Dr Ludmilla Guduff

Dr Patrick Berthault

Dr Carine Van Heijenoort

Jean-Nicolas Dumez
email: jeannicolas.dumez@cnrs.fr

Dr Gaspard Huber
email: gaspard.huber@cea.fr

Dr J.-N Dumez

Single-scan diffusion-ordered NMR spectroscopy of SABREhyperpolarized mixtures

Keywords: analytical methods, NMR, diffusion, parahydrogen, spatially encoded experiments

The analysis of complex mixtures of dissolved molecules is a major challenge, especially for systems that gradually evolve, e.g., in the course of a chemical reaction or in the case of chemical instability. 1D NMR is a fast and non-invasive method suitable for detailed molecular analysis, though of low sensitivity. Moreover, the spectral resolution of proton, the most commonly used and most sensitive stable isotope in NMR, is also quite limited. Spatially encoded (SPEN) experiments aim at creating in one acquisition a 2D data set by simultaneously performing different 1D sub-experiments on different slices of the NMR tube, at the price of an extra loss of sensitivity. Choosing translational diffusion coefficients as the additional dimension (the so-called DOSY approach) helps to recover proton spectra of each molecule in a mixture. The sensitivity limitation of SPEN NMR can, on the other hand, be addressed with hyperpolarization methods. Within hyperpolarization methods, signal amplification by revers ble exchange (SABRE), based on parahydrogen, is the cheapest and the easiest one to set up, and allows multi-shot experiments. Here we show that the spectra of a mixture's components at millimolar concentration are resolved in few seconds by combining the SABRE, SPEN and DOSY concepts.

Introduction

A large number of current analytical methods involve physical separation of the analytes by, e.g., phase separation and/or chromatography steps, as well as derivatization steps. In the case of systems that evolve in time, however, such separation-based methods may not be applicable or may lead to erroneous results. Instability may concern chemical composition and concentrations, e.g., in organic reactions or metabolic pools. [1,2] Also aggregation may gradually occur for dissolved species. It is for example a phenomenon of high biological importance for proteins. [3] There is thus a need for fast analytical methods for the direct, separationfree identification of molecules in a mixture.

Nuclear magnetic resonance (NMR) spectroscopy is a powerful tool for the direct analysis of mixtures, provided that the analysis can be fast compared to the reaction or aggregation timescale. Acquiring a time-series of one-dimensional NMR spectra is the simplest way to record data with high temporal resolution, roughly at the second time-scale. When higher spectral resolution or information content is required, 2D experiments would be appropriate, were it not for the long experiment duration required to sequentially acquire the many 1D spectra from which nD spectra are calculated. For this reason, multiple strategies have been introduced to accelerate the acquisition of multidimensional NMR experiments. [4,5] One of these rely on spatial encoding (SPEN) of the NMR interactions to acquire 2D spectra in a single scan. [4,6] SPEN methods can be seen as the parallelized acquisition of a 2D data set by simultaneously recording different 1D spectra on different slices, each of them experiencing its own NMR sequence.

One of the most widely used multidimensional NMR methods for mixture analysis is diffusion-ordered spectroscopy (DOSY), which discriminates molecules according to their translational diffusion along an axis defined by pulsed field gradients. In its most common implementation, the DOSY method is based on the measurement of signal amplitudes or areas as a function of the diffusion wave vector G (where  is the gyromagnetic ratio, G is the gradient strength and  its duration) for a pair of gradient pulses separated by a fixed delay . This method thus involves the acquisition of several spectra with varying gradient intensities, and typically requires experiment durations of several minutes. The acquisition of DOSY data in a much shorter time, typically in seconds for 0.1 M mixtures, has been demonstrated with various approaches based on multiple echoes induced by a train of gradient or RF pulses. [7][8][9] These methods typically sacrifice spectral resolution and require a long transverse relaxation time.

Fast DOSY experiments based on spatial encoding have also been reported. [10][11][12] With SPEN DOSY, 2D data sets are recorded in less than one second. The applicability of fast nD NMR is, however, also governed by the spectral resolution and sensitivity limitations of the method.

Hyperpolarization (HP) is a method of choice to counteract the low sensitivity of NMR. It consists of transiently increasing population differences between nuclear spin energy levels. For solution-state NMR, two methods in particular have revealed their potential for the analysis of diluted mixtures, [13] namely dissolution dynamic nuclear polarization (D-DNP) [14] and para-hydrogen (p-H2) based signal amplification by reversible exchange (SABRE). [15][16][17][18] Fast nD NMR methods are particular relevant in combination with hyperpolarization, because they are compatible with the transient character of the out-of-equilibrium magnetization even when they are implemented in a single-shot manner. [18][19][20] While SABRE allows multi-shot experiments (with repetition times of ~ 40 s) [15] , the original and still commonly used protocol for SABRE experiments consists of manually shaking a mixture of the substrate, p-H2 and a catalyst, before insertion in the NMR magnet. As a result, polarization levels return to the thermal equilibrium value in a time that is not compatible with the acquisition of nD spectra by conventional means.

Recently, SPEN-DOSY spectra were acquired for substrates polarized by dissolution dynamic nuclear polarization (D-DNP). [21] These substrates were simple metabolites enriched in 13 C on a quaternary-carbon position, thus with a long (ca. 30 s) longitudinal 13 C relaxation time. This enabled acquisition of several SPEN-DOSY spectra in a single D-DNP experiment, at a concentration of 20 mM for each substrate. For SABRE, Reile et al. have shown that the method may be used in combination with conventional DOSY in multi-shot experiments in order to analyse micromolar mixtures, with experiment durations of 35 minutes. [15] In this Article, we study the feasibility of analyzing selfdiffusion of the components of a millimolar mixture of molecules in a single scan with SPEN-DOSY sequences. In this purpose, as a proof-of-concept, we use a mixture of molecules hyperpolarized through the SABRE method. The optimization of this SABRE-SPEN-DOSY concept, including experimental set-up, NMR sequences and parameters, and the biases on the extracted diffusion coefficients originating from convection and methods to fit the diffusion coefficients are examined.

Results and Discussion

The SABRE approach can provide 1 H polarization levels of up to 50% [START_REF] Rayner | Proc. Natl. Acad. Sci[END_REF] and has been applied to several classes of substrates (see for examples refs [16,[START_REF] Adams | [END_REF][24][25] ). It is most efficient for molecules that contain N-heteroaromatic rings, but has recently been extended to substrates containing exchangeable protons (SABRE-RELAY) [26] . At a magnetic field of 11.7 T, corresponding to a 1 H Larmor frequency of 500 MHz, this corresponds to signal enhancements of 12500 at room temperature. The possibility to collect DOSY data in a single scan from SABRE-hyperpolarized molecules is evaluated here on a simple mixture of four small molecules (Scheme 1): pyridine (p), N,N-dimethylnicotinamide (d), 3-ethylpyridine (e) and 4,4'-bipyridyl (b). The 1 H NMR spectrum and their and longitudinal relaxation times, in SABRE conditions, are given in Figure S1 and Table S1. Two signals are almost superimposed, corresponding to the para proton of pyridine py-p and the meta proton of bipyridyl (bpy-m), and the consequences of this will be discussed. The mixture is analyzed either at thermal equilibrium (without catalyst and at a concentration of 150 mM for each substrate), or with SABRE hyperpolarization (with a 1 mM catalyst and 5 mM concentration for each substrate).

Figure 1a depicts the experimental procedure used here for SABRE experiments, which relies on manual sample shaking. The NMR tube containing the liquid solution is degassed to remove oxygen that would otherwise catalyze para-ortho isomerization of dihydrogen. [27] Then enriched pH2 is transferred in the NMR tube that is subsequently shaken in a field of 6.5 mT and quickly introduced in the spectrometer for analysis. For SABRE applications, the dead time that elapses between the end of the shaking step and the start of acquisition should not be too long compared to the longitudinal relaxation time of the aromatic protons. At 11.7 T, their longitudinal relaxation times T1 are in the range 4-21 s in a solution containing 5 mM of each of the four substrates and 1 mM of the catalyst precursor. This T1 value is a weighted average of that of the free substrate and that of the substrate complexed to the iridium metal. A delay of 5 s is chosen here to achieve the lock of the deuterium signal and the recovery of most of the field homogeneity. The tube shaking-NMR experiment procedure may be repeated several times with the same batch of p-H2, albeit with progressively lower sensitivity due to the lowering enrichment of dissolved dihydrogen in the para isomer. Each acquisition cycle induces a decrease of signal intensity of about 30%, as obtained from independent experiments where a 1 H 1D NMR spectrum was recorded after each shaking (Figure S2). This cycle takes less than one minute. The NMR tube can then be filled with freshly prepared parahydrogen. This takes less than 5 minutes and restores the maximum sensitivity.

With this optimized hyperpolarization protocol, we have then investigated the STE (stimulated echo) version of the SPEN-DOSY pulse sequence which is shown on Figure 1b. In this experiment, two 90° pulses bracketed by bipolar gradient pulses separated by the diffusion delay Δ , are used for longitudinal storage of the magnetization during the diffusion delay. A pair of chirp pulses associated to gradient pulses is used to perform spatial encoding of the diffusion information. Acquisition is performed using echo planar spectroscopic imaging (EPSI), with a train of N pairs of gradients pulses. The use of a triple axis gradient probe makes it possible to separate the gradients for diffusion encoding and the gradients for selection of the coherence pathway. [12] Figure 2a shows a conventional DOSY spectrum obtained on a stable, well-shimmed and locked sample of the model mixture. Fitted diffusion coefficients for well-resolved signals are easy to cluster for pyridine and ethyl-pyridine, while the separation is less pronounced between bipyridyl (b) and dimethylnicotinamide (d).

