Alexandre Prola

Zuzana Nichtova

Julie Pires Da Silva

Jérôme Piquereau

Kevin Monceaux

Arnaud Guilbert

Mélanie Gressette

Renée Ventura-Clapier

Anne Garnier

Ivan Zahradnik

Julie Pires

Da Silva

Marta Novotova

Christophe Lemaire
email: christophe.lemaire@u-psud.fr

Endoplasmic reticulum stress induces cardiac dysfunction through architectural modifications and alteration of mitochondrial function in cardiomyocytes

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

INTRODUCTION

Heart failure is a major global health problem and a leading cause of mortality. In response to cardiac stress, several adaptations occur such as hypertrophy and metabolism modifications as an initial compensatory mechanism required for maintenance of cardiac output. However, in the long term these processes may become maladaptive and ultimately lead to cardiac decompensation and heart failure. Despite the considerable attention focused on pathological development of cardiac diseases, the understanding of the transition from adaptive to maladaptive response is still limited.

The rough endoplasmic reticulum (rER) is the site for synthesis and folding of secreted and membrane proteins. Disruption of ER homeostasis leads to accumulation of unfolded/misfolded proteins and ER stress. As a compensatory pro-survival response, the unfolded protein response (UPR) is activated to restore normal ER function. The canonical UPR is initiated by activation of three sensors, the kinase PERK, the transcription factor ATF6 and the kinase/endoribonuclease IRE1, which are normally kept inactive through the interaction with the ER-resident chaperone GRP78/BiP 1 . Upon activation, these sensors induce the transcription of UPR target genes (e.g. atf4, xbp1 and chop) resulting in the downregulation of protein synthesis, upregulation of ER chaperone expression, and upregulation of proteins involved in ERAD (ER Associated protein Degradation). However, in the case of prolonged or severe ER stress, where ER homeostasis cannot be restored, the mitochondrial apoptotic pathway is triggered to eliminate damaged cells [START_REF] Hetz | The unfolded protein response: controlling cell fate decisions under ER stress and beyond[END_REF] .

ER stress-dependent apoptosis was reported to be mediated mainly by the pro-apoptotic transcription factor CHOP, by pro-apoptotic members of the Bcl-2 family and by direct calcium transfer from ER to mitochondria [START_REF] Csordas | Quasi-synaptic calcium signal transmission between endoplasmic reticulum and mitochondria[END_REF][START_REF] Puthalakath | ER stress triggers apoptosis by activating BH3-only protein Bim[END_REF][START_REF] Tabas | Integrating the mechanisms of apoptosis induced by endoplasmic reticulum stress[END_REF] . Thereby, acute activation of ER stress response is protective while prolongation of the response typically leads to apoptosis and contributes to the maladaptive response.

Recently, ER stress has been linked to both physiological and pathological conditions in the cardiovascular system including oxygen and fuel starvation, myocardial infarction, ischemia, dilated cardiomyopathy, pressure overload, hypertrophy, and heart failure [START_REF] Minamino | ER stress in cardiovascular disease[END_REF] . It has been suggested that the ER stress response is cardioprotective as part of the beneficial compensatory mechanism activated in the heart during a stress, while inhibition of this response is deleterious. For example, extinction of the central regulator of the ER stress response GRP78 aggravates insults upon ischemia [START_REF] Shintani-Ishida | Ischemic preconditioning protects cardiomyocytes against ischemic injury by inducing GRP78[END_REF] . Protein disulfide isomerase (PDI), a major component of the UPR, is upregulated in peri-infarct myocardial region in humans and this increase is inversely correlated with the apoptotic rate and the presence of heart failure [START_REF] Severino | Identification of protein disulfide isomerase as a cardiomyocyte survival factor in ischemic cardiomyopathy[END_REF] . However, in the long term, ER stress response triggers apoptosis, which is part of the heart's maladaptive response and contributes to cardiac decompensation [START_REF] Bravo | Increased ER-mitochondrial coupling promotes mitochondrial respiration and bioenergetics during early phases of ER stress[END_REF] . Thus, extinction of the ER stress-activated pro-apoptotic factor CHOP has been shown to reduce the cardiac dysfunction induced by pressure overload in mice [START_REF] Fu | Ablation of C/EBP homologous protein attenuates endoplasmic reticulum-mediated apoptosis and cardiac dysfunction induced by pressure overload[END_REF] . Besides, treatment with the chemical chaperones 4-phenyl butyric acid (4-PBA) or TUDCA, which alleviate ER stress, protects the heart against isoproterenol-and anthracycline-induced cardiotoxicity and against obesity-induced myocardial contractile dysfunction [START_REF] Ayala | Attenuation of endoplasmic reticulum stress using the chemical chaperone 4-phenylbutyric acid prevents cardiac fibrosis induced by isoproterenol[END_REF][START_REF] Ceylan-Isik | Endoplasmic reticulum chaperon tauroursodeoxycholic acid alleviates obesity-induced myocardial contractile dysfunction[END_REF][START_REF] Daosukho | Phenylbutyrate, a histone deacetylase inhibitor, protects against Adriamycininduced cardiac injury[END_REF] .

Although understanding the pathophysiological role of ER stress in cardiovascular diseases has progressed in recent years, the exact physiological effect of ER stress on cardiomyocytes is still poorly understood. In the present study, we evaluated the effect of tunicamycin-induced ER stress on cardiac function, cardiomyocyte ultrastructure and mitochondrial function. Transmission electron microscopy analysis revealed that ER stress-induced cardiac dysfunction is associated with important ultrastructural modifications that manifest extensively at the level of the endomembrane system. Skinned cardiac fibers present slower mitochondrial oxidation rate and a shift from fatty acid to glucose utilization. Taken together, our results show that alteration of the cardiomyocyte ultrastructure and metabolism contributes to the maladaptive response of the heart to severe ER stress.

METHODS

Animals and treatments

To study ER stress in vivo, mice were given i.p. injection of TN 2 mg/kg body weight or the equivalent volume of vehicle (Dextrose 150 mM). Echocardiographic parameters were assessed 72 h after injection and hearts were harvested for molecular studies. Mice were euthanized by cervical dislocation. This procedure was carried out in conformity with the European Community guiding principles in the care and use of animals (Directive 2010/63/EU of the European Parliament). Authorizations to conduct animal experiments were obtained from the French Ministère de l'Education Nationale, de l'Enseignement Supérieur et de la Recherche (n° B9201901, November 3 rd , 2015).

Echocardiography

Transthoracic echocardiography was performed using a 15 MHz transducer under 2.5% isoflurane gas anesthesia. Two-dimensional-guided (2D) M-mode echocardiography was used to determine wall thickness and left ventricular chamber volume at systole and diastole and contractile parameters, such as fractional shortening (FS) or ejection fraction (EF).

Biochemical analysis

Frozen tissues were homogenized with Precellys 24 Bertin technologies in a buffer (50 mg/mL) containing (in mM) HEPES 5, EGTA 1, DTT 1 and 0.1% Triton X-100 and were incubated for 1 h at 0°C for complete enzyme extraction. Activities of total creatine kinase (CK), citrate synthase (CS), hydroxyacyl-CoA dehydrogenase (HADHA) and mitochondrial cytochrome c oxidase (COX) were measured using standard spectrophotometric assays.

Western blot analysis

Frozen tissues were homogenized with Precellys 24 Bertin technologies in RIPA lysis buffer plus a cocktail of protease and phosphatase inhibitors (Roche), and PMSF for 30 min at 4 °C. Proteins (30 μg) were separated by SDS-PAGE and transferred to PVDF membranes (Merck Millipore).

Membranes were incubated overnight at 4°C with the following antibodies: anti-GRP78 (#3183), anti-phospho-eIF2α (#3597), anti-eIF2α (#2103), anti-MCU (#14997), anti-phospho-DRP1 (#6319), anti-DRP1 (#14647), anti-OPA1 (#80471) and anti-CHOP (#2895) from Cell Signaling, anti-IP3R (ab5804), anti-VDAC (ab14734), anti-MFN1 (ab126575), anti MFN2 (ab124773), anti-COXIV (ab14744) and anti-OXPHOS (ab110413) from Abcam, anti-Actin (sc-47778), anti-FIS1 (sc-376447), anti-SEC61α (sc-393182), anti-RIBOPHORIN I (sc-48367), anti-RPS6 (sc-74459) and anti-GADD34 (sc-8327) from Santa Cruz. Proteins were detected on a ChemiDoc XRS (BioRad) by using the ECL method according to the manufacturer's instructions (Merck Millipore). To calculate the relative density (RD), ImageJ software was used and the intensity of each protein was normalized to actin. The data obtained were then expressed as the ratio of the intensity of the protein in treated mice to that of the corresponding protein in vehicle-treated mice (RD: relative density). The level of eIF2α and DRP1 phosphorylation was expressed as the ratio of the phosphorylated protein vs the total protein.

RNA isolation and RT-PCR

RNA was isolated from cultured cells using Zymo Research Quick RNA MiniPrep according to the manufacturer's instructions. Total RNA (1 μg) was reverse transcribed using BioRad iScript reverse transcription kit. cDNA was amplified by the "two-step" SsoFast EvaGreen supermix (BioRad), heated at 95°C for 30 s, followed by 50 cycles of denaturation at 95°C during 2 s and hybridization/elongation at 60°C during 5 s. The PCR primers were obtained from Eurofins and are listed in table S1. The results were quantified according to the Cq value method, where Cq is defined as the quantification cycle of PCR at which the amplified product is detected. The ratio (1+Etarget gene)^-(Cq sample-Cq control)target gene/(1+Ereference gene)^-(Cq sample-Cq control) gene was calculated, where E represents the efficiency of the quantitative PCR reaction.

With this calculation, expression of control was equivalent to one.

Electron Microscopy

Left ventricular papillary muscles were isolated from 3 control and 3 tunicamycin-treated (TN) mouse hearts, fixated with 2% glutaraldehyde in cacodylate buffer (in mM: 150 Na-Cacodylate, 2CaCl2, pH 7.3) for 1 h, postfixated by 1% osmium tetroxide in cacodylate buffer for 30 min and stained with 1% aqueous solution of uranyl acetate. After dehydration in graded ethanol series and acetone, the tissue was embedded in Durcupan (ACM Fluka).

Preparation of sections

Ultrathin (58-60 nm) longitudinal sections were cut using an ultramicrotome (Power-Tome MT-XL, RMC/Sorvall, Tucson, USA). The sections were mounted on formvar-coated copper grids, contrasted with lead citrate and examined with a JEM 1200 electron microscope (Jeol, Tokyo, Japan) at 80 kV. Random images of cardiomyocytes were recorded with a CCD camera (Gatan DualVision 300 W) at a magnification of 15,000× and analyzed using Graphic Cell Analyzer 14 (see below).

Stereological Analysis

Estimation of volume densities (Vv)

Random images of random samples of papillary muscle tissue were analyzed by the point integration method [START_REF] Baddeley | Estimation of surface area from vertical sections[END_REF] . The size of the point test grid generated by the program Graphic Cell Analyzer [START_REF] Parulek | A cell architecture modeling system based on quantitative ultrastructural characteristics[END_REF] was calibrated to the image scale and the point distance set to preferred resolution.

