Clemens Von Scheffer
email: clemens.vonscheffer@abdn.ac.uk

François De Vleeschouwer

Gaël Le Roux

Ingmar Unkel

Mineral dust and lead deposition from land use and metallurgy in a 4800-year-old peat record from the Central Alps (Tyrol, Austria)

Keywords: Alps, Prehistoric metallurgy, Land use, Peat geochemistry, Atmospheric dust, Portable XRF

Humans have occupied the Alps over most of the Holocene. Yet, continuous records on the impact of using montane resources and landscapes are scarce or confined to segregated areas or periods. We present a high-resolution geochemical record of the last 4800 years from the ombrotrophic peatland Piller Moor in the Central Alps (Tyrolean Oberland, western Austria), using inductively coupled mass plasma spectrometry (ICP-MS) and highly efficient inter-calibrated portable X-ray fluorescence analysis (pXRF). Fluctuations of metal enrichment factors (EF) for lead (Pb), copper (Cu), zinc (Zn) and antimony (Sb), accumulation rates of anthropogenic lead (Pbanth AR) and mineral matter (MAR), based on titanium (Ti), are in line with archaeological and pollen evidence for human presence and environmental change. Periods of intensified, erosive land use are indicated by MAR around 4400 cal BP, 3400 cal BP and, very prominently, at 2400 cal BP. After low MAR in the early Middle Ages, soil disturbances reappear around 1200 cal BP (750 CE), after 200 cal BP (1750 CE) and during the 20 th century CE. We found evidence that metallurgy was practised in the area as early as 4450 cal BP, again from 3500 to 2900 cal BP and episodically between 2400 and 1400 cal BP. The Central Alps were presumably a source of increased Pb-emissions in the post-Roman period from 1500 to 1400 cal BP (450-550 CE). Generally, our findings suggest that mining predates archaeological and historical evidence. Following a continuous increase since the Middle Ages, atmospheric Pb EF and Pbanth AR peak around 1980 CE. The record of mineral atmospheric input illustrates the notable impact of human activities on soil erosion and dust entrainment in the Central Alps. Furthermore, links between Little Ice Age cold phases and reduced human impact and mining are established. Our high-resolution peatgeochemistry data quantifies atmospheric deposition of mineral matter and Pb, which act as proxies for landscape evolution and metallurgy on a local and regional scale. It provides new insights and a deeper understanding of the interaction of climate, environment and humans in mountainous landscapes like the Central Alps.

Introduction

Ombrotrophic peatlands are precious palaeoenvironmental archives. Specific characteristics render them reliable geochemical records of certain contaminants like lead (Pb), copper (Cu) or Antimony (Sb) as industrial or metallurgical emissions [START_REF] Damman | Distribution and Movement of Elements in Ombrotrophic Peat Bogs[END_REF][START_REF] De | Atmospheric lead and heavy metal pollution records from a Belgian peat bog spanning the last two millenia: human impact on a regional to global scale[END_REF][START_REF] Forel | Historical mining and smelting in the Vosges Mountains (France) recorded in two ombrotrophic peat bogs[END_REF][START_REF] Jones | Ombrotrophic peat as a medium for historical monitoring of heavy metal pollution[END_REF][START_REF] Nieminen | Enrichment of Cu, Ni, Zn, Pb and As in an ombrotrophic peat bog near a Cu-Ni smelter in Southwest Finland[END_REF][START_REF] Shotyk | Natural and anthropogenic enrichments of As, Cu, Pb, Sb, and Zn in ombrotrophic versus minerotrophic peat bog profiles, Jura Mountains, Switzerland[END_REF][START_REF] Shotyk | Antimony in recent, ombrotrophic peat from Switzerland and Scotland: Comparison with natural background values (5,320 to 8,020 14 C yr BP) and implications for the global atmospheric Sb cycle[END_REF]. They also act as archives of fluctuating mineral atmospheric dust deposition, indicating droughts, storminess or changes in land cover and land use (e.g. [START_REF] Chambers | Development and refinement of proxy-climate indicators from peats[END_REF][START_REF] Hölzer | Silicon and titanium in peat profiles as indicators of human impact[END_REF][START_REF] Lomas-Clarke | Human impact signals from peat bogs-a combined palynological and geochemical approach[END_REF][START_REF] Schofield | An integrated geochemical and palynological study of human impacts, soil erosion and storminess from southern Greenland since c. AD 1000[END_REF]).

Yet, such geochemical studies are rare in the Central Alps, because mires in mountainous landscapes are rather small, heterogeneous, and often disturbed by livestock and drainage [START_REF] Spitale | A warning call from mires of the Southern Alps (Italy): Impacts which are changing the bryophyte composition[END_REF][START_REF] Yang | Qinghai-Tibetan Plateau peatland sustainable utilization under anthropogenic disturbances and climate change[END_REF]. Furthermore, they are affected by natural geomorphological processes or events and peat accumulation can be low due to short vegetation periods.

