Neele S Dellschaft

Marie-Cecile Alexandre-Gouabau

David S Gardner

Jean-Philippe Antignac

Duane H Keisler

Helen Budge

Professor Michael E Symonds
email: michael.symonds@nottingham.ac.uk

Sylvain P Sebert

Effect of pre and postnatal growth and post-weaning activity on glucose metabolism in the offspring

Keywords: IUGR, Perinatal growth, Obesity, Appetite regulation, Insulin, Leptin, Cortisol, Metabolomics, Gene expression

Maternal caloric restriction during late gestation reduces birth weight but whether long-term adverse metabolic outcomes of intra-uterine growth retardation (IUGR) are dependent on either accelerated postnatal growth, or exposure to an obesogenic environment after weaning, is not established. We induced IUGR in twin pregnant sheep using a 40% maternal caloric restriction commencing from 110 days gestation until term (~147 days), compared to mothers fed to 100% of requirements. Offspring were reared either as singletons to accelerate postnatal growth or as twins to achieve standard growth. To promote an adverse phenotype in young adulthood, after weaning, offspring were reared under a low activity obesogenic environment with the exception of a sub-group of IUGR offspring, reared as twins, maintained in a standard activity environment. We assessed glucose tolerance together with leptin and cortisol responses to feeding in young adulthood when the hypothalamus was sampled for assessment of genes regulating appetite control, energy and endocrine sensitivity.

Caloric restriction reduced maternal plasma glucose, raised NEFA, and changed the metabolomic profile, but had no effect on insulin, leptin, or cortisol. IUGR offspring whose postnatal growth was enhanced and were obese showed insulin and leptin resistance plus raised cortisol. This was accompanied by increased hypothalamic gene expression for energy and glucocorticoid sensitivity. These long-term adaptations were reduced but not normalised in IUGR offspring whose postnatal growth was not accelerated and remained lean in a standard post-weaning environment. IUGR results in an adverse metabolic phenotype, especially when postnatal growth is enhanced and offspring progress to juvenile-onset obesity.

Introduction

There is increasing evidence to support the early life programming of adult obesity, type 2 diabetes, and hypertension. The prenatal environment's influence depends on organ-specific windows of susceptibility with some, but not all, outcomes linked to mechanisms affecting size at birth [START_REF] Barker | Fetal nutrition and cardiovascular disease in later life[END_REF][START_REF] Roseboom | Coronary heart disease after prenatal exposure to the Dutch famine, 1944-45[END_REF]. In large mammals, including sheep, pigs, and humans, chronic caloric restriction throughout late gestation results in intra-uterine growth retardation (IUGR) [START_REF] Roseboom | Coronary heart disease after prenatal exposure to the Dutch famine, 1944-45[END_REF][START_REF] Symonds | Nutritional programming of the metabolic syndrome[END_REF]), which contrasts with suboptimal maternal nutrition in earlier gestation, which does not influence birth weight [START_REF] Roseboom | Coronary heart disease after prenatal exposure to the Dutch famine, 1944-45[END_REF][START_REF] Bispham | Maternal endocrine adaptation throughout pregnancy to nutritional manipulation: consequences for maternal plasma leptin and cortisol and the programming of fetal adipose tissue development[END_REF][START_REF] Sharkey | Maternal nutrient restriction during pregnancy differentially alters the unfolded protein response in adipose and renal tissue of obese juvenile offspring[END_REF].

During diet-induced IUGR maternal homeostasis is altered, affecting the metabolic environment in which the fetus develops [START_REF] Tygesen | Late gestational nutrient restriction: effects on ewes' metabolic and homeorhetic adaptation, consequences for lamb birth weight and lactation performance[END_REF]. It is possible that these metabolic adaptations influence fetal growth independently of changes in the feto-maternal endocrine environment. Nutrients not only fulfill energetic requirements but a range of lipids, non-esterified fatty acids (NEFA), and amino acids act as signaling molecules and could, therefore influence epigenetic processes linked to the long-term regulation of metabolic function [START_REF] Mcmillen | Developmental origins of the metabolic syndrome: prediction, plasticity, and programming[END_REF]. In the present study, we examined whether a reduction in maternal food intake in late pregnancy, leading to changes in maternal metabolic homeostasis and birth weight, are essential in programming adult predisposition to the following characteristics: i) altered body composition, ii) central and peripheral insulin resistance, iii) the regulation of food intake, and iv) postprandial and post-absorptive endocrine responses to feeding. Furthermore, the extent to which the impact of IUGR on each of these adaptations is dependent on postnatal growth patterns is not known. This is important as many human studies indicate that the long term impact of reduced birth size, in both term and pre-term infants, can be dependent on early postnatal growth [START_REF] Singhal | Low nutrient intake and early growth for later insulin resistance in adolescents born preterm[END_REF][START_REF] Stettler | Rapid weight gain during infancy and obesity in young adulthood in a cohort of African Americans[END_REF]. In sheep, the relative importance of enhanced postnatal growth on long term outcomes has not been widely examined, although, when combined with IUGR, accelerated postnatal growth differentially affects energy sensing within the stomach and hypothalamus [START_REF] Sebert | Maternal nutrient restriction during late gestation and early postnatal growth in sheep differentially reset the control of energy metabolism in the gastric mucosa[END_REF]. The post-weaning environment is an additional factor which appears to determine the magnitude of the phenotypic response to alterations in maternal diet in pregnancy in rodents [START_REF] Desai | Programmed metabolic syndrome: prenatal undernutrition and postweaning overnutrition[END_REF]. In these studies, the metabolic and related effects in young adult offspring who were nutritionally manipulated in utero are minimal unless adiposity has been promoted. The extent to which similar changes in body composition also apply to large mammals has not been investigated.

Each organ has a set developmental trajectory and therefore they are not all similarly affected by IUGR. The hypothalamus is particularly sensitive to environmental stresses in early life and plays a central role in the regulation of energy homeostasis [START_REF] Adam | Expression of energy balance regulatory genes in the developing ovine fetal hypothalamus at midgestation and the influence of hyperglycemia[END_REF]. Cortisol can influence blood pressure as a consequence of regulating gene expression of arginine vasopressin (AVP) and corticotrophin releasing hormone (CRH), which when suppressed, acts through negative feedback, to reduce cortisol secretion from the adrenals through decreased adrenocorticotropic hormone action [START_REF] Lightman | The neuroendocrinology of stress: a never ending story[END_REF]. Food intake is regulated by changes in the plasma concentration of markers of energy status, including insulin, leptin, and glucose [START_REF] Schwartz | Central nervous system control of food intake[END_REF]. These factors determine the action of neurotransmitters in the arcuate nucleus of the hypothalamus, especially neuropeptide Y (NPY) and pro-opio melanocortin (POMC), which have antagonistic actions in signaling peripheral energy status to other hypothalamic nuclei, the cortico-limbic system and the brain stem, which ultimately determine food intake and physical activity [START_REF] Schwartz | Central nervous system control of food intake[END_REF]. Critically, the fetal hypothalamus shows an orexigenic response by increased NPY signaling to maternal nutrient restriction in late gestation [START_REF] Warnes | Effects of increasing gestation, cortisol and maternal undernutrition on hypothalamic neuropeptide Y expression in the sheep fetus[END_REF]) and an anorexigenic response by increased 5 POMC signaling to maternal and early postnatal overnutrition [START_REF] Muhlhausler | Increased maternal nutrition alters development of the appetite-regulating network in the brain[END_REF]. However, whether these adaptations persist into adulthood is not known. In addition, whilst organogenesis and the developmental maturation of the hypothalamus in altricial species is particularly sensitive to the late gestational nutritional environment [START_REF] Adam | Expression of energy balance regulatory genes in the developing ovine fetal hypothalamus at midgestation and the influence of hyperglycemia[END_REF], hypothalamic maturation continues after birth when it is particularly responsive to the postnatal energetic environment [START_REF] Paus | A primer for brain imaging: a tool for evidence-based studies of nutrition?[END_REF]. Whether specific changes in the early postnatal environment during key windows, i.e. immediately after birth and at weaning, modulate the long-term molecular adaptation of the hypothalamus to IUGR has received no attention. The present study, therefore, not only examines the effects of maternal caloric restriction during late pregnancy on maternal homeostasis but also tests the hypothesis that the adverse effects of IUGR are dependent on the postnatal energetic environment and concomitant differences in peri-partum or post-weaning growth. We investigated the effects of: i) IUGR followed by an accelerated postnatal growth combined with a low activity obesogenic environment after weaning and compared to those offspring born to mothers fed to requirements throughout pregnancy and with the same postnatal treatment, ii) differing postnatal growth rates on adult IUGR offspring submitted to obesogenic conditions, and finally, iii) a differing energetic environment on IUGR offspring submitted to regular postnatal growth rate.

