate. Concerning the two additive masses used for boundary conditions changes, the proposed approach is robust regarding them.

Conformal load-bearing antenna structure (CLAS)

The second test bench realized concerns a CLAS. The dimension of the host structure is 800 × 150 × 2 mm 3 , and it is made up from the same material and number of layers as the composite plates. In addition to the PZTs, an antenna network is bonded on it. Figs. 12(a)-(b) show respectively the antenna network of the CLAS and the seven PZT bonded on it.

Before applying the proposed damage detection methodology, a radiation pattern and a measure of bending and torsion strains using the PZT sensors were conducted with the partners of our project (SMSE 2010). These tests were done simultaneously in an anechoic chamber, and they were conducted in order to check if there is any coupling between the electromagnetic phenomena of the antenna network and the electrical information transmitted by the PZT sensors. First of all, a strain measurement of bending and torsion were conducted before and during the radiation pattern (Fig. 13). Then, a radiation pattern was done before and during the strain measurements (Fig. 14). The results obtained show that the two phenomena can coexist in the same time without any interaction.

Once this study performed, the damage detection procedure was applied. The healthy baseline state was first built. The input excitation consists in a signal pulse with 1ms width, sampling frequency 𝑓 𝑠 = 100 kHz and 𝑁 = 2 16 time samples were recorded. Once the healthy baseline was set, damage was introduced. In this case, a delamination between the antenna part and the host structure was provoked using a buckling device (see Fig. 15(a)-(b)). It is to be noted that the baseline was built through 14 tests with enough time lag between them. Fig. 16 depicts the damage detection results of the CLAS: one can see that the delamination of the antenna array is well detected and distinguished from the healthy tests done.

Discussion

In baseline subtraction SHM methods, one has to deal with two major issues: (a) building and managing online healthy baseline data that includes the effects of varying environmental and operational conditions, (b) finding a good tradeoff between detectability (the smallest detectable damage) and the rate of false alarm. In the present work, an attempt to address these two issues has been proposed. Indeed, an iterative approach relying on instantaneous baseline measurement is proposed to avoid the use of a presorted database for the healthy state. Then the robustness of the detection is enhanced by elaborating a decisions-making based on an analytical threshold, that: (i) includes the effects of environmental perturbations, (ii) does not require any probabilistic models. Typically, the baseline measurements are recorded when the structure is pristine, they are stored for comparison to future tested data for damage detection purpose following the framework depicted in Fig. 3. When no longer damage is detected, the tested data are used as the new baseline.

One concern with the use of this baseline subtraction method is the fact that the data from a missed damage can be incorporated in the new baseline. This could happen if the damage is small and not severe. The severity and the size of the detected damage depend on the frequency range that we use (higher is the frequency; smallest is the damage to be detected). However, as explained in the introduction, low frequency measurements were our interest.

The proposed damage detection is related to the signal sensors acquired. These signals can be either vibratory or ultrasound data (such as Lamb wave), where their choice is related to the size of damage that we look to detect. In real-world application, the relevant smallest size of damage as the Barely Visible Impact Damage is based on expert point of view of the concerned application. Once this smallest size defined, the use of vibratory or ultrasonic data is defined by chosen a welldefined size of sensors/actuators and electronic equipment's. Then, the proposed incremental baseline can be applied.

Conclusions

In this paper, the problem of output-only vibration based damage detection under changing environmental conditions on MAS structures was studied. Through the independent component analysis method, feature matrices were extracted from the data to characterize the behavior of the studied structures and their models, and a damage index (DI) based on angle between subspaces was proposed.

The originality of the present work was: on one hand to develop a new criterion for the decision-making. The key idea behind was to bind analytically using matrix perturbation theory the disturbances that a healthy monitored structure undergoes, without any probabilistic models. Either in FE simulations and experiments, the proposed approach has shown its robustness regarding damage detection and boundary condition changes. On the other hand, this work has shown the possibility of incorporating different capabilities (transmission/receive function and health monitoring) on a MAS structure.