When reconstructing human impact and interaction with mountain landscapes, considering proximate archaeological sites is imperative and a key to proper interpretation. The Piller Moor (Tyrol, Austria, Figure 1) is one of the rare, well-preserved ombrotrophic peatlands in direct vicinity to well-known archaeological sites, which are a bronze-hoard and a ritual fire site [START_REF] Heiss | Weizen, Linsen, Opferbrote -Archäobotanische Analysen bronze-und eisenzeitlicher Brandopferplätze im mittleren Alpenraum[END_REF][START_REF] Tomedi | Der mittelbronzezeitliche Schatzfund vom Piller[END_REF]Tomedi, , 2002a;;[START_REF] Tschurtschenthaler | Das Heiligtum auf der Pillerhöhe[END_REF]. Palynological data is available for the site [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF], while nearby palaeovegetation studies give a good perspective on regional developments (e.g. [START_REF] Festi | Mid and late holocene land-use changes in the Ötztal alps, territory of the neolithic iceman "Ötzi[END_REF][START_REF] Grabherr | Die Via Claudia Augusta in Nordtirol[END_REF][START_REF] Wahlmüller | Die Komperdellalm im Wandel der Jahrtausende. Ein Beitrag zur Vegetationsund Besiedlungsgeschichte des Oberen Gerichts[END_REF][START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF]. Reconstructions of glacier activity and tree line changes from the nearby Kauner Valley (Figure 1) further provide insight on past regional climate variability during the late Holocene [START_REF] Nicolussi | Holocene tree-line variability in the Kauner Valley, Central Eastern Alps, indicated by dendrochronological analysis of living trees and subfossil logs[END_REF][START_REF] Nicolussi | Untersuchungen zur holozänen Gletscherentwicklung von Pasterze und Gepatschferner (Ostalpen)[END_REF]. Although the Eastern Alps became an important mining district during the Bronze Age [START_REF] O'brien | Prehistoric Copper Mining in Europe: 5500-500 BC[END_REF][START_REF] Stöllner | Bergauf Bergab. 10.000 Jahre Bergbau in den Ostalpen[END_REF], there is little known on prehistoric mining activity for this area of the Central Alps [START_REF] Krause | Early tin and copper metallurgy in south-western Germany at the beginning of the Early Bronze Age[END_REF][START_REF] Stöllner | die alpinen Kupfererzreviere: Aspekte ihrer zeitlichen, technologischen und wirtschaftlichen Entwicklung im zweiten Jahrtausend vor christus[END_REF].

In our study, we use geochemical ICP-MS and portable XRF (pXRF) data to identify periods of metallurgy and to assess the degree and scale of human impact at the junction between the Eastern and Western Alps. Portable XRF can be a time and cost-efficient tool to analyse the chemistry of a wide variety of materials (e.g. [START_REF] Kalnicky | Field portable XRF analysis of environmental samples[END_REF][START_REF] Liritzis | Portable XRF of archaeological artifacts: current research, potentials and limitations[END_REF][START_REF] Palmer | Use of field-portable XRF analyzers for rapid screening of toxic elements in FDA-regulated products[END_REF]. However, palaeoenvironmental studies using pXRF remain scarce [START_REF] Gałka | Rich fen development in CE Europe, resilience to climate change and human impact over the last ca. 3500 years[END_REF][START_REF] Kapustová | Peat bog and alluvial deposits reveal land degradation during 16th-and 17thcentury colonisation of the Western Carpathians (Czech Republic)[END_REF][START_REF] Von Scheffer | 6200 years of human activities and environmental change in the northern central Alps[END_REF]. One of the challenges is that preinstalled calibrations rarely cover the highly organic sample matrix of peat. Hence, we developed an (inter)calibration between semi-quantitative pXRF and ICP-MS measurements, following full acid digestion in a clean room. Certified reference materials (CRM) for both methods act as an independent verification of the quality and reliability of our approach. Our geochemical proxy data is supported by pollen data from the same site [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF] and other local palynological and archaeological studies, providing a comprehensive picture of regional human land use, metallurgy and environmental conditions in the past.

Methods

Study area and site

As part of the Tyrolean Oberland, the climate at the Piller Moor is alpine-continental with a mean annual precipitation of ca. 800 mm and main wind directions are between west and south (46%) and north to north-east (18.5%) for the period between 1971 and 2000 CE in Landeck (Central Institution for Meteorology and Geodynamics of Austria, [START_REF] Zamg | Klimadaten von Österreich, 1971 -2000[END_REF]). The Piller Saddle is in the altitudinal lower subalpine zone (c. 1550 m a.s.l.). The Inn River (c. 800 m a.s.l.) approaches the Piller Saddle from the South before joining with the Sanna River at Landeck and turning east (Figure 1). The Kauner, Pitz and Oetz Valleys are south-east of the Saddle. A brook (Pillerbach) drains the mire in north-easterly direction over the Pitze River into the Inn Valley, which divides the Penninic metamorphic zone to the south and the northern Limestone Alps.

The Piller Moor lies within a depression at 1540 m a.s.l., stretching approx. 380 m W to E and 30 to 100 m N to S, with the water-level at approx. 10 cm below surface. Sphagnum spp. dominates the vegetation, together with Andromeda polifolia, Drosera spp., Cyperaceae and Pinus mugo rotundata stands towards the periphery, which is typical for ombrotrophic mires. The surrounding forest consists of Picea spp., Pinus spp. and Larix spp.

Coring and sub-sampling

Coring in the Piller Moor took place in 2017. For the profile Pi17 (47°07'24.85" N, 10°39'45.45" E), a Wardenaar system (10x10 cm; [START_REF] Wardenaar | A new hand tool for cutting peat profiles[END_REF] was used to core the top meter of the mire and a piston corer (Usinger 8 cm barrel; [START_REF] Mingram | Long cores from small lakes -Recovering up to 100 m-long lake sediment sequences with a high-precision rod-operated piston corer (Usinger-corer)[END_REF] was used for the deeper layers. Parallel profiles (A and B) were taken to get a composite core. A maximum depth of 380 cm was reached before hitting an impenetrable layer, supposedly consisting of woody material. The segments were wrapped in cling film, transferred into a PVC-casing and sealed in a plastic hose. Cores A and B were sliced continuously to subsamples of c. 1.1 cm thickness for geochemistry and dating. Dry bulk density was calculated using the dimensions and dry weight of the geochemistry samples. Clean coring and subsampling followed the protocol of [START_REF] De | Coring and sub-sampling of peatlands for palaeoenvironmental research[END_REF] and [START_REF] Givelet | Suggested protocol for collecting, handling and preparing peat cores and peat samples for physical, chemical, mineralogical and isotopic analyses[END_REF]. Three macrofossil samples were picked in ultrapure water for radiocarbon dating at Poznan AMS Radiocarbon Laboratory (Poz), Poland.