For the overlapped signals of the para protons of pyridine (p-p) and the meta protons of 4,4'-bipyridyl (b-m), the estimated diffusion coefficients are close that of the meta proton of bipyridyl. The concentration of these two compounds in the mixture are very close, but there are 4 b-m protons per 4,4'-bipyridyl molecule versus 1 p-p per pyridine molecule, so that b-m has a dominant contribution to this signal, as long as thermal polarizations are considered. It is well known that the molecular mass is not the unique parameter affecting diffusion ; the solvent can have a significant effect. [28] We note that the diffusion coefficients of the 4 substrates are in reverse order of their molecular mass. This is also true for 4,4'-bipyridyl and dimethylnicotinamide whose molecular masses however differ by only 4%. [28] Figure 2b shows the SPEN-DOSY spectrum of the model mixture, also obtained on a stable, well-locked and shimmed sample. The diffusion information has been encoded along the longitudinal axis (z), and the data have been processed in magnitude mode. In this case, the discrimination of the four molecules is hardly possible. The processing in magnitude mode, which is widely used for spatially encoded experiments, induces a decrease of spectral resolution, detrimental for the diffusionbased separation of spectra. While the data acquired in a single scan with echo-planar spectroscopic imaging (EPSI) for UF2D NMR spectra such as UFCOSY are not compatible with pureabsorption processing, the situation is different with SPEN DOSY. Provided that the chemical-shift evolution is refocused at the center of the first acquisition gradient, pure absorption processing should be possible for the so-called odd echoes of the EPSI train that are located at k = 0 in the reciprocal space. Using a modified timing for the pulse sequence and a pure absorption processing of the data, a much better clusterization of the diffusion coefficient values is obtained, except for signals d-5 and e-5 (Figure 2c). However, the extracted diffusion coefficients are lower using the conventional DOSY spectrum (Figure 2a) than using the SPEN-DOSY spectrum (Figure 2c) for 10 out of the 11 signals. This is due in part to the uncorrected non-uniformity of the gradients, since the conventional and SPEN experiments are performed on a different spatial region: the full coil region for the conventional experiments, the central 10 mm for SPEN. In the SPEN spectra, diffusion coefficients are also found to be slightly smaller when the data is processed in magnitude mode than when it is processed in absorption mode for most signals (Figure 2b vs 2c). Indeed, in magnitude mode, the noise is not null in average and induces a systematic overestimate of integrals. The smallest integrals being proportionally more affected, this induces a bias in the extracted diffusion coefficient, as Equation 1 in the Processing Section does not take this effect into account. This is corroborated by a simulation shown on Figure S3. This reinforces the advantage of using pure-absorption rather than magnitude processing, and the former was used in the rest of this study.

The main expected challenge for SABRE DOSY experiments that rely on a sample shaking protocol is the effect of strong liquid motions on scales much larger than the translational diffusion, which can distort the diffusion information. This is illustrated in Figure 2d with a SPEN DOSY spectrum recorded using the STE sequence of Fig. 1b, with diffusion encoding along the z axis, 5 s after having shaken the NMR tube for 15 s outside the magnet. The diffusion coefficients are largely overestimated and the accuracy of the fit decreases, preventing the discrimination of molecules according to their diffusion coefficients. This can be explained by unwanted sample motion that occurs mainly along the z axis, even after tens of seconds. Indeed, while bubbles seen by naked eye reach the liquid surface long before the end of the 5 seconds dead time, their effects may last for a longer duration. An induced vertical convection occurs, acting on the apparent diffusion coefficients (Figure S4). Moreover, micro-bubbles might be created. In that case, their lifetime may be much longer and their rising velocity smaller, acting as a long-term effect on the accuracy of the extracted diffusion coefficients. [29,[START_REF] Tesař | Proc Colloq. Fluid Dyn[END_REF] To avoid the convection effects on the apparent diffusion coefficients, a possible solution would be the use of a double stimulated-echo SPEN DOSY pulse sequence [21] instead of the single stimulated echo used here. Indeed the second diffusionencoding step should cancel the effect of convection. However in this case the results are of a lower quality than for previous studies, even in the absence of sample shaking. [START_REF] Hamdoun | [END_REF] We suspect that scalar couplings involving the detected nuclei, which are more significant in the present study, are responsible of this failure of the DSTE approach. Solutions to deal with motions within the sample, other than using a different pulse sequence, would involve a more elaborate experimental setup, such as a membrane reactor outside the spectrometer [32] , or a capillary plunging into the NMR solution, inside the spectrometer, [33] albeit with a lower NMR signal enhancement factor. [34,35] Another approach to solve the convection problem, which does not require a modified set-up, is to use a transverse axis to encode diffusion. The underlying idea is that unwanted motions are probably more important on the z axis due to the anisotropy of the NMR tube. Processing SPEN DOSY data acquired with transverse encoding needs to consider the spin density profile of the NMR tube. As SPEN experiments can be considered as the simultaneous acquisition of 1D spectra on different slices, the relative volume of these slices should be taken into consideration. Their volume is constant when the longitudinal z axis is used for encoding, in the cylindrical portion of the NMR tube at the coil detection level. On the contrary, the volume of a slice depends on their localization when sequences are recorded along the x (or y) transverse axis. Integrals of signals on each individual 1D spectrum of a SPEN-DOSY spectrum, as illustrated for the ortho protons of pyridine in Figure 3a (red circles), are therefore normalized by the volume of the corresponding slices giving the blue crosses, prior to fit according to the modified Stejskal-Tanner equation (see Experimental Section). For this purpose, a profile along the x axis has been recorded using a gradient echo sequence, shown as a dashed line on Figure 3a.

The impact of sample shaking on diffusion coefficients fitted from data obtained with x-SPEN-DOSY is shown on Figures 3b vs. 3c (obtained with and without sample shaking). A systematic error is observed, compared to data extracted from SPEN-DOSY spectra recorded on z axis, because of gradient non-uniformity and calibration. Within a molecule, these coefficients do not significantly differ and are obtained with comparable deviations. The procedure of recording a SPEN-DOSY spectrum after shaking has been found to be repeatable at 5% or better (Figure S5).

Having optimized both the pulse sequence and the processing steps with the concentrated solution, i.e. 150 mM, SABRE experiments have been performed on a more diluted solution, where each of the four substrates depicted in Scheme 1 is at a concentration of 5 mM, and the catalyst at a concentration of 1 mM. After addition of p-H2, the catalyst structure is modified such that 3 molecules are linked to the metal, each being one of the four substrates. 40 different complexes may be formed, [16] each one of probable micro-molar concentrations, and exhibiting slightly different proton chemical shifts. These signals are not observed on the spectrum and only signals of the free substrates in solution are observable and can be processed. Figure 3d shows the aromatic protons region of a SABRE-SPEN-UFDOSY rebuilt spectrum (processed in absorption mode), with the diffusion dimension along the x axis.

The diffusion coefficients of the different signals for the spectrum shown in Figure 3d are fully compatible with those obtained on a thermal equilibrium sample (Figure 3b, 3c and Table S2). This can, for example, be confirmed by calculating zeta-score [START_REF]Analytical Methods Committee[END_REF] between pairs of signals: as shown in Table S2, the absolute value of the zeta-score is always lower than 2, except for the case where a signal corresponds to two unresolved signals belonging to different molecules. The signal at ca. 7.85 ppm is assigned to para protons of pyridine and meta protons of 4,4'bipyridyl. The diffusion coefficient corresponding to this signal and fitted from the thermally polarized SPEN-DOSY spectrum is not compatible with that fitted from the SABRE-SPEN-DOSY spectrum, as demonstrated by a zeta score much larger, in absolute value, than 2. On the contrary, this diffusion coefficient is fully compatible with the other signals of pyridine, and not compatible with the other signal of 4,4'-bipyridyl, see Table S2. This is explained by the fact that the enhancement coefficient is much higher, by a factor of about 10, for pyridine than for 4,4'bipyridyl. Thus, despite their lower concentration, para protons of pyridine are responsible of most of the intensity of the signal and govern in a large extent the apparent diffusion coefficient in the SABRE-SPEN-DOSY spectrum. If a signal in a SPEN-DOSY spectrum is visible even without SABRE hyperpolarization, the fact that this diffusion coefficient varies in the presence of the metal catalyst may be used as a clue that the corresponding signal indeed results from the superimposition of signals originating from different molecules and having a different signal enhancement factor.