Relative V v of organelles of interest was estimated as the fraction p/P, where p represents the number of test points falling on the structure of interest and P represents the total number of test points falling on profiles of cardiomyocytes in the evaluated image. Altogether, we analyzed 152 images of control and 161 images of TN-treated mice Estimation of mitochondrial environment.

The mitochondrial environment was estimated according to Novotova et al. [START_REF] Novotova | Ultrastructural remodeling of fast skeletal muscle fibers induced by invalidation of creatine kinase[END_REF] by the cycloidal intersection method implemented in the Graphic Cell Analyzer 14 . The intersections of cycloidal curves with the mitochondrion outer surface were counted and classified according to the nearest organelle present at the mitochondrion surface at the point of intersection. For evaluation of mitochondrial environment, we used the relation E = I S /I, where I S corresponds to the number of intersections pertinent to individual nearest organelle at a distance of 20 nm or less and I represents total number of intersections with all mitochondria in the analyzed image. The total number of classified intersections with mitochondrial surface was 10150 (4962 for control vs. 5188 for TN-treated cardiomyocytes). The final image magnification for analysis was 50000x.

Quantification of mitochondrial surface

EM quantification of individual mitochondrial surface in CTL and WT hearts was performed using Image J software on 20 slices (randomly chosen, magnification 15,000×) per animal as previously described [START_REF] Piquereau | Downregulation of OPA1 alters mouse mitochondrial morphology, PTP function, and cardiac adaptation to pressure overload[END_REF] . The mean value of individual mitochondrial surface was obtained on the whole population of mitochondria (for each group), and the distribution of these mitochondrial surfaces calculated for each animal in each group.

Analysis of in situ mitochondrial function

Mitochondrial respiration was studied in situ in saponin-skinned fibers, as previously described [START_REF] Kuznetsov | Analysis of mitochondrial function in situ in permeabilized muscle fibers, tissues and cells[END_REF] .

Briefly, fibers were separated from the endocardial surface of the left ventricle in skinning (S) solution (see below) at 4°C and permeabilized with 50 µg/ml of saponin for 30 min.

Permeabilized fibers were rinsed in (R) solution (see below) for 10 min and transferred into a 3 ml oxygraphic cell (Strathkelvin Instruments, Glasgow, UK). Solutions R and S contained (in mM): 2.77 CaK 2 EGTA, 7.23 K 2 EGTA (100 nM free Ca 2+ ), 1 free Mg 2+ , 20 taurine, 0.5 DTT, and imidazole (pH 7.1). Solution S also contained (in mM) 50 potassium methanesulfonate, (160 mM ionic strength), 5.7 Na 2 ATP, 15 phosphocreatine, while solution R contained 10 glutamate, 4 malate, 3 phosphate, 90 potassium methanesulfonate, 10 sodium methanesulfonate (ionic strength 160 mM) and 2 mg/ml fatty acid-free bovine serum albumin. Experiments were performed at 22°C under continuous stirring. Different experimental protocols were used based on substrate utilization pathways. One protocol determined mitochondrial respiration using fatty acids (0.1 mM Palmitoyl-Coenzyme A) or glycolytic substrate (1 mM pyruvate) in the presence of 2 mM ADP, 4 mM malate. Another protocol was intended to determine the dependency of respiration on external [ADP] in the presence or absence of 20 mM creatine with glutamate and malate.

Fibers were exposed to increasing [ADP], to determine the apparent Km for ADP and maximal mitochondrial respiration (Vmax). The acceptor control ratio (ACR), an index of oxidation phosphorylation coupling, was calculated as Vmax/Vo. Succinate (20 mM) was then added to measure respiration involving complex I and II, amobarbital (2 mM) was added to inhibit complex I and to measure respiration on complex II. Finally, TMPD (0.5 mM) and ascorbate (2 mM) were added to give electrons to complex IV and sodium azide (5 mM) was added to inhibit complex IV. Respiration for complex IV was then calculated as TMPD/ascorbate respiration cut off the remaining azide respiration.

Analysis of in situ mitochondrial calcium uptake

Mitochondrial calcium content was studied in situ in isolated cardiac fibers. Fibers were separated from the endocardial surface of the left ventricle in skinning (S) solution (see analysis of mitochondrial function) at 4°C and then incubated in solution I with 200 nM MitoTracker Green (Life Technologies, France) and 5 µmol/L of the mitochondrial calcium indicator Rhod-2acetoxymethyl ester (Rhod-2-AM; Life Technologies, France) for 60 min at 4°C, and then for 30 min at 37°C [START_REF] Li | Hepatitis C virus core protein increases mitochondrial ROS production by stimulation of Ca2+ uniporter activity[END_REF][START_REF] Trollinger | Selective loading of Rhod 2 into mitochondria shows mitochondrial Ca2+ transients during the contractile cycle in adult rabbit cardiac myocytes[END_REF] . Solution I contained (in mM): 10 K 2 EGTA, 1 free Mg 2+ , 3 K2HPO4, 20 taurine, 0.5 DTT, 54.2 potassium methanesulfonate, (160 mM ionic strength), 3.6 Na2ATP, 12 phosphocreatine 10 glutamate, 4 malate, 60 Bes (pH 7.1) and 6% dextran. With this cold loading/warm incubation procedure, Rhod-2-AM localized to mitochondria. Colocalization of Rhod-2-AM and Mitotracker Green was evaluated with an inverted confocal laser scanning microscope Leica TCS SP8 (Leica, Germany) using a HC PL APO CS2 63x/1.40 oil immersion objective lens and quantified with the Fiji plugin Coloc 2. Rhod-2 (λ excitation: 552 nm, λ emission: 581 nm) and Mitotracker Green (λ excitation: 490 nm, λ emission: 516 nm) fluorescence was acquired in 96-well plates at 37°C in a spectrofluorimeter (TECAN infinite M200, TECAN, Austria).

Public data analysis

Analysis of gene expression using public repository data was performed using BioGPS webtools (http://biogps.org/#goto=welcome), a free scientific web resource [START_REF] Wu | BioGPS: building your own mash-up of gene annotations and expression profiles[END_REF] . We analyzed the microarray of wildtype mice from the dataset E-GEOD-19322. One-way ANOVA test with Benjamini and Hochberg false discovery rate (FDR) correction was applied to the comparison between the conditions, using a 0.05 threshold for statistical significance. Only C57BL/6J data were used.

Statistical analysis

All data are presented as mean±SEM. Data were analyzed using Sigma Stat (Sigma Stat, version 3.0, Systat Software, San Jose, CA, USA). Differences were assessed by Student's t-test when the data follow a normal distribution. Differences were assessed by Mann-Whitney U test when the data distribution was not normal. Differences between groups were considered significant if the P value was less than 0.05. *: P<0.05; **: P<0.01; ***: P<0.005 vs CTL. Microarray analysis was conducted using One-way ANOVA test with Benjamini and Hochberg false discovery rate (FDR) correction, using a 0.05 threshold for statistical significance. Only C57BL/6J data were used.

Correlation coefficient and significance were calculated using Spearman correlation test.

CVR-2017-781

11

RESULTS

ER stress induces cardiac dysfunction in mice

To investigate the effects of ER stress on cardiac function, ER stress was induced in mice by intraperitoneal injection of tunicamycin (2 mg/kg), which inhibits N-linked glycosylation of proteins in the ER. This model is known to elicit activation of the UPR leading to cardiomyocyte apoptosis and development of cardiomyopathy [START_REF] Prola | SIRT1 protects the heart from ER stressinduced cell death through eIF2alpha deacetylation[END_REF][START_REF] Zhang | Activation of Akt rescues endoplasmic reticulum stress-impaired murine cardiac contractile function via glycogen synthase kinase-3betamediated suppression of mitochondrial permeation pore opening[END_REF] . TN injection provoked sustained ER stress and activation of the three arms of the UPR, as demonstrated by increased transcriptional expression of Grp78, Grp94, full-length Xbp1 (Xbp1u), spliced Xbp1 (Xbp1s) and Chop (Figure 1A), upregulation of GRP78, CHOP and GADD34 protein levels and increase in eIF2α phosphorylation (Figure 1B). At the anatomical level, 72 h of ER stress challenge induced a loss of body weight and liver weight (Table S2) but did not overtly affected the weight of other organs. TN-induced ER stress led to a significant impairment of cardiac function as judged by the decrease in ejection fraction and fractional shortening (Figure 1D-E) induced by TN relative to vehicle-treated mice. In contrast, heart rate (Figure 1C), left ventricular internal diameters in diastole and systole or wall thickness were not affected (Table S3). Together, these data indicate that tunicamycin injection is a valuable model to study ER stress-induced cardiac dysfunction.

ER stress induces ultrastructural alterations in cardiomyocytes

To characterize the effects of ER stress induction in heart, ultrastructural analysis of cardiomyocytes was carried out by transmission electron microscopy. Application of vehicle did not induce any ultrastructural changes in control cardiomyocytes. Myofibrils were aligned in the longitudinal direction and sarcomeres were in register. Sub-sarcolemmal as well as intermyofibrillar mitochondria were regular in shape and size and formed columns grouped along myofibrils (Figure 2A). ER stress induction led to modification of the ultrastructure of cardiomyocytes. While some cardiomyocytes were similar to control, we also observed cardiomyocytes with areas characterized by enlarged cytosol (Figures 2D, E, F andS2) and the presence of mitochondrial clusters (Figures 2B andS2).

Ultrastructural alterations of the reticular membrane system

The endomembrane system in control cardiomyocytes consists of a prevailing network of smooth sarcoplasmic reticulum (SR) occurring near the sarcomeres (Figure 2C, 4C), whereas rough endoplasmic reticulum is observed near nuclei and to a lesser extent in regions of I-bands, near the Z-line. ER stress greatly influenced the composition and distribution of the reticular membrane system in cardiomyocytes. Generally, increased amount of the network of rER was observed. Areas presenting enlarged cytosol (Figure 2D) were rich in ribosomes, polyribosomes and branches of rER. These regions were similar by their composition to the growing areas in developing myocytes. The network of smooth SR was maintained in some regions of the A-band, but in other regions of the A-band, network of rER or branches of rER dominated (Figure 2E).

Interestingly, the network of SR and rER sometimes shared their lumen (Figure 2F), indicating continuation of their inner volumes. From the morphological point of view, the character of reticular membrane system has been changed. An increased occurrence of rER in the area of Iband and A-band in TN-treated cardiomyocytes led to substantial ultrastructural changes at the level of dyadic microdomains (Figure 3). Dyads of control cardiomyocytes consist of a central ttubule and of a SR cistern (Figure 3A). Remodeling of dyadic microdomains in TN-treated hearts was manifested by the appearance of ribosomes and polyribosomes on the reticular membranes occurring in a close proximity to the membrane of the central t-tubule (Figure 3B,D) and on the cistern of SR (Figure 3C). The expansion of rER network was also evidenced by the TN-induced increased expression of the ribosomal protein RBP6, the ribosome-binding protein of the ER Ribophorin I and the translocon protein Sec61α (Figure 3E). These observations reveal for the first time a plasticity of the reticulum network in the heart. It seems that the reticulum evolved from a SR to an ER morphology in response to ER stress, probably leading to important modifications of Ca 2+ cycling.