Other samples were selected with the same method, pre-treated at the Gliwice Radiocarbon Laboratory (GdA), Poland and measured at the Rafter Radiocarbon Laboratory, New Zealand.

Geochemistry

143 dry samples for pXRF and 63 samples for ICP-MS analyses, were selected and processed following Le Roux and De Vleeschouwer (2010). The samples were crushed to a homogenous powder in 15-50 ml tubes with eight glass beads of 4 mm using a FastPrep®-24 ball-mill (3x20 s at 6 m*s -1 ). For pXRFanalysis, sample and CRM preparations and measurements were done on dried and homogenised peat, following the protocol in von [START_REF] Von Scheffer | 6200 years of human activities and environmental change in the northern central Alps[END_REF]. The samples were transferred into polystyrene containers, covered with 4-μm thick polypropylene film and measured using a handheld Thermo Fisher Scientific Niton Xl3t, inside a test stand. The pXRF-device was rebooted regularly to account for fluctuations of temperature and atmospheric pressure during the day. The Xl3t was used in soil-mode, running the main and low-filter for 180 s each.

Samples for ICP-MS analyses were digested in a class 100 clean room at "Laboratoire Ecologie Fonctionnelle et Environnement" Toulouse, France. Following the protocol for acid-digestion of peat samples detailed in Vanneste et al. (2015), 100 mg peat powder was treated consecutively with ultrapure chemicals, first with 2 ml of 65 % nitric for 24 h at room temperature and, after adding 0.5 ml hydrofluoric acid, at 110 °C for 48 h, then with 31 % ultrapure peroxide at room temperature for 24 h and lastly in 2 ml 65 % nitric acid at 110 °C for 48 h. Before every step, the mix of dried sample and liquid was treated with ultrasound and the samples were evaporated at 50 °C in between steps. An In/Re spike was added to each sample. Five multi-element standards were run every 10 samples to correct for instrument drift. A blank and two different organic CRMs (NIST-1547a, NIST-1515, GBW-07603, NJV-942, NJV-941) were treated per batch of 21 samples and measured in regular intervals. In addition to the CRMs used in ICP-MS, BCR-060, IAEA-336, IPE-176 and NIST-1575a were used for pXRF.

Computing and calculations

The calculations and regression analyses are performed in R version 4.0.3. (R Core Team, 2021). The Bayesian age-depth model (ADM) is created using the package rbacon version 2.5.3 [START_REF] Blaauw | Flexible paleoclimate age-depth models using an autoregressive gamma process[END_REF] with a 95 % confidence interval and the IntCal20 radiocarbon calibration curve [START_REF] Reimer | THE INTCAL20 NORTHERN HEMISPHERE RADIOCARBON AGE CALIBRATION CURVE (0-55 CAL kBP)[END_REF]. Boundaries are added based on obvious changes in density and humification. Median ages are given as 'cal BP' (calibrated years before 1950). Historical or certain cited ages are given as CE. The peat accumulation rate represents the bulk thickness of one peat sample and the period of time covered (∆thickness/∆time) in mm*year -1 .

Metal enrichment factors (Me EF) for Pb, Sb, Cu and Zn and atmospheric mineral accumulation rates (MAR) are calculated using the conservative behaviour of Ti in peat [START_REF] Nesbitt | Weathering of granodioritic crust, long-term storage of elements in weathering profiles, and petrogenesis of siliciclastic sediments[END_REF], as done in [START_REF] Shotyk | A peat bog record of natural, pre-anthropogenic enrichments of trace elements in atmospheric aerosols since 12 370 14 C yr BP, and their variation with Holocene climate change[END_REF], to detect past metal enrichment and land use change (e.g. [START_REF] Kempter | Ti and Pb concentrations in rainwater-fed bogs in Europe as indicators of past anthropogenic activities[END_REF]. The choice of Ti was also pre-determined by the range of elements of the pXRF. Pb, Sb, Cu, and, sometimes, Zn are commonly used to trace metallurgical or industrial emissions (e.g. [START_REF] Damman | Distribution and Movement of Elements in Ombrotrophic Peat Bogs[END_REF][START_REF] Jones | Ombrotrophic peat as a medium for historical monitoring of heavy metal pollution[END_REF][START_REF] Nieminen | Enrichment of Cu, Ni, Zn, Pb and As in an ombrotrophic peat bog near a Cu-Ni smelter in Southwest Finland[END_REF][START_REF] Shotyk | Natural and anthropogenic enrichments of As, Cu, Pb, Sb, and Zn in ombrotrophic versus minerotrophic peat bog profiles, Jura Mountains, Switzerland[END_REF][START_REF] Shotyk | Antimony in recent, ombrotrophic peat from Switzerland and Scotland: Comparison with natural background values (5,320 to 8,020 14 C yr BP) and implications for the global atmospheric Sb cycle[END_REF].

𝑀𝑒 𝐸𝐹 = ( 𝑀𝑒 𝑇𝑖 ⁄ ) 𝑆𝑎𝑚𝑝𝑙𝑒 ( 𝑀𝑒 𝑇𝑖 ⁄ ) 𝑈𝐶𝐶 𝑀𝐴𝑅 = 100 0.41 ⁄ * 𝑇𝑖 𝑆𝑎𝑚𝑝𝑙𝑒 * δ * PA
δ is the dry bulk density and PA is the peat accumulation rate.