In the work under progress, experiments on changes in other boundary conditions are underway to consolidate the robustness of the proposed method regarding false-positive alarms.

Fig. 1

 1 Fig. 1 BSS applied to damage structural monitoring

  26) Define the following residual matrices: 𝐑 11 = 𝐀𝐕 ̃1 -𝐔 ̃1𝚪 ̃1 = -δ𝐀𝐕 ̃1 (27) 𝐑 21 = (𝐀) 𝑇 𝐔 ̃1 -𝐕 ̃1(𝚪 ̃1) 𝑇 = -(δ𝐀) 𝑇 𝐔 ̃1(28) and evaluate their norms, i.e.:‖𝐑 11 ‖ = ‖δ𝐀𝐕 ̃1 ℎ ‖ (29) ‖𝐑 21 ‖ = ‖(δ𝐀) 𝑇 𝐔 ̃1 ℎ ‖ (30) The scalar 𝜀 is then obtained by: 𝜀 = max(‖𝐑 11 ‖, ‖𝐑 21 ‖)

Fig. 2

 2 Fig. 2 Angle between subspaces

Fig. 4

 4 Fig. 4 Flowchart of the incremental baseline

Fig. 5 :

 5 Fig. 5: (a) Finite element model of the composite plate bounded with PZT, (b) a zoom on the PZT element, (c) a simulated mode of the composite plate

Fig. 6

 6 Fig. 6 Time and frequency characteristics of the input excitation: Signal used for FE simulations and composite plates experiments

Fig. 14

 14 Fig. 14 Radiation pattern measurements (SMSE 2010)

  If it is the case, then the structure is damaged, otherwise it is healthy

				14),
	3.3 for i=1 to 𝑛, repeat the following steps:
	3.3.1 From the measurement matrix 𝐘 ̃𝑖 ℎ , apply the FastICA to calculate the separating
	matrix 𝐀 ̃𝑖
	3.3.2 Apply the SVD to matrix 𝐀 ̃𝑖, following Eq. (14)
	3.3.3. Calculate the variation δ𝐀 ̃𝑖:
			δ𝐀 ̃𝑖 = 𝐀 ̃𝑖 -𝐀
	3.3.4. Calculate the analytical threshold 𝛽 𝐼𝐶𝐴,𝑖 , following Eq. (22),
	3.4 Calculate the mean of the analytical threshold:
			𝜇 𝛽 ,𝐼𝐶𝐴 =	1 𝑛	𝑛 ∑ 𝛽 𝐼𝐶𝐴,𝑖 𝑖=1
	Step 4: Calculation of the damage index DI ICA
	4.1. Take back to step 3.2,
	4.2. From the measurement matrix 𝐘 𝑢 , apply the FastICA to calculate the separating matrix 𝐀,
	4.4. Apply the SVD to matrix 𝐀 following Eq.(15),
	4.5. Calculate the damage index 𝐷𝐼 𝐼𝐶𝐴 following Eq. (20).
	Step 5: Decision-making
	Check if 𝑅 𝐼𝐶𝐴 =	𝐷𝐼 𝐼𝐶𝐴 𝜇 𝛽 ,𝐼𝐶𝐴	> 1.

Step 1: Tests of the structure at the healthy state 1.1 Make a first test of the healthy state, 1.2 Build the measurement matrix 𝐘 0 ℎ , 1.3 Make 𝑛 other tests of the healthy state, with enough time lags between them, 1.4 Build the 𝑛 measurement matrices 𝐘 ̃𝑖 ℎ , 𝑖 = 1. . . 𝑛, Step 2: Test of the structure at an unknown state 2.1 Make one test of the unknown state, 2.2 Build the measurement matrix 𝐘 𝑢 , Step 3: Calculation of the analytical threshold 𝜇 𝛽 ,𝐼𝐶𝐴 3.1 From the measurement matrices 𝐘 0 𝑠 , apply the FastICA Matlab Package to calculate the separating matrix 𝐀, 3.2 Apply the SVD to matrix 𝐀, following Eq. (

