Sénadé Atsou

Célia Schellenberg

Jeremy Lagrange

Patrick Lacolley

Peter J Lenting

Cécile V Denis

Olivier D Christophe

Véronique Regnault

Thrombin generation on vascular cells in the presence of factor VIII and/or emicizumab

Running title: Thrombin generation on vascular cells

Essentials

• Thrombin generation by factor VIII and emicizumab on vascular cells was investigated

• Endothelial and smooth muscle cells support FVIII-and emicizumab-mediated thrombin generation

• Emicizumab activity is limited by an excess of factor IX when phospholipids are limiting

• Anticoagulant components play an important role in controlling FVIII and emicizumab activity

Introduction

Hemophilia A is an X-linked bleeding disorder caused by defects in the gene encoding factor VIII (FVIII), affecting 1-2 per 10,000 male births. [START_REF] Bolton-Maggs | Haemophilias A and B[END_REF] Replacement therapy using plasmaderived or recombinant FVIII-concentrates has proven to be effective in the management of bleedings in hemophilia A. [START_REF] Manco-Johnson | Prophylaxis versus episodic treatment to prevent joint disease in boys with severe hemophilia[END_REF] Nevertheless, replacement therapy is limited by the need for frequent intravenous administrations and the development of neutralizing antibodies (inhibitors) in 15-30% of the severe hemophilia A patients. [START_REF] Gouw | Factor VIII products and inhibitor development in severe hemophilia A[END_REF][START_REF] Peyvandi | A Randomized Trial of Factor VIII and Neutralizing Antibodies in Hemophilia A[END_REF] Bleeding episodes and need for surgery in inhibitor patients were traditionally managed using bypassing agents that act independently of FVIII in the coagulation cascade in order to generate thrombin. These agents include recombinant activated factor VII (rFVIIa) and activated prothrombin complex concentrate (aPCC). However, both aPCC and rFVIIa do not eliminate bleeding or successfully control acute bleeds in all patients with inhibitors. [START_REF] Ewing | Prophylaxis with FEIBA in paediatric patients with haemophilia A and inhibitors[END_REF][START_REF] Ju | The efficacy of bypassing agents in surgery of hemophilia patients with inhibitors[END_REF] To overcome these limitations, novel treatment strategies that act independently of FVIII options have been or are becoming available. Some of these are based on restoring the hemostatic balance by targeting components of the anticoagulant pathway, such as tissue factor pathway inhibitor (TFPI), activated protein C or antithrombin. [START_REF] Sehgal | An RNAi therapeutic targeting antithrombin to rebalance the coagulation system and promote hemostasis in hemophilia[END_REF][START_REF] Chowdary | Anti-tissue factor pathway inhibitor (TFPI) therapy: a novel approach to the treatment of haemophilia[END_REF][START_REF] Polderdijk | Targeting activated protein C to treat hemophilia[END_REF] Alternatively, bispecific antibodies have been developed that aim to mimic FVIII cofactor function. Examples hereof are emicizumab and Mim8. [START_REF] Kitazawa | A bispecific antibody to factors IXa and X restores factor VIII hemostatic activity in a hemophilia A model[END_REF][START_REF] Ostergaard | A factor VIIIa-mimetic bispecific antibody, Mim8, ameliorates bleeding upon severe vascular challenge in hemophilia A mice[END_REF] Emicizumab (approved for clinical use by both FDA and EMA) has shown clinical efficacy in multiple clinical trials, with significantly reduced annual bleeding rates and improved quality of life. [START_REF] Oldenburg | Emicizumab Prophylaxis in Hemophilia A with Inhibitors[END_REF][START_REF] Mahlangu | Emicizumab Prophylaxis in Patients Who Have Hemophilia A without Inhibitors[END_REF][START_REF] Pipe | Efficacy, safety, and pharmacokinetics of emicizumab prophylaxis given every 4 weeks in people with haemophilia A (HAVEN 4): a multicentre, open-label, non-randomised phase 3 study[END_REF][START_REF] Young | A multicenter, open-label phase 3 study of emicizumab prophylaxis in children with hemophilia A with inhibitors[END_REF][START_REF] Oldenburg | The effect of emicizumab prophylaxis on health-related outcomes in persons with haemophilia A with inhibitors: HAVEN 1 Study[END_REF] In vitro activities of both FVIII and emicizumab are usually determined in assays using synthetic phospholipids, such as chromogenic activity assays and thrombin generation assays. [START_REF] Lenting | Laboratory monitoring of hemophilia A treatments: new challenges[END_REF][START_REF] Peyvandi | A critical appraisal of one-stage and chromogenic assays of factor VIII activity[END_REF][START_REF] Schultz | The effect of emicizumab and bypassing agents in patients with hemophilia -An in vitro study[END_REF][START_REF] Bravo | Non-additive effect on thrombin generation when a plasma-derived factor VIII/von Willebrand factor (FVIII/VWF) is combined with emicizumab in vitro[END_REF][START_REF] Dargaud | Use of thrombin generation assay to personalize treatment of breakthrough bleeds in a patient with hemophilia and inhibitors receiving prophylaxis with emicizumab[END_REF][START_REF] Kizilocak | Comparison of bypassing agents in patients on emicizumab using global hemostasis assays[END_REF] However, emicizumab and FVIII are exposed to vascular cells within the circulation, like endothelial cells and, upon vascular breaching, smooth muscle cells. These cells display a different phospholipid signature compared to synthetic phospholipids, while also expressing both pro-and anti-coagulant proteins, including TFPI, thrombomodulin and tissue factor. In this study, we therefore aimed to explore the contribution of primary vascular arterial cells to emicizumab-and FVIII-supported thrombin generation. Our data show that both endothelial cells and vascular smooth muscle cells support FVIII-and to a lesser extent emicizumabdependent thrombin generation. Interestingly stimulation of endothelial cells by tumor necrosis factor-a (TNFa) resulted in an increase of both pro-and anti-coagulant activity, resulting in a net reduced potential to stimulate FVIII-and emicizumab-dependent thrombin generation. In all cases, combining emicizumab with aPCC resulted in exaggerated thrombin generation.

Materials and Methods

Cell culture

Primary human aortic endothelial and vascular smooth muscle cells (hAECs and hVSMCs), human umbilical vein endothelial cells (hUVECs) and human microvascular endothelial cells (hMVECs) were purchased from Lonza and grown in Endothelial Cell Growth Medium-2 BulletKit™ and SmGM™-2 Smooth Muscle Cell Growth Medium-2 BulletKit™ (Lonza, Basel, Switzerland), respectively during 3 passages. Batches of three different individuals were used in this study. Cells were used between passages 3 to 7 to reduce phenotypic drift. Cells (6,500-7,500/well) were seeded in 96-well tissue culture flat-bottom plates, (MICROTEST -96), grown to sub-confluence a day before use. We have previously established that cells seeded above 2500/well generates homogeneous thrombin generation parameters. [START_REF] Mao | Cyclic stretch-induced thrombin generation by rat vascular smooth muscle cells is mediated by the integrin alphavbeta3 pathway[END_REF] Cells were washed with 20 mM HEPES, 140 mM NaCl, pH 7.35 containing 5 mg/mL albumin (HBS-buffer) before use.

In some experiments, hAECs were activated by incubating with 5 nM TNF-alpha in growth medium for 4 hours before use.

Flow cytometry

Cells were harvested with trypsin-EDTA and then incubated 1h with an anti-Endothelial Protein C receptor (EPCR) antibody (cat # 563624; BD Biosciences), an anti-thrombomodulin antibody (cat # MAB3947; R&D Systems) or an anti-tissue factor pathway inhibitor (TFPI) antibody (cat Ab260041; Abcam) in PBS/BSA 1%. After washing, cells were resuspended in PBS/BSA1% and measurement was performed with Celesta Sorp flow cytometer (BD Biosciences). Cells (10,000) were routinely counted, and cell population was defined based on forward-side scatter characteristics. Data were analyzed with the Kaluza analysis 2.1 software. Non-labelled cells were used as negative controls

Antigen and activity assays

Tissue factor (TF) and tissue factor pathway inhibitor (TFPI) activities were measured in 200 μL HBS incubated for 1 h at room temperature with hAECs or hVSMCs using the Actichrome-TF and Actichrome-TFPI activity assay respectively (American Diagnostica, Stamford, CT). To measure cell surface TF or TFPI activity, washed adherent cells were overlaid with HBS-buffer.

The reaction was stopped with glacial acetic acid and the absorbance read at 405 nm.

The chromogenic assay measuring the phosphatidylserine (PS)-equivalent in hAECs and hVSMCs was performed as described previously for VSMCs. Briefly, washed adherent cells were incubated with 50 µl of 20 mM HEPES, pH 7.35 containing 60 mg/mL bovine serum albumin (BSA), 50 µL of FXa-FVa-CaCl2 and 50 µL of bovine prothrombin (6 µM) plus Z-Gly-Gly-Arg-AMC substrate (1.25 mM) in 20 mM HEPES pH 7.35 containing 60 mg/mL BSA. The plate was placed in the Fluoroskan Ascent fluorometer and allowed to warm to 37°C for 5 min before kinetic readings were taken over 10 min. Phospholipid concentration was estimated from the initial rate of thrombin formation by reference to a standard curve constructed with a mixture of phosphatidylserine (PS), phosphatidylethanolamine (PE) and phosphatidylcholine (PC) (20:20:60 mol%), and expressed as PS equivalents.

The Quantikine Human Thrombomodulin Immunoassay (cat # BDCA-3; R&D Systems) was used to measure human Thrombomodulin in cell culture lysates as instructed.