An anthropogenic Pb accumulation rate (Pbanth AR) is calculated following [START_REF] Weiss | Atmospheric Pb deposition since the industrial revolution recorded by five Swiss peat profiles: Enrichment factors, fluxes, isotopic composition, and sources[END_REF]. First, the concentration of Pb in local and natural soil dust (Pbnat)are determined for every sample.

𝑃𝑏 𝑛𝑎𝑡 = 𝑃𝑏 𝑆𝑎𝑚𝑝𝑙𝑒 * ( 𝑃𝑏 𝑇𝑖 ⁄ )

𝑈𝐶𝐶

Pbnat is then subtracted from every sample to obtain the anthropogenic contribution Pbanth., which is then used to calculate Pbanth AR as follows:

𝑃𝑏 𝑎𝑛𝑡ℎ. 𝐴𝑅 = 𝑃𝑏 𝑎𝑛𝑡ℎ. * δ * PA
The upper continental crust (UCC) concentrations [START_REF] Mclennan | Relationships between the trace element composition of sedimentary rocks and upper continental crust[END_REF] are used as reference or background values to calculate MAR, metal EFs and Pbanth AR with Ti (4100 mg*kg -1 ), Pb (17 mg*kg -1 ), Cu (25 mg*kg -1 ), Zn (71 mg*kg -1 ) and Sb (0.2 mg*kg -1 ). Using the UCC-values is partly because of the heterogenous geology of the Alps and their surroundings as potential dust sources, but it also makes the results more comparable to similar studies. Furthermore, the mineral base was not reached to get a local sediment reference and defining a natural reference level within our samples would be difficult within the age range of the peat record.

Model estimates are made in all unmeasured peat samples from the continuous profile by linear interpolation between measurements. These modelled data-points are of course not included in the main data and figures, but they allow a simple approximation of the cumulative anthropogenic Pbdeposition and of both the average MAR and Pbanth AR over time.

The chronological interpretations are separated into five different periods from Neolithic until present, which largely correspond to cultural periods in the central Alps, also used by [START_REF] Röpke | Late-holocene land-use history and environmental changes at the high altitudes of st antönien (switzerland, northern alps): Combined evidence from pollen, soil and tree-ring analyses[END_REF].

Results

Chronology

Sphagnum spp. mosses dominate throughout the core sections. The deepest section of profile B was fitted and merged to the deepest section of profile A, using density, geochemistry and radiocarbon dates (Table 1).

The age-depth-model (Figure 2) provides a median age of 4750 cal BP for the core bottom. Up to 182 cm depth (2000 cal BP), the peat accumulation rate (AR) remained mostly below 0.7 mm*a -1 before increasing to 0.8-1.2 mm*a -1 until 91 cm (1200 cal BP). A significant decrease to less than 0.4 mm*a -1 prevails from 91-61 cm (1200-100 cal BP). In the uppermost part, the AR increases to over 10 mm*a -

1

. The most recent part of the model relies upon a single bomb-pulse date (GdA-5492), which reduces the uncertainty in the upper 50cm.

Geochemistry

Dry bulk density, raw pXRF and ICP-MS results (data vs depth and calibrated ages) are given in Table SI_1. The raw data output of the analyses is presented as ICP-MS vs pXRF (Figure 3) for the purpose of visual comparison and performing regression analyses.

Quality control

The data relevant for quality control is provided in the supplementary information (Table SI_1).

Concentrations in the blanks attest clean sample processing. Measurements of Ti, Pb, Zn, Rb, K, Sb, Fe, Sr and Cu deviate less than 20 % from certified values in ICP-MS. In contrast, raw pXRF results of the CRMs are generally much higher than their certified concentrations. Yet, only the pXRF-measurements of Cu, Zn, and K show standard deviations (sd) over 20 % in certain organic CRMs (e.g NJV-941).

Elements that are not detectable with pXRF in most samples, for example due to detection limits, or which produced arbitrary results, were not considered further in the regression analysis. This is the case for Cu and Sb leaving only Fe, K, Pb, Rb, Ti, Zn and Sr for further use.

Regression Analysis

von Scheffer et al. ( 2019) demonstrate the general reliability and cost and time efficiency of pXRF analyses for Ti and Pb in peat. In the same way, we here performed an individual regression analysis of pXRF versus ICP-MS and CRMs on a broader set of elements. The regression functions of CRMs, ICP-MS and pXRF-results (Figure 3) show a good linear fit for Ti (R²=0.98), Pb (R²=0.99), Sr (R²=0.99), K (R²=0.98), Rb (R²=0.97), Zn (R²=0.92) and Fe (R²=0.86). Although pXRF-results are above certified values, these elements can be cross-calibrated with quantitative methods or by using appropriate organic CRMs. Depending on the elements in question, a regression analysis could be based on a larger set of CRMs alone (red symbols in Figure 3).

Elemental profiles

The relevant concentration vs depth profiles (Figure 4) and further interpretation are based on the pXRF data calibrated for quantification via ICP-MS using the regressions (Figure 3). The pXRF profiles have a higher depth resolution, except for Cu and Sb which were only measured by ICP-MS (Figure 4).