Table 2

 2 Mechanical properties of the composite material

	Property	(GPa) 𝐸 1 (GPa) 𝐸 2 = 𝐸 3	(GPa) 𝐺 12 = 𝐺 13	𝐺 23 (GPa) 𝜈 12 = 𝜈 13 𝜈 23 𝜌 (𝐾𝑔/𝑚 3 )
	Value	127.7	7.217	5.712		2.614	0.318	0.38	1546
	Table 3 Mechanical and electrical properties of the piezoelectric patches PZ29 (Ferroperm 2009)
	Property E (GPa) Value 58.8	ν 0.3	𝜌 (𝐾𝑔/𝑚 3 ) 7460	d 31 (C/N) -2.43 × 10 -10 5.74 × 10 -10 d 33 (C/N)	Curie temperature C° 235

Table 4

 4 Negentropy of the measured noise for different sensors: healthy composite plate

	Sensor	1	2	3	4	5	8	9	10
	Sensor	1	2	3	4	5	8	9	10

Negentropy 1.7845 1.7849 1.7977 1.8632 2.1086 1.8464 2.0650 2.7648 Table 4 Negentropy of the measured noise for different sensors: damaged composite plate Negentropy 1.7835 1.7847 1.7883 1.8044 3.1618 1.7476 1.7904 1.7908

Acknowledgments

This work was supported by the project: Smart Materials and Structures for Electromagnetics (SMSE) funded by the consortium Aerospace Paris Région "ASTech". The authors wish to thanks all the persons involved in this project.


Decker

Lallier, F.H E 4 Leize--Wagner

Olu K 1 & Andersen
email: andersen@sb--roscoff.fr

Globin's structure and function in Vesicomyid bivalves from the 1 Gulf of Guinea cold seeps, as an adaptation to life in reduced sediments. 2 3

Keywords: hemoglobin, myoglobin, mass--spectrometry, oxygen--affinity, symbiosis, clams 44 45 46

Vesicomyid bivalves form dense clam--beds both at deep--sea cold--seeps and hydrothermal vents. The 28 species diversity within this family questions about niche separation and specific adaptations. To 29 compare their abilities to withstand hypoxia we have studied the structure and function of 30 erythrocyte hemoglobin (Hb) and foot myoglobin (Mb) from two Vesicomyid species : 31 Christineconcha regab and Laubiericoncha chuni, collected from the Regab pockmark in the Gulf of 32 Guinea at a depth of 3000 m. L. chuni possesses three monomeric globins, G1 (15361 Da), G2 (15668) 33 and G3 (15682) in circulating erythrocytes (Hb), and also three globins, G1, G3 and G4 (14786) in foot 34 muscle (Mb). Therefore globins G2 and G4 appears to be specific for erythrocytes and muscle, 35 respectively, but globins G1, and G3 are common. In contrast, C. regab lacks erythrocyte Hb 36 completely, and only possesses globins monomers G1' (14941 Da), G2' (15169 Da) and G3' (15683 37 Da) in foot muscle. Thus two Vesicomyid species, C. regab and L. chuni, show a remarkable diversity 38 in globin expression when examined by ESI--MS. Oxygen binding affinities reveal extremely high 39 oxygen affinities (P 50 <1 Torr, from 5 to 15°C at pH7.5), in particular L. chuni globins, which might be 40 an advantage for L. chuni to dig deeply for sulfides and remain buried for long time in reduced 41 sediments. 42 43

Introduction

51

Foot tissue samples: 156 Feet of C. regab and L. chuni were weighed, and crushed in 1 mL/g ice--cold HEPES--buffer as those 157 prepared by [START_REF] Childress | Sulfide and carbon dioxide uptake by 475 the hydrothermal vent clam, Calyptogena magnifica and its chemoautotrophic symbionts[END_REF]. The homogenate was centrifuged 3 times at 10000 rpm for 10 158 minutes at 4°C, and the supernatant was kept after each centrifugation. When the volume of 159 homogenate was insufficient for analysis, we pooled and crushed the feet of 3 specimens from a 160 same collection site (Table S1). The feet homogenates supernatant of L. chuni were directly purified 161 on serially connected Superose 12 and Superdex 75 columns, the latter with a fractionation range of 162 3 to 70 kDa. Each heme--containing peak was collected separately and concentrated in a micro--163 centrifugal filter device Centricon--3kDa (Millipore).