Finally, the zeta-score can be used to determine the compatibility of diffusion coefficients within a molecule, and the capability to differentiate molecules. Table S3 shows z-scores between all pairs of fitted diffusion coefficients of the SABRE-SPEN-DOSY spectrum depicted in Figure 3d. Within a molecule, the zeta-score, in absolute value, is always smaller than 2 (even less than 1.2), showing the intra-molecular compatibility of diffusion coefficients. Moreover, it is statistically possible to distinguish the individual molecules, except between the b and d molecules (zeta-score of 1.6). This can be explained by the close values of their diffusion coefficients, differing by only 5%, a value close to the separation limit of the SPEN-DOSY method. This separation is not statistically sufficient but remains higher than the intra-molecular zeta-scores. Therefore, the diffusion dimension of SABRE-SPEN-UFDOSY spectra helps at assigning signals to each molecule in a mixture, as does conventional SPEN-DOSY, but on a solution 20 times less concentrated.

Conclusion

In this Article, we demonstrate the feasibility of the analysis of a mixture of dissolved molecules by one-scan spatially-encoded diffusion ordered NMR experiment, consecutive to hyperpolarization through the SABRE method. Specific challenges have been overcome: the use of a transverse axis to encode diffusion avoids the effect of convection that occurs mainly along the z-axis. The use of pure absorption processing of the data improves signal separation along the diffusion dimension. This has been validated on a SABRE-hyperpolarized mixture and systematic errors on the fitted diffusion coefficients have been investigated. A factor 20 in the solute concentrations has been gained while preserving the capacity to discriminate these solutes by their diffusion coefficients. Low-field SABRE has undeniable qualities. It needs a simple and cheap set up, is applicable to non-isotopically enriched molecules, and may be repeated within minutes. In the near future, the SABRE-SPEN-DOSY method will certainly take advantage from recent developments, including SABRE-Relay [26] that may be applicable to a much larger range of molecules than conventional SABRE, as only the occurrence of an exchangeable proton is required.

Experimental Section

Materials and solutions

The catalyst precursor [Ir(COD)(IMes)Cl] (1) (IMes = 1,3-bis(2,4,6trimethylphenyl)imidazole-2-ylidene, COD = cyclooctadiene) was purchased from the Centre for Hyperpolarization in MRI of the University of York (UK). Pyridine (py), 4,4'-bipyridyl (bpy), N,N-dimethylnicotinamide (dmni) and 2-ethylpyridine (2-epy) were purchased from Sigma-Aldrich. Methanol-d4 was purchased from Cambridge Isotope Laboratories. All chemicals were used as supplied.

Two solutions were prepared in methanol-d4. Thermal-equilibrium analyses were performed on a solution of the four selected substrates, namely pyridine, 4,4'-bipyridyl, N,N-dimethylnicotinamide and 2ethylpyridine, each at ca. 150 mM, both solutions in 3.95 mm NMR tube equipped with Teflon valves from Young Scientific Glassware Ltd. For SABRE experiments, an NMR tube of 5 mm o.d. and 3.95 mm i.d., equipped with Teflon valves from Young Scientific Glassware Ltd was used. A 450 l methanol-d4 solution was prepared, for a final concentration of 5 mM of each of the 4 substrates. A solution of the catalyst precursor was prepared under air, quickly transferred to the NMR tube for a final concentration of 1.0 mM, and quickly degassed by three sequences of gas phase expansion-tube shaking, taking overall less than 2 minutes.

Experimental proceedings

The NMR experiments were performed on a Bruker Avance II spectrometer operating at a frequency of 500.13 MHz and equipped with an inverse triple resonance broad band probe head with xyz gradients. Experiments were performed at 298K. The conventional DOSY spectrum of figure 2a was recorded using a double stimulated echo sequence with bipolar gradient pulses with additional longitudinal eddy current delay and spoil gradients, [37] with 8 diffusion encoding values linearly spaced along a ramp ranging from 0.019 T/m to 0.135 T/m, along x axis. The diffusion time was set to 100 ms. The duration of the bipolar gradient pulses for diffusion encoding was 1.4 ms. The conventional data were acquired with 16384 points, 4 dummy scans, 32 scans, a spectral width of 7500 Hz and a relaxation delay of 5 s, resulting in a total experiment duration of 27 min.

The SPEN DOSY spectra with x encoding were acquired using the SPEN STE pulse sequence, using a chirp pulse with a bandwidth of 70 kHz and a duration of 1 ms, sweeping over a region of 3.95 mm thanks to a gradient of 0.3627 mT/m. The post-chirp gradient had a duration of 0.9 ms and the encoding gradient strength was 0.3627 T/m. The acquisition gradient was set to 0.2325 T/m. The diffusion delay was 100 ms. Additional delay for symmetry purpose was 1.93 ms for  and 5.59 ms for '. A selective 180° pulse was used with a duration of 5.915 ms centered at 7.94 ppm. The acquisition time was 66 ms for 65536 points, 128 loops, Ta=0.256 ms leading to a spectral width of 1953 Hz.

The DOSY spectra with z encoding over a region of 3.95 mm were acquired using the SPEN STE pulse sequence with the same parameters as before, excepted for the acquisition gradient that was set to 0.3375 T/m. The reference profile was acquired with a double-spin echo imaging pulse sequence using a chirp pulse with a 70 kHz bandwidth and 1 ms duration, an encoding gradient of 0.4050 T/m along z and 0.3627 T/m along x, an acquisition gradient of 0.3375 T/m along z and 0.2325 T/m along x, a number of 1024 points for an acquisition duration of 1.024 ms.

For SABRE-polarized experiments, 51%-enriched p-H2 was produced in less than 5 minutes according to the procedure and home-built setup previously described. [18] It was then transferred without shaking into the NMR tube. The H2 final pressure was about 4 bar. As dissolution of hydrogen in methanol is slow on the minute time-scale, as checked in a separate experiment, the exact magnetic field where this transfer proceeds was considered unimportant. Then, the NMR tube was manually shaken during 15 s for catalyst activation, giving [Ir(H)2(IMes)(S1)(S2)(S3)] molecules, where S1, S2 and S3 were among the four substrates present in solution. As the total substrate concentration was well above three times that of the catalyst, binding of methanol solvent was neglig ble. [38] Shaking was performed at about 6.5 mT, a field close to the optimum for signal enhancement of pyridine when [Ir(COD)(IMes)(Py)] is the catalyst precursor. [39] The NMR tube was then introduced in the spectrometer. The total delay between the shaking and the start of the NMR acquisition was about 5 s during which the deuterium lock was established and the solution tended to stabilize. NMR acquisitions either used SPEN-DOSY sequences such as that shown in Figure 1b, or slightly modified by putting diffusion encoding and decoding gradients along the z-axis, or a series of 90° spectra acquired each 3 s. This shaking-acquisition sequence was repeated up to 6 times. For further experiments, the gas phase of the NMR tube was expanded in a degassed volume in order to decrease the pressure by a factor of ca. 15, prior to the transfer of fresh p-H2. This procedure took less than 5 minutes.

Processing

Conventional DOSY spectra were processed with the DOSY Toolbox, in pure-absorption mode. [40] For all SPEN DOSY experiments, data were processed in Matlab (The Mathworks, Natick, U.S.A.) using home-written routines, part of which adapted from the DOSY Toolbox. [40] The procedure had been improved since the previous report, [21] and contained the following steps: data were read from Bruker files, then sorted and reshaped in order to get a 2D matrix. Cosine apodization and zero-filling were used in the spectroscopic dimension. Only the odd echoes were retained, and Fourier transformation was performed along the k and t2 dimensions. After phase correction of the spectra, the peak maxima were selected graphically and the spatial profile for each peak was obtained. Correction by a reference profile was performed. The diffusion was measured in a region of 2.8 mm depth. Calibration constant of Gmax=0.675 T/m and Gmax=0.465 T/m were used for z and x axis, respectively. The data were fitted against the following modified Stejskal-Tanner equation, with S0 and D as adjustable parameters: S(x) = S 0 exp(-𝐷 ∆ ′ (𝐴𝑥 + 𝐵) 2 )

(1)

where A and B were calculated according to:

𝐴 = -2𝛾𝐺 𝑒 𝑇 𝑒 𝐿 ⁄ 𝐵 = 𝛾𝐺 𝑒 𝑇 𝑝
with Ge is the encoding gradient strength, Te is the duration of chirp pulse, L is the length of the region swept by the pulse, and Tp is the duration of the post-chirp gradient. [12]

Scheme 1 .

 1 Scheme 1. Structure and nomenclature of substrates used in this study. The abbreviations indicate: pyridine (p), N,Ndimethylnicotinamide (d), 3-ethylpyridine (3) and 4,4'-bipyridyl (b).

Figure 1 .

 1 Figure 1. Description of the SABRE-SPEN-DOSY experiments. a) Timing of the experiment: NMR tube shakings, noted s, NMR acquisitions, noted exp., "low" means magnetic field of 6.5 mT, "high" means 11.7 T. i and j denote the potential repetition of NMR experiments on he same sample. b) SPEN STE-DOSY pulse sequence. Gradients are shown on 3 logical channels with diffusion encoding and decoding gradients on the SPEN line, and ctp1 and ctp2 correspond to the coherence transfer pathway (CTP) selection. 180° are chirp pulses.

Figure 2 .

 2 Figure 2. Aromatic regions of the rebuilt DOSY 1 H NMR spectra of the solution containing the four substrates at ca. 150 mM. a) Conventional DOSY spectrum. Projection on the spectral axis is displayed. b-d) SPEN-DOSY spectra with diffusion measured according to the z axis. Spectra acquired with optimized shims and limited convection for b) and c), and recorded just after having shaken the NMR tube for d). The data are processed using magnitude mode for b), and using absorption mode, for a), c) and d). The linewidth in the diffusion dimension denotes the standard deviation obtained from the fit. Signal assignment according to nomenclature in Scheme 1. Each colored line corresponds to one molecule.