Thrombin generation

Lyophilized FVIII deficient plasma (SYSMEX/HYPHEN Biomed) was reconstituted with distilled water and kept for 30 min at room temperature.

Thrombin generation was essentially performed as described by Hemker et al. [START_REF] Hemker | The calibrated automated thrombogram (CAT): a universal routine test for hyper-and hypocoagulability[END_REF] In brief, 20 µl of 20 mM Hepes (pH 7.4)/140 mM NaCl/5 mg/ml bovine serum albumin (HBS-BSA) and 80 µl FVIII-deficient plasma, alone or supplemented with FVIII (0.25-1.5 U/ml), emicizumab (10-80 µg/ml) or aPCC (1 U/ml) was added to wells (polypropylene 96-well microtiter plates; Nunc, Thermo Fischer Scientific) containing non-stimulated hAECs, TNFa-stimulated hAECs or hVSMCs previously washed with HBS-BSA. Cell-counts were between 10,000 and 11,000 hVSMCs/well and between 8,000 and 9,000 hAECs/well. After incubation for 5 min at 37°C, thrombin generation was initiated by the addition of 20 µl pre-warmed Fluo-substrate (20 mM Hepes (pH7.4)/0.1 M Z-Gly-Gly-Arg-AMC/2.5 mM CaCl2/60 mg/ml BSA). Thrombin generation curves were recorded continuously with a microtiter-plate fluorometer (Fluoroskan Ascent, Thermo Labsystems, Helsinki, Finland) under control of Thrombinoscope software (Thrombinoscope BV, Maastricht, The Netherlands), filtered for excitation at 390 nm and emission at 460 nm. A calibrator assay was done using FVIII deficient plasma included on wells with a 20-µl solution that contained a known concentration of thrombin-α2-macroglobulin complex (thrombin calibrator, Stago, France). In total, four to six experiments were performed in duplicate at three different dates (with 1-2 experiments/day) for each cell-type. Control experiments using normal pooled plasma were performed to establish reproducibility of the cell-based thrombin generation assay. Intra-assay coefficients of variability (CV) for hVSMCs based on 30 values were 6.1%, 2.5%, 6.4% and 5.5% for lag-time, endogenous thrombin potential (ETP), peak height and time to peak, respectively. Inter-assay CV for hVSMCs based on 35 values were 13.0%, 8.6%, 10.8% and 7.9% for lag-time, endogenous thrombin potential (ETP), peak height and time to peak, respectively. Intra-assay coefficients of variability (CV) for hAECs based on 30 values were 5.8%, 7.6%, 8.1% and 6.0% for lag-time, endogenous thrombin potential (ETP), peak height and time to peak, respectively. Inter-assay CV for hAECs based on 35 values were 10.3%, 9.9%, 13.7% and 11.8% for lag-time, endogenous thrombin potential (ETP), peak height and time to peak, respectively.

FX activation

Phospholipid vesicles (60% phosphatidylcholine, 20% phosphatidylserine, 20% phosphatidylethanolamine) were incubated in 25 mM Hepes pH 7.2, 120 mM NaCl, 2.5 mM CaCl2, 0.1% BSA with FIXa in the absence or presence of FIX for 10 min at 37°C in 60% of the final volume. We then added FVIII in the presence of thrombin or emicizumab. After 1 min, FXa generation was initiated by the addition of the substrate FX and hirudin (to inactivate thrombin). At this point, volume was at 100% for all incubations, with the final concentrations being: phospholipids 50 nM or 1 µM, 9 nM FIXa, 90 nM FIX, 0.1 nM FVIII, 5 nM thrombin, 50 µg/ml emicizumab, 120 nM FX and 2 U/ml hirudin. At various times after initiation, samples were taken and FXa generation was quenched by the addition of EDTA (10 mM), and FXa concentrations were determined using the synthetic substrate pNAPEP-1065. An active-site titrated FXa preparation was used to relate substrate hydrolysis to FXa concentrations.

Results

Characterization of vascular cells

Two types of human cells of aortic origin were used in this study: endothelial cells (hAECs) and vascular smooth muscle cells (hVSMCs). Flow cytometric analysis showed that hAECS were positive for thrombomodulin, TFPI and EPCR, whereas hVSMCs only proved positive for EPCR (Fig. 1). Quantitative analysis further revealed that hVSMCs displayed about 10-fold more TF antigen than hAECs (1.1±0.12 µg/mg cell protein versus 0.13±0.04 µg/mg cell protein), whereas TF activity was approximately 2-fold higher in hVSMCs compared to hAECs (19±3 pM vs 8±1 pM; Table 1). Both cell types expressed similar levels of phosphatidylserine (PS)-equivalent (34±7 nM vs 53±20 nM; Table 1). With regard to anti-coagulant proteins, hVSMCs exposed low levels of thrombomodulin and TFPI just above the limit of detection (1±1 ng/mg cell protein and 0.04±0.01 µg/mg cell protein), much less than in hAECs (9±1 ng/mg cell protein and 0.31±0.04 µg/mg cell protein, respectively; Table 1).

A stimulation of hAECs by TNFa (5 nM; 4 hours) resulted in an 11-fold increase in TF antigen (from 0.13±0.04 µg/mg cell protein to 1.4±0.1 µg/mg cell protein), with a relative minor increase in TF activity being noted (10±2 pM). Furthermore, a 4-fold increase in PS-equivalent (197±99 nM) was measured. Perhaps unexpectedly, an increase in thrombomodulin and TFPI expression was also observed (16±1 ng/mg cell protein and 0.47±0.04 µg/mg cell protein, respectively). These data suggest that the pro-and anticoagulant balance in hAECs remains seemingly unchanged upon stimulation by TNFa. Furthermore, hVSMCs display a more procoagulant profile compared to hAECs, due to a lack of anticoagulant components thrombomodulin and TFPI.

Thrombin generation on vascular cells in FVIII-deficient plasma

To investigate the effect of FVIII concentrations on thrombin generation at the surface of vascular cells, FVIII-deficient plasma was spiked with different concentrations of recombinant FVIII. No external phospholipids, TF or FXIa were added to the reactions, which were therefore dependent on the amounts of TF and phospholipids exposed by the cells. Thrombin generation was first determined in FVIII-deficient plasma alone to establish background values. In the absence of any addition, minimal amounts of thrombin were generated when using hAECS or TNFa-stimulated hAECs, even when this was slightly increased in the stimulated cells (Fig. 2A-B). ETP values were 35±9 nM•min and 120±45 nM•min for hAECS and TNFa-stimulated hAECs, respectively (see Table 2). At the surface of hVSMCs, thrombin generation was significantly higher (ETP 768±70 nM•min; Table 2; Fig. 2C), in keeping with the more procoagulant nature of these cells.

Thrombin generation on vascular cells in the presence of FVIII

The addition of FVIII resulted in a dose-dependent increase in thrombin generation (Fig. 2A-C). Thrombin generation-related parameters (lag-time, thrombin peak and ETP) changed in a dose-dependent manner for all three cell-types (p-trend <0.05; Fig. 2D-L; summarized in Table 2). Between the lowest and highest concentration of FVIII tested (0.25 and 1.5 U/ml), the ETP increased from 1022±19 to 1475±112 nM•min on hAECs, from 574±71 to 1166±247 nM•min on TNFa-stimulated hAECs, and from 1079±65 to 1287±55 nM•min on hVSMCs. Thus, the extent of thrombin generation was dependent on the amount of FVIII for each of the cell-types investigated.

Thrombin generation on vascular cells in the presence of emicizumab

In a next series of experiments, FVIII-deficient plasma was spiked with emicizumab (10-80 µg/ml), knowing that a concentration of 50 µg/ml represents the average therapeutic emicizumab level. The presence of 10 µg/ml emicizumab did not increase thrombin generation above the levels of FVIII-deficient plasma when tested in TNF-stimulated hAECs (Fig. 3B).

Concentrations of 25, 50 and 80 µg/ml increased thrombin generation for all three cell types.

Interestingly, the largest increase in thrombin generation was observed for non-stimulated hAECs, increasing ETP from 35±9 nM•min to 686±195 nM•min for emicizumab at 50 µg/ml (Fig. 3A; Table 3). Increased thrombin generation was also observed for TNFa-simulated hAECs in the presence of 50 µg/ml emicizumab, albeit to a lesser extent (ETP: from 120±45 nM•min to 262±59 nM•min). When added to FVIII-deficient plasma exposed on hVSMCs, emicizumab induced a less pronounced increase in thrombin generation as compared to the endothelial cells, although the absolute ETP was higher than for both other conditions. For example, the ETP increased from 768±70 nM•min to 900±38 nM•min at 50 µg/ml emicizumab (Table 3). Together, this shows that, emicizumab is less efficient in comparison to FVIII in promoting thrombin generation at the surface of vascular cells. Nevertheless, it shares with FVIII that its capacity to enhance thrombin generation is dependent on cell type.

Effect of FIX on FIXa-mediated FXa generation

The PS-equivalent on hVSMCs and hAECs is lower compared to the PS-equivalent used in traditional thrombin generation assays (30-200 nM versus 1.6 µM). We tested therefore if the limiting phospholipid-surface affects FXa-generation by FIXa/FVIIIa or FIXa/emicizumab in the absence or presence of FIX using purified proteins. With regard to the FIXa/FVIIIa complex, FXa generation was unaffected by the presence of FIX, irrespective whether a low or high PSequivalent was used (Fig. 4). In contrast, when FIXa was combined with emicizumab, it appeared that FXa generation was more efficient in the absence compared to the presence of exaggerated thrombin generation, and that this process may also occur at the surface of vascular cells.