Ultrastructural alterations of mitochondrial population

Mitochondria of control cardiomyocytes had a typical cylindrical shape extended along the axis of the cell. In comparison to control (Figure 4A), the mitochondria of the intermyofibrillar region of TN-treated cardiomyocytes appeared to be heterogeneous in shape and size (Figure 4B). Inner mitochondrial membrane of some mitochondria was changed, and fragmentation of mitochondrial cristae was observed (Figure 4E). Moreover, quantification of mitochondrial surface revealed a significant increase of the proportion of small mitochondria (<0.2 µm²) associated with a decrease of large mitochondria (>0.5 µm², Figure 4G). To investigate whether a more fragmented network would be triggered by increased profission or reduced profusion signals, we quantified the expression level of the main regulators of these processes. While the transcriptional expression of Mfn2, Opa1 and Fis1, the protein levels of MFN1, OPA1 and FIS1 and the phosphorylation of DRP1 were not modified by ER stress, we observed an increase of the total expression of DRP1 associated with a decrease of MFN2 protein level (Figure S1A and4H-I).

ER stress induces mitochondrial dysfunction

We reasoned that changes in mitochondrial architecture induced by ER stress may produce changes in the oxidative capability of the heart. We therefore measured mitochondrial respiration rates and substrate preference in situ in permeabilized fibers. Basal respiration in the presence of substrates but without ADP in the respiratory medium (Vo) and thus without ATP production, was not modified by TN treatment. In contrast, maximal coupled respiration rate with ADP in the medium was decreased in the presence of glutamate (complex I), succinate (complex I+II), amytal (complex II) and TMPD/ascorbate (complex IV) (Figure 5A). Consequently, the coupling between oxidation and phosphorylation estimated by the ratio of maximal respiration on basal respiration was decreased following ER stress induction (Figure 5B). This low respiratory efficiency was associated with reduced enzymatic activity of citrate synthase (CS) and cytochrome c oxidase (COX) (Figure 5C,D). The reduced mitochondrial capability to generate ATP was accompanied by a dramatic inhibition of mitochondrial biogenesis as the transcriptional expression of the master coordinator of mitochondrial biogenesis Pgc-1α and its targets Nrf1, Tfam, Cs, CoxIV were profoundly decreased by ER stress (Figure 5E). The decrease of mitochondrial mass suggested by the decrease of CS activity was also evidenced by reduced protein levels of the subunits of complex I, II, IV and V of the respiratory chain (Figure 5F), the mitochondrial calcium uniporter (MCU) and the porin VDAC (Figure S1C). Stereological analysis revealed a significant decrease of the volume density of lipid droplets in cardiac muscle tissue in TN-treated mice (Table S4), while no significant change in other components of cardiomyocytes were found. The volume of lipid droplets significantly decreased from 1.25 ± 0.38 % of the unit cell volume in controls to 0.87 ± 0.18 % in TN-treated cardiomyocytes. This result suggests a modification of the lipid metabolism by ER stress.

Mitochondrial respiration was decreased when fueled by palmitoyl-Coenzyme A or by glutamate and succinate (Vmax) but not changed when fueled with the glycolysis-derived substrate pyruvate (Figure 6A). Consequently, in TN-treated mice the relative oxidation of fatty acids (FA) was significantly decreased, whereas the relative oxidation of pyruvate was increased (Figure 6B). Accordingly, the activity of the lactate dehydrogenase involved in glycolysis was increased, whereas the activity of the fatty acid β-oxidation enzyme HADHA was decreased (Figure 6C,D).

Moreover, mRNA level of the master regulator of FA oxidation PPARα, as well as the βoxidation enzyme MCAD, were markedly decreased after TN injection (Figure 6E). The transcriptional expression of mitochondrial FA transporters CPT1, CPT2 and CD36 remained unchanged, suggesting that the decreased oxidation rate of FA induced by ER stress is not the result of FA transport alterations but is rather due to a global decrease of mitochondrial βoxidation (Figure 6E).

In cardiomyocytes, a localized crosstalk between energy producing and energy consuming sites is required to ensure proper cardiac contractility. This phosphotransfer is achieved by creatine kinase much more efficiently than by simple diffusion of nucleotides through the bulk cytosol [START_REF] Kaasik | Energetic crosstalk between organelles: architectural integration of energy production and utilization[END_REF] .

We thus assessed the functionality of the creatine kinase shuttle. We first measured creatine kinase enzymatic activity and we reported a decrease after TN injection (Figure 6F). We next analyzed the mitochondrial respiration regulation by ADP in the presence or absence of creatine to estimate the Km to ADP. Whereas Km to ADP was not modified in the absence of creatine, TN injection induced an increase of the Km after creatine addition (Figure 6G), showing a decreased efficiency of mitochondrial creatine kinase. These results suggest that ER stress induces an alteration of the creatine kinase energy transfer function that could contribute to ER stress-mediated metabolic alterations in cardiomyocytes.

Mitochondrial environment

We then sought to determine the mechanism that led to mitochondrial dysfunction in response to ER stress. As we observed substantial cytoarchitectural modification in response to TN treatment, we first performed a morphometric analysis of the mitochondrial environment, which corresponds to the presence of organelles at a distance of 20 nm or less from mitochondrial surface. As shown in Table S5, the most common structures close to mitochondria in control and TN-treated cardiomyocytes were myofibrils (41.3±9.2 % vs. 36.5±2.2 %, respectively) and neighboring mitochondria (29.9±6.1 % vs. 35.0±6.9 %, respectively). The remaining environment of mitochondria was represented by SR, rER and mixed smooth and rough reticulum, ribosomes and polyribosomes, dyads and transversal tubules, cytoplasm, plasma membrane and lipid droplets (Table S5). Among the different organelles found in the mitochondrial environment, only the proportion of rER that lies in close contact with mitochondria, the so-called mitochondria-associated-membranes fraction (MAM), was increased by ER stress induction from 0.7 ± 0.2 in control to 2.1 ± 0.6) while the total occurrence of reticular network (smooth and rough) near mitochondria was not changed.

Mitochondrial calcium homeostasis

Given that MAM plays a key role in the transport of calcium from the SR/ER to mitochondria, the mitochondrial calcium content in response to ER stress was examined. Assessment of specific mitochondrial calcium loading with Rhod-2-AM was performed on isolated cardiac fibers. With our staining protocol, fluorescent dye showed a specific mitochondrial staining, overlapping with the mitochondrial marker MitoTracker Green (Manders coefficient >97%, Figure S1B). First, we observed that when cardiac fibers isolated from control mice were treated with TN (40 µg/ml), a fast and progressive increase of the Rhod-2-AM signal was induced, indicating that acute ER stress induces a rapid mitochondrial calcium uptake (Figure 6H). Second, when cardiac fibers were isolated from mice challenged for 72 h with vehicle (CTL) or with TN, we observed that the mitochondrial calcium content, normalized to mitochondrial mass (MitoTracker Green), was unchanged (Figure 6I-J). Calcium fluxes between ER and mitochondria were then monitored upon histamine stimulation (IP3R-dependent ER Ca 2+ efflux activator), in order to release calcium from ER through the IP3R. Mitochondrial Ca 2+ uptake induced by histamine was significantly reduced in TN-treated mice by comparison with CTL (Figure 6I-K). The alteration of Ca 2+ flux between ER and mitochondria was associated with unchanged IP3R1 protein level but decreased VDAC and MCU contents (Figure S1C). Altogether, these results demonstrate that 72 h after ER stress, the Ca 2+ transfer between SR/ER and mitochondria is impaired.

ER stress and cardiac disease

The important alteration of mitochondrial function should represent a major pathological event contributing to cardiac dysfunction. Therefore, we reasoned that ER stress could contribute to the alteration of mitochondrial function reported in cardiac diseases. To support these results, we conducted a search of public gene expression repositories on BioGPS (http://biogps.org/#goto=welcome) to identify a possible link between ER stress and mitochondrial function. [START_REF] Wu | BioGPS: building your own mash-up of gene annotations and expression profiles[END_REF] Using microarray analyses of the dataset E-GEOD-19322 [START_REF] Hunt | Early postmyocardial infarction survival in Murphy Roths Large mice is mediated by attenuated apoptosis and inflammation but depends on genetic background[END_REF] , we reported an activation of the ER stress response in a mouse model of myocardial infarction (MI) (Figure 7A). Interestingly, the expression profile of genes of the ER stress response was heterogeneous. The increased expression of some genes was transient and reached a maximum 1 day after MI and returned to normal level 5 days after MI (e.g. Chop, Grp78, Xbp1, Atf3 and Atf4), whereas the expression of other genes increased progressively (e.g. Edem1, P58ipk, Pdia4

and Calreticulin) (Figure 7A). Given that the expression of all members of the PGC-1α pathway were dramatically decreased upon TN injection, we paid a specific attention to PGC-1α expression in the context of MI. PGC-1α expression varies highly among the different conditions of the dataset (Sham and MI, infarct and border region, 1 day or 5 days after MI) and in agreement with our data, a dramatic decrease of PGC-1α mRNA in the stressed region 1 day and 5 days after MI was observed (Figure 7B). Consequently, the expression of citrate synthase, (Cs), Tfam and CoxIV were decreased. Moreover, a strong negative correlation between the expression of genes of the UPR and Pgc-1α was observed (Figure 7C-M). Interestingly, the negative correlation between the IRE1 and ATF6 branches of the ER stress response and Pgc-1α is strong and highly significant (Figure 7C One purpose of this study was to evaluate the effect of acute ER stress in the heart in vivo. Our results demonstrate that TN-induced ER stress triggers a rapid phosphorylation of eIF2α and an increase in the expression of the ER stress markers GRP78, CHOP and GADD34 in cardiomyocytes. Furthermore, TN injection resulted in the reduction of cardiac contractility after 72 h and thus represents a valuable tool to evaluate the early effects of ER stress in cardiomyocytes. In a previous study, it was reported that ER stress impairs intracellular Ca 2+ homeostasis and excitation-contraction coupling in cardiomyocytes [START_REF] Yang | Antioxidant metallothionein alleviates endoplasmic reticulum stress-induced myocardial apoptosis and contractile dysfunction[END_REF] . However, the mechanisms underlying these defects were not investigated. Here, we show that early effects of ER stress are accompanied by a reorganization of the reticulum network. Importantly, we evidenced the presence of rough instead of smooth reticulum at the interfibrillar space. The presence of tubules covered by ribosomes/polyribosomes in the vicinity of myosin myofilaments (A band) in TN-treated mice shows the possible changes of the properties of the endomembrane network in adult cardiomyocytes and could be an adaptive response to ER stress. The increased occurrence of rER in TN-treated cardiomyocytes at the level of dyads suggests higher protein synthesis in these areas and reorganization of the dyadic microdomains. Our findings suggest that structural alterations of the excitation-contraction coupling apparatus could be involved in ER stressmediated cardiac dysfunction and that ER stress could contribute to the depressed Ca 2+ cycling observed in cardiac diseases.