Figure 3 .

 3 Figure 3. SPEN-DOSY recorded along the x axis. a-c) with the solution containing the four substrates depicted in Scheme 1, at ca. 150 mM each, using the absorp ion mode for processing. a) 1 H NMR signal as a function of he x coordinate. Red circles: raw data, blue crosses: data corrected by the 1 H spatial density (profile of the tube along the x axis given by the dashed line), continuous line: fitted diffusion curve for the p-o signal. b) Reconstructed spectrum acquired with optimized shims and limited convection. Projection on spectral axis is displayed. c) Reconstructed spectrum acquired 5 s after having shaken the NMR tube. d) SABRE-SPEN-UFDOSY spectrum on a 1 mM catalyst solution, each 4 substrates concentrated at 5 mM, and processed in absorption mode. Assignment of signals according to nomenclature in Scheme 1. Color lines stand for each molecules.

Acknowledgements

Dr. Florent Malloggi is acknowledged for the acquisition of the video shown in Figure S4. This research was supported by the Région Ile-de-France and the Agence Nationale de la Recherche (ANR-16-CE29-0012).


Zhongliang Li
email: zhongliang.li@lsis.org

Rachid Outbib
email: rachid.outbib@lsis.org

Stefan Giurgea
email: stefan.giurgea@utbm.fr

Daniel Hissel
email: daniel.hissel@univ-fcomte.fr

Samir Jemei

Alain Giraud
email: alain.giraud@cea.fr

Sebastien Rosini
email: sebastien.rosini@cea.fr

Online implementation of SVM based fault diagnosis strategy for PEMFC systems

Keywords: PEMFC system, Fault diagnosis, SVM classification, System in Package, Online implementation

In this paper, the topic of online diagnosis for Polymer Electrolyte Membrane Fuel Cell (PEMFC) systems is addressed. In the diagnosis approach, individual cell voltages are used as the variables for diagnosis. The pattern classification tool Support Vector Machine (SVM) combined with designed diagnosis rule is used to achieve fault detection and isolation (FDI). A highly-compacted embedded system of the System in Package (SiP) type is designed and fabricated to monitor individual cell voltages and to perform the diagnosis algorithms. For validation, the diagnosis approach is implemented online on PEMFC experimental platform. Four concerned faults can be detected and isolated in real-time.

Introduction

The environment and resource issues have been drawing increasing attention of the world.

Global warming and non-renewable resource exhaustion are two problems need to be addressed urgently. One of the main causes of these issues is the high dependence of the fossil fuels in the current energy structure. Since hydrogen can be produced from diverse sources, such as renewable resources and nature gas, large-scale use of hydrogen-based fuel cells is considered as one of the most significant solutions dedicated to slacking the dependence on fossil fuels [START_REF] Park | A review of the gas diffusion layer in proton exchange membrane fuel cells: Durability and degradation[END_REF][START_REF] Sun | A numerical study on the effects of temperature and mass transfer in high temperature PEM fuel cells with ab-PBI membrane[END_REF]. Amongst various fuel cells, Polymer Electrolyte Membrane Fuel Cell (PEMFC) is potentially beneficial for a wide range of applications, thanks to its attractive advantages, such as high efficiency, high power density, in-situ zero-emission, low operating temperature, and quick response to load changes [START_REF] Jang | Dynamic cell performance of kW-grade proton exchange membrane fuel cell stack with dead-ended anode[END_REF][START_REF] Raga | Black-box model, identification technique and frequency analysis for pem fuel cell with overshooted transient response[END_REF]. Especially, fuel cell electric vehicle (FCEV), which is equipped with PEMFC stack as the main energy generator, is a powerful competitor in the future automobile market. Compared to the battery based electric vehicles, FCEVs have the advantages of quick recharging (refueling) and long running range [START_REF] Simons | A life-cycle perspective on automotive fuel cells[END_REF][START_REF] Xuewei | Novel bidirectional snubberless naturally commutated soft-switching current-fed full-bridge isolated dc/dc converter for fuel cell vehicles[END_REF]. However, several bottlenecks of PEMFC technologies, such as reliability and durability, still exist and impede the widely commercial exploitation of the PEMFC products [START_REF] Wu | A review of PEM fuel cell durability: Degradation mechanisms and mitigation strategies[END_REF][START_REF] Chen | Lifetime prediction and the economic lifetime of Proton Exchange Membrane fuel cells[END_REF].

Fault diagnosis, i.e., fault detection and isolation (FDI), is playing an increasingly important role in several kinds of modern industrial systems [START_REF] Cai | Multi-source information fusion based fault diagnosis of ground-source heat pump using Bayesian network[END_REF][START_REF] Yin | A Review on Basic Data-Driven Approaches for Industrial Process Monitoring[END_REF][START_REF] Liu | Multiblock Concurrent PLS for Decentralized Monitoring of Continuous Annealing Processes[END_REF][START_REF] He | Adaptive Extended Kalman Filter Based Fault Detection and Isolation for a Lithium-Ion Battery Pack[END_REF]. It has been found that various faults involving different components of PEMFC systems can occur and cause performance degradations. For instance, the faults related to reactants supply subsystems and the ones related to water management. During the last decades, fault diagnosis devoted to improving the reliability and durability performance of PEMFC systems has drawn the attention of both academic and industrial communities [START_REF] Petrone | A review on model-based diagnosis methodologies for PEMFCs[END_REF][START_REF] Zheng | A review on non-model based diagnosis methodologies for PEM fuel cell stacks and systems[END_REF]. Through an efficient diagnosis strategy, more serious faults can be avoided thanks to an early fault alarm. With the help of diagnosis results, the downtime (repair time) can be reduced. Moreover, the precise diagnosis information can help to speed up the development of new technologies [START_REF] Li | Data-driven fault diagnosis for pemfc systems[END_REF].

Several fault diagnosis strategies have been studied during the last decade [START_REF] Escobet | Model-based fault diagnosis in PEM fuel cell systems[END_REF][START_REF] Lira | LPV observer design for PEM fuel cell system: Application to fault detection[END_REF][START_REF] Benouioua | Fuel cell diagnosis method based on multifractal analysis of stack voltage signal[END_REF][START_REF] Kim | State-of-health diagnosis based on hamming neural network using output voltage pattern recognition for a PEM fuel cell[END_REF][START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF][START_REF] Zheng | A double-fuzzy diagnostic methodology dedicated to online fault diagnosis of proton exchange membrane fuel cell stacks[END_REF][START_REF] Hua | Proton exchange membrane fuel cell system diagnosis based on the multivariate statistical method[END_REF][START_REF] Li | Diagnosis for pemfc systems: A data-driven approach with the capabilities of online adaptation and novel fault detection[END_REF]. The general model based fault diagnosis theoretical base seems to be well established and some positive results have been obtained by using these methods for some PEMFC systems [START_REF] Escobet | Model-based fault diagnosis in PEM fuel cell systems[END_REF][START_REF] Lira | LPV observer design for PEM fuel cell system: Application to fault detection[END_REF]. Nevertheless, building a model with first principle is not a trivial task. The internal parameters, which are essential for modeling, are not evident to be found or estimated. In addition, model structures and parameters may differ among different designs of fuel cell stacks and other system components. Apart from the model based diagnosis, the application of data based methodologies for the diagnosis of PEMFC systems has been drawing the attention of researchers [START_REF] Benouioua | Fuel cell diagnosis method based on multifractal analysis of stack voltage signal[END_REF][START_REF] Kim | State-of-health diagnosis based on hamming neural network using output voltage pattern recognition for a PEM fuel cell[END_REF][START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF][START_REF] Zheng | A double-fuzzy diagnostic methodology dedicated to online fault diagnosis of proton exchange membrane fuel cell stacks[END_REF][START_REF] Hua | Proton exchange membrane fuel cell system diagnosis based on the multivariate statistical method[END_REF][START_REF] Li | Diagnosis for pemfc systems: A data-driven approach with the capabilities of online adaptation and novel fault detection[END_REF]. Avoiding the sophistical modeling process, the data based diagnosis seems to be more practical in most cases. Actually, the data based diagnosis has been utilized in a number of industrial processes [START_REF] Rauber | Heterogeneous Feature Models and Feature Selection Applied to Bearing Fault Diagnosis[END_REF][START_REF] Amar | Vibration Spectrum Imaging: A Novel Bearing Fault Classification Approach[END_REF][START_REF] You | WPD-PCA-Based Laser Welding Process Monitoring and Defects Diagnosis by Using FNN and SVM[END_REF].