Discussion

We have analyzed the capacity of human aortic vascular cells (smooth muscle cells (hVSMCs) and endothelial cells (hAECs)) to support thrombin generation in the presence of FVIII and/or emicizumab. We observed that independent of the cell type analyzed, low concentrations of FVIII (0.25 U/ml) are more efficient than emicizumab to enhance thrombin generation. Adding emicizumab to FVIII at physiological concentrations (1 U/ml) does not seem to further increase thrombin generation. However, combining emicizumab with aPCC resulted in markedly increased thrombin generation, similar as what has previously been observed when using synthetic phospholipid vesicles.

For this study, primary cells were used originating from the aorta, isolated from at least three different individuals. Characterization of the hAECs and hVSMCs revealed a clear difference in balance between pro-and anti-coagulant proteins, with TFPI and thrombomodulin being virtually absent in hVSMCs. The lack of anticoagulant potential was visible when comparing the background thrombin generation using FVIII-deficient plasma: the ETP was 20-fold higher in hVSMCs compared to hAECs. These data are illustrative for the interest of exploring cellbased thrombin generation assays compared to the standard assays that use synthetic phospholipids. The extent of phospholipid-exposure and the absence or presence of pro-and anticoagulant cellular components may modulate FVIII-and emicizumab-dependent thrombin generation. This was particularly apparent when testing similar TF concentrations (10 pM) in combination with synthetic phospholipids. FVIII-deficient plasma, FVIII (0.25 or 1 U/ml) and emicizumab all generated similar amounts of thrombin (Supplementary Table S3). Indeed, there is sufficient TF/FVIIa complex to bypass FIXa-dependent FX activation under these conditions and cellular anticoagulant components are absent to dampen this process.

Together, these data provide insight into how local conditions (the balance between pro-and anti-coagulant components) within the vascular tree are of relevance to control thrombin generation TNFa-mediated stimulation of hAECs resulted in a 15-fold increase in TF antigen and a 1.8fold increase in PS-exposure. Nevertheless, thrombin generation remained very low in FVIIIdeficient plasma, with peak levels being 3±1 nM and 4±1 nM for non-stimulated and TNFastimulated hAECs, respectively. In the absence of FVIII or emicizumab, a minor increase in ETP for the stimulated cells was observed, which is most likely due to the increased phospholipid-exposure. Increased phospholipid-exposure also allowed for a more sensitive response to different doses of FVIII. In non-stimulated hAECs (53±20 nM PS-equivalent), no significant difference in thrombin generation parameters were observed between 0.25 and 1.0 U/ml. In contrast, a significant difference in peak height (p=0.006), ETP (p=0.046 and time to peak (p=0.0013) was observed for TNFa-stimulated hAECs.

Unexpectedly, when FVIII-deficient plasma was spiked with FVIII or emicizumab, thrombin generation on TNF-a-stimulated hAECs was consistently lower compared to non-stimulated hAECs. A potential explanation is that despite the 15-fold increase in TF antigen, TF activity was only minorly increased, from 8 to 10 pM. Indeed, TF can exist in an active or a cryptic nonfunctional form, and it has been reported that the majority of the TF exposed at the cellular surface is in its cryptic conformation. [START_REF] Rao | Tissue factor encryption and decryption: facts and controversies[END_REF] It seems conceivable that the majority of the newly synthesized TF is in its cryptic conformation and does not contribute to coagulation. A second, not mutually exclusive explanation is that the increased pro-coagulant potential is compensated by the increased anti-coagulant potential by virtue of increased TFPI and thrombomodulin levels. In particular, the increased TFPI availability may interfere with FVIIa and FXa activity on the TNFa-stimulated hAECs. It is tempting to speculate that the increased anti-coagulant potential may exist to avoid exaggerated coagulation to occur under conditions of inflammation.

An intriguing question that came up during the study was whether or not the use aortic endothelial cells would be representative for other endothelial cell types. In particular, expression of thrombomodulin may differ between tissues, as for instance its expression is particular limited in brain tissue. [START_REF] Maruyama | Thrombomodulin is found on endothelium of arteries, veins, capillaries, and lymphatics, and on syncytiotrophoblast of human placenta[END_REF] However, when testing additional endothelial cell types (hUVECs and hMVECs), we observed that not only thrombomodulin levels, but also TFPI, TF and phosphatidyl-serine exposure was similar to those of hAECs. The thrombomodulin levels being similar is in keeping with a previous report showing that thrombomodulin expression is not controlled by vessel type, but rather that thrombomodulin expression is highest on continuous endothelium and reduced on fenestrated or sinusoidal endothelium. [START_REF] Ford | Thrombomodulin is preferentially expressed in Balb/c lung microvessels[END_REF] In addition, similar thrombin generation data were observed by using these cells. This suggests that our observations seem to be representative for a large portion of the endothelial cell population throughout the vascular tree. Under all conditions tested, emicizumab promoted significantly lower thrombin generation than FVIII (25%-150% rFVIII), whether it be on hVSMCs or hAECs (Supplementary Table S2). This seems in contrast to results obtained using classic thrombin generation assays using synthetic phospholipids, in which the addition of emicizumab to hemophilia A plasma nearly or completely normalizes the ETP. [START_REF] Bravo | Non-additive effect on thrombin generation when a plasma-derived factor VIII/von Willebrand factor (FVIII/VWF) is combined with emicizumab in vitro[END_REF][START_REF] Dargaud | Use of thrombin generation assay to personalize treatment of breakthrough bleeds in a patient with hemophilia and inhibitors receiving prophylaxis with emicizumab[END_REF] Classic thrombin generation assays differ from cell-based thrombin generation assays by the absence of cellular components (cell-derived TFPI and thrombomodulin) and the different concentrations of TF and/or factor XIa that are used to trigger thrombin generation. It is further important to mention that the PS-equivalent on the vascular cells used in this study is markedly lower compared to regular thrombin generation assays: 30-200 nM versus 1.6 µM, suggesting that the phospholipid-surface may become a limiting factor in the formation of the enzyme/substrate complex. Indeed, levels of FIX will exceed those of FIXa (probably in a 10:1 ratio, with FIX levels being 80-100 nM), and the affinities of both for PS-containing phospholipids are 15-20 nM. [START_REF] Mertens | Binding of human bloodcoagulation Factors IXa and X to phospholipid membranes[END_REF][START_REF] Panteleev | Factor VIIIa regulates substrate delivery to the intrinsic factor X-activating complex[END_REF] It is likely that FIX rather than FIXa will occupy most of the available binding sites in the absence of FVIIIa. In contrast, FIXa binds with higher affinity (about 2 nM) in the presence of FVIIIa (which itself binds phospholipids with an affinity of <1 nM), and will display preferential binding over FIX. In addition, the presence of both FVIIIa and FIXa reduces the affinity of FX for phospholipids about 10-fold. [START_REF] Panteleev | Factor VIIIa regulates substrate delivery to the intrinsic factor X-activating complex[END_REF] Emicizumab differs from FVIIIa in that it will not enhance binding of FIXa over FIX to the limited phospholipid-surface, which will therefore result in less efficient FXa generation compared to what is seen in traditional thrombin generation assays. This explanation is supported by our experiments using purified proteins (Figure 5). At low PSequivalent (50 nM), FIX reduced the efficiency of FIXa/emicizumab-mediated FXa generation but not that of FIXa/FVIIIa-mediated FXa generation. At high PS-equivalent (1 µM), the presence of FIX did not affect FXa generation by either complex. Similar observations were made when we analyzed thrombin generation under conditions of low and high PS-equivalent (Supplementary table S3).

Several studies have evaluated the effect of aPCC on thrombin generation in the presence of emicizumab. [START_REF] Schultz | The effect of emicizumab and bypassing agents in patients with hemophilia -An in vitro study[END_REF][START_REF] Bravo | Non-additive effect on thrombin generation when a plasma-derived factor VIII/von Willebrand factor (FVIII/VWF) is combined with emicizumab in vitro[END_REF][START_REF] Dargaud | Use of thrombin generation assay to personalize treatment of breakthrough bleeds in a patient with hemophilia and inhibitors receiving prophylaxis with emicizumab[END_REF][START_REF] Kizilocak | Comparison of bypassing agents in patients on emicizumab using global hemostasis assays[END_REF][START_REF] Meyer | Analyses of thrombi in acute ischemic stroke: A consensus statement on current knowledge and future directions[END_REF] Consistent findings in these studies is the exaggerated thrombin formation when combining emicizumab and aPCC. A similar synergistic effect of aPCC and emicizumab has also been observed in our study. The mechanism by which aPCC enhances emicizumabmediated thrombin formation could be multiple: First, increased concentrations of the substrate of the prothrombinase-complex, i.e. prothrombin, promote thrombin generation. [START_REF] Allen | Impact of procoagulant concentration on rate, peak and total thrombin generation in a model system[END_REF] Second, by increasing concentrations of FIX and FX, more ternary complex with emicizumab can be formed. [START_REF] Kitazawa | Factor VIIIa-mimetic cofactor activity of a bispecific antibody to factors IX/IXa and X/Xa, emicizumab, depends on its ability to bridge the antigens[END_REF] Third, aPCC contains substantial concentrations of FIXa, which will also result in higher concentrations of the active ternary complex. One question that is of course relevant to address is whether such synergistic thrombin generation also occurs when combining aPCC and emicizumab in vivo. Recently, Kizilocak and colleagues administered aPCC (up to 75 U/kg) to hemophilia A patients who were treated with emicizumab. Twenty minutes after infusion, blood samples were taken, and plasma samples were analyzed for thrombin generation. In none of the samples tested, exaggerated thrombin generation was observed, in contrast to samples from the same patients that were spiked with aPCC in vitro. [START_REF] Harkins Druzgal | Neutralizing antidrug antibody to emicizumab in a patient with severe hemophilia A with inhibitors: New case with detailed laboratory evaluation[END_REF] This can potentially be explained by the rapid elimination of FIXa when infused into the circulation. [START_REF] Fuchs | Regulation of factor IXa in vitro in human and mouse plasma and in vivo in the mouse. Role of the endothelium and the plasma proteinase inhibitors[END_REF] Not only is FIXa rapidly inhibited by antithrombin, but both the FIXa/antithrombin complex and free FIXa are ligands for the clearance-receptor LRP1. [START_REF] Neels | Activation of factor IX zymogen results in exposure of a binding site for low-density lipoprotein receptor-related protein[END_REF] If the FIXa component of aPCC is rapidly cleared, how then to explain the development of thrombotic microangiopathy in patients that received aPCC in combination with emicizumab? [START_REF] Oldenburg | Emicizumab Prophylaxis in Hemophilia A with Inhibitors[END_REF] An important difference between the Haven-1 study (in which those complications were first described) and the study by Kizilocak et al., is that the patients who developed thrombotic microangiopathy not only received higher doses of aPCC (100 U/kg) but also multiple doses over a 24h-period. [START_REF] Oldenburg | Emicizumab Prophylaxis in Hemophilia A with Inhibitors[END_REF] This may have resulted in an accumulation of FIXa. It should also be noted that not all patients developed such complications, suggesting that perhaps other factors have played a role. In our study, we observed that emicizumab-mediated thrombin generation in the presence of aPCC was particularly amplified when using TNFa-stimulated hAECs (10-fold) compared to non-stimulated hAECs and hVSMCs (both 3-fold). It is possible therefore that an inflammatory status of endothelial cells could have contributed to the amplifying effect of aPCC when added to emicizumab.