Materials and Methods

Animals and experimental design

All animal procedures were performed in accordance with the UK Animals (Scientific Procedures) Act 1986 with approval from the Local Ethics Committee of the University of Nottingham. The experimental nutritional intervention has previously been described in detail [START_REF] Sebert | Maternal nutrient restriction during late gestation and early postnatal growth in sheep differentially reset the control of energy metabolism in the gastric mucosa[END_REF]. In brief, 28 Bluefaced Leicester cross Swaledale twin bearing sheep (ovis) were individually housed at 100 days of gestation (dGA) and, at day 110 dGA, randomly allocated to the experimental groups (Figure 1). All pregnancies continued normally until term (~145 ± 1 days) and produced heterozygous twins. They included a control group (C, n=9) that were fed to requirements through pregnancy (i.e. from 0.46 MJ/kg.BW 0.75 at 110 days gestation, increasing to 0.72 MJ/kg.BW 0.75 at dGA 130), whilst the remaining 19 mothers were caloric restricted (R) and were pair-fed to 60% of control intake, based on their body weight. All mothers were individually weighed once a week prior to feeding in order that their total food requirements could be adjusted. From birth, the offspring born to C mothers were then reared to promote accelerated (A) early postnatal growth (CA, n=8, 4 males and 4 females), accomplished by only one twin being reared by its mother. The offspring born to R mothers were reared to promote an accelerated (RA n=9, 2 males and 7 females) or a regular (RR, n=17) early postnatal growth rate, accomplished by being reared together as twins. After weaning, all offspring were kept in a low activity environment until 17 months of age in order to promote obesity (O, 6 animals on 19 m 2 , fed ad libitum on straw nuts and a micronutrient supplement) with the exception of 9 RR offspring that were kept in a normal physical activity environment, in order to remain lean (RRL, n=9, 5 males and 4 females, 6 animals on 1125 m 2 , ad libitum access to grass and a micronutrient supplement; RRO n=8; 2 males and 6 females; Figure 1). Discrepancies between the total number (n) of mothers and offspring are due to additional offspring for independent intervention groups for 7 the twins that were removed from their mother on the first day of birth. This included formula-reared twins within the CAO and RAO offspring, which were not included in the present study. The numbers of twin bearing mothers entered into the study for each nutritional group were predicted to be sufficient to produce enough numbers of male and female offspring for each of the postnatal intervention groups. However due to the uneven distribution of male and females born to R mothers there were fewer male offspring available than anticipated. The resulting groups permit us to draw comparisons between animals with and without IUGR (RAO vs. CAO) and, within those with IUGR, to investigate the effects of early postnatal growth (RAO vs. RRO) and of post-weaning environment (RRO vs. RRL).

Timing of samplings and in vivo challenges

Maternal blood sampling: At 130 dGA, jugular venous blood samples (5 ml) were collected from the ewes in the morning, prior to, and two hours after, feeding. Venous blood was collected into heparinized or K + EDTA coated tubes and the plasma was immediately separated by centrifugation (2500 g x 10 min at 4˚C) and stored at -80˚C until analysis.

Offspring blood sampling: Venous blood samples (prepared and stored under identical conditions as described above) were collected after an overnight fast (≥18h) at both 7 and 16 months of age. Jugular catheters were inserted by percutaneous venepuncture 1-2 days before sampling. Additional blood samples were collected at 16 months of age following the presentation of a mix of high and low energy-dense feed (3 kg straw nuts, 8.5 MJ/kg and 800 g concentrate pellets, 12.5 MJ/kg) to study the post absorptive and postprandial response at 2, 4, 8, and 24 h after feeding.

Determination of insulin sensitivity:

Glucose tolerance tests (GTT) were undertaken on all offspring at 7 and 16 months of age in which jugular vein catheters had been previously inserted and the area under the curve (AUC) calculated. Animals were fasted overnight (≥18h) and injected intravenously with 0.5 g/kg glucose. Glucose and insulin concentrations were measured in plasma samples before and at 10, 20, 30, 60, 90, and 120 minutes, after the intravenous glucose [START_REF] Gardner | Programming of glucose-insulin metabolism in adult sheep after maternal undernutrition[END_REF]). The homeostatic model assessment for insulin resistance (HOMA-IR) index was calculated by multiplication of glucose (mmol/L) and insulin (µg/L) concentrations measured in fasted plasma (Wallace et al. 2004).

Determination of body composition, physical activity, and food intake at 16 months of age: Total body fat was determined when the animal was sedated (intramuscular injection of 1.5 mg /kg ketamine with 0.1 mg /kg xylazine) and scanned in a transverse position using a Lunar DPX-L (fast-detail whole body smartscan, GE Healthcare, Little Chalfont, UK). The level of spontaneous physical activity in adulthood in their respective environments was determined using uniaxial accelerometers (Actiwatch; Linton Instrumentation, Diss, UK).

Average total food intake was measured in 24h intervals over a 10 day period with all animals kept in individual pens and with ad libitum access to feed, straw nuts (8.5 MJ/kg) and concentrate pellets (12.5 MJ/kg).

Post mortem procedures and hypothalamic collection:

At 17 months of age, all offspring were euthanazed by electrical stunning and exsanguination after an overnight fast. The entire hypothalamus was dissected according to anatomic landmarks [START_REF] Sebert | Maternal nutrient restriction between early and midgestation and its impact upon appetite regulation after juvenile obesity[END_REF], snap frozen, and stored at -80°C until analyzed. The use of entire hypothalamus allows analysis of the entire hypothalamic response but cannot be extrapolated to responses that would require nuclei-specific analyses.

Laboratory analysis

Plasma metabolites and hormones

Plasma glucose, triglycerides, and NEFA were measured by colorimetric assays (Randox, Crumlin, UK). Insulin was assayed using an ovine specific ELISA assay (Mercodia, 9 Diagenics Ltd, Milton Keynes, UK). Leptin [START_REF] Delavaud | Plasma leptin determination in ruminants: effect of nutritional status and body fatness on plasma leptin concentration assessed by a specific RIA in sheep[END_REF] and cortisol (DPC coat-acount, Siemens, Camberley, UK) were determined by a radio-immunoassay.