Within the scope of data based fault diagnosis, a number of pattern classification techniques have been widely used since FDI can be considered as a classification problem [START_REF] Amar | Vibration Spectrum Imaging: A Novel Bearing Fault Classification Approach[END_REF][START_REF] You | WPD-PCA-Based Laser Welding Process Monitoring and Defects Diagnosis by Using FNN and SVM[END_REF]. Some classification based diagnosis strategies have been proposed for PEMFC systems (see [START_REF] Benouioua | Fuel cell diagnosis method based on multifractal analysis of stack voltage signal[END_REF][START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF][START_REF] Zheng | A double-fuzzy diagnostic methodology dedicated to online fault diagnosis of proton exchange membrane fuel cell stacks[END_REF][START_REF] Li | Diagnosis for pemfc systems: A data-driven approach with the capabilities of online adaptation and novel fault detection[END_REF] for instance). Different variables, feature extraction and classification methods have been studied using the historical data. In [START_REF] Benouioua | Fuel cell diagnosis method based on multifractal analysis of stack voltage signal[END_REF], the classification was supposed to be carried out in the feature space which is generated using multifractal analysis on stack voltage. In [START_REF] Zheng | A double-fuzzy diagnostic methodology dedicated to online fault diagnosis of proton exchange membrane fuel cell stacks[END_REF], the fuzzy classification method was utilized to analyze Electrochemical Impedance Spectroscopy. In our previous study [START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF], selecting individual cell voltages as the variables for diagnosis, several classification and feature extraction techniques were compared from the perspectives of classification accuracy and computational complexity. The classification method Support Vector Machine (SVM) was selected as the most suitable classification tool in the case.

The strategy was further developed by extending the capabilities of novel fault detection and online adaptation [START_REF] Li | Diagnosis for pemfc systems: A data-driven approach with the capabilities of online adaptation and novel fault detection[END_REF].

After elaborating the diagnosis strategy, the objective of this work is the online implementation. To do so, three aspects must be considered specially aiming at online implementation.

First, for practical applications, such as FCEVs, reducing the volume and cost of hardwares is always required [START_REF] Chan | A novel polyphase multipole square-wave permanent magnet motor drive for electric vehicles[END_REF][START_REF] Kang | Dynamic simulation of a fuel cell hybrid vehicle during the federal test procedure-75 driving cycle[END_REF]. The embedded system which fulfills the measurements and computation should be designed with compact layout and limited components. Second, the diagnosis approach programed in the embedded system is performed in real-time, which requires the diagnosis algorithms being saved in limited memory space and being handled in a sufficiently short diagnosis cycle [START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF]. Third, the diagnosis results should be sufficiently reliable and robust. The importance of online implementation cannot be over-emphasized to make the work closer to industrial applications. The paper is organized as follows: In Section 2, the general development of a classification based diagnosis strategy is summarized. Section 3 is dedicated to introducing the experimental platform. Then, the diagnosis algorithms, including the classification method SVM and the diagnosis rule, is presented in Section 4. The online implementation of diagnosis approach is described in Section 5. The diagnosis results are also provided and analyzed in the same section.

Finally, the conclusion is made in Section 6.

Development process of classification based online fault diagnosis

The development process of the classification based online fault diagnosis strategy for PEMFC systems consists of three stages. Fig. 1 shows the different components and their tasks concerned in different stages, and the data flows in-between these components.

Algorithm training: In this stage, the historical data sampled in the experiments of different health states, i.e. normal operating state and different concerned faulty states, are analyzed using the computer and the software such as Matlab. The objective is to train and verify the diagnostic algorithms offline using the historical data.

Algorithm integration: In this stage, the programs for performing the diagnosis algorithms are coded and burnt into an embedded system, which is designed in consideration of specificities of both the objective PEMFC system and the characteristics of diagnosis algorithms. The embedded system equipped with diagnosis algorithms is then tested using the historical data. Thus, the obtained results can be compared with the results from the computer. The objective of this step is to ensure the algorithm can be loaded and run correctly in the embedded system.

Online realization: After the first two stages, the embedded system integrated with diagnosis approach is installed into the real PEMFC systems. The online tests are carried out using the real-time data. This step is operated just as the real situation. The objective is to make sure the different subsystems can cooperate as expected.

Generally speaking, in the literature (see for instance [START_REF] Benouioua | Fuel cell diagnosis method based on multifractal analysis of stack voltage signal[END_REF][START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF][START_REF] Zheng | A double-fuzzy diagnostic methodology dedicated to online fault diagnosis of proton exchange membrane fuel cell stacks[END_REF][START_REF] Li | Diagnosis for pemfc systems: A data-driven approach with the capabilities of online adaptation and novel fault detection[END_REF]), the strategy is tested offline, i.e., the first stage. Here, we consider the feasibility of the second stage dedicated to the integration of the algorithm of classification, and the third stage, which is the online realization on the real process. Hence, the complete process of implementation is realized.

Diagnosis strategy development platform

As Fig. 2 shows, the development platform dedicated to online implementation of the diagnosis strategy consists of the following parts:

• PEMFC system
The schematic of the whole PEMFC system is shown in Fig. 3. The core of the system is for automotive application. The nominal operating conditions of the stack are summarized in Table 1. In normal or fault free state, all the operating parameters should be maintained at the nominal values with small variation caused by system noises. It is considered in our case that a fault in the PEMFC system occurs when the operating parameters are out of the normal range. Notice that the faults defined in our case are not limited to the fuel cell stack but cover the health states of the whole system. Certain faults, such as air pressure exceeds the normal range, may not cause obvious degradation with respect to fuel cell stack. The air is supplied from the environment. Thanks to the compressor, valve and mass flow regulator, the air flow rate and the pressure at inlet can be regulated. By using a humidifier, the hygrometry level of the fed air can be regulated to the required value.

Hydrogen is supplied from a high pressure tank. The pressure at the hydrogen inlet can be controlled thanks to the pressure regulator; namely a valve. The hydrogen flow rate can also be set through the regulator located at downstream of the stack.

The system is equipped with a temperature regulation subsystem in which the thermal exchanging medium is deionized water. The temperature measured at the water outlet is considered as the temperature of the stack.

The system is operated through the Labview interface. The parameters such as pressures, flow rates, relative humidities, temperatures of reactants, cell voltages can also be monitored and saved through the same interface.

• DC load

The load current can be flexibly varied through an electronic load.

• Measuring and computing unit

The measuring and computing unit is devoted to measuring the variables for diagnosis and performing online the diagnosis approach. The core component is the specially-designed SiP chip (yellow square component shown in Fig. 2). The structure of the SiP is shown in Fig. 4. Here, the upper layer (see Fig. 4) can be seen as the "main board" which is equipped with a Smartfusion on-chip system developed by Microsemi. The device integrates an FPGA fabric, ARM Cortex-M3 Processor, and programmable analog circuitry [START_REF]Smartfusion introduction[END_REF]. Another two chips of 16 M memory are also added to the system. With the abundant connecting ports, several kinds of communications can be realized with other devices. This on-chip system is ideal hardware for embedded designers as it provides more flexibility than traditional fixed-function microcontrollers [START_REF]Smartfusion introduction[END_REF]. The other two layers, which are equipped with Giant MagnetoResistive (GMR) sensors, are used for measuring individual cell voltages precisely [START_REF] Rothan | A low power 16-channel fully integrated GMRbased current sensor[END_REF].

The block of SiP is settled on an electric board which is equipped only with some LED lights, test points, and connectors.

• Diagnosis interface

The measurements and the calculation results obtained from the measuring and computing unit are exported to an output interface. In the presented application, the output interface has been materialized by an computer equipped with Labview software. With the help of Labview, the real-time cell voltage signals and the diagnosis results can be visualized on the screen. The real-time data can also be saved for advanced analysis. [START_REF] Giraud | Embedded smart sensors for measurement and diagnosis of measurement and diagnosis of multicells PEMFC[END_REF] of the fuel cells, such as the current density distribution, electrochemical characteristics, temperature, fluidic conditions, and aging effect. Voltage signals are therefore crucial for inspecting the health states of the fuel cells. Second, it is observed that the voltages of the cells located at different positions are usually different [START_REF] Rodatz | Operational aspects of a large PEFC stack under practical conditions[END_REF]. It is somehow necessary to monitor every single (or several) cell voltage(s) other than only the global stack voltage to get the knowledge of the local health states. Third, from our previous studies, it is observed that different faults lead to different magnitudes and distributions of cell voltages [START_REF] Li | Fault diagnosis and novel fault type detection for pemfc system based on spherical-shaped multiple-class support vector machine[END_REF]. This characteristic is in accordance with the objective of the FDI. Moreover, the designed SiP is equipped with GMR sensors which facilitate the precise measurement of individual cell voltages.

Principle of the diagnosis approach

The principle of the proposed diagnosis approach can be summarized in Fig. 5. In the offline training process, the SVM classifier is trained based on the training dataset in which the data are collected in both normal and faulty states. In the online performing phase, the real-time data are handled using the trained SVM model. The diagnosis inference can be obtained based on the classification results and according to the diagnosis rule.

SVM classification

SVM is a classification method developed in the late 20 th century [START_REF] Platt | Sequential Minimal Optimization : A Fast Algorithm for Training Support Vector Machines[END_REF]. It has been successfully used in a wide applications range during the last two decades [START_REF] Widodo | Support vector machine in machine condition monitoring and fault diagnosis[END_REF]. Thanks to its excellent characteristics, SVM is a suitable diagnosis oriented classification tool. For instance, SVM has better generalization capability than conventional classification methods, such as artificial neural networks [START_REF] Widodo | Support vector machine in machine condition monitoring and fault diagnosis[END_REF]. Concerning fault diagnosis, it is usually impossible to obtain the sufficient samples in faulty conditions. In such cases, SVM can provide more reliable results with a small number of learning samples. Regarding the training procedure of SVM, the global optimal solution can be guaranteed. In addition, the solution of SVM is usually represented using a small proportion of training samples, which makes the performing calculation light enough for realtime use [START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF].