165

Mass Spectrometry of the purified globins 166 Samples of hemolymph and foot tissue for mass spectrometry were purified as described previously, 167 but in an ammonium acetate buffer at 50 mM pH 6.2. ESI--MS analyses were performed in denaturing 168 conditions to search for eventual disulfide bonds and in non--denaturing conditions to preserve the 169 native structure. Ten individuals of each species (L. chuni or C. regab) were analyzed.

170

For the denaturing analyses, each sample was dissolved at a final concentration of about 0.1 mg/ml For non--denaturing analyses, samples were purified using mini--gel filtration columns (Microbiospin 181 30, Biorad) in 200 mM or 50 mM ammonium acetate (pH7.5). ESI--MS measurements were performed 182 on an electrospray time--of--flight mass spectrometer (MicrOTOF LC , Bruker Daltonic, Germany). The

204

Heme--assay analyses: heme and protein concentrations 205 10 µL of purified hemoglobin were diluted in 2mL of the purification HEPES--buffer (Childress et al. 206 1991). 10 µL of potassium ferricyanide solution (0.01 mol. L -1 ) were added to 2ml of this diluted 207 solution, and incubated for 5min at room temperature to oxidize the hemoglobin completely into 208 met--hemoglobin. 10µL of potassium cyanide (0.05 mol. L -1 ) was then added to obtain the cyan--met--209 hemoglobin derivative. The solution was analyzed in a spectrophotometer at 540 nm. Absorbance 210 was measured at 540 nm and the extinction coefficient of 11.0 L.mmol 1 cm 1 was used to calculate 211 heme concentration. The Bradford method was used for protein quantification [START_REF] Bradford | A Rapid and Sensitive Method for the Quantitation of Microgram Quantities of 455 Protein Utilizing the Principle of Protein--Dye Binding[END_REF].

213

Oxygen binding measurements Oxygen--binding properties

284

Oxygen binding properties were measured on the purified Hbs and Mbs of L. chuni, (Table 2). At 5°C, 285 the value of the P 50 was significantly higher for circulating Hb (0.45 ± 0.18 Torr at pH 6.65 ± 0.07, 286 n=3), than for foot Mb (0.19 ± 0.02 Torr at pH 6.27 ± 0.4, n=3) (Wilcoxon Mann--Whitney, W=9, 287 p<0.08). Consequently, the oxygen affinity is higher for cytosolic Mb than for circulating Hb in L.

288

chuni. As expected for monomeric globins, there was no cooperativity in any of the molecules as n 50 289 was close to 1 (Table 2).

290

A slight temperature effect was observed for the hemoglobin with a tendency of the affinity to 291 decrease with a temperature rise from 5 to 15°C, (Figure 7a), however not statistically significant in 292 our sampling (Kruskal--Wallis: X²=4.7, p=0.1). Foot myoglobin affinity remained stable with an 293 increase of temperature (Kruskal--Wallis: X²=3.7, p=0.2) (Figure 7a). Variation of pH had no effect on 294 hemoglobin affinity (Figure 7b), (Kruskal--Wallis, X²=13.37, p=0.42)

295

C. regab myoglobin affinity was about 0.85 Torr ± 0.09 at pH= 6.63 and T°=5°C, n=3 and with this high 296 value its affinity was lower than the affinity of L. chuni Mb and Hb (Wilcoxon Mann--Whitney: W=9, 297 p<0.08). As for L. chuni no cooperativity was measured (Table 2) and a drop of affinity was observed 298 with an increase of temperature (Figure 8a), but no Bohr effect was observed (Figure 8b).