Analysis of the plasma metabolome

Fasted heparin-treated plasma samples taken from mothers at dGA 130 were analyzed for a wide spectrum of metabolites by liquid chromatography coupled to high resolution mass spectrometry (LC-HRMS). Plasma was defrosted on ice and filtered by centrifugation (Nanosep Omega, Pall, Port Washington, NY) to remove high molecular weight species, proteins in particular (over 10kDa). Metabolomic LC-HRMS profiles were acquired from 15 µL of each filtered serum sample using an Agilent 1200 TM HPLC system equipped with a 150

x 2.1 mm Uptisphere HDO-C 18 column with 3 µm particle size (Interchim, Montluçon, France) coupled to a high resolution LTQ-Orbitrap hybrid mass spectrometer (Thermo Fisher Scientific, Bremen, Germany) fitted with an electrospray source operated in the positive ion mode. The detailed conditions applied both for the HPLC separation and mass spectrometric signal acquisition were previously described [START_REF] Courant | Development of a metabolomic approach based on liquid chromatography-high resolution mass spectrometry to screen for clenbuterol abuse in calves[END_REF][START_REF] Courant | Offspring metabolomic response to maternal protein restriction in a rat model of intrauterine growth restriction (IUGR)[END_REF]. Quality control standards and samples were randomly included five times into the sequence of injection.

Metabolomic data processing

Open-source XCMS software [START_REF] Smith | XCMS: processing mass spectrometry data for metabolite profiling using nonlinear peak alignment, matching, and identification[END_REF]) was used for non-linear alignment of the generated raw data and automatic integration and extraction of the signal intensities measured for each mass-retention time ([m/z; rt]) feature constituting these metabolomic fingerprints, which each represent one ion. The XCMS parameters were implemented with the algorithm "match-filter" using default settings except for the interval of m/z value for peak picking which was set to 0.1, the noise threshold set to 6, the group band-width set to 10 and the 10 minimum fraction set to 0.5 as previously described (21). After XCMS processing, the signal abundances observed for identical ions in two groups of samples were statistically analyzed and annotation then subsequent identification of putative metabolites of interest were achieved using an in-house reference databank (34).

Gene expression measurements

Offspring hypothalami were homogenized and RNA isolated, using the RNeasy Plus kit (Qiagen, Hilden, Germany). An aliquot of 4 µg of RNA was reverse transcribed with the High Capacity RNA-to-cDNA kit (Applied Biosystems, Foster City, CA, USA). The resulting cDNA was amplified in a real-time thermocycler (Quantica, Techne, Burlington, NJ, USA) using a SYBR green system in Taq polymerase reaction mix (ABsolute blue QPCR SYBR green, Thermo Scientific, Epsom, UK). Specificity of primers was confirmed by sequencing PCR product (Supplementary Information Table 1). Hypothalamic gene expression was assessed for the following pathways: a) orexigenic neurotransmitters: neuropeptide Y (NPY); agouti-related peptide (AGRP), b) insulin and leptin signaling: protein tyrosine phosphatase non-receptor type 1 (PTP1B); suppressor of cytokine signaling 3 (SOCS3); insulin receptor (IR); and leptin receptor (OBRB), c) intracellular energy signaling: AMP-activated kinase (AMPKΑ2); mammalian target of rapamycin (MTOR); and fat mass and obesity-related gene (FTO), d) cortisol regulation: glucocorticoid receptor (GCR); corticotropin releasing hormone (CRH); and arginine vasopressin (AVP). Ribosomal RNA 18S showed a stable expression and was used as a housekeeping gene. Gene expression was calculated by using the 2 -∆∆Ct method [START_REF] Livak | Analysis of Relative Gene Expression Data Using Real-Time Quantitative PCR and the 2-∆∆CT Method[END_REF].

Statistical analysis

Metabolomic data: All multivariate data analyses and modeling were performed using SIMCA-P+software (v 12, Umetrics Inc., Umeå, Sweden) on log-transformed (van den [START_REF] Van Den Berg | Centering, scaling, and transformations: improving the biological information content of metabolomics data[END_REF]) and Pareto-scaled [START_REF] Cloarec | Statistical total correlation spectroscopy: an exploratory approach for latent biomarker identification from metabolic 1H NMR data sets[END_REF]) data as previously described [START_REF] Courant | Offspring metabolomic response to maternal protein restriction in a rat model of intrauterine growth restriction (IUGR)[END_REF]. The susceptibility of the metabolic phenotypes of the mothers to caloric restriction in late pregnancy was assessed by using a supervised method, Partial Least Squares Discriminant Analysis (PLS-DA), which was applied to the transformed data set to reveal the potentially existing discrimination between sample groups to be compared within the data set, and to point out the variables more importantly involved in this discrimination.

PLS-DA was combined with a multivariate preprocessing filter called Orthogonal Signal Correction (OSC). By removing within-class variability and confounders that may interfere with chemometric analysis, such as LC-MS technical variability, OSC can significantly improve PLS-DA performance, yielding a better discrimination of the clusters [START_REF] Wagner | Metabonomics and biomarker discovery: LC-MS metabolic profiling and constant neutral loss scanning combined with multivariate data analysis for mercapturic acid analysis[END_REF]). The quality of the generated OSC-PLS-DA model was classically evaluated by several goodness-of-fit parameters and criteria including: R 2 (X), the proportion of the total variance of the dependent variables that is explained by the model; R 2 (Y), defining the proportion of the total variance of the response variable (i.e. the class of the samples) explained by the model; and the predictive ability parameter Q 2 (Y), which was calculated by a seven-round internal cross-validation of the data. In addition, a permutation test (n=100) was carried out to validate, and test, the degree of over fitting for OSC-PLS-DA models. The score values from OSC-PLS-DA were subjected to ANOVA to test the model and the validation was considered successful with P<0.01. The variables that discriminate the metabolic signatures most significantly were pinpointed by their loadings on PLS-DA.

For non-metabolomic outcomes: Statistical analysis of the data was performed using PASW ® statistics software (v 17.02, IBM, Chicago, USA). Kolmogorov-Smirnoff tests were realized on every parameter analyzed to determine the Gaussian distributions of the variables.

The influence of maternal nutrition (CAO vs. RAO), early postnatal growth (RAO vs. RRO), and obesogenic environment (RRL vs. RRO) were determined, according to parametric distribution, using ANOVA with a pairwise a priori test or Mann-Whitney U tests. Of the metabolites and hormones measured over 24 hours, changes over time were tested with the use of a paired t-test. Data is expressed as mean values with their standard errors. To address the limitations of multiple testing, statistical trend was accepted with a 95% interval of confidence (P<0.05) and significance was accepted with a confidence interval of 99% (P<0.01). Correlations were tested with the non-parametric Spearman's test and slope of the correlation was reported on the linear fit. Each variable was tested for sex. Body weight and fat mass are known to differ, in absolute scale, between male and female sheep [START_REF] Bloor | Sex differences in metabolic and adipose tissue responses to juvenile-onset obesity in sheep[END_REF]) thus sex-specific Z-score transformation was used prior to analyses. Specifically, we saw no indication of a difference in male and female offspring in glucose homeostasis, which is consistent with earlier studies [START_REF] Gardner | Programming of glucose-insulin metabolism in adult sheep after maternal undernutrition[END_REF]. Moreover, comparison for each variable between groups for females only demonstrated similar outcomes, although without reaching statistical significance, hence data for each sex were combined for further analyses and greater statistical power.