A limitation of our study is that we have not investigated the role of another anticoagulant component in this study, i.e. heparan sulphate proteoglycans, which may promote antithrombin-mediated inhibition of FIXa, FXa and thrombin. The presence of these molecules may differ between cell types, and thereby their capacity to inhibit the activity of these proteases.

In conclusion, by testing thrombin generation on primary vascular cells, we have found that hAECs that line the aortic wall display a low procoagulant potential, mainly due to the presence of sufficient anticoagulant components, like thrombomodulin and TFPI. This is in line with previous findings that the FIXa/FVIIIa complex plays a little, if any, role in the basal activation of coagulation in vivo, but is relevant for thrombin generation upon injury. [START_REF] Bauer | Factor IXa-factor VIIIa-cell surface complex does not contribute to the basal activation of the coagulation mechanism in vivo[END_REF] Furthermore, we show that emicizumab shows lower procoagulant activity compared to FVIII on non-stimulatedand TNFa-stimulated hAECs as well as on hVSMCs. Vascular cells (hAECs, TNFa-stimulated hAECs and hVSMCs) were incubated with FVIIIdeficient plasma (black lines) supplemented or not with various concentrations of recombinant full-length FVIII (Pink: 0.25 U/ml; Green: 0.5 U/ml; Blue: 1.0 U/ml and Red: 1.5 U/ml) for 5 min before initiation of thrombin generation. Thrombin generation was initiated by the addition of CaCl2, without any other activating agents. Panels A-C depict representative thrombograms for each of the conditions tested. Panels D-F show the calculated lag-times, panels G-I the calculated thrombin peak and panels J-L the endogenous thrombin potential (ETP). P-trend was calculate using a one-way ANOVA test with trend analysis. Vascular cells (hAECs, TNFa-stimulated hAECs and hVSMCs) were incubated with FVIIIdeficient plasma (black lines) supplemented or not with various concentrations of emicizumab (Pink: 10 µg/ml; Green: 25 µg/ml; Blue: 50 µg/ml and Red: 80 µg/ml) for 5 min before initiation of thrombin generation. Thrombin generation was initiated by the addition of CaCl2, without any other activating agents. Panels A-C depict representative thrombograms for each of the conditions tested. Panels D-F show the calculated lag-times, panels G-I the calculated thrombin peak and panels J-L the endogenous thrombin potential (ETP). P-trend was calculate using a one-way ANOVA test with trend analysis. Data for FVIII-deficient plasma are similar to those presented in Figure 2.

Figure 1 :

 1 Figure 1: Cell-surface expression of TFPI, thrombomodulin and EPCR on hAECs and hVSMCs. Cell-surface expression of Tissue Factor Pathway Inhibitor (TFPI), Thrombomodulin (TM) and Endothelial Protein C-Receptor (EPCR) on non-stimulated human aortic endothelial cells (hAECs) and human aortic vascular smooth muscle cells (hVSMCs) was determined by flow cytometry. Shown are representative flow cytograms of 3-5 analyses. Red cytograms represent cells incubated with isotype-control antibodies, and blue cytograms represent cells incubated with TFPI-, TM-or EPCR-specific antibodies.

Figure 2 :

 2 Figure 2: Thrombin generation in the presence of FVIII.

Figure 3 :

 3 Figure 3: Thrombin generation in the presence of emicizumab.

Figure 4 :

 4 Figure 4: FXa generation by FIXa/FVIIIa and FIXa/emicizumab in the absence or presence of FIX FX (120 nM) was activated by FIXa (9 nM) in the presence of FVIIIa (0.1 nM; panels A & B) or emicizumab (50 µg/ml; panels C & D). Mixtures contained phospholipids (PS-equivalent 50 nM

Figure 5 :

 5 Figure 5: Thrombin generation in the presence of emicizumab in combination with FVIII or aPCCVascular cells (hAECs, TNFa-stimulated hAECs and hVSMCs) were incubated with FVIIIdeficient plasma (black lines) supplemented or not with emicizumab (Green: 50 µg/ml), FVIII (Red: 1.0 U/ml), aPCC (Red: 1 U/ml) or with a combination of emicizumab with FVIII (Blue: 50 µg/ml & 1.0 U/ml) or emicizumab with aPCC (Blue: 50 µg/ml & 1.0 U/ml). Data for FVIIIdeficient plasma, emicizumab and FVIII were taken from figures 2 & 3.

  Figure 1 Atsou et al

  Figure 2 Atsou et al

Table 1 : Expression of pro-and anticoagulant proteins in different cell types

 1

			hAECs
	hVSMCs	Non-stimulated	TNFa-stimulated	hUVECs	hMVECs

hAECs: human aortic endothelial cells; hVSMCs: human aortic vascular smooth muscle cells; hUVECs: human umbilical endothelial cells; hMVECs: human dermal microvascular endothelial cells; TF: tissue factor; PS-exposure: phosphatidylserine-exposure; TFPI: tissue factor pathway inhibitor. N represents number of independent wells have been analyzed for each of the components.

Table 3 : Summary of thrombin generation parameters in FVIII-deficient plasma spiked with Emicizumab ± FVIII or aPCC.

 3

	hAECs

Funding: This study received funding from Institut Roche (Boulogne-Bilancourt, France).

Acknowledgements:

The authors thank Mrs Huguette Louis & Cindy Lerignon for expert technical assistance. We thank the Flow Cytometry Core facility of UMS2008/US40 IBSLor (Université de Lorraine-CNRS-Inserm) for assistance in flow cytometric experiments.

Data analysis

All data were presented as mean ± standard deviation (SD) unless stated otherwise.

The statistical analyses were performed using Prism-9 for MacOS (Graphpad Software; San Diego, USA) as specified in the legends.

FIX (1.0±0.2 nM/min vs 2.2±0.5 nM/min; p<0.0001; Figure 5). This inhibitory effect of FIX was elevated when using 1 µM PS-equivalent (33±8 nM/min vs 32±4 nM/min; p=0.73). Apparently, under conditions where phospholipids are limiting, the presence of FIX reduces the efficiency by which the FIXa/emicizumab complex is able to generate FXa.

Thrombin generation on different endothelial cells

Since endothelial cells may vary in phenotype, we tested thrombin generation also using two other endothelial cells: hUVECs and hMVECs. Levels of thrombomodulin, TFPI, EPCR, TF activity, TF antigen and PS-equivalent were similar as for the unstimulated hAECs (Table 1; Supplementary Figure S1). In addition, thrombin generation was in the same order of magnitude for these cells, irrespective whether FVIII (0.25 or 1.0 U/ml) or emicizumab (50 µg/ml) was used (Supplementary Table S1). This suggests that the data obtained using hAECS might be extrapolated to various other types of endothelial cells.

Thrombin generation on vascular cells in the presence of both FVIII and emicizumab

We next investigated the effect of combined FVIII and emicizumab on thrombin generation using the same three cell-types. FVIII-deficient plasma spiked with both FVIII (1.0 U/ml) and emicizumab (50 µg/ml) generated thrombograms that were similar to those of FVIII alone, irrespective of the cell types on which thrombin generation was analyzed (Fig. 5; Table 3; Supplementary Table 1). Apparently, the contribution of emicizumab to thrombin generation in the presence of physiological FVIII concentrations is limited, if present at all under these conditions.