317

In our sampling of L. chuni hemolymph has two or three types of globin monomers of slightly 318 increasing masses that apparently do not dimerize naturally. As Hb is circulating through the blood 319 vessels and capillaries irrigating the foot muscle, it might be difficult to sort out the circulating 320 globins from the cytosolic muscle globins, and this might explain the similarity of the globins found in 321 both hemolymph and foot muscle. However, G4, with a lighter mass of about 14 kDa is only observed 322 in the foot muscle, and thus seem to be a specific cytosolic Mb, whereas globin G2, when present, is 323 only found as circulating Hb. In purified circulating Hb the lightest chain G1 can form a homodimer.

324

This covalent homodimer is probably due to the presence of cysteine residues in the primary 325 sequence, forming disulfide bridges between two globin chains, which has to be confirmed by 326 sequencing. On the contrary no dimerization is observed in L. chuni's foot homogenate. In L. chuni 327 and C regab, the number or globin chains of different masses vary according to the specimens.

328

Having various globins within an organism might enable a fine--tuning of the O 2 binding, as the 329 various globins might differ in their O 2 affinities or in other functional properties. Moreover, most of 330 the bivalves possess two hemoglobins, one with a higher affinity than the second one (Nagel 1985; 331 Weber and Vinogradov 2001). The globin diversity within an organism could thus enable a 332 modulation of the oxygen affinity even as monomers, to fit to the oxygen levels of the surrounding than that of the tetrameric Hb of the vent clam "Calyptogena" magnifica (P 50 = 7.6 ± 0.23 Torr at pH 362 6.78 and 10°C) (Terwilliger et al. 1983). However a tetrameric Hb transports 4 times more O 2 per 363 molecule than a monomer, but the oxygen supply finally relies on their respective heme 364 concentration in the hemolymph that is from 0.1--0.4mM in L. chuni, which seems rather comparable 365 to those measured in "C". magnifica (<0.4mM) (Powell and Arp, 1989). Although tetrameric, the vent 366 clam Hb has a low cooperativity, (n=1.24), and both the affinity and the cooperativity vary little with 367 a temperature increase from 2° to 11°C (Terwilliger et al. 1983). These figures contrast with the 368 properties found in the monomeric Hb of L. chuni. The globins of L. chuni and C. regab do not show 369 any cooperativity (n 50 = 1) at all the temperatures tested and no Bohr effect, i.e. no drop of affinity 370 when the pH drops, aligns with the monomeric state of the globins that do not interact together in 371 the hemolymph. This is also consistent with what is observed in most bivalves' red blood cell Hb 372 (Weber and Vinogradov 2001). Functionally it means that a pH drop in the tissues when they 373 become acidic will not result in an increase of oxygen delivery from the globins to the tissues.

374

On the contrary, when the temperature increases, the affinity of Hb in L. chuni drops. However, 375 based on the exothermic nature of heme--oxygenation, P 50 must increase at higher temperatures. The 376 heat or enthalpy change (ΔH) due to the oxygen binding on the globins can be directly derived from 377 the integrated Van't Hoff equation: ΔH= --2.303R *Δlog P50/Δ(1/T), where R is the universal gas 378 constant and T is the absolute temperature. Using this equation, we have calculated the enthalpy of 379 the Hb--O 2 complex derived from our P 50 data, at various temperatures. Between 5 and 15°C, at pH 380 7.5, the enthalpy changes for the Hb of L. chuni is --69 kJ.mol --1 . Moreover this high negative value is 381 consistent with an absence of Bohr effect, as oxygenation--linked proton dissociation is endothermic, 382 and would lower the overall enthalpy value. Comparatively, the heat liberated upon oxygen binding 383 to alpha or beta human Hb monomers alone, is about --66 kJ.mol --1 (Ackers 1980). Our enthalpy value 384 is very close to that value and also comparable to those from the large Hb molecules in the Oxygen affinity is higher in L. chuni (circulating hemoglobin and foot myoglobin: 0.45 and 0.19 Torr 388 respectively) than in C. regab (0.85 Torr). It is noteworthy that the affinity of the myoglobin in L.