13

Results

Mothers

Relative to their weight at the beginning of the caloric restriction, R mothers gained less weight up to term compared with C mothers (Figure 2A). At 130 dGA, plasma glucose was reduced in fasted R mothers but there was a greater increase after feeding (Table 1A). Plasma NEFA concentrations were higher in fasted R mothers but did not differ between groups after feeding, whilst plasma triglycerides, cortisol, insulin, and leptin were unaffected by maternal diet (Table 1A). Metabolomic analysis showed a specific biological signature associated with the caloric restricted mothers, with a strong overall difference between the groups (OPLS-DA model of all the 2629 [m/z, rt] features detected, using 2 latent factors for maternal plasma metabolomic profiles (describing 43% of variable information); C mothers n=7 and R mothers n=17; Validation parameters: R 2 X (cum) = 0.434, R 2 Y (cum) = 0.999, Q 2 (cum) = 0.994, permutation test (n = 100) with R 2 intercept = 0.331 and Q 2 intercept=-0.333, ANOVA P-value = 9.9x10 -19 ), and of the 2629 detected features constituting these metabolomic profiles, 133 differed significantly (P<0.01). Of these, 95 were upregulated with a fold change (expressed as a ratio of the mean abundance in R group compared to the mean abundance in the C group) of >1.4 and only 7 were downregulated with a fold change of <0.71. Due to species-specific technical constraints, only five of these compounds could be precisely identified (Table 1B) as phenylalanine, tryptophan, and three forms of o-acetylcarnitine which were all upregulated in R mothers.

Offspring

The primary characteristics of each offspring group over the study are summarized in Table 2. Offspring of R mothers were smaller at birth and, when subjected to an intervention of accelerated early postnatal growth (RA), gained weight faster before weaning than either CA 14 or RR groups, suggesting that nutrient restriction during late pregnancy did not diminish milk production. By 7 months of age, body weight was similar between groups. At 16 months of age, as expected, physical activity was higher in those offspring kept in an unrestricted environment (RRL vs RRO) but did not differ between those maintained within an obesogenic environment. RRL animals were further smaller and consumed less feed each day.

Insulin sensitivity: At 7 months of age, the glucose AUC during the GTT was higher in obese compared to lean animals (RRO vs RRL, Figure 3 and Table 3). RAO offspring showed twice the insulin response to a standard glucose challenge in comparison to RRO. By 16 months of age, glucose AUC did not differ between groups but the insulin response during the GTT was significantly higher in RAO compared to CAO (P<0.05), as was the HOMA-IR, an index of insulin resistance, which was also higher in RAO than in the RRO offspring (P<0.01).

Effect of feeding on plasma profiles of leptin and cortisol:

Prior to the feeding challenge, plasma leptin was higher in RAO than in RRO (Figure 4A). In the RAO group, plasma leptin initially declined on feeding (P<0.05), to gradually increase between 8 and 24 h after feeding (P<0.05). This effect was not observed in any other group as plasma leptin remained unchanged. Plasma glucose and insulin differed between RRO and RRL animals during the 24h of measurements (P<0.05) but not between groups raised in an obesogenic environment (Figure 4B and4C). Plasma cortisol both peaked 4 hours after feeding and was highest in RAO compared with CAO offspring, a difference that persisted until at least 8 h after feeding (Figure 4D).

Hypothalamic gene expression:

Expression of appetite regulatory genes was unchanged, whilst AMPKA2, MTOR, and FTO were all higher in RAO compared to CAO groups (Table 4). A statistically significant negative correlation between anorexigenic circulating hormones insulin and leptin and the expression of orexigenic genes NPY and AGRP was observed in RAO and RRO, but not CAO or RRL groups. Taken together, these different relationships suggest a potential change in insulin and leptin sensitivity within the hypothalamus after IUGR (Table 5). Gene expression of both AVP and CRH was higher in RAO offspring as compared to CAO. Expression of NPY was three times higher and of PTP1B, AMPKA2, MTOR, and GCR was lower in the RRL offspring as compared to RRO. Importantly, postnatal growth rate (RAO vs RRO) did not have any effect on hypothalamic gene expression in any of the pathways investigated.

Discussion

We have established that the long-term adverse outcomes of IUGR on insulin sensitivity can be dependent on exposure to accelerated early postnatal growth together with an obesogenic post-weaning environment. Accelerated early postnatal growth and post-weaning obesity following IUGR resulted in central resistance to insulin and leptin and was accompanied by an upregulation of gene expression for markers primarily recruited in energy sensing. In an absence of adult obesity, the detrimental effects of IUGR appeared to be much less pronounced. We have, therefore, indicated the important association between raised plasma insulin and in utero programmed changes of hypothalamic sensitivity previously observed following juvenile onset obesity [START_REF] Sebert | Maternal nutrient restriction during late gestation and early postnatal growth in sheep differentially reset the control of energy metabolism in the gastric mucosa[END_REF].

Both acute and chronic reductions in maternal food intake in late gestation stimulate maternal catabolism resulting in hypoglycemia, ketoacidosis [START_REF] Herrera | Lipid metabolism in the fetus and the newborn[END_REF][START_REF] Tygesen | Late gestational nutrient restriction: effects on ewes' metabolic and homeorhetic adaptation, consequences for lamb birth weight and lactation performance[END_REF]) and an increased lipolysis [START_REF] Symonds | Lipid metabolism in shorn and unshorn pregnant sheep[END_REF]). In the present study, caloric restriction over the same period not only induced fasting hypoglycemia but was accompanied by a more pronounced rise in plasma glucose immediately after feeding. These substantial fluctuations in maternal plasma glucose are likely to be paralleled within the fetus, and thus possibly resetting metabolic homeostasis. We, therefore, propose that the metabolic stimuli following maternal nutrient restriction in late gestation not only promotes NEFA oxidation [START_REF] Symonds | Lipid metabolism in shorn and unshorn pregnant sheep[END_REF]) but stimulates protein catabolism as indicated by raised plasma acetylcarnitine identified in the metabolomic analysis. This is the first study to analyze the maternal metabolomic response to caloric restriction in any species. Given the substantial dichotomy in the maternal metabolic profiles with maternal nutrient restriction or free access to food, the present study suggests that the source of energy 17 available to the fetus may be a primary determinant of long term energy homeostasis in the offspring, especially when subsequently exposed to an obesogenic environment. The brain is dependent on the availability of glucose and ketone bodies [START_REF] Robinson | Physiological roles of ketone bodies as substrates and signals in mammalian tissues[END_REF] and this switch in energy source may be essential to hypothalamic plasticity. Although insulin resistance following maternal caloric restriction can be exacerbated further with age [START_REF] Kongsted | Programming of glucose-insulin homoeostasis: long-term consequences of pre-natal versus early post-natal nutrition insults. Evidence from a sheep model[END_REF], at 16 months of age we observed an effect of both postnatal growth rate and a clear influence of exposure to an obesogenic environment.

Despite higher insulin and leptin concentrations, IUGR offspring raised in an obesogenic environment (RAO vs CAO) did not exhibit alterations in gene expression for orexigenic neurotransmitters such as NPY and AGRP and correlations between plasma leptin with NPY and AGRP suggest a blunted response in RAO as compared to CAO, i.e. early-onset hypothalamic resistance to leptin [START_REF] Schwartz | Leptin and the brain: then and now[END_REF]. No reduction in gene expression for insulin and leptin receptors was found, which could have suggested a potential mechanism. Whether these effects are mediated through changes in downstream signaling has yet to be confirmed. We were unable to detect any significant changes in expression of PTP1B or SOCS3, suggesting further mechanistic studies are required.