In the heart, the SR has been widely considered as just a different name for the ER, but recent biochemical and ultrastructural analysis support the concept of functionally distinct SR and ER compartments. [START_REF] Minamino | ER stress in cardiovascular disease[END_REF] In agreement, we observed in control mice distinct SR and ER systems. In response to ER stress, an increase in the amount of rough endoplasmic reticulum was observed in the intermyofibrillar region. This observation might appear surprising because a hallmark of the UPR via the PERK/eIF2α axis is translational arrest to prevent overloading of ER with nascent proteins. In fact, as a consequence of UPR induction, a continued association, rather than release, of ER-bound ribosomes has been reported [START_REF] Stephens | Stable ribosome binding to the endoplasmic reticulum enables compartment-specific regulation of mRNA translation[END_REF] . In addition, the authors showed that when UPR is elicited, mRNA translation is sustained in the ER compartment, whereas it is suppressed in the cytosol. Therefore, the increased rER and ribosome content after TN treatment observed in cardiomyocytes could be considered as a compensatory mechanism to cope with ER stress. We also observed ultrastructural continuity between rough and smooth reticulum that were shown to share their lumen, indicating that the endomembrane system may form one continuous network.

These observations reveal that the reticular network not only is a dynamic membrane system but also may have a high plasticity evolving from smooth to rough morphology to adapt to cellular conditions.

Optimal mitochondrial ATP production is essential in normal cardiac function and it is now established that mitochondrial biogenesis and function is altered in numerous cardiac diseases including heart failure [START_REF] Neubauer | The failing heart--an engine out of fuel[END_REF][START_REF] Ventura-Clapier | Bioenergetics of the failing heart[END_REF] . However, the pathological mechanisms associated with alteration of the mitochondrial function in cardiac diseases remain not fully understood. In this study, we demonstrate that ER stress induces important alterations of the mitochondrial oxidative function.

In functional experiments on permeabilized cardiac fibers, alteration of the mitochondrial respiration induced by ER stress is not specific to a respiratory complex as values for complex I, I+II, II and IV dependent-respiration are similarly decreased. Remarkably, this global alteration of mitochondrial function is only visible in phosphorylating state suggesting a decrease in ATP production. This is accompanied by an increase in mitochondrial network fragmentation as suggested by the increased occurrence of small mitochondria, associated with an increase of the profission factor DRP1 and a decrease of the profusion factor MFN2, although it cannot be excluded that small mitochondria represent protrusions of large mitochondria. These results suggest that ER stress could contribute to the development of cardiac diseases by impairing mitochondrial structure and functions.

It has been demonstrated that cardiac dysfunction is associated with a shift from fatty acid to glucose utilization for ATP generation [START_REF] Nascimben | Mechanisms for increased glycolysis in the hypertrophied rat heart[END_REF][START_REF] Osorio | Impaired myocardial fatty acid oxidation and reduced protein expression of retinoid X receptor-alpha in pacing-induced heart failure[END_REF] . The implication of this metabolic shift in the pathogenesis of cardiac diseases is still debated as both activation and inhibition of fatty acid oxidation are considered as potential therapeutic strategies. [START_REF] Abdurrachim | Good and bad consequences of altered fatty acid metabolism in heart failure: evidence from mouse models[END_REF] In any cases, the decrease of fatty acid oxidation is interpreted as an oxygen-sparing mechanism, but the mechanism that triggers this shift is still poorly understood. We demonstrate here that ER stress induced a shift from fatty acid oxidation to glucose utilization as evidenced by an increase of the lactate dehydrogenase activity and a decrease of β-oxidation capacity after TN treatment. ER stress could thus represent a new mechanism underlying the metabolic shift observed in cardiac disease.

One other important finding of this study is the dramatic ER stress-induced decrease in expression of proteins involved in mitochondrial biogenesis that are regulated by the co-activator PGC-1α. This alteration of PGC-1α levels could represent a major insult in the pathological development of the disease. This hypothesis is supported by the bioinformatic study that we conducted on a mouse model of myocardial infarction [START_REF] Hunt | Early postmyocardial infarction survival in Murphy Roths Large mice is mediated by attenuated apoptosis and inflammation but depends on genetic background[END_REF] that revealed a similar alteration of PGC-1α expression. Importantly, we found strong negative correlations between several members of the IRE1 and ATF6 branches of the UPR and PGC-1α expression, suggesting that one member of these pathways may be a direct regulator of PGC-1α expression at the transcriptional level. The high similarity of the activation IRE1 and ATF6 pathways probably reflect their interconnection through XBP1. These results also evidenced that the PERK pathway is less connected to the other branches and present its own kinetic of activation. Interestingly, a decrease of PGC-1α expression was reported upon induction of ER stress in liver [START_REF] Purushotham | Hepatocyte-specific deletion of SIRT1 alters fatty acid metabolism and results in hepatic steatosis and inflammation[END_REF] , suggesting that this alteration is not organ specific. A link between CHOP and PGC-1α has also been recently evidenced in diabetic CVR-2017-781 20 embryopathy 34 . However, additional studies are needed to confirm the close relationship between the UPR and PGC-1α expression in cardiac diseases. Although mitochondrial biogenesis was decreased upon ER stress, the short onset of apparition of mitochondrial dysfunction associated with the fact that in the heart, mitochondria are stable organelles with a half-life of 5.6 to 6.2 days, suggest that mitochondrial alteration could not be entirely explained by a mitochondrial self-renewal defect and that other mechanisms may underlie this process.

The main physiological role of Ca 2+ uptake in mitochondria is to increase the activity of ratelimiting enzymes of the Krebs cycle and ATP production [START_REF] Bravo | Increased ER-mitochondrial coupling promotes mitochondrial respiration and bioenergetics during early phases of ER stress[END_REF] . Oppositely, mitochondrial Ca 2+ overload uncouple oxidations from phosphorylation and triggers opening of the mitochondrial Permeability Transition Pore (mPTP) leading to apoptotic cell death [START_REF] Filadi | The endoplasmic reticulum-mitochondria coupling in health and disease: Molecules, functions and significance[END_REF] . Several studies have shown that alterations in organelles' functional tethering is a common hallmark in different pathologies, such as metabolic syndrome, cancer and neurodegenerative diseases [START_REF] Filadi | The endoplasmic reticulum-mitochondria coupling in health and disease: Molecules, functions and significance[END_REF] . Indeed, Ca 2+ transfer between ER and mitochondria are altered in diabetic mice and the restoration of this flux improves hepatocytes insulin sensitivity [START_REF] Tubbs | Mitochondria-associated endoplasmic reticulum membrane (MAM) integrity is required for insulin signaling and is implicated in hepatic insulin resistance[END_REF] . Similarly, the restoration of this interorganelle Ca 2+ transfer improves muscle contractility in a mouse model of Duchenne muscular dystrophy [START_REF] Pauly | ER stress disturbs SR/ER-mitochondria Ca(2+) transfer: Implications in Duchenne muscular dystrophy[END_REF] .

Altered ER-mitochondria associations are also observed in various neurodegenerative diseases including Alzheimer, Parkinson and amyotrophic lateral sclerosis and it is thought that correcting damaged ER/mitochondria association may correct damage to other neurodegenerative diseaselinked features [START_REF] Joshi | The entangled ER-mitochondrial axis as a potential therapeutic strategy in neurodegeneration: A tangled duo unchained[END_REF] . In the heart, Ca 2+ crosstalk between SR/ER and mitochondria has been involved in myocardial reperfusion injury [START_REF] Garcia-Dorado | Calciummediated cell death during myocardial reperfusion[END_REF] and the inhibition of SR/ER/mitochondria interactions protects cells against reperfusion injury [START_REF] Paillard | Depressing mitochondria-reticulum interactions protects cardiomyocytes from lethal hypoxia-reoxygenation injury[END_REF] . Here, we demonstrated that acute ER stress challenge provokes a rapid mitochondrial calcium uptake, as previously described in other cell types [START_REF] Deniaud | Endoplasmic reticulum stress induces calcium-dependent permeability transition, mitochondrial outer membrane permeabilization and apoptosis[END_REF] . Intriguingly, despite increased contact between rER and mitochondria, a prolonged ER stress (72 h) leads to a decrease of mitochondrial Ca 2+ uptake in response to histamine-induced rER calcium release. We reasoned that acute ER stress induces mitochondrial Ca 2+ overload leading to a reduction of mitochondrial membrane potential that in turn, reduces mitochondrial Ca 2+ uptake. This hypothesis is in agreement with the demonstration that ER stress slows intracellular Ca 2+ clearance in cardiac cells [START_REF] Yang | Antioxidant metallothionein alleviates endoplasmic reticulum stress-induced myocardial apoptosis and contractile dysfunction[END_REF] . Decreased mitochondrial calcium content and membrane potential may thus explain decreased respiration rates. Besides, we measured a decrease of MFN2 expression after 72 h of ER stress induction. Although the role of MFN2 in the ER-mitochondria CVR-2017-781

21

tethering is still debated [START_REF] Filadi | Mitofusin 2 ablation increases endoplasmic reticulum-mitochondria coupling[END_REF][START_REF] Naon | Critical reappraisal confirms that Mitofusin 2 is an endoplasmic reticulum-mitochondria tether[END_REF] , its decrease could explain the alteration of Ca 2+ transfer between the two organelles.

It was recently showed that the three subsets of heart mitochondria (i.e. intermyofibrillar, subsarcolemmal and perinuclear mitochondria) are morphologically different and respond differently to ischemic stress [START_REF] Kalkhoran | Unique morphological characteristics of mitochondrial subtypes in the heart: the effect of ischemia and ischemic preconditioning[END_REF] . In our model of ER stress induction, the reduction of mitochondrial size was detected only in the intermyofibrillar region, in which the occurrence of rER as well as rER-mitochondria interactions was increased. Our observations that TN induces a rapid mitochondrial Ca 2+ uptake and a decrease of mitochondrial size, suggest that increased Ca 2+ transfer from rER to mitochondria can participate in mitochondrial fragmentation, as reported for other cells [START_REF] Rizzuto | Ca(2+) transfer from the ER to mitochondria: when, how and why[END_REF] .

In conclusion, we identified ultrastructure modifications of cardiomyocytes in response to ER stress with reticulum network disorganization. An important finding was that after 72 h, ER stress reduces mitochondrial Ca 2+ uptake and triggers an alteration of all components of cardiac energy metabolism, from the substrate utilization to the oxidative phosphorylation and the transport of energy to the myofibrils. These results provide evidence that ER stress could represent an early mechanism that contributes to the impaired energy metabolism reported in most cardiac diseases.