The basic SVM theory comes from the binary classification problem. As Fig. 6 In the performing phase, which class a test sample belongs to can be told according to its location.

Support vectors

Training sample in health state 1 Training sample in health state 2

Maximum margin

The optimal separating hyperplane

Space constituted by individual cell voltages

Test sample

F (x) = i, i ∈ {0, 1, 2, . . . C} (1)
For performing, a real-time sample can be classified into one of the known classes thanks to [START_REF] Park | A review of the gas diffusion layer in proton exchange membrane fuel cells: Durability and degradation[END_REF].

The binary SVM corresponding to the first two classes is summarized as Algorithm 1. For more details on SVM theory, the reader is referred, for instance, to [START_REF] Platt | Sequential Minimal Optimization : A Fast Algorithm for Training Support Vector Machines[END_REF] and references therein.

Algorithm 1 Binary SVM

Training:

1: Initialize D, σ.

2: Collect x 1 , x 2 , . . . , x N distributed in 1st and 2nd classes.

3: Solve the quadratic problem:

min J(a) = 1 2 N n=1 m=1 a n a m g n (x)g m (x)k(x n , x m ) - N n=1 a n s.t. N n=1 a n g n (x) = 0, 0 ≤ a n ≤ D for n = 1, . . . , N (2)
with

g n (x) = 1 if x ∈ Ω 1 and g n (x) = -1 if x ∈ Ω 2 .
where a = [a 1 , a 2 , ..., a N ] T are the Lagrange multipliers, and the Gaussian kernel function is defined as

k(x n , x m ) = exp - ||x n -x m || 2 σ (3)
4: Save support vectors x s 1 , x s 2 , . . . , x s S and corresponding g n and a n denoted by {g s n } and {a s n }) for which a n > 0, where S is the number of support vectors.

Performing:

For a new sample x,

F (x) =              1, if sign        S n=1 a s n g s n k(x s n , x) + b        = 1 2, elsewhere (4)
where

b = 1 S S j=1        g s j - S n=1 a s n g s n k(x s n , x s j )       
To extend the binary classifier to multi-classification situations, there are several ways (see for instance [START_REF] Hsu | A Comparison of Methods for Multiclass Support Vector Machines[END_REF] and references therein). The method "One-Against-One" has been adopted in this study. Actually, up to C(C + 1)/2 binary SVMs can be constructed based on the training data in C + 1 classes. For classifying a new sample, first its classification results corresponding to all the binary SVMs are obtained. After that, the final classification result is obtained by voting all the binary classification results (see [START_REF] Hsu | A Comparison of Methods for Multiclass Support Vector Machines[END_REF] for more details).

Diagnosis rule

In a general way, the classification results are used directly as the diagnosis results. However,

in
Fd i (k) = k n=k-N i lag +1 (F (x n ) == i) N i lag , i ∈ {1, . . . , C} (5)
The fault degree of fault i, i.e., Fd i (k), is then calculated and compared to the pre-defined threshold denoted by T h i . The fault occurrence at time k can be justified if the threshold is exceeded. The diagnosis rule can be expressed as Algorithm 2. Notice that diagnosis window size N i lag and threshold T h i need to be initialized to realize this rule. Collect F (x k-N i lag +1 ), . . . , F (x k ) 3:

Calculate Fd i according to [START_REF] Simons | A life-cycle perspective on automotive fuel cells[END_REF] 4:

if Fd i ≥ T h i then 5:

Fault i detected 6:

else 7:
No fault i 8:

end if 9: end for

Online implementation of the diagnosis strategy

Offline training and algorithm integration

Knowing that classification based diagnosis belongs to supervised learning methods, the data from various classes were needed for training. To prepare the training dataset, several faults were produced deliberately. Table 2 summarizes the operations in the experiment of training data preparation. Notice that all the concerned faults are recoverable ones caused by faulty operations. The faults consist of the ones of gas supply subsystems and those on water management.

Constrained by the measuring capability of the initially designed SiP and configuration of connectors between the stack and SiP, the voltages of 14 cells can be measured and used as the variables for diagnosis. These cells are numbered by [START_REF] Park | A review of the gas diffusion layer in proton exchange membrane fuel cells: Durability and degradation[END_REF][START_REF] Jang | Dynamic cell performance of kW-grade proton exchange membrane fuel cell stack with dead-ended anode[END_REF][START_REF] Simons | A life-cycle perspective on automotive fuel cells[END_REF][START_REF] Xuewei | Novel bidirectional snubberless naturally commutated soft-switching current-fed full-bridge isolated dc/dc converter for fuel cell vehicles[END_REF][START_REF] Wu | A review of PEM fuel cell durability: Degradation mechanisms and mitigation strategies[END_REF][START_REF] Cai | Multi-source information fusion based fault diagnosis of ground-source heat pump using Bayesian network[END_REF][START_REF] Yin | A Review on Basic Data-Driven Approaches for Industrial Process Monitoring[END_REF][START_REF] Liu | Multiblock Concurrent PLS for Decentralized Monitoring of Continuous Annealing Processes[END_REF][START_REF] He | Adaptive Extended Kalman Filter Based Fault Detection and Isolation for a Lithium-Ion Battery Pack[END_REF][START_REF] Benouioua | Fuel cell diagnosis method based on multifractal analysis of stack voltage signal[END_REF][START_REF] Kim | State-of-health diagnosis based on hamming neural network using output voltage pattern recognition for a PEM fuel cell[END_REF][START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF][START_REF] Zheng | A double-fuzzy diagnostic methodology dedicated to online fault diagnosis of proton exchange membrane fuel cell stacks[END_REF][START_REF] Hua | Proton exchange membrane fuel cell system diagnosis based on the multivariate statistical method[END_REF], counting from the negative pole of the stack. were initialized respectively as D = 19000 and σ = 2000 according to cross validation [START_REF] Cawley | Fast exact leave-one-out cross-validation of sparse least-squares support vector machines[END_REF].

Classifying the training data with the trained SVM, the global classification accuracy rate is 84.98%. More detailed results can be summarized as a confusion matrix, shown quantitatively in Table 3 and visually in Fig. 8. It could be observed that the false alarm rate (FAR), i.e., the rate of the samples in normal state wrongly diagnosed into the fault classes, is relatively low. The diagnosis accuracy for the data in F3 is also high. A considerable part of data in classes F1, F2, and F4 are wrongly classified into the normal class. From Fig. 8, it can be seen the classification results vibrate between the corresponding faults and normal classes. Actually, faults F1, F2, and F4 are relatively light ones compared to the faults such as F3. In these states, the data vary lightly from the normal state. The overlaps between the normal and faulty states exist. It can also be observed that some overlaps exist between class F1 and F4. The diagnosis procedure tested by using a computer or by coding into the memory of SiP, respectively, provides 100% accordant results. Besides, the diagnosis algorithm could be calculated within a sampling cycle (i.e., 1s) using the SiP. That is to say, the diagnosis approach is successfully integrated into the SiP.

Online validation

To realize online validation, the programed SiP was tested online with the real-time data during another experiment. The operations during this experiment are summarized in Table 6, and the measured cell voltages, i.e., the variables for diagnosis are plotted in Fig. 10. are also summarized quantitatively as the confusion matrix shown in Table 7.

To show the effect of the proposed diagnosis rule, the raw classification results are also provided here. The global classification accuracy of online validation data is 85.93%. The detailed classification results corresponding to online validation are summarized in Table 8. By comparing Table 8 and7, it can be seen that the diagnosis accuracy for the data in F1, F2 and F4

classes can be increased from the raw classification results by using the proposed diagnosis rule.

However, the FAR is also a little increased. Although the robustness performance and accuracy are improved by using the proposed diagnosis rule, it should be mentioned that some delays are also introduced. These delays are the main factors which cause the diagnosis error. As Fig. 12 shows, when the diagnosis rule is launched, to formulate the first diagnosis window for the detection of fault i (i = 1, . . . , C), the initial delay which is of the length N i lag is introduced. When fault i occurs, the fault can be diagnosed after N i lag T h i sample periods in ideal case. The data during the diagnosis delay are wrongly diagnosed into the normal state. When fault i is eliminated, the diagnosis result of the corresponding fault will continue N i lag (1-T h i ) more sample periods. The data related to recovery delay are wrongly diagnosed into the fault state and lead to the increase of FAR.

Notice that the three delays are all determined by diagnosis window size N i lag . To shorten the delays, N i lag must be initialized with a small value. On the contrary, a relatively big N i lag is usually required to improve the robustness and accuracy performance. Hence, a compromise needs to be made to parameterize N i lag .