Peaks in Ti exceeding 400 mg*kg -1 and 600 mg*kg -1 appear at 312.5 and 200 cm (4140 and 2330 cal BP), respectively, with some minor peaks of 400 mg*kg -1 and 260 mg*kg -1 at 88 cm and 62 cm (1050 and 110 cal BP). Rb resembles the course of Ti, staying mostly below 5 mg*kg -1 except for the five peaks parallel to Ti, indicating stronger terrigenous influx into the mire during these periods. A slight increase in Rb is also recorded in the surface layers. K ranges between 300 and 700 mg*kg -1 , with peaks at 312.5 cm (3000 mg*kg -1 ) and again at 200 cm, followed by 2300 and 1500 mg*kg -1 at 88 cm and 62 cm. A rising trend shows in the uppermost 25 cm. Sr gradually rises from 10 mg*kg -1 to a maximum of 30 mg*kg -1 at 200 cm (2330 cal BP). After a local minimum of 2 mg*kg -1 , a declining trend sets in at 155 cm (1770 cal BP). Fe doubles from 1500 mg*kg -1 at the bottom to approx. 3000 mg*kg -1 at 125 cm depth before decreasing again.

Pb concentrations remain low around 3 to 10 mg*kg -1 between 350 and 100 cm (4710-1260 cal BP).

An increase to 20 mg*kg -1 appears around 328 cm. In three subsequent peaks in the uppermost metre, the maximum concentration increases from 35 mg*kg -1 at 90 cm (1120 cal BP) to 70 mg*kg -1 at 39 cm (-29 cal BP). Cu peaks at 326 cm (39 mg*kg -1 ) and 282 cm (23 mg*kg -1 ). Smaller increases appear at 310, 262 and 200 cm. However, a decreasing trend is obvious towards the surface. Sb increases to 3 mg*kg -1 at 326 cm but is mostly below 1 mg*kg -1 until 90 cm. A maximum of 7 mg*kg -1 at 67 cm is followed by concentrations over 1 mg*kg -1 . Zn is on a level between 10 and 20 mg*kg -1 , rises to c. 30 mg*kg -1 at 312.5, 270, 200 and 62 cm (4140, 3500, 2330 and 110 cal BP) and exceeds 40 mg*kg -1 nearsurface.

The dry bulk density gradually increases from 0.05 to 0.1 g*cm -3 in the lowest 100 cm and sharply returns to 0.05 g*cm -3 at 250 cm. A density peak to over 0.1 g*cm -3 covers 90 to 62 cm.

Accumulation rates and enrichment factors

MAR stays mostly below or around 1.5 g*a -1 *m -2 , but remarkable peaks of c. 9 g*a -1 *m -2 appear at 2350 cal BP and again in in the last century (Figure 5). Moderate increases in MAR appear prior to 4000, and around 3400, 1600, 1100 and 200 cal BP.

A peak of Pbanth AR around 4400 cal BP (approx. 0.8 mg*a -1 *m -2 ) is followed by a slowly rising trend from 4000 until 3250 cal BP to 0.5 mg*a -1 *m -2 . After another single peak around 1450 cal BP (approx. In Table 2, the estimated averages of accumulation rates as well as the estimated cumulative loads of Pbanth during the five periods (discussed in section 3.3) are summarised.

4. Peatland and landscape evolution and human impact

Trophic status and atmospheric input

The low dry bulk density and low concentrations of Sr paired with the observed Sphagnum spp.

Dominance suggest ombrotrophic conditions over the full profile Although the Sr-concentration profile fluctuates from top to bottom, it does return to low concentrations in the deepest section of our record, which is unlike a typical profile of a fen. Furthermore, the deepest section of the peat record is not the mineral bottom, as we hit an impenetrable layer of wood. Rather gentle slopes around the peatland and the fact that the core was taken in the peatland's centre, makes surface input unlikely.

Even with a spatially restricted higher availability of nutrients from the more mineral rich layers (e.g. 60-90 cm and 200 cm), which would favour other Sphagnum species or more vascular plants, the main elements used for interpretation (Ti, Pb) show a generally conservative behaviour in peat. While the immobility of Ti is well accepted and often used as a conservative reference element [START_REF] Bao | Recent atmospheric dust deposition in an ombrotrophic peat bog in Great Hinggan Mountain, Northeast China[END_REF][START_REF] Sapkota | Six millennia of atmospheric dust deposition in southern South America (Isla Navarino, Chile)[END_REF][START_REF] Shotyk | A peat bog record of natural, pre-anthropogenic enrichments of trace elements in atmospheric aerosols since 12 370 14 C yr BP, and their variation with Holocene climate change[END_REF], Pb also remains largely immobile even when affected by strongly fluctuating water tables [START_REF] Rothwell | Storage and behavior of As, Sb, Pb, and Cu in ombrotrophic peat bogs under contrasting water table conditions[END_REF] and it shows the strongest adsorption to organic matter in peat [START_REF] Koivula | Sorption of Pb(II), Cr(III), Cu(II), As(III) to peat, and utilization of the sorption properties in industrial waste landfill hydraulic barrier layers[END_REF][START_REF] Krumins | Biosorption of Metallic Elements onto Fen Peat[END_REF]. In contrast, the increasing trend of Cu with depth could indicate some mobility, which is why it is interpreted with caution.

On first sight, Pbanth AR and Pb EF (figure 5) can appear inconsistent when, for example, anthropogenic Pb input is masked (diluted) by local soil dust input with a low natural background signature. Or, during times of low energy dust entrainment and deposition (MAR), the consequently finer particles could bear higher concentrations of Pb or trace metals [START_REF] Shotyk | A peat bog record of natural, pre-anthropogenic enrichments of trace elements in atmospheric aerosols since 12 370 14 C yr BP, and their variation with Holocene climate change[END_REF][START_REF] Ujević | Trace metal accumulation in different grain size fractions of the sediments from a semi-enclosed bay heavily contaminated by urban and industrial wastewaters[END_REF]. The former can be assumed when Pbanth AR is high and Pb EF low. The latter is to consider with Pbanth AR being low and Pb EF high. Pb-enriched atmospheric dust could also be more distal or very small, and therefore not increasing significantly the total accumulation significantly. With simultaneously rising Pbanth AR and Pb EF, and especially in prehistoric times, local or regional metallurgy is very likely. In any event, most of the interpretation is based on the more robust Pbanth AR.