  -I), whereas the correlation with the PERK branch of the UPR is less (Atf4 and Atf3, Figure7J, K) or not (Gadd34 and Chop, Figure7L, M) significant. This suggests that a member of the IRE1 or ATF6 pathway could directly regulate Pgc-1α expression.Altogether, these results demonstrate that ER stress induces a robust alteration of mitochondrial function and biogenesis and suggest that the well described decrease of PGC-1α expression during cardiac disease could be induced by ER stress.DISCUSSIONDifferent studies have demonstrated the importance of ER stress in the development of cardiac diseases, but the lack of a reliable model raises the difficulty to more specifically delineate the effects of ER stress per se from other pathophysiological processes. Because the ER stressor tunicamycin specifically affects N-linked glycosylation of proteins in the ER, intraperitoneal injection of TN constitutes an interesting model to study the functional effects or ER stress in the heart but was never precisely characterized. Here, we provide evidence that TN injection corresponds to a valuable model and reveal undescribed early adaptations of cardiomyocytes to ER stress. A limitation of this in vivo model is that the changes induced by TN treatment may be compensatory responses secondary to cardiac dysfunction and not due to ER stress.However, our model was designed to minimalize secondary side effects, and in vitroexperiments on isolated fibers support our conclusions that most modifications reported here are direct responses to ER stress induction. We demonstrated that ER stress induces an important alteration of the ultrastructure of cardiomyocytes that presented as early signs of cardiomyopathy phenotype, accompanied by a reorganization of the endomembrane system and modifications of mitochondrial structures. ER stress induced a profound inhibition of mitochondrial biogenesis pathway, an inhibition of mitochondrial respiration and a decrease in mitochondrial fatty acid utilization. These metabolic alterations may play an important role in the ER stress-induced cardiac dysfunction.

Figure 1 .

 1 Figure 1. Tunicamycin increases ER stress markers and induces cardiac dysfunction.

Figure 2 .

 2 Figure 2. Ultrastructural alterations of the reticular membrane network induced by ER stress in cardiomyocytes.

Figure 3 .

 3 Figure 3. ER stress induces alteration of the dyadic microdomains in cardiomyocytes.

Figure 4 .

 4 Figure 4. Ultrastructural alteration of the mitochondrial environment induced by ER stress.

Figure 5 .

 5 Figure 5. Cardiac energy metabolism of control and TN-treated mice.

Figure 6 . 30 Figure 7 .

 6307 Figure 6. Cardiac lipid metabolism and energy transfer of control and TN-treated mice.

ACKNOWLEDGEMENTS

We thank F. Lefebvre for helpful technical assistance and V. Domergue-Dupont and the animal core facility of IPSIT for efficient handling and preparation of the animals. We thank L. Novota for skillful technical assistance and preparation sections for electron microscopy. We thank A.

Vandestienne for technical assistance for western blots. We gratefully acknowledge Dr AM.

Gomez and Dr R. Fischmeister for continuous support.

FUNDING

This work was funded by the grant ANR-10-LABX-33 as members of the Laboratory of Excellence LERMIT, FRM (Fondation pour la Recherche Médicale) to A. Garnier (#DPM20121125546), Région Ile de France CODDIM to R. Ventura-Clapier (#cod110153) and by grant VEGA 2/0110/15, APVV-15-0302 and SK-FR-2015-0007 to M. Novotova. A. Prola received a fellowship from Groupe de Réflexion sur la Recherche Cardiovasculaire (GRRC). A. Guilbert received a fellowship from Région Ile de France CORDDIM.

CONFLICT OF INTEREST

No potential conflicts of interest were disclosed by the other authors. Table S4: Quantification of the cardiomyocyte composition.

Supplementary Figures

Mice were injected i.p. with TN (2 mg/kg) or with vehicle (150 mM dextrose) for 72 h and stereological analysis were performed at the test grid point distance of 280 nm to quantify the cardiomyocyte composition. The volume density of organelles is presented as mean percentage ± SEM. n=3 (152 images of control and 161 images of TN-treated mice were analyzed). * P<0.05 vs control (Mann-Whitney U test).

Table S5: Environment of mitochondria in control and TN-treated mice.


Pakedam Lare

Siyamak Sarabi

Claude Delpha

Demba Diallo

Diagnosis of stator windings short-circuits with PCA and Nuisance Attribute Projection

Keywords: Fault detection, PMaSynRM Inter-turn shortcircuit fault, NAP

Among the data-driven techniques for abnormalities detection in complex systems, Principal Component Analysis (PCA) is popular because of its simplicity and it does not require prior knowledge. However, the used of PCA is limited to stationary data. This work proposes a methodology to address this limitation. It consists of applying Nuisance Attribute Projection (NAP) in the preprocessing stage before the fault features are transformed with PCA to remove the nonstationarity effects due to the variable operating conditions. The proposal is evaluated to detect inter-turn short-circuits in the stator of a Permanent Magnet Assisted Synchronous Reluctance Motor (PMaSynRM) used in the powertrain of electric vehicles. The variances of the phase currents, computed in moving windows, are used as fault features. The results, obtained with seven fault severities and three load conditions, show that monitoring the Hotelling T 2 in the principal subspace leads to good performance, with probabilities of missed detection and false alarms lower than 0.02 and 0.05, respectively. To provide a safety metric, an estimate of the fault level is obtained with an analytical model of the evolution of the slope of the CUmulative SUM decision function with an accuracy greater than 97%.

I. INTRODUCTION

In process control of multivariate systems, Principal Component Analysis (PCA) is widely used because it requires no prior knowledge and is efficient to highlight the correlation among variables [START_REF] He | Process fault detection and diagnosis based on principal component analysis[END_REF]. However, its application lies on the assumption that the variables are stationary (constant mean and variance over all the data time-series observations) and follow Gaussian distribution. [START_REF] Rato | Defining the structure of DPCA models and its impact on process monitoring and prediction activities[END_REF]. Nevertheless, in a dynamic environment such electric vehicles, the variables have nonstationary properties mostly related to the varying operation conditions. To address this limitation, extensions based on the analysis of time-series segmentation with fixed or moving windows have been proposed. For example, the Dynamic Principal Component Analysis (DPCA) has been proposed in [START_REF] Ku | Disturbance detection and isolation by dynamic principal component analysis[END_REF] to deal with autocorrelations. PCA is applied to a new expanded data matrix with time-shifted duplicate vectors for all variables. However, it has been shown in [START_REF] Kruger | Improved principal component monitoring of large-scale processes[END_REF] that the resultant score variables of the DPCA can still be correlated. Consequently, the Probability of False Alarm (P F A) is higher when using the Hotelling's T 2 statistic as fault index. Multi-scale methods known as Multi-Scale PCA (MSPCA) have also been proposed for feature extraction for dynamic systems: each variable is extended to different forms of the variable at different scales. For example, in [START_REF] Bakshi | Multiscale PCA with application to multivariate statistical process monitoring[END_REF] wavelets are used to decompose the variables into various scale representations. Then PCA is used to obtain the coefficients for wavelet reconstitution. The PCA algorithm is applied to the reconstructed data for fault detection. However, the accuracy of this methodology highly depends on the wavelet coefficients, which are not always optimal [START_REF] Malluhi | Enhanced multiscale principal component analysis for improved sensor fault detection and isolation[END_REF]. These extensions of the usual PCA come with some weaknesses like long response time, computational complexity, and their effectiveness is not always guaranteed. Determining the severity level of the defect is one of the crucial operations of the diagnosis. Indeed, it allows making the appropriate safety decision. The CUSUM decision function has proven to be an effective tool for estimating the severity of faults in electrical systems [START_REF] Delpha | Multiple incipient fault diagnosis in three-phase electrical systems using multivariate statistical signal processing[END_REF]. This work proposes a simple method for detecting short circuit faults between the turns of a PMaSynRM for different mechanical load conditions and levels of fault severity. The Nuisance Attribute Projection (NAP) is applied to the raw data in the preprocessing step to eliminate the data variabilities related to the load variation. This helps to get fault features that are only sensitive to the fault occurrence. The features are then normalized before being transformed with PCA to detect the fault. The effectiveness of the proposal will be evaluated in terms of probability of false alarm P F A and probability of missed detection (P M D). Once the defect is detected, the estimation of the severity level is obtained by the inversion of the analytical model of the evolution of the slope of the CUSUM decision function. The rest of the paper is organized as follows: In Section II, after recalling the basics of PCA for fault diagnosis, NAP is presented, and the proposal is described. Section III presents the results and performance of the fault detection and fault severity estimation. Section IV concludes the paper.

II. FAULT DETECTION METHODOLOGY

Let us assume that the original data has N observations for n measured variables, that are arranged in a data matrix X ∈ R N ×n . In this matrix, each vector is written as x T i = [x 1,i , . . . , x N,i ] where x j,i is the jth observation of the ith variable. In this approach, the collected data in healthy operating conditions are used to build the reference model that will be used to evaluate the current data. The PCA and the NAP are first described, and the proposed fault detection strategy is further derived.

A. Principal Component Analysis for fault detection

Basically, PCA is used to reduce data dimensionality by grouping correlated variables in a set of new uncorrelated ones [START_REF] Jolliffe | Principal component analysis for special types of data[END_REF]. For a system with different physical variables of different magnitudes and scales, the original variable data set must be processed to give equal importance to all the variables. One way to achieve this is to give to all variables the same variance regardless of their magnitudes by using the normalization method. The normalization of vector x i is done as follows:

µ xi = 1 N N j=1 x ji σ xi = 1 N -1 N j=1 (x ji -µ xi ) 2 xij = xji-µx i σx i (1)
where µ xi and σ xi are the mean and standard deviation of x i respectively, and xij is the re-scaled observation. In the rest of the paper, the scaled data are considered without bar notation for simplicity. The normalized data is then subject to a linear transformation matrix T to express the variation in the observations such as T = XP, with T ∈ R N ×n the principal component matrix and P ∈ R n×n the eigenvectors matrix containing the eigenvalues λ i of the correlation matrix Σ of X such as:

Σ = P∧P T (2)
where ∧ = diag(λ 1 , . . . , λ n ) is a diagonal matrix whose elements are sorted in decreasing magnitude order. The reduced ldimensional space of the data is obtained by retaining only the principal components that correspond to the l-highest eigenvalues of the covariance matrix. They represent the feature space where most of the patterns in the data are represented (generally up to a given percentage of cumulated variance).

The remaining components with the smallest eigenvalues represent the noise contribution. Once the number of components l to retain is determined, the eigenvectors matrix P and the principal component matrix T are partitioned into the form:

P = Pl P n-l T = Tl T n-l (3)
X is the principal part of the data explained by the l first eigenvectors and the residual part X is explained by the residual components [START_REF] Tharrault | Fault detection and isolation with robust principal component analysis[END_REF]:

X = Pl PT l X X = P n-l P T n-l X (4)
They respectively lead to the principal and residual subspaces used for fault diagnosis. A process monitoring with PCA uses Hotelling's T 2 and Q statistics also called Squared prediction error (SP E) to detect abnormal behaviors. Hotelling's T 2

and SP E represent the variability in the Principal Component Subspace (PCS) and the Residual Subspace (RS), respectively. T 2 can be expressed by using the estimated value Σ of the correlation matrix as follows [START_REF] Engelen | A comparison of three procedures for robust PCA in high dimensions[END_REF]:

T 2 = XT Σ-1 X (5)
Under normal conditions, if the data set is multivariate Gaussian distributed, the T 2 can be approximated by a χ2 distribution with l degrees of freedom and a significance level (1-α).