Extendability of the approach

Here, four different faults are concerned in the study. It should be noticed that other types of faults than the given ones could also be encountered. For instance, the fault of catalyst poisoning which is usually caused by the CO mixed in the entered hydrogen [START_REF] Wagner | Change of electrochemical impedance spectra (EIS) with time during CO-poisoning of the Pt-anode in a membrane fuel cell[END_REF][START_REF] Farrell | Experimental and modelling studies of CO poisoning in PEM fuel cells[END_REF], the faults related to the temperature subsystem, and the faults occurs at the electric circuit [START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF]. The discriminative information contained in the individual cell voltage signals is the key factor that determines whether a fault can be efficiently detected and isolated from other faults. Actually, in our previous study [START_REF] Li | Fault detection and isolation for Polymer Electrolyte Membrane Fuel Cell systems by analyzing cell voltage generated space[END_REF], it has been demonstrated that the CO catalyst poisoning fault, the fault related to temperature management, and the fault in electric circuit fault can be accurately diagnosed thanks to our diagnostic approach. Nevertheless, it should also be emphasized that the data corresponding to the concerned faults must be collected in prior to implement an efficient diagnosis. It is usually difficult or impossible to carry out the experiments in all the faulty cases. This could be considered as the main drawback of all the data based approaches. To alleviate this defect, we proposed previously a procedure which enables the recognition of a novel fault even the corresponding data have not appeared in the training phase [START_REF] Li | Fault diagnosis and novel fault type detection for pemfc system based on spherical-shaped multiple-class support vector machine[END_REF].

Ageing effect

The performance degradations involving a PEMFC system also result from the ageing effect other than the regular faults. When the ageing effect is taken into account, the diagnosis results could be impacted. For instance, the data in normal state are not stationary. Using the originally developed diagnosis approach, the normal data might eventually be diagnosed as the ones in faulty states as time goes on. In order to maintain the performance, a self-adaptation method is proposed for the diagnosis in our previous work [START_REF] Li | Diagnosis for pemfc systems: A data-driven approach with the capabilities of online adaptation and novel fault detection[END_REF].

Concerning the ageing effect, several studies have been launched and focused on the strategy of prognosis which is dedicated to describing the degradation tendency related to ageing effect and predicting the residual useful life far ahead [START_REF] Zhang | An unscented kalman filter based approach for the health-monitoring and prognostics of a polymer electrolyte membrane fuel cell[END_REF][START_REF] Jouin | Prognostics and Health Management of PEMFC State of the art and remaining challenges[END_REF][START_REF] Petrone | Accelerated stress test procedures for PEM fuel cells under actual load constraints: State-of-art and proposals[END_REF].

Conclusion

In this paper, a classification based diagnosis strategy is proposed for PEMFC systems and the results of online realization are demonstrated. According to the obtained results, the following conclusions can be made:

1. A satisfying online diagnosis results can be obtained with individual cell voltages serving as the variables for diagnosis.

2. In the diagnostic approach, SVM classification method and the designed diagnosis rule are performed successively in the diagnostic process. The efficiency of the approach is validated in the perspectives of diagnosis accuracy and online implementability. More especially, it is demonstrated that, by post-processing raw classification results using the proposed diagnosis rule, more robust and accurate diagnosis results can be obtained.

3. The specially designed SiP can fulfill the tasks of precisely measuring individual cell voltages and implementing the diagnostic approach online. Thanks to the compact design, it is promising to be used in practical applications like FCEVs.

  This study is dedicated to realizing the online implementation of a classification based fault diagnosis strategy for PEMFC systems. The approach employs individual cell voltages as the variables for diagnosis and SVM as the classification tool. Apart from the classification algorithm, a diagnosis rule is designed to obtain the diagnosis results based on the raw classification results. An embedded system of the System in Package (SiP) type is designed to precisely monitor the individual cell voltages and perform the diagnosis approach. The diagnosis approach is then integrated into the SiP and verified online in a PEMFC system. Four different faults which are generated deliberately are detected and isolated in real-time.

Figure 1 .Figure 2 .

 12 Figure 1. Developing process of classification based online fault diagnosis strategy

Figure 3 .

 3 Figure 3. Schematic of the PEMFC system

4. Diagnosis approach 4 . 1 .Figure 4 .

 414 Figure 4. Embedded system designed for PEMFC system diagnosis[START_REF] Giraud | Embedded smart sensors for measurement and diagnosis of measurement and diagnosis of multicells PEMFC[END_REF]

Figure 5 .

 5 Figure 5. Flowchart of the diagnosis approach

Figure 6 .

 6 Figure 6. Schematic diagram of SVM dedicated to fault diagnosis

Algorithm 2 rule 1 :

 21 Diagnosis for i = 1 to C do 2:

  The evolutions of individual cell voltages of the training data are shown in Fig.7(a). The cell voltage details in a period of 100 s are shown in Fig.7(b) (sample time 1 s). It can be observed that the magnitudes and behaviors of the voltages vary between different cells. Besides, a cycle property can be observed from the curves. Actually, it is related to the process of anode purge whose periodic time is 90 s.

Figure 8 .

 8 Figure 7. Cell voltages in training dataset

Figure 9 .

 9 Figure 9. Fault degrees and diagnosis results corresponding to the training data

Figure 10 .Figure 11 .

 1011 Figure 10. Cell voltages measured during online validation

Figure 12 .

 12 Figure 12. Delays introduced by diagnosis rule

Table 1 .

 1 Nominal conditions of the stacks

	Parameter

  some practical cases, overlaps usually exist among different health states and the samples in classes can not be perfectly classified. In such cases, an additional diagnosis rule should be designed to provide more reliable and consistent diagnosis results. In this study, an additional degree of freedom is introduced to achieve this goal. The general idea is to use a sequence of classification results instead of a single one to determine the current health state. Specifically concerning the fault class i, i ∈ {1, . . . , C}, at time k, the diagnosis results of the last N i lag samples

(i.e. F (x k-N i lag +1 ), . . . , F (x k )), named diagnosis window, are taken into account. Fault degree, denoted Fd, corresponding to a specific fault is defined as the rate of the fault is diagnosed:

Table 2 .

 2 Experimental procedure for the preparation of the training dataset

	Starting time Ending time Operation	Health state
	0	879 Nominal condition	Normal state (Nl)
	880	1675 Pressure of 1.3 bar at each side	Low pressure fault (F1)
	1676	2618 Back to nominal condition	Normal state (Nl)
	2619	3499 Pressure of 1.7 bar at each side	High pressure fault (F2)
	3500	4892 Back to nominal condition	Normal state (Nl)
	4893	6288 Lower relative humidity	Drying fault (F3)
	6289	7518 Back to nominal condition	Normal state (Nl)
	7519	8287 St. Air 1.5	Low air stoichiometry fault (F4)
	8288	8955 Back to nominal condition	Normal state (Nl)

With the training dataset, the SVM classifier is trained. Parameters D and σ in Algorithm 1

Table 3 .

 3 Confusion matrix for classification results of training data

			Predicted classes
		Nl	F1	F2	F3	F4
		Nl 4762 29	25	68	11
		F1 406 373	0	0	17
	Actual classes	F2 300 F3 157	0 11	800 0	0 1228	0 0
		F4 239	82	0	0	448
	To improve the robustness and accuracy performance, the diagnosis rule is designed based
	on the classification results (refer Section 4.4). Parameters N i lag and T h i were initialized based on

Table 4 .

 4 Parameter initialization for the design of diagnosis rule

		F1	F2 F3 F4
	N i lag	100 100 1 100
	T h i 0.3 0.3	1	0.3

Table 5 .

 5 Confusion matrix of diagnosis results of training data

			Predicted classes
		Nl	F1	F2	F3	F4
		Nl 4729 57	7	68	34
		F1 138 658	0	0	0
	Actual classes	F2 F3 168 10	0 0	1090 0	0 1228	0 0
		F4 114	13	0	0	642

Table 6 .

 6 Experimental procedure for online validation

	Starting time Ending time Operation					Health state
	0	3660 Nominal condition				Normal state (Nl)
	3661	4543 Pressure of 1.3 bar at each side	Low pressure fault (F1)
	4544	5374 Back to nominal condition		Normal state (Nl)
	5375	6541 Pressure of 1.7 bar at each side	High pressure fault (F2)
	6542	8128 Back to nominal condition		Normal state (Nl)
	8129	8909 St. Air 1.5					Low air stoichiometry fault (F4)
	8910	9841 Back to nominal condition		Normal state (Nl)
	9842	11909 Lower relative humidity			Drying fault (F3)
	11910	12459 Back to nominal condition		Normal state (Nl)
		Nl	F1 Nl F2	Nl	F4	Nl	F3	Nl

Table 7 .

 7 Confusion matrix of diagnosis results corresponding to online validation

			Diagnosed classes
		Nl	F1	F2	F3	F4
		Nl 7266 19	250	0	28
		F1 101 782	0	0	0
	Actual classes	F2 F3 173 77	0 0	1090 0	0 1890	0 0
		F4 101	0	0	0	680

Table 8 .

 8 Confusion matrix of classification results corresponding to online validation

			Diagnosed classes
		Nl	F1	F2	F3	F4
		Nl 7302 31 220	0	10
		F1 446 432	0	1	4
	Actual classes	F2 477 F3 132	0 28	690 5	0 1890	0 8
		F4 363	14	14	0	390
	5.3. Discussion
	5.3.1. Delays caused by the diagnosis rule

CEA: Alternative Energies and Atomic Energy Commission

Acknowledgment

This work is a contribution to the ANR DIAPASON2 project (fuel cell diagnosis methods for vehicle and stationary applications 2nd phase). The authors would like to thank their partners for their contribution.