Lean IUGR offspring (RRL vs RRO) were characterised as exhibiting reduced hypothalamic gene expression for PTP1B but the abundance of the orexigenic neurotransmitter NPY was raised, reflecting a high central sensitivity to insulin and leptin, as expected in animals of normal body weight [START_REF] Ahmad | Alterations in skeletal muscle protein-tyrosine phosphatase activity and expression in insulin-resistant human obesity and diabetes[END_REF]. Glucose homeostasis and the hormonal response to feeding in RRL were similar to CAO offspring. Taken together, these findings indicate a degree of maladaptation as lean IUGR individuals would be expected to exhibit lower plasma concentrations of fasted metabolites and hormones and show a smaller response to those challenges than obese animals, at least in terms of NEFA, insulin, and leptin [START_REF] Sebert | Maternal nutrient restriction between early and midgestation and its impact upon appetite regulation after juvenile obesity[END_REF]. One hypothalamic outcome of IUGR was increased expression of genes involved in energy sensing, which were also higher in the offspring reared within an obesogenic, compared with a lean environment (RRO vs RRL). In the lean IUGR group, the expression for those genes was reduced to values very similar to obese controls, even though FTO is known to be more highly expressed in obese than lean sheep [START_REF] Sebert | Influence of prenatal nutrition and obesity on tissue specific fat mass and obesity-associated (FTO) gene expression[END_REF]. This further suggests that IUGR has a long-term effect which is not fully corrected with exposure to a high activity environment. However, these assumptions will need to be tested further with a more appropriate control group and in both male and female offspring.

IUGR also resulted in raised gene expression for hypothalamic genes involved in cortisol regulation, i.e. CRH and AVP which, when combined with the higher plasma cortisol response to feeding seen in the obese IUGR group subject to an accelerated postnatal growth rate, may be indicative of reduced negative feedback control [START_REF] Lightman | The neuroendocrinology of stress: a never ending story[END_REF]. The same higher expression of AVP and CRH was observed in the obese IUGR animals subjected to a slower postnatal growth rate and lean IUGR animals, which both had a lower cortisol response to feeding. Therefore, we did not see a similar loss of negative feedback in these latter offspring. This difference in cortisol regulation is novel and requires further investigation. It has recently been described that female sheep with juvenile-onset obesity have elevated plasma cortisol concentrations [START_REF] Bloor | Sex differences in metabolic and adipose tissue responses to juvenile-onset obesity in sheep[END_REF]), a difference not found in the present study.

All offspring raised in an obesogenic environment became equally obese irrespective of their in utero diet, and this may reflect the more physiological, long term exposure we adopted to induce this condition. Both twin and singleton pregnancies are common in sheep, leading to differences in birth weight and post weaning growth [START_REF] Hancock | Size at birth and adult fat mass in twin sheep are determined in early gestation[END_REF]. Only twin bearing mothers were selected for the present study, so it is not possible to ascertain whether similar interventions designed to impact on postnatal growth rates would lead to identical outcomes in singleton offspring. Our study demonstrates, however, that both the postnatal and post weaning environments are important determinants of long-term outcomes following IUGR. To date, there are no large animal studies which have looked at the developmentally exacerbated effects of adult onset obesity together with the extent to which all symptoms of the metabolic syndrome become manifest. This is due to a number of practical considerations which include the extended time period required, well beyond the three year time frame of most project grant awards and the very high cost of such studies. In addition, the sex of the offspring is not predictable in naturally conceived pregnancies. A study designed to analyze the biological interaction between the sex of the offspring and the outcomes of fetal programming would clearly require a much larger number of mothers to reach the appropriate number of male and female offspring. Given the current limitations and knowledge, our present data support the evidence that some long term impacts of fetal programming are common to both sexes. However, future studies that are able to include sufficient numbers of males and females are warranted to analyze further the effect of the sex of the offspring and its interaction with the fetal and postnatal environments.

In conclusion, in sheep, manipulation of the maternal metabolic status alone, without significant changes in maternal plasma insulin, leptin and cortisol, is sufficient to have long term consequences for the offspring's health. The adverse phenotype of IUGR is enhanced by accelerated postnatal growth and exposure to an obesogenic environment in juvenile life.

Figure Titles

Figure 1: Schematic depiction of the study design. Twin pregnant ewes were randomly assigned to one of two diets for late gestation (110-145 days): C diet meeting requirements or macronutrient-restricted diet meeting 60% of caloric requirements (R). After birth twins were either both reared by their mother (regular early postnatal growth rate, R) or separated with only one twin being reared by the mother (accelerated early postnatal growth rate, A). After weaning a majority of animals were kept in restricted space, representing a mildly obesogenic (O) environment but a proportion of the RR group were kept within an unrestricted space, leading to lean (L) animals. Discrepancies between numbers (n) of mothers and offspring are due to additional offspring intervention groups which were not included in the present study. Offspring of C and R mothers were subjected to an accelerated (CA, n=8; RA, n=8) or regular growth (RR, n=15) during lactation. After weaning, offspring were then exposed to an obesogenic environment (O) with the exception for a subset of RR, which remained lean (RRL,n=8;RRO,n=7). Open square, CAO; filled square, RAO; open circle, RRO; filled circle, RRL. Values are mean ± SEM. Significant differences between groups P<0.05; * between CAO and RAO; # between RAO and RRO; ‡ between RRO and RRL. Insert in D depicts the relative change in plasma cortisol concentrations between 2h and 4h after feeding in the intervention groups.

Offspring of C and R mothers were subjected to an accelerated (CA, n=7; RA, n=8) or regular growth (RR, n=14) during lactation. After weaning, offspring were then exposed to an obesogenic environment (O) with the exception for a subset of RR, which remained lean (RRL, n=7; RRO, n=7). Open square, CAO; filled square, RAO; open circle, RRO; filled circle, RRL. Values are mean ± SEM. Significant difference between time points P<0.05; a within RAO. Significant differences between groups P<0.05; * between CAO and RAO; # between RAO and RRO; ‡ between RRO and RRL.

Table Titles

Table 1: Effect of maternal diet in late gestation commencing on 110 days gestation on plasma endocrine and metabolic characteristics. Plasma was sampled from mothers at 130 days gestation and (A) concentrations of metabolites and hormones, determined immediately prior to and 2 hours after feeding and (B) metabolites in pre-feeding samples that were identified by metabolomic fingerprinting to have significantly changed with maternal diet (Mann-Whitney test, p<0.01).

Twin-pregnant sheep were either fed to requirements (C, n=9) or pair-fed to 60% of that amount from 110 days gestation (R, n=19). *P<0.05; **P<0.01; ***P<0.001. M, monoisotopic mass; all compounds were identified using authentic standards. Fold change of each feature is reported as mean ± SEM of the abundance for caloric restricted mothers relative to controls.