The system operation is considered healthy if

T 2 ≤ T 2 α . T 2 α = χ 2 l,1-α (6)
A variation of the variables' correlation indicates abnormal behavior. Under this condition, the sample matrix X increases its projection to the RS, and the magnitude of X reaches abnormal values compared to those obtained during healthy conditions. SP E is the magnitude of X and is written as:

SP E =∥ X ∥ 2 (7)
The process is considered healthy if the SP E statistic is under its control limit which is expressed as SP E ≤ SP E α :

SP E α = (μ + σz 1-α ) 3 (8)
with z 1-α as the (1 -α) significance level of a Gaussian distribution Φ. μ and σ are the estimated mean and standard deviation of SP E 2/3 [START_REF] Engelen | A comparison of three procedures for robust PCA in high dimensions[END_REF], respectively.

B. Nuisance Attribute Projection

Originally applied to reduce the signal interference from different channels in speaker recognition, it has been recently applied to condition-based maintenance to improve fault diagnostic. Its principle is explained graphically in Figure 1. The raw data are organized in the matrix X while X ′ is the data matrix from which the nuisances have been removed. Therefore, it is expected that X ′ is representative of the fault information. The transformation from X to X ′ is obtained with NAP as follows:

X ′ = PX (9)
where P ∈ R N ×N is the projection matrix.

P = I - d i=1 ∆ i ∆ T i ( 10
)
where I is an N × N identity matrix, ∆ i represents the i th NAP direction, d is the number of NAP directions to be removed from the feature space and d ≤ N . The parameter d can be determined by making a compromise between the computational complexity and the projection effect. Indeed, larger is d, better is the projection effect (nuisance mitigation) but higher is the computation time. The main objective of the NAP is to minimize the Projection Effect (PE) defined as follows:

PE = i,j W ij P • x i -P • x j (11)
W ij is a weight coefficient that quantifies the relation between two feature vectors. It is defined as follows [START_REF] Campbell | SVM based speaker verification using a GMM supervector kernel and NAP variability compensation[END_REF]:

W ij = 1 if x i ̸ = x j 0 otherwise (12)
The minimization of PE in equation 11 can be transformed into finding the leading eigenvectors of the following eigenproblem [START_REF] Ma | A fault diagnosis approach for rolling bearing based on convolutional neural network and nuisance attribute projection under various speed conditions[END_REF]:

X(W -diag(WU))X T ν = λν ( 13
)
where U is an identity column vector, W the matrix of weight coefficients W ij , λ the eigenvalues, and ν the eigenvectors. The solution to this problem is established in [START_REF] Campbell | SVM based speaker verification using a GMM supervector kernel and NAP variability compensation[END_REF].

C. Elimination of attributes related to varying operating conditions

In our proposed fault detection methodology, a preprocessing step based on NAP is added to the conventional PCA to address its limitation to deal with dynamic processes. Initially, the stator three-phase currents are collected in the time domain under different mechanical loads. For feature extraction with less burden of large data, the sliding windows variance, on consecutive non-overlapping windows of fixed size is proposed to collect the data statistical features. The sliding windows variance is applied to the three-phase current signal in the time domain to get the data matrix X. For a stator phase current signal I (s) , the jth observation of the ith variable x j,i of the matrix X is derived as follows [START_REF] Villarreal-López | A new scheme for multiple fault detection and isolation for rotational mechatronic systems, by means of analytical redundancy and adaptive filtering[END_REF]:

x i,j = 1 ω -1 N I (s) m ∈Ωj I (s) m -μ 2 ( 14
)
where μ is the mean of the samples window Ω j = {I (s) (j-1)ω+1 , . . . , I (s) j×ω }. To guarantee the data features properties, and to not violate the non-stationarity property of the data, the window size should be quite small. In this case study, the window size equals to the period of the phase current is used. For a variable speed drive the window size equivalent to the largest velocity series identified would be recommended.

The features are extracted for the healthy and test data using the moving variance. The NAP projection is at first computed using the healthy data to get the model P, which is independent of the dynamic load variations. To compute the projection matrix P, the weight matrix W is generated to make the features independent. The minimization of the projection Effect (PE) is then achieved by setting the columns of ν to be the σ most principal eigenvectors of the eigenvalue analysis in Equation 13. In our case, we set σ = min(dim X , d), dim X as the dimension of the features, and d as the number of the NAP directions. The model projection matrix P is used to remove from the healthy and actual features the effects of dynamic load variations. The transformed features are then used as inputs to the PCA for fault detection. The flowchart displayed in Figure 2 summarizes the proposal.

III. RESULTS AND DISCUSSIONS

In this section, the proposed methodology is applied to the detection of stator inter-turn short-circuits in a PMaSynRM.

A. Data generation and feature extraction

To evaluate the proposal, the model of the PMaSynRM presented in [START_REF] Lare | Stator winding inter-turn short-circuit and air gap eccentricity fault detection of a permanent magnet-assisted synchronous reluctance motor in electrified vehicle[END_REF] and [START_REF] Lare | Modelling of a pma-synrm for the detection of inter-turn short-circuit[END_REF] is used. The characteristics of the electrical machine, and simulation parameters are displayed in Table I. The PMaSynRM winding under an inter-turn shortcircuit fault in phase a is shown in Figure 3.

Under this faulty condition, the phase a current i a is divided into: i s the current in the defective part of the winding and i f the current in the inter-turn fault's contact branch. L a1 and L a2 represent the inductances of the healthy and faulty subcoils of the phase a winding, respectively. M a1b and M a1c are the mutual inductances between the healthy sub-coil L a1 and the coils L b , and L c , respectively. On the other hand M a1a2 , M a2b and M a2b represent the mutual inductances between the sub-coil L a2 and the healthy sub-coil L a1 , and coils L b , and L c , respectively. Three load conditions (Γ 1 = 18N m, Γ 2 = 134N m, Γ 3 = 260N m), each 3s long, are simulated at a controlled rotating speed of 1500rpm. The short-circuits are emulated by changing the stator resistances and inductances. The faults of 1s duration are introduced after 1s for each case study. Seven severity levels are considered in this study, ranked from 2 to 8. This rank is related to the number of turns short-circuited in the winding of phase a.

Figure 4 displays the current flowing in the phase windings a of the PMaSynRM under healthy and faulty (fault severity level 2) conditions for the three different load cases.

Healthy data collection

Healthy features extraction

Moving variances of healthy data

NAP

Find nuisance projection matrix P

Faulty data collection

Faulty stator 3-phase currents The fault characteristics are the variances of the phase currents. They are calculated using a moving window whose length is equal to the period of the currents, and stored in the data matrix X.

Faulty data features extraction

Moving variances of faulty data

Faulty data features transformation

Nuisance attributes elimination

Healthy data features transformation

B. Simulation results

As displayed in Figure 2, the procedure is composed of two parts: the first one (on the left side) uses the healthy data to obtain the projection matrix P that is used to transform the actual data (test data) for fault detection. The number of NAP directions is set to d = 3. Figure 5 displays for the healthy data the original features and the projected ones for three different loads. It can be clearly seen that after projection with the NAP, the new features are insensitive to load variations. The new healthy features are used to design the model for the PCA. The threshold of the cumulative percentage variance is set to 90%. Figure 6 shows that the first two principal components capture 98.67% of the information. Therefore, in the PCA model, the principal subspace is spanned with the first two components while the third one defines the residual subspace. The Hotelling T 2 and the squared prediction error SP E will be used as fault indicators. The thresholds T 2 α and SP E α are set at 1-0.99 confidence level, are for χ2 and z distributions, respectively. The results for the fault level 2 are shown in Figure 7. The dashed lines represent the thresholds.

Figure 8 shows the overall performance comparison of the T 2 and SP E monitoring in terms of probability of missed [START_REF] Weber | Increasing effectiveness of model-based fault diagnosis: A dynamic bayesian network design for decision making[END_REF]. In Figure 8, these typical values are highlighted with dashed lines. For all case studies, it is observed that with the T 2 , the fault detection performance is 100%. However, with SP E, the P M D is higher than the threshold for severities 2 and 5. These results show that for detecting inter-turn short circuits in an electrical machine, monitoring the Hotelling T 2 in the principal subspace is more efficient. This analysis indicates that, in our case study, the system modelling errors are projected onto the residual component which makes it less sensitive to the fault.

C. Fault estimation

Let us consider µ T 2 0 as the mean value of the selected fault index T 2 under healthy condition. As it can be observed in Figure 7 the average value undergoes an abrupt change to a new value denoted as µ T 2 1 when the defect appears. Under the assumption that the variance σ 2 T 2 of T 2 is constant, the instantaneous likelihood ratio s(i) of the i th observation of the distribution of T 2 is given as follows [START_REF] Basseville | Detection of abrupt changes: theory and application[END_REF]:

s(i) = µ T 2 1 -µ T 2 0 σ 2 T 2 T 2 (i) - µ T 2 1 + µ T 2 0 2 (15)
The CUSUM function S N for the N observations of T 2 and the CUSUM decision law D S N are given as follows [START_REF] Basseville | Detection of abrupt changes: theory and application[END_REF]:

S N = N i=1 s(i) D S N = S Ni -min 1≤t≤i (S Nt ) (16)
A fault is detected when D S N is greater than the threshold T 2 α . The top of the Figure 9 shows a clear change in the T 2 , despite fluctuations, while the bottom of the figure shows the evolution of the CUSUM decision function for the fault level 2. The latter also provides a relevant fault indicator. Compared to T 2 monitoring shown in Figure 8, the CUSUM monitoring leads to similar performance. Fig. 9: CUSUM for fault monitoring

The severity of the faults varies from 0.25 to 1, corresponding to the number of short-circuited turns from 2 to 8. Figure 10 shows the evolution of the slope of the CUSUM decision function as a function of fault severity for the three load levels. It can be observed that the slope of the decision function increases monotonically with the severity of the defect regardless of the mechanical load. Therefore, it is a relevant characteristic that can be used to estimate the fault severity. For the three load conditions, the evolution of the slope of the CUSUM decision dS N as a function of fault severity f can be approximated by an exponential function as follows:

dS N = ae b×f (17)
where a and b are coefficients determined from the three load conditions. The upper section in Figure 11 shows the evolutions of the actual and analytical approximation of dS N for the three load conditions. At the bottom, the actual and estimated fault severities are shown. The estimation performance IV. CONCLUSION In this paper, a fault detection methodology is proposed for inter-turn short-circuit fault monitoring in an electrical drive. An accurate model of the electrical powertrain is used to generate the dataset composed of measured phase currents under seven fault severities for three different loads. The variances of the currents flowing in the windings of the electrical machine are used as fault features. They are computed in a moving window whose length is equal to the period of the phase currents. The fault detection methodology combines the Nuisance Attribute Projection (NAP) with Principal Component Analysis (PCA). NAP is used in the preprocessing stage to remove from the fault features the effects of load variations, which are inherent in electric drives. This extra step only causes 2.12% increase of the computation time of the fault diagnosis. The probabilities of missed detection and false alarms (P F A and P M D) are computed to evaluate the method's performance when using the Hotelling T 2 or the Squared Prediction Error SP E as fault indexes. The results show that monitoring the T 2 in the principal subspace is the most efficient. An analytical model of the slope of the CUSUM decision function is derived, from which the fault severity is estimated. Compared to the actual fault level, the accuracy of the estimation is higher than 97%.