Riad Ladjel
email: riad.ladjel@inria.fr

Nicolas Anciaux
email: nicolas.anciaux@inria.fr

Guillaume Scerri
email: guillaume.scerri@uvsq.fr

Philippe Pucheral
email: philippe.pucheral@uvsq.fr

Secure and distributed computations for a personal data management system

INTRODUCTION

A large amount of economically valuable data is produced every day. Whether they come from smartphones, connected devices, sensors or smart meters, this data is a gold mine for the people holding it. This data is often stored in centralized servers, servers that usually belong to large corporations that collected it in the first place (Google, Amazon, Facebook, insurance companies etc.) The result of this situation is that users lose control over their own data. This represents a real threat to privacy, whether it is intentional (misuse, malicious attack), or just by negligence (data leakage, mismanagement). These threats point to the need for personal platforms which allow their users to collect, manage and share their own data. This is the essence of the self-data movement. Thanks to smart disclosure initiatives, users can access their personal data from the companies or government agencies that collected them. Concurrently, personal data management system (PDMS) solutions are flourishing. Their goal is to empower users to leverage their personal data for their own good. While storing data in PDMS increases user control over data, in the PDMS context collaborative use of data is often overlooked. The benefits derived from exploiting data are considerable. A user may want to share her GPS position to have accurate traffic prediction [START_REF] Lv | Traffic flow prediction with big data: a deep learning approach[END_REF], or her medical records to train a shared neural network so that it can detect several diseases [START_REF] Joseph | Applications of machine learning in cancer prediction and prognosis[END_REF]. She may also want to adapt her energy contract based on her actual consumption without jeopardizing her privacy [START_REF] Molina-Markham | Private memoirs of a smart meter[END_REF].A naive approach to this problem is to send personal data to a trusted third party who will perform said collaborative computations. This, however involves very strong trust in the third party's honesty. The goal of this work is to overcome this unrealistic trust assumption and propose a privacy preserving distributed computation framework for performing collaborative computations over a large number of PDMS. Our objective is to propose a secure distributed computation protocol offering the same guaranties as secure multi-party computation (SMC) [START_REF] Cramer | Secure multiparty computation[END_REF] while keeping a profit-to-cost ratio as low as possible in case of an attack. In other words, it should be possible for parties to compute any function f (x 1 , x 2 , ..., x n ) over their inputs while keeping them private. An individual cannot infer any information other than what she can infer from her own input and the final result. The result should be exact and not approximate. Unlike SMC, the proposed protocol should be scalable, with respect to the number of parties and the complexity of the computation. This research is supported by the ANR PersSoCloud grant no ANR-16-CE39-0014.

SHORTCOMINGS OF EXISTING SOLUTIONS

Secure multi-party computation (SMC) [START_REF] Cramer | Secure multiparty computation[END_REF] allows N users to perform a secure computation on their personal data. The users involved learn nothing more than what they can infer from their input and the result. SMC is based on complex cryptographic techniques, which limit their scalability, in particular for very large number of parties. Ad-hoc SMC protocols have been proposed but these are not generic and do not allow all types of computations. Fully Homomorphic Encryption (FHE) [START_REF] Gentry | A fully homomorphic encryption scheme[END_REF] schemes allow one to compute arbitrary functions over encrypted data without a decryption key. Given c 1 and c 2 ciphertexts of m 1 and m 2 , one can compute f (m 1 , m 2 ) by decrypting f (c 1 , c 2 ). FHE is not suitable in our context due to its high cost and because users need to have the same encryption key, which creates serious security issues. Schemes based on gossip protocols [START_REF] Allard | Lightweight privacy-preserving averaging for the internet of things[END_REF] Gossip protocols are based on a communication technique that works the same way a rumor spreads. On every round each node randomly selects a node from its neighborhood to exchange information, after a sufficient number of rounds, the result of each node converges to the final result. Gossip protocols scale well but are not generic in terms of possible computations, which make them unsuitable for our case.

OUR APPROACH

We propose a protocol for secure distributed computations based on Trusted Execution Environments (TEE). A TEE is a secure part of the processor, which guarantees confidentiality by providing isolated enclaves and integrity provided by attestation mechanisms 1 . Code executed inside a TEE is protected against all elements outside it, including the operating system. Several vendors propose their own Trusted Execution Environment : Platform Security Processor for AMD , TrustZone for ARM and Software Guard Extensions for Intel, the latter one will be used for the implementation and evaluation of our protocol. To be usable in our protocol a TEE must be able to do Attested Computation. Our architecture is composed of a querier and several users who agree to contribute to the computation. They are all equipped with a TEE. The use of TEE increases the cost of an attack while distributing the computations over plenty of nodes decreases the benefits of attacking a single computation node. Threat model. The threat model in our context is different from SMC one. In SMC, the adversary is honest-but-curious. But in our context, data involved in the computation is stored and managed inside an isolated enclave. This makes the computation node honest even in the presence of curious or malicious PDMS owner.

Figure 1: overview of the architecture

The first step in our study was to identify and propose a welladapted threat model. We consider two different ones (1) honest computation node held by honest-but-curious participants and/or querier who may try to infer some information without breaking the security of the TEE and (2) malicious participants and/or querier who may perform a side channel attack (e.g., cache attack using technique presented in [START_REF] Götzfried | Cache attacks on Intel SGX[END_REF]) to retrieve some information from the TEE. They may also either participate to the computation with many TEEs to infer more information than they should or try to run another code then the expected one. Problem statement. Based on the previous threat model and taking advantage of the confidentiality and the integrity guarantees provided by TEEs, we propose adopting a manifest based protocol. The manifest will be used to specify how the distributed computation will unfold. The protocol should ensure that the computation is respected as described in the manifest. This is not trivial, for the following reasons: (1) Each user should have the possibility to check the global correctness of the computation from her local view (local correctness checking basis). (2) The execution should be zero knowledge. In other words, in the case of data oriented operations where the dataflow depends on the data value (e.g., hashing or sorting as part of joins), an attacker able to observe the data exchanges should not be able to infer users' personal data. (3) Finally, the protocol should be massive leak resilient. More specifically, in case of a successful side channel attack, a user or a set of colluding users, should not be able to compromise a large amount of data nor targeting a specific user. Such attacks should be taken into account by the protocol by adding again a set of countermeasures to reduce the benefit-to-cost ratio.

THE PROTOCOL

Let us take as a simple example the case of a group by computation. A naive secure execution approach based on TEEs could consist in participants sending their personal data to a single node which perform the computation. This approach is not massive leak resilient nor can it enforce a local correctness checking basis. Another approach could be participants sending their data to different nodes, where a node is in charge of computing data belonging to the same group, this obviously is not a zero knowledge execution. Our approach aims at designing a protocol that supports execution of any distributed computation, on a potentially large number of participants, while providing strong security guarantees. The protocol is organized in three phases (see Fig. 1). The first phase is to set up the environment; the querier broadcasts the function to be computed, together with the organization of the distributed computation. Users who want to participate to the computation register with the querier . When the number of participants is sufficient, the querier and participants collaborate to produce an execution table, which is a list of tasks to do for each participant (e.g. user 1 executes f 1 on user 2 data and sends her output to user 3 ). The list of participants, the topology and the execution table form a manifest. This manifest has to be public, so that everyone can verify it. Thanks to attestation, the manifest is generated with strong guarantees of integrity. In the second phase, participants establish links between them following the manifest. Users leverage attestation to prove that they are executing their assigned tasks from the manifest. Finally, the last phase is the actual computation and it depends of the algorithm implemented. This protocol provides strong integrity guarantees, as breaking integrity means compromising a tamper resistant TEE. Moreover, if a malicious participant performs a side channel attack, retrieving the content of its TEE, it only has access to a limited amount of data as prescribed by the manifest. As long as the distributed computation is organized in a sensible way, no party should have access to large amount of personal data, and the threat of large scale attacks is this mitigated. Additionally, note that all computations are done on clear data, the results produced are thus exact. Moreover, only simple cryptographic operations and bookkeeping inside TEE are required in addition to the actual computation. This allows for a limited overhead w.r.t. performing the computation in the clear between mutually trusted parties.

FURTHER WORK

As further work, we aim at designing a protocol solving the three problems defined above. In other words, a protocol giving guarantees on the global integrity of the computation while taking into account side channel attacks against TEEs2 . Moreover, the protocol should be validated for three different kinds of computation, computation with static built of the manifest, those where the manifest has to be built dynamically (group by query based on hash) and iterative computation (such as training a shared neural network).

"Attestation is the process of demonstrating that a piece of software has been properly instantiated on the platform. In Intel SGX it is the mechanism by which another party can gain confidence that the correct software is securely running within an enclave on an enabled platform"[START_REF] Anati | Innovative technology for CPU based attestation and sealing[END_REF]

In[START_REF] Van Bulck | Foreshadow: Extracting the Keys to the Intel SGX Kingdom with Transient Out-of-Order Execution[END_REF] the authors present an attack against SGX which does not rely on software vulnerability and show that they can extract full cryptographic keys from enclaves and break the confidentiality and the integrity guarantees for remote computation. An expected microcode patches from intel may give solution against this attack.