Thrombin generation of vascular cells in the presence of emicizumab and aPCC

Based on previous findings that combining emicizumab and aPCC have a synergistic effect on thrombin generation when using synthetic phospholipids [START_REF] Hartmann | In vitro studies show synergistic effects of a procoagulant bispecific antibody and bypassing agents[END_REF] , it was of interest to evaluate their combination on vascular cells as well. The addition of aPCC alone (1 U/ml) increased thrombin generation on non-stimulated and TNFa-stimulated hAECs (ETP: from 35±9 nM•min and 120±45 nM•min to 575±36 nM•min and 794±108 nM•min, respectively; Fig. 5; Table 3; Supplementary Table 1). On hVSMCs, the addition of aPCC resulted in a minor increase in thrombin generation (ETP: from 768±70 nM•min to 845±70 nM•min; Fig. 5; Table 3). However, combining aPCC (1 U/ml) with emicizumab (50 µg/ml) resulted in a massive increase in thrombin generation on each of these three cell types. ETP values were 2087±332 nM•min, 2704±135 nM•min and 2623±39 nM•min for hAECs, TNFa-stimulated hAECs and hVSMCs, respectively. These data confirm that the combination of aPCC and emicizumab provokes


Abdenour Soualhi

Maawad Makdessi

Ronan German

Francklin Rivas

Hubert Razik

Ali Sari

Pascal Venet

Guy Clerc

Heath Monitoring of Capacitors and Supercapacitors Using Neo Fuzzy Neural Approach

Keywords: prognosis, ageing, capacitor, supercapacitor, artificial neural network, fuzzy logic, time series prediction, health monitoring, parameter estimation

come

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I. INTRODUCTION

Currently, most of transportation systems contain embedded electronics equipment providing various functions (conversion, energy storage, control, etc.) [START_REF] Yhua | Split Converter-Fed SRM Drive for Flexible Charging in EV/HEV Applications[END_REF]- [START_REF] Bojoi | Control of Shaft-Line-Embedded Multiphase Starter/Generator for Aero-Engine[END_REF]. For an increased lifetime expectation and safety of these components, strong efforts have therefore been devoted to improve reliability of power electronic systems with cost-effective and sustainable solutions [START_REF] Shibuya | Designing Methods of Capacitance and Control System for a Diesel Engine and EDLC Hybrid Powered Railway Traction System[END_REF]- [START_REF] German | Prediction of supercapacitors floating ageing with surface electrode interface based ageing law[END_REF].

Condition monitoring and health management present fundamental ways to improve the lifetime expectation of power devices. In this paper, we focus our study on the health monitoring of energy storage systems (ESS), particularly on metallized polymer film (MPF) capacitors and supercapacitors (SCs). The reliability of these components is a major issue since chemical solvents (such as acetonitrile, which is classified as hazardous) used for SCs and acetylene (noxious gases) for MPF capacitors may be released in the case of breakdown. Thus, the degradation of (ESS) performance must be monitored in order to avoid power breakdown or system malfunctioning.

SCs [START_REF] Hammar | Study of Accelerated Aging of Supercapacitors for Transport Applications[END_REF] are intermediate components between batteries (used for their very high energy density) and capacitors (mostly used for high frequency filtering). These components, also called ultracapacitors or electrochemical double layer capacitors, use an electrostatic mode to store energy (double layer effect). SCs present higher cyclability and higher specific power than other ESS based on electrochemical transformation such as batteries [START_REF] Schaltz | Influence of Battery/Ultracapacitor Energy-Storage Sizing on Battery Lifetime in a Fuel Cell Hybrid Electric Vehicle[END_REF]; which is why SCs are appreciated in applications requiring a short duration power boost, such as regeneration of braking energy or stop and start systems.

MPF capacitors, on the other hand, present higher power density but lower energy density than SCs. Such components offer great advantages compared to other capacitor technologies, since they have the ability to self-heal. Indeed, thanks to this feature, MPF capacitors tend to generally fail within an open-circuit failure mode (gradual loss of electrode surface) rather than in a short-circuit one. MPF capacitors are also known for their low dissipation factor and high dielectric stability with frequency and temperature, which are important factors for filtering, power factor correction, and high temperature applications.

Accelerated ageing tests conducted on both capacitors and SCs showed that most of their failure modes can be monitored by the evolution of their precursor parameters of equivalent series resistance (ESR) and capacitance (C) [START_REF] Ahmad | An online technique for condition monitoring of capacitor in PV system[END_REF]- [START_REF] Amaral | A Simple Offline Technique for Evaluating the Condition of Aluminum-Electrolytic-Capacitors[END_REF]. Thus, an effective and reliable monitoring method must be based on the double estimation and/or prediction of these electrical parameters.

Even though failure modes and failure mechanisms are well known for a component, their estimation/prediction remains difficult to obtain, especially when electrical and environmental stresses are combined together. These constraints require the use of suitable diagnostic or prognostic methods to analyze the C and ESR in order to improve the health monitoring of SCs and MPF capacitors.

The objective of this paper is to limit such drawbacks and to show that with the same model (MPF capacitors and SC in our case), it is possible to detect potential deterioration drifts of different energy storage devices

II. CHOICE OF A HEALTH MONITORING METHOD

Model-based (or physics-based) methods and data-driven methods are often used to monitor ESS degradation [START_REF] Lawder | Battery Energy Storage System (BESS) and Battery Management System (BMS) for Grid-Scale Applications[END_REF]- [START_REF] German | Novel Experimental Identification Method for a Supercapacitor Multipore Model in Order to Monitor the State of Health[END_REF]. The model-based method uses an analytical model to estimate and predict electrical parameters of components, while the data-driven method does not require a physical modeling of the components and aims to model the relationship between the measured data and the component degradation. The choice of a method is based on the complexity of the studied component and also on the availability of information about the component. Research conducted by [START_REF] Venkat | A review of process fault detection and diagnosis: Part iii: Process history based methods[END_REF] allowed extracting a comparison between these methods. The obtained Abdenour Soualhi, Maawad Makdessi, Ronan German, Francklin Rivas, Hubert Razik, Senior Member, IEEE, Ali Sari, Pascal Venet, Senior Member, IEEE, Guy Clerc, Senior Member, IEEE.

Heath Monitoring of Capacitors and Supercapacitors

Using Neo-Fuzzy Neural Approach results led to favor in our case the data-driven method; although this mainly depends on the application. From literature, artificial intelligence is the most popular data-driven method used for health monitoring. More specifically, artificial neural networks (ANNs) appear as a reliable technology for diagnosis and prognosis. Two types of ANNs exist: the feed forward neural networks and the recurrent neural networks [START_REF] Sahoo | Voltage stability monitoring based on Feed Forward and Layer Recurrent Neural Networks[END_REF]. These two types of ANNs have been successfully used for diagnosis and prognosis. However, some authors highlight some drawbacks:

-ANNs are black boxes and it is not possible to explain and analyze the relationship between inputs and outputs;

-ANNs are prone to over fitting. Thus, to overcome these weaknesses, researchers combined the ANNs with fuzzy logic to obtain the neuro-fuzzy system (NFS). The use of the NFS for diagnosis/prognosis purposes requires taking into account the time factor and therefore generates a great computational burden. In this context, we propose to improve the architecture of the NFS by a new architecture named the neo-fuzzy neuron model (NFN). To explain how the NFS architecture is improved, consider an adaptive neuro-fuzzy system (ANFIS) with four inputs denoted {x0, x1, x2, x3} and one output denoted x (see Fig. 1).

If two fuzzy sets (defined by triangular, trapezoidal or Gaussian membership functions) are associated with each input, the system will contain 16 fuzzy rules (4 2 ) =16. These rules are given as follows:

( ) ( ) ( ) ( ) 0 0 1 1 2 2 3 3 0 1 2 3 0 0 1 1 2 2 3 3 4 Rule ( ): If is and is and is and is , 1 , 2 Then ( , , , ) , 1, 2,
...16

j j j j k k k k k k k k x x x x j x f x x x x c x c x c x c x c k µ µ µ µ = = = + + + + =
Where (k = 16) is the number of rules, xi for (i = 0, 1, 2, 3) is the i th input and ˆk x is the output of rule (k). ji µ is the j th membership function of the input xi and 0 1 2 3 4 { , , , , }

k k k k k c c c c c
are the coefficients of rule (k). The structure of the ANFIS predictor contains five layers including the input layer (see Fig. 1). They are defined as follows: Layer 1 membership function (MF): each input is associated with a MF which evaluates the membership degree of the j th fuzzy partition with the i th input variable. Here, the MF can be any function (triangle, trapezoid or Gaussian). For a Gaussian function, we have:

x 2 N MF MF MF MF MF MF MF MF Π Π Π Π Π Σ x 0 x 3 x 1 x 3 x 2 x 1 x 0 ω k ω k x ˆk k x ω
2 ( ) exp i ji ji i ji x m x b µ     -   = -          (1)
with (mji, bji), the Gaussian function parameters (premise parameters). Layer 2 (Π): in this layer, the weight ωk of each rule (k) is associated with the MF of each input by using a T-norm. The most widely used T-norm is the product:

( ) ( ) ( ) ( ) 0 0 1 1 2 2 3 3 k j j j j x x x x ω µ µ µ µ = ⋅ ⋅ ⋅ (2)
Layer 3 (N) : the purpose of this layer is the normalization of the different weights. The normalization is expressed as follows:

16 1 k k k k ω ω ω = =  (3)
Layer 4 : this layer computes the contribution of each rule (k) by a first-order input function (Takagi-Sugeno approach):

( )

0 0 1 1 2 2 3 3 4 ˆk k k k k k k t p k x c x c x c x c x c ω ω + = ⋅ + + + + (4)
The goal of the ANFIS system is to form an adaptive network able to approximate an unknown function through the learning data and then find the precise values of the parameters above (consequent and premise parameters). The characteristic of this approach is that ANFIS applies a hybrid learning algorithm. The hybrid learning algorithm is an association between the gradient descent method and the least squares method. The gradient descent method is used to adjust the premise parameters (mji, bji), whereas the least squares method is used to identify the consequent parameters

0 1 2 3 4 { , , , , } k k k k k c c c c c .
The inconvenient of the ANFIS system is related to a slow convergence of the learning step when the number of membership functions is big and/or when the number of inputs is big. To solve this problem, we propose the use of a new NFS called the NFN [START_REF] Yamakawa | A neo fuzzy neuron and its applications to system identification and prediction of the system behavior[END_REF]. The architecture of a NFN is quite close to an artificial neural network architecture with several inputs. However, instead of the usual synaptic weights, it contains nonlinear synapses. Among the most important advantages of the NFN model are the high rate of learning, simplicity of calculation, and also that it is characterized by the fuzzy rules of "if-then". The present paper is focused on the monitoring of MPF capacitors and SCs. More precisely, the objective of this paper is to show how it is possible to use the NFN model to estimate the ESR in the case of the MPF capacitor and to predict the evolution of the ESR and C in the case of SCs.