Figure 2 :

 2 Figure 2: Maternal characteristics of diet-induced intrauterine growth restriction.

Figure 3 :

 3 Figure 3: Influence of fetal intrauterine growth restriction, accelerated postnatal

Figure 4 :

 4 Figure 4: Influence of fetal intrauterine growth restriction, accelerated postnatal

Table 2 :

 2 Influence of fetal intrauterine growth restriction, accelerated postnatal growth, and obesity on offspring body weight and on adult body composition, physical activity, and food intake as measured at 16 months of age. Offspring of C and R mothers were subjected to an accelerated (CA, n=8; RA, n=9) or regular growth (RR, n=17) during lactation. After weaning, offspring were then exposed to an obesogenic environment (O) with the exception for a subset of RR, which remained lean (RRL, n=9; RRO, n=8). Values are mean ± SEM. Significant differences between groups represented by different superscripts, a vs b P<0.05; c vs d P<0.01. NEFA, non-esterified fatty acids; TG, triglycerides. Table 3: Influence of fetal intrauterine growth restriction, accelerated postnatal growth, and obesity on the onset of insulin resistance in the offspring. Plasma glucose and insulin responses to an intravenous glucose injection at 7 (i.e. puberty) and 16 months (i.e. young adulthood) of age. Offspring of C and R mothers were subjected to an accelerated (CA, n=8; RA, n=8) or regular growth (RR, n=15) during lactation. After weaning, offspring were then exposed to an obesogenic environment (O) with the exception for a subset of RR, which remained lean (RRL, n=8; RRO, n=7). Values are mean ± SEM. Significant differences between groups represented by different superscripts, a vs b P<0.05; c vs d P<0.01. Table 4: Effect of maternal caloric restriction, accelerated postnatal growth, and juvenile-onset obesity on the regulation of energy balance and endocrine sensitivity in the hypothalamus of young adults. Offspring of C and R mothers were subjected to an accelerated (CA, n=5; RA, n=8) or regular growth (RR, n=15) during lactation. After weaning, offspring were then exposed to an obesogenic environment (O) with the exception for a subset of RR, which remained lean (RRL, n=8; RRO, n=7). Values are mean ± SEM and n=5-8 per time point. Statistical significance for the effect of maternal diet (i.e. CAO vs RAO), accelerated postnatal growth (i.e. RAO vs RRO) and obesity (i.e. RRO vs RRL). NS, not significant. NPY, neuropeptide Y; AGRP, agouti-related peptide; PTP1B, protein tyrosine phosphatase, non-receptor type 1; SOCS3, suppressor of cytokine signalling 3; IR, insulin receptor; OBRB, leptin receptor, long form; AMPKA2, AMP-activated protein kinase α2; MTOR, mammalian target of rapamycin; FTO, fat mass and obesity associated gene; GCR, glucocorticoid receptor; CRH, corticotropin releasing hormone; AVP, arginine vasopressin. 29 Table 5: Correlations between plasma insulin and leptin concentrations and hypothalamic gene expression for NPY and AGRP (2^-∆ ∆ ∆ ∆∆ ∆ ∆ ∆Ct) at 16 months of age. Offspring of C and R mothers were subjected to an accelerated (CA, n=5; RA, n=8) or regular growth (RR, n=15) during lactation. After weaning, offspring were then exposed to an obesogenic environment (O) with the exception for a subset of RR, which remained lean (RRL, n=8; RRO, n=7). *P<0.05; **P<0.01. Slope is expressed as a) *10 -5 and b) *10 -6 .AGRP, agouti-related peptide; NPY, neuropeptide Y.

Table 1 A

 1

	Variables	Control	Restricted
	Glucose (mmol/L)
		Fasted 3.6 ± 0.6	2.3 ± 0.2 *
		2H-fed 4.3 ± 0.9	7.0 ± 0.4 **
		Change 1.4 ± 1.0	4.7 ± 0.5 **
	NEFA (mmol/L)
		Fasted 0.34 ± 0.05	0.85 ± 0.08 ***
		2H-fed 0.74 ± 0.12	0.65 ± 0.09
		Change 0.50 ± 0.05	-.31 ± 0.12 ***
	Triglycerides (mmol/L)
		Fasted 0.32 ± 0.01	0.33 ± 0.01
		2H-fed 0.30 ± 0.02	0.32 ± 0.01
		Change -0.02 ± 0.03	-0.01 ± 0.02
	Fasted insulin (µg/L)	0.3 ± 0.01	0.3 ± 0.01
	Fasted leptin (ng/ml)	1.5 ± 0.3	1.0 ± 0.1
	Fasted cortisol (nmol/L)	17 ± 3		22 ± 3
	B
	Metabolites (LC-HRMS)	M	Fold change	P
	o-Acetyl-carnitine [M+H] +	203.11	1.8 ± 0.2	0.0003
	o-Acetyl-carnitine [M+Na]	203.11	2.7 ± 0.4	0.0008
	o-Acetyl-carnitine [2M+H] +	203.11	2.9 ± 0.3	0.0011
	Tryptophane [M-NH 3 +H] +	204.09	2.9 ± 0.3	0.0011
	Phenylalanine [M+H] +	165.08	1.2 ± 0.1	0.0085

Acknowledgements

This work was supported by the European Union Sixth Framework Program for Research and Technical Development of the European Community, The Early Nutrition Programming Project FOOD-CT-2005-007036, the Nutricia Research Foundation, and the Nottingham Respiratory Biomedical Research Unit. S.P.S. was also supported by a Wellcome Trust Value-in-People award.

Declaration of Interest:

The authors have nothing to disclose.


Keywords: Benchmark, Active Control Performances, Active Control Algorithm Comparison

ABSTRACT

The literature on active control, which has developed abundantly since the last 20 years, suffers from a lack of methodologies to compare the performance of different proposed algorithms. More precisely, the criteria introduced to evaluate them are often specific to their field of application, which makes them unsuitable for objective comparison with other algorithms. This work proposes a unified method which intensively compares algorithm performances. It relies on the definition of applicationindependent descriptors that reflect performances in the time domain both for transient and steady regimes. This evaluation method adapts to the user's needs by letting him choose the signals on which the algorithms are tested and by allowing him to adjust the weight of descriptors in the final score. The method is used to compare two feedforward adaptive control algorithms for vibration cancellation: the FxLMS and an adaptive algorithm using the Youla-Kučera parametrisation. Test signals are extracted from an experimental test bench, designed to mimic a museum stand, consisting of a cantilever beam driven at one end with a vibration shaker and controlled at the other end with an actuator. The results show through several examples how the choice of descriptors' weight can be influenced by the user's needs and can affect the final score assigned to the algorithms.

INTRODUCTION

This article introduces the basis of a benchmark designed to objectively assess active control performances. In here, active control refers to the technology that has been designed to cancel an unwanted vibration created by a disturbance source, thanks to an electronic system that creates an anti-vibration of equal amplitude and opposite phase [START_REF] Kuo | Review of dsp algorithms for active noise control[END_REF]. It can be either acoustics noise cancellation in the case of sound waves or active control of structures in the case of waves propagation through solid materials.

Moreover, it can be either feedfoward control when a well correlated signal with the disturbance source is available, or feedback when only the information of the target sensor is used. Finally, the benchmark is designed for adaptive algorithms, which use real-time information to update the controller. This article will only face the case of SISO (Single Input Single Output) active control.

Since the booming of papers about active control in the 80s and the proposition of the so-called FxLMS by Burgess [START_REF] Burgess | Active adaptive sound control in a duct: A computer simulation[END_REF], hundreds of active adaptive control algorithm have been developed [START_REF] George | Advances in active noise control: A survey, with emphasis on recent nonlinear techniques[END_REF][START_REF] Lu | A survey on active noise con-trol in the past decade-part i: Linear systems[END_REF]. However, this growth has not been followed by the development of tools to objectively assess, and so to compare, algorithm performances. Most of the time, when a new algorithm is proposed, its performances are compared to references algorithms, following a paper-specific protocol. The discrepancy of protocols make it very complicated to consciously choose an algorithm when facing a new situation.