Fig. 1 :

 1 Fig. 1: Schematic diagram of NAP principle

Fig. 2 :Fig. 3 :Fig. 4 :

 234 Fig. 2: Flowchart of the NAP-based PCA methodology

Fig. 5 :

 5 Fig. 5: Comparison of features before and after NAP

Fig. 6 :

 6 Fig. 6: Variance captured by each principal component

Fig. 7 :F a u lt le v e l 2 F a u lt le v e l 3 F a u lt le v e l 4 F a u lt le v e l 5 F a u lt le v e l 6 F a u lt le v e l 7 FF a u lt le v e l 2 F a u lt le v e l 3 F a u lt le v e l 4 F a u lt le v e l 5 F a u lt le v e l 6 F a u lt le v e l 7 F a u lt le v e l 8 0Fig. 8 :

 723456723456788 Fig. 7: Fault level 2 detection with NAP-based PCA Performance comparison of T 2 and SPE monitoring

Fault level 2 Fault level 3 Fault level 4 Fault level 5 Fault level 6 FaultFig. 10 :

 2345610 Fig. 10: Slope of CUSUM decision function

Fig. 11 :

 11 Fig. 11: Fault severity estimation

TABLE I :

 I The PMaSynRM characteristics

	Motor characteristics
	Number of poles	8
	Number of PMs per pole	5
	Rated power [kW ]	208
	Maximum operating speed [rpm]	14000
	Number of turns	8
	Stator phase winding resistance value at 20 • [mΩ]	6.1
	Simulation parameters
	Permanent Magnet flux amplitude [W b]	6.24 ×10 -2
	Moment of inertia [kgm 2 ]	0.0357
	Input DC voltage amplitude [V ]	412

Actual fault level 10 2 10 4 10 6 Analytical model under load 2 condition

	CUSUM slope	10 4 10 6	Analytical model under load 1 condition dS N y=59.844e 9.2375x		dS N y=70.5831e 8.9419x				10 4 10 6	Analytical model under load 3 condition dS N y=6.3113e 10.6439x
														10 2
			0.2	0.4	0.6	0.8	1	0.2	0.4	0.6	0.8	1	0.2	0.4	0.6	0.8	1
					Actual fault level									Actual fault level
	Estimated fault level	0.2 0.2 0.4 0.6 0.8 1	0.4 Estimation under load 1 condition 0.6 0.8	1	0.2 0.2 0.4 0.6 1 0.8	0.4 Estimation under load 2 condition 0.6 0.8	1	0.2 0 0.5 1	0.4 Estimation under load 3 condition 0.6 0.8 Actual value Estimated value	1
					Actual fault level			Actual fault level				Actual fault level

Authorized licensed use limited to: Centrale Supelec. Downloaded on January 17,2024 at 10:31:04 UTC from IEEE Xplore. Restrictions apply.


Lu Zhang
email: lu.zhang@centralesupelec.fr

Claude Delpha
email: claude.delpha@centralesupelec.fr

Demba Diallo
email: demba.diallo@centralesupelec.fr

Performance of Fault Severity Estimation in 7-Phase Electrical Machines under Noisy Conditions

Keywords: Fault severity estimation, 7-phase machines, Stationary frames, Noisy environment, CUSUM, Natural frame: 7 phases denoted

This work proposes a method for estimating fault severity in the presence of noise using the measured currents for a 7-phase electrical machine. The method is based on analytical models in stationary reference frames and analysis of the DC and fundamental components in the four fictitious machines. The slope of the decision function from the CUSUM algorithm, which will be noticeably different depending on the fault severity, is used to assess the performance of the fault severity estimation rapidly. The effects on the decision function's slope of the fault severity estimation for different noise levels are evaluated. The simulation results show that even in presence of high noise levels, the decision function is an efficient fault estimation indicator. When the noise level is high, the decision function and its slope are noisier. Conversely, the decision function and its slope are less noisy when the noise level is low. The results also show that for the three fault types under study (gain fault, phase shift fault, and mean value fault), the current components of the fictitious machines in the stationary frames have distinct robustness to noise.

I. INTRODUCTION

Studies in the last decades, particularly monitoring of electrical machines, have provided important information on Fault Detection and Diagnosis (FDD), which is decomposed into fault detection, isolation and estimation [START_REF] Basseville | Detection of abrupt changes: theory and application[END_REF]. Despite the continued dominance of three-phase machines, there is a growing trend towards designing and utilizing machines with five, seven, or nine phases, driven by their inherent ability to tolerate faults and distribute power more effectively [START_REF] Diallo | Current-based analytical model derivation to analyse fault effects in 5-phase pmsm[END_REF], [START_REF] Semail | Vectorial formalism for analysis and design of polyphase synchronous machines[END_REF]. This paper will focus on a seven-phase electrical machine whose main application areas are air and sea transport or wind turbines.

The detection, isolation, and estimation of faults involve extracting and analyzing fault signatures or features from measured or estimated variables or parameters. The features can be extracted in the time, frequency, or time-frequency domain, depending on fault types. Reference [START_REF] Delpha | Multiple incipient fault diagnosis in three-phase electrical systems using multivariate statistical signal processing[END_REF] proposes a time-domain approach to detect and diagnose multiple faults in a three-phase electrical machine. Reference [START_REF] Zhang | Current-based analytical model for fault detection and diagnosis in 7-phase machines[END_REF] introduced an analytical current flow model for a seven-phase machine and fault analysis performed in time and frequency domains.

The authors would like to thank China Scholarship Council for funding.

After the fault is detected and isolated, the estimation of its severity is crucial for maintenance and control reconfiguration. The estimator's performance depends on the accuracy of the estimation model and the quality of the measurements. Indeed, as the systems are increasingly complex, it is more challenging to develop accurate models [START_REF] Kay | Fundamentals of statistical signal processing: estimation theory[END_REF], [START_REF] Stoustrup | Fault estimation : a standard problem approach[END_REF]. In [START_REF] Zhu | Fault estimation for a class of nonlinear systems based on intermediate estimator[END_REF], the authors designed an intermediate estimator to estimate the state and fault simultaneously by exploiting the properties of the fault distribution matrix. The authors in [START_REF] Jiang | Fault estimation and accommodation for linear mimo discrete-time systems[END_REF] developed a new real-time fault estimation module. This work is a follow up of [START_REF] Zhang | Current-based analytical model for fault detection and diagnosis in 7-phase machines[END_REF] in which an analytical fault model is derived. The fault characteristics are processed through Cumulative Sum (CUSUM) algorithm. The slope of the decision function will be used as fault indicator. The performance of the fault estimation will be analyzed under noisy conditions and varying fault severities.

The contributions of this paper are: 1) Development of accurate analytical models in the stationary frames for phase currents, which are affected by faults that alter their amplitude, phase, or mean value. 2) Assessment of the fault severity estimation performance under various levels of noise and different fault types. Fig. 1 describes the flowchart of the estimation procedure. The rest of this paper is structured as follows: Section II (right side of the flowchart) outlines the extraction of the theoretical relationship between fault severity and fault parameters in the absence of noise. Section III presents the CUSUM approach. Section IV explains how the fault severity is estimated from fault parameters under different noise levels, and estimation features also contained. In section V, the evaluation of the estimation performance, based on the analysis of the slope of the decision function from CUSUM algorithm, is provided in the different fictitious machines. The conclusions are given in section VI.

II. NOISE-FREE PHASE CURRENTS ANALYSIS

A. Introduction

The currents in the 7-phase machine can be modeled using three representation spaces as an extension of the usual space vector definition used for 3-phase systems [START_REF] Semail | Vectorial formalism for analysis and design of polyphase synchronous machines[END_REF], [START_REF] Zhang | Current-based analytical model for fault detection and diagnosis in 7-phase machines[END_REF], [START_REF] Semail | Right harmonic spectrum for the back-electromotive force of an n-phase synchronous motor[END_REF]

℧ -1 (•) = ℧ -1 ( )
Fig. 1. Flowchart of fault estimation

• Stationary (α, β) frame: one-phase Homopolar Machine (HM) with variable i 0 with three two-phase independent fictitious machines, including a Principal Machine (PM) with i pα and i pβ , a Secondary Machine (SM) with i sα and i sβ , and a Tertiary Machine (TM) with i tα and i tβ . • Synchronous (d, q) frame: a one-phase HM and three d-q orthogonal coordinate fictitious machines. In this paper, the study is limited to the stationary space, and to the analysis of the DC component (0F ) and/or fundamental component (1F ) of the phase currents. The healthy and faulty currents in the natural frame are expressed as follows, respectively [START_REF] Zhang | Current-based analytical model for fault detection and diagnosis in 7-phase machines[END_REF]:

i j(j=1...7)h = I √ 2sin(θ + (1 -j)φ) (1)
i j(j=1...7)f = I √ 2(1 + △i j )sin(θ + (1 -j)φ + ϕ j ) + γ j (2)
where, θ = ωt, ω is the angular frequency; t is the current time; φ is the natural phase shift equals to 2π 7 in the 7-phase machine; I is the RMS value of the phase current; △i j will result in a gain fault, which is a modification of the current amplitude; ϕ j will lead to a phase shift fault, which modifies the initial phase of the current; and γ j , which represents a bias in the mean value of the current. The lower scripts h and f stand for the healthy and faulty conditions, respectively. Equation ( 2) is used to simulate the different fault effects on phase currents.

B. Analytical model for fault severity estimation

By combining (2) with the Clarke transformation in (3), the analytical expressions of the phase currents in the stationary frames can be derived. The detailed derivation process can be found in [START_REF] Zhang | Current-based analytical model for fault detection and diagnosis in 7-phase machines[END_REF].

Under healthy conditions, there is no current in the SM, TM, and HM. However, under faulty conditions, there are new components and/or frequency distortions in the actual phase currents. The frequency analysis is summarized in TABLE I. It can be observed that [START_REF] Zhang | Current-based analytical model for fault detection and diagnosis in 7-phase machines[END_REF]:

1) The spectrum of the faulty current in the stationary frames includes DC (0F ) and/or fundamental component (1F ). 2) Only the mean value fault introduces a DC (0F ) component in the four fictitious machines.

0F 1F 0F 1F H PM ipα × G PM ipα × ipβ × ipβ × SM isα SM isα × isβ isβ × (1) TM itα TM itα × itβ itβ × (1) HM i0 HM i0 × PS PM ipα × MV PM ipα × × ipβ × ipβ × (2) × SM isα × SM isα × isβ × (1) isβ × (3) TM itα × TM itα × itβ × (1) itβ × (3)
HM i0 × HM i0 × H: healthy; G: gain fault; PS: phase shift fault; MV: mean value fault. (1) For phase 1, no 1F component for isβ and itβ . (2) For phase 1, no 0F component for ipβ . (3) For phase 1, no 0F component for isβ and itβ .