4.2 Neolithic-Bronze Age transition (Period 1 from 4800 to 4000 cal BP)

Land use: Increases of mineral matter input at 4450 and 4150 cal BP from less than 0.5 to c. 2 and 5 g*a -1 *m -2 , respectively, are in line with indicators for forest clearances, increased pastoralism indicators and burning in the area [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF][START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF]. [START_REF] Wahlmüller | Die Komperdellalm im Wandel der Jahrtausende. Ein Beitrag zur Vegetationsund Besiedlungsgeschichte des Oberen Gerichts[END_REF] suggests first human impact in the region near Serfaus southwest of the Piller Moor around 4250 cal BP.

Around the same time, agricultural terraces [START_REF] Zoller | The history of vegetation and land use in the Lower Engadine (Switzerland). Pollen records of the last 13000 years[END_REF] and alpine pasture systems [START_REF] Reitmaier | Letzte Jäger, erste Hirten[END_REF] From a climatic perspective, the peaks in MAR around 4450 and 4150 cal BP coincide with minimum glacier stands in the region [START_REF] Nicolussi | Untersuchungen zur holozänen Gletscherentwicklung von Pasterze und Gepatschferner (Ostalpen)[END_REF]. Afterwards, a continuously declining tree line in the Kauner Valley [START_REF] Nicolussi | Holocene tree-line variability in the Kauner Valley, Central Eastern Alps, indicated by dendrochronological analysis of living trees and subfossil logs[END_REF] could have resulted from both climate and human forcing and contributed to an increasing trend of MAR, starting around 4000 cal BP. Yet, it is still the period with the lowest estimated average MAR (1.01 g*a -1 *m -2 , Table 2).

Metallurgy: Only few hints for prehistoric mining exist in western Tyrol (e.g. [START_REF] Grutsch | Die Nordtiroler Kupfererzvorkommen westlich von Schwaz als Rohstoffpotential der Bronzezeit[END_REF]. Even the ancient mining districts of the Eastern Alps bear only limited evidence before 3750 cal BP (O'Brien, 2015), although copper mining could have started around 4450 cal BP [START_REF] Knierzinger | Late Holocene periods of copper mining in the Eisenerz Alps (Austria) deduced from calcareous lake deposits[END_REF][START_REF] Knierzinger | Anthropogenic and climate signals in late-Holocene peat layers of an ombrotrophic bog in the Styrian Enns valley (Austrian Alps)[END_REF]. Metallurgy in general was already present in the Alps at that time [START_REF] Höppner | Prehistoric copper production in the Inn Valley (Austria), and the earliest copper in Cental Europe[END_REF].

Ore extraction is suggested for the Southern Alps [START_REF] Artioli | A lead-isotope database of copper ores from the Southeastern Alps: A tool for the investigation of prehistoric copper metallurgy[END_REF] and Cu-mining is suggested for the Eastern Alps [START_REF] Knierzinger | Anthropogenic and climate signals in late-Holocene peat layers of an ombrotrophic bog in the Styrian Enns valley (Austrian Alps)[END_REF]. In the Piller Moor record, an increase of Pbanth AR to 0.8 mg*a -1 *m -2 between 4500 and 4200 cal BP is the highest until the end of the Middle Ages. This pronounced signal also coincides with synchronously enriched Pb and Sb and with the MAR and pollen indicators mentioned above, which suggests a link between these proxies of human impact. A lake record to the south-west (Meidsee) [START_REF] Thevenon | Pre-) historic changes in natural and anthropogenic heavy metals deposition inferred from two contrasting Swiss Alpine lakes[END_REF] shows Pb-isotope supported evidence for metallurgy, which shows that the technology was around. However, the coincidence of proxies with the marked rise of Pbanth AR indicates that the inputs of the Piller Moor peat record had a proximate source at that time. Various polymetallic ore deposits in the area contain Cu, Ag, Pb, As and Sb, and some had been exploited over the last millennium [START_REF] Grutsch | Die Nordtiroler Kupfererzvorkommen westlich von Schwaz als Rohstoffpotential der Bronzezeit[END_REF][START_REF] Hammer | Über Gelbbleierz im Oberinntal[END_REF][START_REF] Hanneberg | Galmei und schöne Wulfenite: Der Blei-Zink-Bergbau rund um den Fernpass in Tirol[END_REF][START_REF] Neuhauser | Argentifodinam seu montem dictum Mùntafùne , -1000 Jahre Bergbau im südlichen Vorarlberg[END_REF][START_REF] Vavtar | Die Erzanreicherungen im Nordtiroler Stubai-, Ötztal-und Silvrettakristallin[END_REF][START_REF] Weber | Metallogenetische Karte von Österreich[END_REF]. Local small-scale metallurgy is therefore likely, but it would predate any direct archaeological evidence and the possibility of remote transport cannot be ruled out completely. Despite the depth, influence of minerotrophic conditions on the estimated Pbanth AR average of 0.26 mg*a -1 *m -2 (Table 2) is unlikely, as the described Pb-peak is very distinct from the background level and the Sr-concentration profile is very low.