First, depending on the active control application, dif-ferent features might be privileged: convergence time, global reduction, robustness to source variation, low complexity, low spillover (or waterbed effect)... Unfortunately, most article evaluate only some of these descriptors. Also, the methodology to extract these features is often only partially covered. Thus, the descriptors introduced in most publications only allow for a qualitative assessment of the performance of control algorithms, but not for a quantitative comparison.

The need for a robust benchmark of active control technology was first mentioned in 2003 [START_REF] Ogonowski | Benchmarking of active noise control[END_REF]. To the knowledge of the authors only one article provide a large scale benchmark, in the case of active vibration control with feedback adaptive algorithms [START_REF] Landau | Benchmark on adaptive regulation-rejection of unknown/time-varying multiple narrow band disturbances[END_REF].

The purpose of the following work is not to propose a definitive method to get an complete benchmark, but to start a reflection on how such a benchmark must be built. First, methods to extract performance descriptors are introduced. Then, an application of this benchmark in a museal context is discussed.

PERFORMANCE DESCRIPTORS

The descriptors introduced in this section are designed to assess performances when the disturbance signals are stationary. Even though a complete benchmark must tackle the problem of nonstationnary perturbations, this case will not be treated in this article.

Notations

A very simple and reduced active control structure is introduced in Figure 1. The purpose of the control device is to minimize the error signal e(n), measured at a specific position thanks to a so called error transducer. This signal is the sum of the disturbance d(n) with the contribution of the electronic system y(n), equal to the command u(n) filtered by H, the transfer function including the electrical response of the actuator and the physical path between the actuator and the error transducer. The command is defined by filtering a measured reference x(n) with a time-varying control filter W (n).

In the following e open (n) will represent the open-loop error, i.e. when the active device is disabled (W (n) = 0, thus u(n) = 0), while e close (n) will represent the controlled signal in closed loop, i.e. when the active device is turned on. Signals are all treated as digital signal, and e(n) represents the value of the n-th samples of the signal e. The control device is assumed to be turned on at sam-ple n = 0, and the recording stops at sample n = n last . The sampling frequency is noted f s . x(n) u(n), y(n), d(n) and e(n) represent respectively the measured reference, the control signal, the contribution of the control device, the disturbance signal and the error signal. The control filter is W (n), while H represents the secondary path.

In the following, the operator rms () represents the root mean square:

rms(e(1 : N )) = 1 N N n=1 e(n) 2 (1)

Static descriptor: Global Reduction GR

Static descriptors are performance indicators used to estimate the control performance once the steady state has been reached. They can represents both time domain or frequency domain behaviors. Here, only the global reduction, which is a time domain descriptors, will be introduced. The search for frequency domain descriptors will be the treated in future works.

The global reduction (GR), which represents the attenuation in terms of energy, is computed by: GR = 20 log 10

rms (e open (n last -3f s : n last )) rms (e close (n last -3f s : n last ))

(2) By definition, this descriptor only applies to signals which reached their steady state for more than 3 seconds. A preliminary study performed by the author on test signals pointed out that computing the root mean square over three seconds of signals is enough to significantly reduce the influence of white noise randomness.

Then this envelope is fitted with a decreasing exponential function f (n) of the form:

f (n) = (1 -r) × exp -n τ N + r (4)
where r and τ N , respectively corresponding to the final value and the convergence of the envelope, are deduced from an optimization procedure. On our experimental test bench (see section 3), we observe that τ N has a linear and increasing dependence with N , beyond a threshold value of N, usually around N = 1000. In addition, the intercept of this linear fit, which is by definition not depending on the window length, corresponds to the convergence time that an exponentially decreasing envelope would have in the absence of noise. We propose to use this value, which does not depend on any parameter of the algorithm, as a definition of the convergence time (Figure 2). In practice, to find the threshold value of N above the one the function f (N ) = τ N is linear, a first linear fit is performed with all N . Then the lowest value of N are successively removed until the Pearson correlation coefficient of the linear fit becomes higher than 0.99.

Combining the descriptors

The proposed descriptors quantify independent performances of the control algorithm. Its evaluation requires a weighting of these descriptors values, which depends on the control application. In the following, a systematic method of weighting is proposed, consisting of answering three questions for each descriptor:

1. What is the lowest acceptable value D imin for the descriptor D i ?

2. Which value D imax for the descriptor D i is considered to be fully satisfactory? 3. How important is this descriptor compared to the other ones?

Q1 & Q2 aim to convert each descriptor value into a satisfaction index expressed as a percentage. Then these indexes are weighted according to the values given by the answer to Q3. As instance, let's imagine a user decides to set the Global Reduction parameters such as the lowest value equals GR min = 10 dB, the fully satisfactory value equals GR max = 30 dB. Then, the satisfaction index related to the global reduction µ GR is computed such as:

   µ GR = 1 when GR > 30 µ GR = 0 when GR < 10 µ GR = GR-10 30-10 otherwise (5)
Finally, all satisfactory indexes are combined to get a global index performance:

I = i µ Di × w Di i w Di (6)
where D i represents a descriptor and w Di is the associated weight defined by the user at Q 3.

Defining Test signals

As descriptors must be computed from controlled signal, it is necessary to define the test signals used as disturbance signal. Descriptors are indeed strongly influenced by properties of test signals such as bandwidth, amplitude, center frequency, stationarity.... As it is expected that every change within these parameters will result in different control performances, the test signals must be chosen carefully.

In some cases, the sources can be fully determined and it is possible to reproduce them only with a few test signals. In other situations however, the encountered sources are diverse and test signals which are representative of these sources must be carefully designed.

APPLICATION

In this section, an experimental application of the benchmark is described. The test bench, composed of a cantilever beam, and equipped with two sensors and one actuator, cf. Fig. 3, is a mockup of stand used in museum to display artworks (jewelries, coins or other lights objects are often exposed to the tip of spikes). Two control algorithms are implemented to cancel out the vibrations of the stand, and their performances are compared.

Protocol

Control Algorithms

The first algorithm is the well known FxLMS algorithm [START_REF] Burgess | Active adaptive sound control in a duct: A computer simulation[END_REF]. The second one uses the Youla-Kuc ¸era parametrisation, and has been intensively studied by Landau et al. [START_REF] Landau | Adaptive and robust active vibration control[END_REF]. The Youla-Kučera parametrisation used in this article is the simplest version, with a scalar adaptation gain, a finite impulse response filter as control filter, and no central regulator (called YKFIR in [START_REF] Landau | A youla-kucera parametrized adaptive feedforward compensator for active vibration control with mechanical coupling[END_REF]). It will be noted as FIRYK in the rest of the article. Presentation of the control algorithms are out of the scope of this article and readers seeking for further information can refer to the above references.

Test Bench

The cantilever beam is made out of wood, is 200 mm long (from clamp to tip), 35 mm large and 19mm thick. It is excited at its fixed extremity with a vibration exciter, driven by signals designed to have similar properties to the signals measured in situ. The control system is composed of two accelerometers ((Bruel& Kjaer, type 4374), with their charge conditioning amplifier (Brüel & Kjaer, type 2635), an audio actuator (PUI Audio, ASX05404-HD-R), and a controller (dSpace MicrolabBox DS 1202). The first accelerometer is placed 1 cm away from the vibration exciter to get an image of the incoming disturbance. The second one is fixed at 4 cm from the other extremity with the actuator, where the object is to be placed, to measure the residual error. A drawing and a picture of the test bench are available Figures 3 and4.