III. HEALTH MONITORING OF SCS

A. SCs ageing indicators

From literature, SCs ageing leads to C decrease and ESR increase (see Fig. 2). The decrease in C and the increase in ESR are not totally linked together as they are not related to the same phenomena (storage surface decrease for C and separator gas storage, internal pressure increase and contact degradation for ESR). Some publications define end of time parameters for SC life prediction [START_REF] Kreczanik | Study of Supercapacitor Aging and Lifetime Estimation According to Voltage, Temperature, and RMS Current[END_REF], but we will focus on the study of C and ESR through time. So instead of having only one information (i.e., the lifetime), one can monitor and predict the evolution of SC parameter through time.

B. SCs ageing factors

As SC ageing time is quite long under nominal conditions, some accelerated ageing tests are performed [START_REF] Kreczanik | Study of Supercapacitor Aging and Lifetime Estimation According to Voltage, Temperature, and RMS Current[END_REF], [START_REF] Kovaltchouk | Enhanced Aging Model for Supercapacitors Taking Into Account Power Cycling: Application to the Sizing of an Energy Storage System in a Direct Wave Energy Converter[END_REF]. The goal of those tests is to shorten the ageing test duration without implying any new ageing mode. Basically, they need voltage to take place and temperature plays the role of an acceleration factor [START_REF] El Brouji | Ageing quantification of ultracapacitors during calendar life and power cycling tests using a physically-based impedance model[END_REF], as long as the temperature is within the operating range of the SC [START_REF] Kreczanik | Study of Supercapacitor Aging and Lifetime Estimation According to Voltage, Temperature, and RMS Current[END_REF]. For out of bonds temperatures, new ageing mechanisms will happen but it is not the target of this paper.

Two kinds of accelerated ageing tests are usually performed. They are called cycling and floating ageing [START_REF] El Brouji | Ageing quantification of ultracapacitors during calendar life and power cycling tests using a physically-based impedance model[END_REF]. Cycling ageing consists of charging and discharging the SC in cycles. The loss of C and increase of ESR are very fast, but ageing is mainly reversible [START_REF] Brouji | Impact of calendar life and cycling ageing on supercapacitor performance[END_REF]. The acceleration factors for cycling ageing are depth of discharge, temperature and the root mean square (RMS) value of the current [START_REF] Kreczanik | Study of Supercapacitor Aging and Lifetime Estimation According to Voltage, Temperature, and RMS Current[END_REF]. Floating ageing consists of maintaining the voltage and temperature of SC as constant as possible through time. Thus, only temperature and voltage are ageing factors, since RMS current is near to 0 A. This kind of ageing is mainly irreversible.

Our study will focus on floating ageing since it is the main ageing mode for personal vehicles (95% of the time) and uninterruptible power supplies (99% of the time) and because it is an irreversible ageing mode. Thus, we will not study variable ageing constraints.

Fig. 2 presents averaged ageing results for floating ageing tests for 3 groups of three SCs aged with different constant voltage and temperature constraints. The results are presented in percent compared to the manufacturer rated C and ESR. The effect of temperature and voltage can be easily deduced. The reference test (60°C, 2.8 V) showed that a lower temperature (50°C, 2.8 V) or a lower voltage (60°C, 2.3 V) led to lower ageing speed.

As most of the SC used in hybrid and electric vehicles are based on the acetonitrile/activated carbon technology, the increase of ESR and the decrease of C through time have the same shape. Thus, although the parameter values from the learning database will not be the same for another SC, the method developed in this paper is applicable to other acetonitrile/ activated carbon SCs.

C. Prediction of the ESR and C for SCs

The C and resistance of the tested SC were measured at 100 mHz by electrochemical impedance spectroscopy (EIS) [START_REF] Brouji | Impact of calendar life and cycling ageing on supercapacitor performance[END_REF]. For any high power/ high C of SC, the impedance behavior is similar to the impedance of distributed porous electrodes [START_REF] Song | The effect of pore size distribution on the frequency dispersion of porous electrodes[END_REF]. The C of SC is frequency dependent and goes to its maximum value at low frequency [START_REF] El Brouji | Ageing quantification of ultracapacitors during calendar life and power cycling tests using a physically-based impedance model[END_REF]. Testing the SC at 100 mHz was a good compromise between capacitance estimation and acquisition time. Thus we used that frequency for C and ESR calculation. @100 1 . Im( )

SC mHz C j Z ω = - (6)
@100 Re( )

SC mHz ESR Z = (7)
with Im(ZSC) and Re(ZSC) the imaginary and real parts of the SC impedance (ZSC) measured at 100 mHz. This kind of estimation for C and ESR has the advantage of taking only experimental data without any other data treatment. With the selected SCs and the measurement tools used for the paper, the reproducibility of the extracted C and ESR were inferior to 0.5%. Other publications use data fitting for the identification of the SC model [START_REF] Bohlen | Ageing behaviour of electrochemical double layer capacitors Part I. Experimental study and ageing model[END_REF], [START_REF] El Brouji | Ageing quantification of ultracapacitors during calendar life and power cycling tests using a physically-based impedance model[END_REF]. The fitting is used to analyze experimental curves. It consists on constructing a curve from mathematical functions and adjusting the parameters of these functions to approximate the measured curve. For simple cases, the linear regression is used if the curve is linear for all parameters, or polynomial regression when using a polynomial to simulate the phenomenon (the degradation of SCs in our case). Conventional regression methods make possible to determine the mathematical functions from the data of the curve but are inapplicable if the function takes into account physical parameters not available in the curve, such as the temperature and the supply voltage, which are necessary to provide a good estimation of ESR and C.

As mentioned previously, the ageing of SCs can be predicted by estimating the evolution of ESR and C. This estimation is based on the following assumption.

Consider a set of measures denoted "X" performed on a SC. These measures are used to estimate an unobservable measure denoted ˆt p x + via the function f(X). This function is expressed as follows:

( ) t t 3 2 2 ˆ( ) ( , , , , , ) t p t r t r t r t t n r x f X f V x x x x x θ + - - - -- = = … (8)
ˆt p

x + is a measure "x" estimated for a horizon of prediction denoted p. The measure "x" corresponds to the ESR if the unobservable measure is ˆt p ESR + and corresponds to the C if the unobservable measure is ˆt p C + . xt is a measure acquired at time t. xt-r is a measure acquired at time t-r, where r is the interval between two measures (expressed in hours). xt-(n-2)r is a measure acquired at time t-(n-2)r, where n represents the number of measures. Vt, θt are respectively the supply voltage Vt and the temperature θt. The ageing estimation of the SC is illustrated in Fig. 3 for ˆt p C + with r=100, n=7 and p=2600, 3000 h... Figure 4 represents the architecture of the proposed NFN model. The output of the NFN is expressed as follows:

0 n t p i i i x f ( X ) f ( x ) + = = =  (9)
Where f(X) results by the sum of nonlinear functions fi( i x ). Each function fi is related to a normalized input i

x which represents the i th position of the series "X". The last and before the last position of the series "X" represent respectively the supply voltage and the temperature of the SC,

n t x V = , 1 ( n ) t
x .

θ -= The normalized input i x is comprised between 0 and 1 (0≤ i x ≤1) and is defined by the following formula:

i i max x x x = ( 10
)
where xmax is the maximal value recorded in the training step. The function i i f ( x ) depends on the interconnecting weights ωji between the i th input i x and the j th membership value ji i ( x ) µ

. The function i i f ( x ) is expressed as follows:

1

h i i ji ji i j f ( x ) ( x ) ω µ = = ⋅  ( 11
)
Where h is the number of MF. The membership values are obtained from triangular functions spaced equivalently according the number (h) of MFs as shown in Fig. 5.

ω hi i x 1 ( n ) x - 0 x n x 0 0 f ( x ) i i f ( x ) 1 1 n ( n ) f ( x ) - - n n f ( x )
Fig. 4. Architecture of a neuro-fuzzy neuron model for the prediction of equivalent series resistance and capacitance.

Triangular membership functions μ ji

1 0 τ 0,i =0 τ 1,i τ j,i τ h-1,i τ h,i=1 ji ir ( x ) µ ir x 1i µ ji µ 1 h i µ - hi µ 1 1 i ji µ µ + =
Neighboring membership functions Fig. 5. General view of triangular membership functions.

τ0,i , τ1,i,..., τj,i,, τh,i are the positions of the triangular functions with τh,i= 1. They are comprised between 0 and 1 (0≤τj,i ≤1). They are defined according to the number of the MF h. For h MFs, the position τj,i is equal to j/h.