389

chuni is particularly high, even higher than that of the circulating Hb, and surprisingly less variable to 390 temperature differences (as there is no Bohr effect to create an endothermic dissociation of protons 391 to compensate for the natural exothermic oxygen binding to the heme). The higher oxygen affinity in 392 the Mb than in the Hb indicates a biologically advantageous oxygen transfer from Hb to Mb to enable 393 oxygen storage in the muscle, as known in vertebrate animals and described in literature for some 394 invertebrates that have both these pigments (Wittenberg, 1970). The high affinity of Mb to oxygen 395 might also indicate a great importance of binding oxygen within the foot, in particular during sulfide 396 uptake from the sediments, to avoid oxidation of sulfide before they are transported through the 397 hemolymph and reach the symbionts, in the gills.

398

In conclusion the two sympatric species at the cold seep pockmark Regab vary greatly in their of the lucinids and solemyids (Kraus 1990;Kraus et al. 1996) remains to be investigated. However it is possible that the great molecular mass molecule, eluted in the void volume of the column during 414 the purification of the hemolymph, could be a Sulfide Binding Component comparable to the SBC 415 lipoprotein isolated in "Calyptogena" magnifica [START_REF] Zal | while sulfide is carried by a lipoproteic sulfide--binding 74 component dissolved in the hemolymph[END_REF].

417

Compared to the majority of the blood clams found at vent and seeps, it is questionable how C.

Supporting information:

Table S1: Localization of studied sites, cruises, dives, specimen identification, sampled tissues and sample processing. * Foot tissue pooled before analyses.

  183 capillary exit voltage was set to optimize the desolvation process while preventing dissociation of the 184 non--covalent species (values from 100 to 200 V were tested). Samples were diluted 10 times in 185 100 mM ammonium acetate and continuously infused into the ESI ion--source at a flow rate of 186 3 µl/min through a Harvard syringe pump (Harvard Apparatus model 11). Acquisition mass range was 187 1000--10,000 mass/charge--units. Calibration was performed using a concentrated solution of Cesium 188 Iodide (1mg/ml in water: isopropanol 1:1). Masses were calculated and averaged for all ions 189 distributed in the ionized state. 190 Direct infusion ESI--MS data were complex to interpret, as globin masses were similar and thus 191 generated very close and multiple charged ions. To simplify our interpretations we had to separate 192 the different globin chains, using reverse phase--Liquid Chromatography Mass Spectrometry (rp--193 LCMS). Samples were injected into a HP1100 HPLC (Agilent Technologies). The globins were 194 separated on a 2,1 x 125 mm, 5 µm, 300 Å, Nucleosil ® C 18 column (Macherey--Nagel) prior to 195 introduction into the mass spectrometer. Mobile phases were: A: 0.1% TFA, and B: 0.08% TFA in 196 acetonitrile. A linear gradient from 5% B to 60% B in 65 min, then to 80% B in 5 min, was used for 197 separation, at a flow rate of 300 µL/min. Column temperature was kept at 25°C. UV trace was 198 monitored at a wavelength of 214 nm, typical for peptide--bond absorption. 1/20 th of the eluted 199 solution coming out of the UV detector was sent to the mass spectrometer by a T--split. The other 200 19/20 th were manually collected each time a globin was eluted from the column (shown by the UV 201 detector); These collected fractions, were systematically re--injected on a MicrOTOF--Q II (Bruker--202 Daltonik GmbH, Bremen, Germany) to confirm our LCMS measurements.