Test signals

The characteristics of the test signals used as a disturbance source are selected from previous measurements found in the literature [START_REF] Zini | Experimental analysis of the traffic-induced-vibration on an ancient lodge[END_REF][START_REF] Cigada | Protecting pietà rondanini against environmental vibrations with structural restoration works[END_REF] or recorded by the authors. Since the spectral content of the sources ranges from 10 Hz to 370 Hz, and the cutoff frequency of the actuator is around 70 Hz, the frequency band of interest is chosen to be 70-370 Hz. It is then decided to divide this band into three distinct sub-bands (70-170 Hz; 170-270 Hz and 270-370 Hz), as sources frequency bandwidth is usually around 100 Hz. To assess performances of the control system in the worst case (the broader the bandwidth, the lower the performances are expected [START_REF] Ardekani | On the convergence of real-time active noise control systems[END_REF]), a fourth signal covering the full bandwidth of interest is created. To create the test signals, a pseudo random binary sequence is filtered by a 20th order pass-band filter whose cutoff frequencies are chosen accordingly to the ones given above.

Test procedure

The sampling frequency of the controlled system is set to 2500 Hz. The test signals are designed to be 65 seconds long. Prior to each recording, the amplitude of the source is varied until the amplitude of the acceleration at the position of the error sensor is around 2mm/s 2 . This value has been chosen because it is the maximum acceleration measured in situ by the authors and it represents a limit from which damage to cultural objects has been noticed [START_REF] Thickett | Vibration damage levels for museum objects[END_REF].

For every test signal, the vibration shaker is driven while the active control is disabled for the whole duration, to record first the error sensor signal in the absence of control. Then, a second measurement is performed: the active control, which is initially disabled, is now activated after 5 seconds. The error sensor signal is recorded from this instant, considered at the origin of time.

Benchmark set

Table 1. Four different sets used to compute the benchmark performance index I.

GR (dB) CT (s)

Set 1

D i min 12 X D imax 18 X w D i 1 X Set 2 D i min 12 0.5 D imax 18 3 w D i 1 1
Set 3

D i min 12 0 D imax 18 1 w D i 1 1
Set 4

D i min 12 0 D imax 18 1 w D i 1 3
Four different benchmark sets, including different values for D imin , D imax , and w Di for the descriptors GR and CT, are proposed to evaluate the control performances (see Table 1). The first one only focuses on static performances. One can imagine that this kind of set is used when sources are stationary, therefore dynamic performances are not that important and only performances in steady state matter. The second set includes the convergence time which is a relevant descriptor when the disturbance source is not stationary. The third set is a variation of the second one, but this time expectations related to convergence time are higher. This set can be used when the source show fast variation, thus it is necessary to have a fast adaptation algorithm. Finally, the last set is the same as the third with one difference: the weight given to the convergence time is increased, what means the user gives priority to the convergence time descriptor over the global reduction descriptor.

Preliminary Results

Descriptors

Global reduction obtained for both FxLMS and FIRYK is shown in Figures 5, and convergence time is shown in Figure 6. In each diagram, one vertical bar evaluates a performance of the algorithm for one of the four test signals used, whose spectral content is reminded in the inset box

Benchmark Performances Index

Performances index I, computed for every proposed set in Table 1, are available in Table 2. One can see that regarding performances in stationary sources (Set 1), FIRYK must be chosen. However, in cultural heritage condition, most of sources are not stationary. In this case, it might be interesting to look at the second set, which gives equal importance to static and dynamic descriptors. For these benchmark parameters, the FxLMS definitely outperforms the FIRYK. In cultural heritage context, some sources can vary very quickly, both regarding temporal and frequency aspects, so more demanding convergence time parameters can be used (Set 3 vs. Set 2). In this case, the FIRYK appears to be better, even though both algorithms are probably not appropriated as they show poor global performance index. Finally, increasing the weight of the convergence time (Set 4) seems to increase the relevance of using FxLMS, thanks to its better capacity to adapt. As a conclusion, these different sets show how performances parameters can influence the global performance index, as both a change in the min/max values or in the related weight can have a strong impact and change the final choice. Therefore, these parameters must be set carefully to match the user's requirements.

CONCLUSION

In this article, a method to objectively and quantitatively assess control performance has been proposed. This method relies on the extraction of time performance de- scriptors, which reflect specific properties of controlled signals, both in dynamic and static behavior. Then, parameters' weighting allows the user to tune the benchmark parameters according to his own needs and quantitatively compare several algorithms for a specific application. An application to a museum control condition has been proposed to compare performances of two algorithms (FxLMS and FIRYK). Results show that depending on the user requirements, performance indexes can vary a lot and does not always consider the same algorithm as the best. Future work will address the relevance of using frequency descriptors to help discriminate the two algorithms performances.

STATEMENTS AND DECLARATIONS

This research was supported by Paris Seine Graduate School of Humanities, Creation, Heritage, Investissements d'Avenir ANR-17-EURE-0021-Foundation for Cultural Heritage Science.

A

  UNIFIED APPROACH TO COMPARE ACTIVE VIBRATION CONTROL PERFORMANCES AND ITS APPLICATION IN A MUSEAL CONTEXT Loïc Forma 1 * Henri Boutin 2 Marguerite Jossic 3 Nicolas Wilkie-Chancellier 1 Sandie Le Conte 4 1 SATIE, CY Cergy Paris Université, 5 mail Gay Lussac, 95000 Neuville, France 2 STMS -Sorbonne Université -Ircam, 1, place Igor Stravinsky, 75004 Paris, France 3 ECR team, Musée de la Musique, CRC UAR3224, 221 Avenue Jean-Jaurès, 75019 Paris, France 4 Institut National du Patrimoine, 124 rue Henri-Barbusse, 93300 Aubervilliers, France

Figure 1 .

 1 Figure 1. Reduced active control block diagram.x(n) u(n), y(n), d(n) and e(n) represent respectively the measured reference, the control signal, the contribution of the control device, the disturbance signal and the error signal. The control filter is W (n), while H represents the secondary path.

2. 3

 3 Dynamic descriptor: Convergence Time CT Dynamic descriptors are performance indicators used to estimate the control performance when a change in the control condition occurs. Here, only the convergence time will be presented. The proposed algorithm is divided in two parts. The first algorithm starts with the extraction of an envelope E N (n) which represents the energy reduction over a window of length N E N (n) = rms (e close (n -N : n)) rms (e open (n -N : n))

Figure 2 .

 2 Figure 2. Convergence time of the envelope τ N in function of N for different experimental controlled error signals. These signals are obtained using four experimental conditions (a b, c and d), which differ according to the algorithm, the position of the reference, the disturbance signal, etc. The grey dashed lines represent linear fit of the curves, excluding the first points.

Figure 3 .

 3 Figure 3. Drawing of the test bench used during experiments.

Figure 4 .

 4 Figure 4. Photo of the test bench used during experiments.

Figure 5 .

 5 Figure 5. Global Reduction Results. The colours stands for the different test signals described in section 3.1.3.

Figure 6 .

 6 Figure 6. Convergence time.The colours stands for the different test signals described in section 3.1.3.

Table 2 .

 2 Benchmark performance indexes obtained for different sets.

	FxLMS FIRYK
	Set 1 39.2%	64.1%
	Set 2 64.1%	54.8%
	Set 3 32.6%	35.1%
	Set 4 29.3%	20.6%

Turin, Italy • 11 th -15 th September 2023 • Politecnico di Torino