The membership value ji i ( x ) µ is obtained according to the i th input in the intervals

1 j ,i ji , τ τ -     and 1 ji j ,i , τ τ +     . ji i ( x )
µ is expressed as follows:

1 1 1 1 1 1 0 otherwise i j ,i i j ,i ji ji j ,i j ,i i ji i i ji j ,i j ,i ji x , x , x ( x ) , x , τ τ τ τ τ τ µ τ τ τ τ - - - + + + -   ∈    -  -    = ∈    -    (12)
Based on equation [START_REF] Rigamonti | Particle Filter-Based Prognostics for an Electrolytic Capacitor Working in Variable Operating Conditions[END_REF] and Fig. 5, the output value of the nonlinear synapse i i f ( x ) depends only on two neighboring MFs (j, j+1). fi( i x ) is expressed as follows:

1 1 i i ji ji i j ,i j ,i i f ( x ) ( x ) ( x ) ω µ ω µ + + = ⋅ + ⋅ (13)
Finally, the estimation of t p x + is given by:

60 0 0 t p i i n n x f ( x ) f ( x ) ... f ( x ) + = + + + (14)
where t denotes current time instant, t p x + is the estimated value at the horizon t+p.

The interconnecting weights are calculated in the training step after ℓ-iterations by considering equation [START_REF] Schaltz | Influence of Battery/Ultracapacitor Energy-Storage Sizing on Battery Lifetime in a Fuel Cell Hybrid Electric Vehicle[END_REF], where the output of the NFN model is expressed as follows:

0 0 1 ˆ( ) ( ( )) ( 1) ( ( )) n n h t p i i ji ji i i i j x f x x ω µ + = = = = = -   ℓ ℓ ℓ ℓ (15)
The output ˆ( )

t p
x + ℓ depends on the MFs ji i ( x ) µ and the adjustable weights ωji(ℓ-1) obtained from the previous iteration. Therefore, there are n×h weights to be adjusted according to a criterion. This criterion consists on updating the synaptic weights by minimizing the quadratic error function E(ℓ) which is expressed as follows:

2 2 2 0 1 1 1 ( ) ( ( ) ( )) ( ) 2 2 1 ( ( ) ( 1) ( ( ))) 2 t p t p n h t p ji ji i i j E x x e x x ω µ + + + = = = - = = - -  ℓ ℓ ℓ ℓ ℓ ℓ ℓ (16)
The quadratic error is minimized by the gradient descent algorithm which allows calculating ωji by the following formula:

0 1 ( 1) ( ) ( 1) ( ( 1)) ( 1) ( 1) ( ) ( ( 1)
)

ji ji ji i n h t p ji ji i i j e x e x x ω ω ρ µ ω µ + = = + = + + + + = + - +  ℓ ℓ ℓ ℓ ℓ ℓ ℓ ℓ (17)
This equation depends on three parameters. The first parameter is the learning rate ρ, comprised between 0 and 1, used to control the convergence of the learning process. The second parameter is the MF ji µ calculated in equation [START_REF] Kreczanik | Study of Supercapacitor Aging and Lifetime Estimation According to Voltage, Temperature, and RMS Current[END_REF].

The third is the real measure xt+p.

IV. HEALTH MONITORING OF MPF CAPACITORS

A. MPF ageing MPF ageing leads to a variation in C and ESR. Table I resumes the ESR and C evolutions depending on the applied stresses [START_REF] El-Husseini | Improving pulse handling capability of metalized polypropylene films capacitors[END_REF]. Based on the different failure mechanisms shown in Table I, it seems extremely important to monitor both the ESR and C, since all of the failures mechanisms can be detected through the evolution of these electrical parameters.

B. MPF ageing factors

Different factors may have an irreversible impact on performance of MPF capacitors with time and deteriorate their operating lifetime. Among the numerous ageing factors, voltage and temperature are the most prevalent stresses [START_REF] Brown | Electrical and Thermal Modelling of Low Power Metallised Polypropylene Capacitors[END_REF].

Two kind of accelerated ageing test are usually performed. (i) Standard ageing by "floating", at a fixed temperature and voltage. This makes possible to analyze the behavior of the capacitor parameters as a function of time and therefore determining the acceleration factors of voltage and temperature. (ii) Ageing by current ripple with the application of a zero DC voltage. This type of ageing generates degradation of the metallization by electrochemical corrosion with superposition of a DC voltage to the above mentioned current ripple [START_REF] Brinkmann | Corrosion phenomena on evaporated metal layers under electric stress[END_REF], [START_REF] Brown | Electrical and Thermal Modelling of Low Power Metallised Polypropylene Capacitors[END_REF]. This test combines the constraints of the tests mentioned above (tests with the application of a current ripple and "floating") and consists of applying to the capacitor similar stresses encountered in a power electronics application. It makes it possible to study the impact of using the capacitor as a filter element of a static energy converter. In the following, standard ageing by "floating" is used to accelerate the ageing of MPF capacitors.

C. Estimation of the ESR and C for MPF capacitor

The health monitoring of an MPF capacitor consists of estimating the ESR and C. This estimation is obtained from the capacitor impedance, extracted within the frequency domain analysis. Indeed, if we plot Bode diagrams of a MPF 15µF-400 V capacitor at different ageing states, we note, as shown in Fig. 6, two distinct frequency regions separately dominated by ESR and C.

From the plotted curves, one can notice an evolution of the ESR and C for different ageing states. From theses curves, one can observe that the decrease of the capacitor impedance at low frequencies is followed by a decrease of the capacitance impedance at the resonant frequency (fres). This is interpreted by a link between the C and ESR. The C is estimated using [START_REF] Venkat | A review of process fault detection and diagnosis: Part iii: Process history based methods[END_REF] at low frequencies where 1/(2πfC) >> ESR:

1 | | 2 MPF C Z f π = ⋅ (18)
The ESR, estimated on the basis of its relation with C, is given by the NFN model where the output of the model is the ESR estimated at a time t denoted t ÊSR and the inputs are a series of impedances noted Zfi measured at different frequencies. This estimation is obtained by considering the following assumption.

Consider a series of impedances "Z" measured from an MPF capacitor. These measurements are used to estimate an unobservable parameter noted t Ê SR via a function f(Z). This function is expressed as follows: ˆ( ) ( ... )

2 1 t fn f f ESR f Z f Z , ,Z ,Z = = ( 19
)
where n represents the number of impedance measures used for the estimation of the t Ê SR . In the case of the MPF capacitor, n = 4 corresponds to the impedances Zf1 ,Zf2 ,Zf3 and Zf4 measured respectively at 200, 300, 400 and 500 Hz at time t. The choice of the frequencies 200, 300, 400 and 500 Hz is justified by the fact that the impedance of the capacitor for frequencies higher than 500 Hz will be disturbed because of the low amplitudes of harmonics (i.e., Fig. 13). The t Ê SR is the NFN output which corresponds to the ESR at the resonant frequency (~1 MHz). Since ESR values may differ from one capacitor to another (due to contact resistance), an additional input was introduced to the NFN model, that is Zf0 = ESR0 corresponding to the ESR of the monitored component at its healthy state (t=0). Very often, most of the diagnostic techniques require the knowledge of the component initial state regardless of the exploited physical quantity. Fig. 7 illustrates the inputs and output of the NFN model. The output of the NFN is expressed as follows: f ( Z ) is formulated as follows:

0 i n t i f i Ê SR f ( Z ) = =  (20)
1 h i fi ji ji fi j f ( Z ) ( Z ) ω µ = = ⋅  ( 21
)
Where ωji are the interconnecting weights between the i th input fi Z and the j th membership value ji fi ( Z ) µ .

As for SCs, the membership values ji fi ( Z ) µ are extracted from triangular functions spaced equivalently according the number (h). ji fi ( Z ) µ is expressed as follows:

1 1 1 1 1 1 0 otherwise fi j ,i fi j ,i ji ji j ,i j ,i fi ji fi fi ji j ,i j ,i ji Z , Z , Z ( Z ) , Z , τ τ τ τ τ τ µ τ τ τ τ - - - + + + -   ∈    -  -    = ∈    -    (22)
The function i i f f ( Z ) depends only on two neighboring membership functions (j, j+1). It is expressed as follows:

1 1 i fi ji ji fi j ,i j ,i fi f ( Z ) ( Z ) ( Z ) ω µ ω µ + + = ⋅ + ⋅ ( 23
)
The weight ωji is updated by a learning process based on the same principle of [START_REF] German | Novel Experimental Identification Method for a Supercapacitor Multipore Model in Order to Monitor the State of Health[END_REF]. . Finally, The estimation of t ÊSR is given by:

1 f Z fi Z 0 f Z fn Z 0 0 f f ( Z ) i fi f ( Z ) n fn f ( Z ) 1 1 f f ( Z )
0 0 f i fi n fn Ê SR f ( Z ) ... f ( Z ) ... f ( Z ) = + + + + (24)
V. EXPERIMENTAL SETUP

A. Health monitoring of SCs 1) SC test bench for ESR and C prediction

Fig. 8 shows the test bench used to obtain the experimental ageing results for ESR and C evolution. Nine independent DC voltage sources were used to maintain a fixed voltage constraint for 9 SCs. A first group of 3 SCs was aged at 2.8 V, 3 other SCs were aged at 2.7 V and the last 3 SCs group was aged at 2.3 V. A programmable thermal chamber allowed fixing a temperature constraint equal to 60°C for all SCs. Then a second batch of 9 SCs was aged at 50 °C within the same voltage constraints. Thus, a total amount of 18 SCs were tested. Those ageing results were used for building the learning and test database. A 4-point connection was realized due to the impedance of the SC which was in the same order of magnitude as the electrical wires (0.1 mΩ). An impedance spectrometer was used for the characterization of SCs. Some of the experimental results are presented in Fig. 2.