Bronze Age (Period 2 from 4000 to 2800 cal BP)

Land use: Towards 3400 cal BP, increasing land use activity is suggested by rising MAR, which is in good agreement with Cerealia pollen in the Piller mire [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF] as well as open landscape and pastoral indicators in nearby study sites [START_REF] Wahlmüller | Die Komperdellalm im Wandel der Jahrtausende. Ein Beitrag zur Vegetationsund Besiedlungsgeschichte des Oberen Gerichts[END_REF][START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF]. Coinciding elevated charcoal values in these studies are in line with an increased fire clearance in the Alps [START_REF] Valese | Fire, humans and landscape in the European Alpine region during the Holocene[END_REF].

Local archaeological evidence of Bronze Age buildings in Fließ [START_REF] Tomedi | Denkmalschutzgrabungen am bronzezeitlichen Haus von Fliess-Silberplan[END_REF] and Kaunerberg [START_REF] Staudt | Zur Besiedlungsgeschichte der Ostalpen in der Mittel-bis Spätbronzezeit: Bestand, Kolonisation und wirtschaftlicher Neuanfang in der mittleren und späten Bronzezeit in Nordtirol[END_REF], and the ritual site on the Piller Saddle dating between 3450 and 3230 cal BP [START_REF] Tschurtschenthaler | Das Heiligtum auf der Pillerhöhe[END_REF][START_REF]source: Stamen Design under CC-BY-3.0 and OSM contributors under ODbl. B) Selection of references in discussion. Palaeoenvironmental studies a) to d), metallurgy and Pb-accumulation e) to o)[END_REF][START_REF] Shotyk | Natural and anthropogenic enrichments of As, Cu, Pb, Sb, and Zn in ombrotrophic versus minerotrophic peat bog profiles, Jura Mountains, Switzerland[END_REF], indicate extensive human activity in the study area, which was probably responsible for the doubling of the estimated average MAR (1.94 mg*a -1 *m - 2 ).

A pulse of stronger human activity is also evident in other regional records from the Central Alps [START_REF] Dietre | Palaeoecological evidence for Mesolithic to Medieval climatic change and anthropogenic impact on the Alpine flora and vegetation of the Silvretta Massif (Switzerland/Austria)[END_REF][START_REF] Festi | Mid and late holocene land-use changes in the Ötztal alps, territory of the neolithic iceman "Ötzi[END_REF][START_REF] Röpke | Late-holocene land-use history and environmental changes at the high altitudes of st antönien (switzerland, northern alps): Combined evidence from pollen, soil and tree-ring analyses[END_REF][START_REF] Von Scheffer | 6200 years of human activities and environmental change in the northern central Alps[END_REF]. In the Eastern Alps, intensified human impact is documented [START_REF] Knierzinger | Anthropogenic and climate signals in late-Holocene peat layers of an ombrotrophic bog in the Styrian Enns valley (Austrian Alps)[END_REF][START_REF] Viehweider | Mining-related land use changes since the Neolithic in the region of Kitzbühel (Tyrol)[END_REF], possibly to sustain copper mining operations [START_REF] Stöllner | die alpinen Kupfererzreviere: Aspekte ihrer zeitlichen, technologischen und wirtschaftlichen Entwicklung im zweiten Jahrtausend vor christus[END_REF].

Following on glacier progression around 3600 cal BP, a recession until 3350 cal BP [START_REF] Nicolussi | Holocene tree-line variability in the Kauner Valley, Central Eastern Alps, indicated by dendrochronological analysis of living trees and subfossil logs[END_REF] could have promoted land use at higher elevations mentioned earlier. Inferred from low MAR and pollen [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF][START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF], local and regional land use declined after 3200 cal BP, possibly induced by a cooling trend (e.g. [START_REF] Ivy-Ochs | Latest Pleistocene and Holocene glacier variations in the European Alps[END_REF].

Metallurgy: Slightly elevated but fluctuating EFs for Pb, Cu and Zn are recorded between 3750 and 3450 cal BP, while Pbanth AR slowly rises to 0.5 mg*a -1 *m -2 until 3400 cal BP, before dropping again (Figure 5). Compared to sites in the Vosges, Alpine Foreland and Swiss Jura, with max. Pbanth ARs of c. 0.2, 0.016 and 0.075 mg*a -1 *m -2 respectively [START_REF] Forel | Historical mining and smelting in the Vosges Mountains (France) recorded in two ombrotrophic peat bogs[END_REF][START_REF] Kern | Persistent, multisourced lead contamination in Central Europe since the Bronze Age recorded in the Füramoos peat bog, Germany[END_REF][START_REF] Shotyk | History of atmospheric lead depostion since 12,37014C yr BP from a Peat bog[END_REF], the estimated average of 0.33 mg*a -1 *m -2 in our record is considerably higher during this period. Not far from the Piller Saddle, Bronze Age ceramic mixed with copper slag found near a malachite ore deposit suggests local metallurgy and mining (Tomedi, 2002b). A large Middle or Late Bronze Age bronze hoard and unworked copper were found nearby [START_REF] Tomedi | Der mittelbronzezeitliche Schatzfund vom Piller[END_REF], 2002a[START_REF] Nicolussi Castellan | Das bronzezeitliche Haus von Fließ-Silberplan[END_REF]. The chemical signature of this hoard's artifacts largely corresponds to the well-studied Mitterberg mining district in the Eastern Alps [START_REF] Pernicka | Bronze Age Copper Produced at Mitterberg, Austria, and its Distribution[END_REF], although the main wind directions make trajectories from there to the Piller Moor less likely. In any case, the lack of characterisations (e.g. isotopy, composition) of local polymetallic ores around the Piller Moor makes tying any artifacts to nearby sources impossible. A Pb-isotope record from a peatland in southern Germany suggests

Iberian ores as the main source of atmospheric Pb fluxes during this time [START_REF] Kern | Persistent, multisourced lead contamination in Central Europe since the Bronze Age recorded in the Füramoos peat bog, Germany[END_REF]. However, more proximate and thus more likely source regions like the Alps or Black Forest, have not been considered so far. The behaviour of Pb EF and AR is challenging to interpret in this period and pointing out a source even more, but the combined evidence suggests that metallurgy was practised regionally.