The fault severity x ∈ [0, 1] corresponds to the modification of parameters △i j , ϕ j , and γ j for gain, phase shift, and mean value faults, respectively. The function y = ℧(x) expresses the relationship between the fault severity x and the amplitude of the components y for 0F and 1F , as shown in TABLE II to TABLE IV. These functions, obtained noise-free conditions are then used to estimate the fault parameter from noisy faulty features (Fig. 1).

i 0F 1F ipα / y = 1 2 * 1 7 * 2x(x + 7)(1 + cos(j -1)2φ) + 49 * I ipβ / y = 1 2 * 1 7 * 2x(x + 7)(1 -cos(j -1)2φ) + 49 * I isα / y = kx, k = 1 2 * 2 7 * 1 + cos(j -1)6φ * I isβ / y = kx, k = 1 2 * 2 7 * 1 -cos(j -1)6φ * I itα / y = kx, k = 1 2 * 2 7 * 1 + cos(j -1)4φ * I itβ / y = kx, k = 1 2 * 2 7 * 1 -cos(j -1)4φ * I i0 / y = kx, k = 1 2 * 2 7 * I III. CUSUM ALGORITHM
The CUSUM algorithm was first proposed by Page in 1954 [START_REF] Page | Continuous inspection schemes[END_REF]. It is based on the sequential likelihood ratio analysis. The idea is to accumulate information from the sampled data in such a way as to amplify any mismatch that may occur. Let us assume n statistically independent samples of the vector Y = { y k , k = 1, • • • , n}. Each sample follows a probability distribution p( y k , ϑ) depending on a deterministic parameter ϑ. An abrupt change is modeled by an instantaneous modification of ϑ at the change time n c . Before the change time n c , ϑ = ϑ h , and after the change time, ϑ = ϑ f [START_REF] Basseville | Detection of abrupt changes: theory and application[END_REF]. A binary hypothesis is considered as follows:

         i0 ipα ipβ itα itβ isα isβ          = 2 7          1 √ 2 1 √ 2 1 √ 2 1 √ 2 1 √ 2 1 √ 2 1 √ 2 1 cos(φ)
                  i1 i2 i3 i4 i5 i6 i7          (3)
+ (j -1)2φ) * I isα / y = 1 2 * 1 7 * 4 * (1 + cos(j -1)6φ -cosφx) -2 * (cos(φx -(j -1)6φ) + cos(φx + (j -1)6φ)) * I isβ / y = 1 2 * 1 7 * 4 * (1 -cos(j -1)6φ -cosφx) + 2 * (cos(φx -(j -1)6φ) + cos(φx + (j -1)6φ)) * I itα / y = 1 2 * 1 7 * 4 * (1 + cos(j -1)4φ -cosφx) -2 * (cos(φx -(j -1)4φ) + cos(φx + (j -1)4φ)) * I itβ / y = 1 2 * 1 7 * 4 * (1 -cos(j -1)4φ -cosφx) + 2 * (cos(φx -(j -1)4φ) + cos(φx + (j -1)4φ)) * I i0 / y = 1 7 * √ 1 -cosφx * I TABLE IV EVOLUTION OF FAULT SEVERITY UNDER MEAN VALUE FAULT i 0F 1F ipα y = kx, k = 2 * 1 7 * |cos(j -1)φ)| * I y = √ 7 2 * I ipβ y = kx, k = 2 * 1 7 * |sin(j -1)φ)| * I y = √ 7 2 * I isα y = kx, k = 2 * 1 7 * |cos(j -1)3φ)| * I / isβ y = kx, k = 2 *
under H 0 , ϑ = ϑ h , 1 ≤ k ≤ n under H 1 , ϑ = ϑ h , 1 ≤ k ≤ n c ϑ f , n c + 1 ≤ k ≤ n (4)
The probabilities of Y under hypotheses H 0 and H 1 are:

p( Y |H 0 ) = n k=1 p( y k , ϑ h ) p( Y |H 1 ) = nc k=1 p( y k , ϑ h ) n k=nc+1 p( y k , ϑ f ) (5)
The deterministic parameter ϑ, can be the mean value µ or the variance σ 2 of a signal following a Gaussian distribution N (µ, σ 2 ):

p( y k , ϑ) = 1 √ 2πσ 2 exp - ( y k -µ) 2 2σ 2 (6)
The Gaussian distribution N (µ, σ 2 ) under two hypotheses are:

H 0 : Y = { y k , k = 1, ..., n} ∽ N (µ h , σ 2 h ) H 1 : Y = Y h = { y k , k = 1, ..., n c } ∽ N (µ h , σ 2 h ) Y f = { y k , k = n c + 1, ..., n} ∽ N (µ f , σ 2 f ) (7)
Note that before the change time n c , mean and variance are µ h and σ 2 h , and after change time n c , mean and variance are µ f and σ 2 f . The instantaneous log-likelihood ratio s k at time k, which represents the difference between the log-likelihood of the observed data under two different hypotheses, is defined:

s k = ln( p( y k , ϑ f ) p( y k , ϑ h ) ) (8)
Therefore combining ( 6) and ( 8), s k can be calculated through the following expressions:

s k = ln σ h -ln σ f + ( y k -µ h ) 2 2σ 2 h - ( y k -µ f ) 2 2σ 2 f ( 9
)
• if there is only mean change, σ h = σ f , it can be simplified:

s k = µ f -µ h σ 2 h × ( y k - µ f + µ h 2 ) (10)
• if there is only variance change, µ h = µ f , it can be simplified:

s k = ln σ h -ln σ f + ( 1 σ 2 h - 1 σ 2 f ) × ( y k -µ h ) 2 2 (11)
The cumulative sum, used to compute the decision function in (13), is as follows:

S n = n k=1 s k (12)
The decision function represents the deviation of the signal from a reference value over time. The decision function should stay close to zero if the signal is stable and does not change over time. However, if there is a change in the signal, such as a shift in the mean or the variance value, the decision function will follow a linear evolution whose slope is sensitive to the amplitude of the change.

G n = S n -min 1≤nc≤n S nc-1 (13)

IV. NOISY PHASE CURRENTS ANALYSIS A. Settings for the numerical model

A white Gaussian noise is added to the phase currents to simulate realistic measurements, and the noise level is defined by considering the Signal to Noise Ratio (SNR):

SN R = 10 × log 10 σ 2 s σ 2 υ ( 14
)
where, σ 2 s is the variance of the signal, and σ 2 υ is the variance of the Gaussian distributed noise υ ∼ N (0, σ 2 υ ). In the following simulations, the SNR is set to 20, 15, 10 and 5 dB, respectively. When the SNR decreases, the noise level increases. The fault levels are set to [5% to 30%] for the three cases, corresponding to gain fault △i j varying from 0.05 to 0.3; phase shift fault ϕ j varying from 0.05φ to 0.3φ; and mean value fault γ j varying from 0.05I √ 2 to 0.3I √ 2. Two hundred simulations are run for the healthy conditions and for each faulty severity and noise level (three single fault types and four SNR values).

Without loss of generality, the RMS value of the phase current is set to 4A, and only the results for faults occurring in the fourth phase of the machine are presented.

B. Fault estimation features

The fault severity estimation under noisy conditions is performed in two steps:

1) The function ℧ -1 (•) is obtained under noise-free conditions using the analytical models and the fault features (y, amplitude of DC and 1F components) and actual fault severity x.

2) The estimated the fault severity x is obtained from the fault amplitudes y extracted from noisy measurements, expressed as x = ℧ -1 ( y). Fig. 2 shows the estimated fault severity plotted against the actual fault severity for gain fault case using i pα under two different SNR levels, 20 dB and 5 dB. Each simulation (three single fault types and four SNR values) is repeated 200 times. The red dots represent the average values of the estimated. Indeed, they are found to be close to the actual fault level.

It can be also observed that the variance increases with the noise level and remains stable with increasing fault severity as confirmed by the histograms displayed in Fig. 3. They show that the estimations follow a Gaussian distribution, as expected. Fig. 4 confirms the stable trend of the variance with increasing fault severity. The same computations are performed for all the components in stationary frames of the phase currents in the four fictitious machines.

V. FAULT ESTIMATION EVALUATION

In the following, the first 200 samples represent the healthy cases, while the subsequent 200 ones stand for the faulty cases, as shown in Fig. 5.

The previous analysis showed that only the mean value is affected by the fault occurrence. The histograms in Fig. 3 also showed that we can assume the Gaussian distribution for the estimates. Therefore, the CUSUM algorithm can be applied using [START_REF] Semail | Right harmonic spectrum for the back-electromotive force of an n-phase synchronous motor[END_REF], (12), and (13) to measure the magnitude of the change in the signal and detect changes. Fig. 6 and Fig. 7 shows the results for 5% and 30% fault severity with i pα under gain fault when SNR equals to 20 dB and 5 dB, respectively. The following conclusions can be drawn: the abrupt change in the fault estimate is clearly detected by the decision function, even if the noise level is high (SNR = 5 dB), and the slope of the decision function is sensitive to the fault severity. The slope's evolution along fault severity for different noise levels is plotted in Fig. 8 and Fig. 9. We can make the following comments:

1) The slope increases with the fault severity.

2) The difference in slope between two fault severities is more significant when the noise level is lower. 3) For the same noise level and fault severity, the slope for the three fault types is sorted as follows: mean value fault > gain fault > phase shift fault. 4) Particular attention need to be paid to i pα , i pβ and i sα components. For gain fault, i pβ and i sα are more sensitive to the noise; for phase shift fault, i pα , i pβ , and i sα are more sensitive to the noise; and for mean value fault, i pβ and i sα are more sensitive to the noise.

VI. CONCLUSION

This paper analyzed the performance of fault severity estimation under noisy conditions in a 7-phase electrical machine. The estimation model assumed that the faults affect the characteristics (amplitude, phase shift, and mean value) of the winding currents, whose components are derived in the stationary reference frames. The relationships between the fault severity and fault features (DC and 1F components) are first extracted in noise-free conditions. These relations are then used to estimate the fault severities from noisy features. The performance of the estimation is evaluated with the CUSUM algorithm. Indeed, the simulation results for different fault severities (0 to 30%) and different noise levels (20 dB to 5 dB) showed that the decision function is an efficient fault indicator and that its slope is proportional to the fault severity.

The results also show the sensitivity to noise depending on the components of the currents in the different fictitious machines used for fault severity estimation.

Fig. 2 .

 2 Fig. 2. Fault severity estimation with ipα under gain fault

Fig. 3 .Fig. 4 .Fig. 5 .

 345 Fig. 3. Histograms with ipα under gain fault

Fig. 6 .Fig. 7 .

 67 Fig. 6. Fault estimation and decision function with ipα under gain fault and SNR = 20 dB

Fig. 8 .Fig. 9 .

 89 Fig. 8. CUSUM slope using ipα for fault estimation

  Healthy current and Faulty time series phase current

	Noise v	Addition of White Gaussian Noise
		in the currents
		Noisy current in the natural frame	Noise-free current in the natural frame
		Frame transformation	Frame transformation
		with numerical simulation	with analytical model
		Noisy current in the	Noisy-free current
		stationary frame	in the stationary frame
		Domain transformation and	Domain transformation and
		component selection	component selection
		Noisy amplitude of	Noisy amplitude of
		the frequency	the frequency
		components	components y 0F and y 1F
		0F and 1F	Equation inversion for
			analytical estimation model derivation
		Fault severity estimation calculation with noisy components
		Performance evaluation of the estimated fault severity

TABLE II EVOLUTION

 II OF FAULT SEVERITY UNDER GAIN FAULT


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