SCs are characterized by galvanostatic mode EIS (sinewave current imposed and voltage amplitude and phase measured) at ageing voltage (2.3 V, 2.7 V or 2.8 V). (10 kHz) to the low frequency (10 mHz). The capacitor and the resistance were characterized at low frequency (100 mHz), see eq. ( 6) and [START_REF] German | Prediction of supercapacitors floating ageing with surface electrode interface based ageing law[END_REF], as the SC is used for low frequency applications (1 to 10 s power supply, braking energy recovery in electric vehicles, etc.).

2) Prediction of the ESR and C evolution

The prediction of the ESR and C passed by three steps: database creation, learning and validation.

-Step 1. Database creation: The learning database was created from 12 identical SCs of 3000 F and 2.7 V placed in a thermal chamber regulated at 60°C for the first batch of 6 SCs and 50°C for the second batch of 6 SCs. Each batch was divided into two groups, in which each one was supplied with a specific voltage (2.8 V for group 1 and 2.3 V for group 2). The ageing evolution of these components showed that SCs of the same group followed the same ageing evolution. These results validated our measuring method and therefore validated the learning database. This was obtained by characterizing each SC thanks to an impedance spectrometer.

-Step 2. Learning: To show the learning capability of the NFN model, consider a database composed of two SCs noted SC1 and SC3 supplied respectively with 2.8 V and 2.3 V at 60°C. Based on the learning database created in step 1, two NFN models were created based on the ageing of the 12 SCs supplied at 2.3 V and 2.8 V and placed at 50°C and 60°C. The first model was used to estimate the ageing of the ESR and the second model to estimate the ageing of the C. The input of the first NFN model included the time series XESR for SC1 and SC3. The interval between each measure was expressed in hours. This time series is defined as follows:

400 300 200 100 { , , , , , , } ESR
t t t t t t t X V ESR ESR ESR ESR ESR θ - - - - =
The second model included the time series XC for SC1 and SC3. These time series are defined as follows:

400 300 200 100 { , , , , , , } C
t t t t t t t X V C C C C C θ - - - - =
The interval r between each measure was fixed to 100 h (r=100), (n-2) = 4, θt=60°C,Vt=2.3V for SC3 and Vt=2.8V for SC1. The output of the two models corresponded respectively to the estimation of the ESR and C, for a horizon of prediction (p) equal to 2600 h.

Two hundred triangular MFs (h=200) were used for each input of the NFN model. The interconnecting weights were updated in order to match the estimations values (prediction) with the desired ones.

The learning rate ρ was fixed according to normalized root mean square error (NRMSE). The NRMSE is the error between the estimation and the measure of the ESR and C. It is formulated as follows:

( )

2 1 1 N i i i max min ŷ y N NRMSE y y = - = -  (25)
where N represents the number of predicted values, i y and Results of Table II show that the values of the NRMSE for the ESR and C are very small and therefore demonstrated that the introduction of the voltage and temperature in the time series of the ESR and C is a good strategy to predict the ageing of SCs. The peak in the ESR located after 5500 h (see Fig. 10(b)) was due to a stop of two weeks in the ageing process. The effect of ageing perturbation disappeared after a few times of relaunching. After that, the ESR increased normally.

The decrease in the C value indicated the degree of degradation in the contact surface between the electrolyte and the electrode of the SC. This decrease was interpreted by a decrease in energy storage capability.

The ageing of the ESR depends on the quality of contacts which are linked to the internal pressure of the SC. The increase in pressure causes a deformation of the SC, which can induce a breakdown in contacts. This defect is observable in Fig. 10 (a) where the value of the ESR jumps after 3500 h. This defect was not observable in the evolution of the C. This is why it is necessary to monitor simultaneously the evolution of the ESR and C.

B. Health monitoring of capacitors 1) MPF test bench

The test bench used for the ESR estimation was a switched mode power supply 230V AC/24V DC, 0-iSmax as described in the block diagram of Fig. 11. Each of the input capacitors C1, C2, C3 and C4 was made of two MPF capacitors 15µF-400V connected in parallel.

V ~ 50 Hz

u C 1 C 2 i e i c1 C 3 C 4 i c2 i 1 u s = 24 V C s L s I s = 0-16 A

2) Estimation of the ESR -Step 1. Database creation:

The database was created from 8 identical MPF capacitors of 15µF-400V. These capacitors were subjected to a temperature constraint varying between 85°C and 100°C and a voltage constraint varying between 1.1 and 1.3•UR. UR is the capacitor rated voltage. The database was obtained by evaluating the impedance from the fast Fourier transform (FFT) of the current and voltage signals. The C was then calculated by using [START_REF] Venkat | A review of process fault detection and diagnosis: Part iii: Process history based methods[END_REF] at the low frequency and the ESR was estimated by the NFN model.

-Step 2. Learning: This step considered the database of the MPF capacitor #1 (15µF-400V) supplied with 1.1•UR at 85°C. This database was composed of an impedance series corresponding respectively to the frequencies (fres, 200 Hz, 300 Hz, 400 Hz and 500 Hz) and acquired at different time intervals (hours) during the ageing process. This database is summarized in Table III.

To test the accuracy estimation of the ESR by the NFN model, three MPF capacitors of 15µF-400V subjected to different electrical and thermal stresses were tested. The constraints are defined in Table IV.

ESR estimation results are given in Table V. The obtained results show that estimation errors of the ESR were small (error<5.8%). In addition, these results show that the introduction of ESR0 in the impedance series allowed estimating the ESR of MPF capacitors subjected to electrical and thermal stresses which differed from those used in the learning phase.

-Step 3. Validation: Online health monitoring

Health monitoring was validated by measuring online the current and voltage across the capacitor C3 where one of its MPF capacitor has been replaced by an aged component. The ageing process was simulated by replacing at specified Figure 12 shows the curve of the current and voltage measured across the aged capacitor. After performing a FFT on the current and voltage signals, the impedance series Zfi located at the frequencies (fres, 200 Hz, 300 Hz, 400 Hz and 500 Hz) was extracted. The ESR0, located in the resonance frequency was deduced before the ageing process thanks to an impedance spectrometer. Figure 13 shows the curve of the impedance ZMPF. The blue curve represents the impedance identified online from the current and voltage signals. The red curve represents the impedance of the MPF capacitor measured from the impedance spectrometer. One can observe that the two curves are identical in the low band frequencies. This is why the impedance series is limited from 200 to 500 Hz. The estimated ESR and C given in Table VI show that the estimated values of ESR and C are coherent with those measured with an impedance meter, which proves the effectiveness of our approach.

VI. CONCLUSION

A model for the health monitoring of MPF capacitors and SCs based on the NFN model has been proposed in this paper. The bibliographical research showed that monitoring ESR and C is the best way for tracking the ageing of these components. For SCs, a time series composed by the ESR or C has been used in the NFN model. The obtained results showed that the introduction of temperature and voltage in this time series allow obtaining good predictions of ESR and C and therefore an accurate estimation of the remaining useful life. The same model was proposed for the estimation of ESR in the case of MPF capacitors. A series of impedances located in the low frequencies were used in the NFN model. Since ESR values may differ from one capacitor to another, an additional input was added to the impedance series, that is the ESR0 corresponding to the healthy state. This strategy allows a robust and accurate estimation of the ESR. The proposed approach requires a database creation step and a learning step on a healthy and aged state. Further research is currently underway to implement the NFN predictor in complex industrial facilities and to develop new strategies for health monitoring and to generalize it to all ESS devices (batteries).

Fig. 1 .

 1 Fig.1. Architecture of adaptive neuro-fuzzy system for four inputs and two membership functions (MF).

  this linear combination and are called consequent parameters.Layer 5 (Σ): the output of this layer is the sum of all incoming rules.

  ESR ageing evolution. Fig.2. Impact of ageing on supercapacitor capacitance (C) and equivalent series resistance (ESR) for different accelerated calendar ageing test.

Fig. 3 .

 3 Fig. 3. Prediction of the capacitance until a horizon p from XC.

Fig. 6 .

 6 Fig. 6. Impact of ageing on capacitance (C) and equivalent series resistance (ESR) of a metallized polymer film capacitor for different accelerated ageing tests.

  impedance (observation) situated in the i th position of the impedance series. The first position of the impedance series represents the normalized ESR at the healthy state 0

Fig. 7 .

 7 Fig. 7. Neo-fuzzy neuron (NFN) architecture for the equivalent series resistance (ESR) estimation.

Fig. 8 .Frequency

 8 Fig. 8. Test bench for supercapacitor ageing.The characterization frequency went from high frequency

iŷFig. 9 (Fig. 9 (Fig. 10 (

 9910 Fig.9 (a). Learning result of the equivalent series resistance (ESR) neo-fuzzy neuron model for SC1 (2.3 V, 60°C) and SC3 (2.8 V, 60°C) with a horizon p=2600 h.

Fig. 10

 10 Fig. 10(b). Prediction of the equivalent series resistance (ESR) evolution for an accelerated ageing test of SC2 (2.7 V, 60°C).

Fig. 11 .

 11 Fig. 11. Representation of the switched mode power supply.

Fig. 12 .

 12 Fig. 12. Voltage and current signals corresponding to an aged capacitor.

Fig. 13 .

 13 Fig. 13. Comparison between the impedance obtained from the voltage and current signals (blue curve) and the impedance measured by an impedance meter (red curve).

TABLE II NORMALIZED

 II ROOT MEAN SQUARE ERROR (NRMSE) OF THE EQUIVALENT SERIES RESISTANCE (ESR) AND CAPACITANCE C FOR SC2

	intervals (1300 h, 413 h, 113 h) the component forming C3 by
	the MPFs (#2, #4, #6).
	Horizon of prediction p	NRMSE (%)
	(hours)	ESR	C
	100	0.126	0.036
	1100	0.249	0.041
	16000	0.253	0.041
	26000	0.290	0.043
	46000	0.813	0.049