  pockmark, the dominant species Christineconcha regab is the first recorded vesicomyid 303 clam from a chemosynthetic environment with clear hemolymph, i.e that is not a "blood--clam".304However the deep--red foot of this species contains myoglobin. The other vesicomyid clam found at 305 regab, Laubiericoncha chuni, is a regular blood--clam having both intracellular circulating hemoglobin 306 and also myoglobin in its foot muscle. Both species also have deep--red adductor muscles, probably 307 containing Mb too.308L. chuni and C. regab have monomeric globinsmore: from 14 to 19 kDa[START_REF] Bruneaux | The Structural Analysis of Large 457 Noncovalent Oxygen Binding Proteins by MALLS and ESI--MS: A Review on Annelid Hexagonal Bilayer 458 Hemoglobin and Crustacean Hemocyanin[END_REF] Weber and Vinogradov 2001). Thus our results fit 314 within the normal mass range for invertebrate globins. The three other cold seep vesicomyid species 315 have likely globins of about 15--16kDa but they are associated as homodimers(Kawano et al. 2003; 316 Suzuki and Ohta 2000; Suzuki et al. 1989a).

  399modes to bring oxygen to their symbionts: C. regab transports the oxygen dissolved in its hemolymph 400 as a regular coastal bivalve, whereas L. chuni has a greatly enhanced transport capacitance with its 401 Hb as oxygen--carrier within red blood cells, as all the blood--clams. In fact Hb can both ensure the 402 oxygen transport and its storage in the hemolymph during hypoxic periods when the clam remains 403 closed, or when a greater oxygen demand occurs during burying. This oxygen storage might enable L.404chuni to bury deeper into the sediment to reach a larger source of sulfides. This hypothesis would be 405 in favor of the deep position of L. chuni which siphons are only rarely seen at the sediment surface, 406 while it could nonetheless ensure an aerobic metabolism. This also could explain the distribution of 407 both species along the pockmark according to the depth of the sulfide production. Indeed L. chuni is 408 more abundant in the southwestern part of the pockmark (site 3), where the lower methane fluxes 409(Decker et al. 2012a; Pop Ristova et al. 2012) and deeper AOM maximum rates (Pop Ristova et al. 410 2012) may drive sulfide production deeper in the sediment, than at the most active central venting 411 site 2, as observed at other seep sites (Fischer et al. 2012). Whether its Hb could bind sulfide as those 412

418Figure 1 :Figure 2 :Figure 3 :Figure 4 :Figure 5 : 614 Figure 7 :Figure 8 :

 1234561478 Figure Captions

PANGAEA

Table 1 :

 1 Summary of globin chains identified in L. chuni circulating Hb and foot muscle samples, and

	620
	621	in C. regab foot homogenate.
	622

Table 2 :

 2 Oxygen binding properties of L. chuni hemoglobin and myoglobin and C. regab myoglobin at

	623
	624	15°C.

Table 2 :

 2 Oxygen binding properties of L. chuni hemoglobin and myoglobin and C. regab myoglobin at 5°C.

	Species	Specimens or samples	Type	pH	p50	n50
		425--V1		6.7	0.26	0.83
		425--V2 425--V3	Hemoglobin	6.57 6.67	0.48 0.61	0.91 0.71
	L. chuni	Mean (SD) Lc1		6.65 (0.07) 6.02	0.45 (0.18) 0.17	0.82 (0.1) 1
		Lc2 Lc3	Myoglobin	6.05 6.74	0.2 0.2	1.09 1.55
		Mean (SD)		6.27 (0.40)	0.19 (0.02)	1.20 (0.29)
		Chr1		6.78	0.95	0.98
	C. regab	Chr2 Chr3	Myoglobin	6.55 6.55	0.8 0.79	0.92 0.82
		Mean (SD)		6.63 (0.13)	0.85 (0.09)	0.91 (0.08)

exposed to variable environmental conditions has a relatively high affinity for oxygen(Terwilliger et

al. 1983), but may nevertheless greatly facilitate oxygen transport needed for the chemoautotrophic

pockmark, 8 km North of the Congo canyon, at a depth of 3100 m (Ondreas et al 2005). The cruises

indicative of protein and heme concentrations respectively. Every heme--containing protein peak was

collected separately and concentrated in micro--centrifugal filter devices Centricon--3kDa (Millipore). 154

in a mix of water/acetonitrile/formic acid at (50:50:1 in volume). Mass data were obtained using a

MicroTOFLC (Bruker--Daltonik GmbH, Bremen, Germany) mass spectrometer fitted with Z--spray

electrospray ion source, and operated in positive ion mode. MS data were acquired from 500 to 2000

m/z. Mass calibration was performed using a mix of Tune Low (Agilent Technologies # G1969--8500)

and a solution of horse heart--myoglobin at 20 fmol/µL (Sigma, # M--1882). Data were processed with

the Data Analysis software: Bruker Daltonik (GmbH, Bremen, Germany) and multiple ionized spectra

were deconvoluted with MaxEnt tool to generate molecular mass spectra. All molecular masses were

calculated from the raw data multiple ionized peaks.

Oxygen--binding affinities of hemoglobins and myoglobins were obtained in a gas--diffusion chamber

(Sick and Gersonde 1969). Small samples (5µL) of purified globin solution were equilibrated with pure 216 N 2 for the deoxygenated state, and pure O 2 for the fully oxygen saturated state, and mixtures of 217 these gases were added stepwise by the Muti--gaz--controller mks 647C (Instruments Deutschland ) to

shown). Two homo--dimeric chains of G1'--G1' and G2'--G2' were also observed in two specimens from

the central site (Table1).

monomeric structure is also found in the vesicomyid P. nautilei from Japan's trench, but its molecular

mass is higher: about 18kDa, as determined from cDNA sequence(Kawano et al. 2003). In fact, 312 compared to the stable molecular mass of vertebrate globins, those of invertebrates vary much

environment. This diversity could either result from a structural genetic diversity at the population 334 level, or come from modulations in the transcription of the globin genes, due to individual metabolic

Wittenberg 1990). Compared at the same temperature of 10°C and within the same pH range, the

values of L. chuni's monomeric Hb is 0.22 Torr, and corresponds surprisingly to a much higher affinity

pulmonate mollusk Biomphalaria glabra (ΔH=--49 to --77 kJ.mol --1 )[START_REF] Bugge | Oxygen binding and its allosteric control in hemoglobin of the 460 pulmonate snail, Biomphalaria glabrata[END_REF], and in an

hydrothermal copepod (ΔH=--68.7 kJ.mol --1 )(Hourdez et al, 2000).

(UBO) on the 6 th of December 2011. The authors also wish to thank the referees for their

constructive remarks that greatly improved the manuscript.

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Cosel, R.v., and K. Olu --Le Roy. 2008. A new genus and new species of Vesicomyidae (Mollusca,

Bivalvia) from cold seeps on the Barbados accretionary prism, with comments on other species.

Zoosystema 30: 929--944.

Cosel, R.v., and K. Olu. 2009. Large Vesicomyidae (Mollusca: Bivalvia) from cold seeps in the Gulf of

Guinea off the coasts of Gabon, Congo and northern Angola. Deep Sea Research II 56: 2350--2379.

Decker, C., J.C. Caprais, A. Khripounoff and K. Olu. 2012a. First respiration estimates of cold--seep

vesicomyid bivalves from in situ total oxygen uptake measurements. Comptes rendus biologies 335:

261--270.

Decker, C., K. Olu, S. Arnaud--Haond and S. Duperron. 2013. Physical proximity may promote lateral

acquisition of bacterial symbionts in vesicomyid clam PlosONE 8: e64830.

doi:64810.61371/journal.pone.0064830.

Decker, C., K. Olu, R.L. Cunha and S. Arnaud--Haond. 2012b. Phylogeny and diversification patterns

Rathburn. 2003. Spatial heterogeneity of macrofauna at northern California methane seeps:

influence of sulfide concentration and fluid flow. Marine Ecology Progress Series 265: 123--139.

Acknowledgments

426

We are indebted to the people who provided us with the vesicomyid samples, firstly the Chief 427 Scientists of the three cruises: Dr. Antje Boetius (GUINECO M76/3 2008), Dr. K. Olu (WACS 2011), and

Dr. Christophe Rabouille (CONGOLOBE 2011(CONGOLOBE --2012)). We thank the pilots and crew from the research