Iron Age (Period 3 from 2800 to 2000 cal BP)

Land use: Around 2400 cal BP, [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF] reports increased abundances of charcoal, Plantago spp., Poaceae, Cyperaceae and Cerealia at the Piller Moor as evidence of land use change, fitting to similar palaeoecological signals of increased human impact at Fließ [START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF] and Serfaus [START_REF] Wahlmüller | Die Komperdellalm im Wandel der Jahrtausende. Ein Beitrag zur Vegetationsund Besiedlungsgeschichte des Oberen Gerichts[END_REF]. The drastic rise of MAR to more than 9 g*m -2 *a -1 illustrates the intense human impact, with strong deforestation and agro-pastoralism, followed by heavy soil destabilisation.

Archaeological sites on and around the Piller Saddle show widespread human occupation in this area [START_REF] Lutz | Eisenzeitliche Nutzung alpiner Kupferlagerstätten[END_REF][START_REF] Staudt | Rätisches Haus in Wenns[END_REF][START_REF] Sydow | Der hallstattzeitliche Bronzehort von Fliess im Oberinntal, Tirol. Fundberichte aus Österreich[END_REF][START_REF] Tschurtschenthaler | Das Heiligtum auf der Pillerhöhe[END_REF][START_REF] Zemmer-Plank | Ein Waffenopfer der Fritzens-Sanzeno-Kultur in Wenns im Pitztal[END_REF], explaining the strong impact on the Piller Moor .

Metallurgy: Pb EF does not suggest local metallurgical activity during the early Iron Age. However, strong mineral input masked increased Pb input around 2400 cal BP. This is shown by simultaneously elevated Pbanth AR, which remains on a higher level afterwards. This period has the lowest estimated average Pbanth AR with 0.16 mg*a -1 *m -2 , but the trend largely agrees with records from Black Forest, and the Vosges [START_REF] Forel | Historical mining and smelting in the Vosges Mountains (France) recorded in two ombrotrophic peat bogs[END_REF][START_REF] Le Roux | Recent atmospheric Pb deposition at a rural site in southern Germany assessed using a peat core and snowpack, and comparison with other archives[END_REF]. Although direct evidence is lacking for the Central Alps, silver production as early as 2250 cal BP is suggested for the Swiss Wallis [START_REF] Guénette-Beck | New insights into the ancient silver production of the Wallis area, Switzerland[END_REF], making also local mid or late Iron Age metallurgy in the study area a possibility.

Roman Period to Early Middle Ages (Period 4 from 2000 to 1400 cal BP)

Land use: In agreement with an initial MAR minimum at Piller Moor, larger forests and reduced pastoralism are reported once the region fell under Roman influence around 1950 cal BP [START_REF] Bortenschlager | Vegetationsgeschichte im Bereich des Rotmoostales[END_REF][START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF][START_REF] Wahlmüller | Die Komperdellalm im Wandel der Jahrtausende. Ein Beitrag zur Vegetationsund Besiedlungsgeschichte des Oberen Gerichts[END_REF][START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF]. This is reflected in the estimated average MAR of 1.41 g*a -1 *m -2 being lower than the pre-Bronze Age and the Iron Age estimated averages (periods 3 and5). Yet, MAR fluctuations around 1750 cal BP match indicators for burning and landscape openings in Fließ [START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF]. Just prior to a MAR peak around 1660 cal BP, increased charcoal values in the Piller Moor [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF] indicate reoccupation of the higher slopes, coinciding with crisis in the Roman Empire [START_REF] Wierschowski | Die historische Demographie -ein Schlüssel zur Geschichte? Bevölkerungsrückgang und Krise des Römischen Reiches im 3[END_REF]. [START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF] and [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF] document a significant forest recovery and absence of cultural indicators around 1400 cal BP, when the MAR declines below 1 g*m -2 *a -1 . This gap of human impact agrees with other observations in the Central Alps (e.g. von [START_REF] Von Scheffer | 6200 years of human activities and environmental change in the northern central Alps[END_REF] and is connected to a cold climate extreme referred to as Late Antique Little Ice Age [START_REF] Büntgen | Cooling and societal change during the Late Antique Little Ice Age from 536 to around 660 AD[END_REF][START_REF] Helama | Dark Ages Cold Period: A literature review and directions for future research[END_REF][START_REF] Ivy-Ochs | Latest Pleistocene and Holocene glacier variations in the European Alps[END_REF].

Metallurgy: Compared to the Iron Age, the mean estimated Pbanth AR of 0.25 mg*a -1 *m -2 during this period is significantly higher. Elevated Pbanth AR and Pb EF during the earlier part of this period are likely associated with distal origin and diffuse Roman influence (e.g. [START_REF] Longman | High variability between regional histories of long-term atmospheric Pb pollution[END_REF], in contrast to peaks of Pb EF and Pbanth AR (c. 0.7 mg*a -1 *m -2 ) around 1450 cal BP. Similar signals are registered across Western and Central Europe, for example in the Bernese Alps [START_REF] Carvalho | Reconstruction of mining activities in the Western Alps during the past 2500 years from natural archives[END_REF], and in the northern Central Alps [START_REF] Von Scheffer | 6200 years of human activities and environmental change in the northern central Alps[END_REF], but also in Eastern Europe [START_REF] Bohdálková | Atmospheric metal pollution records in the Kovářská Bog (Czech Republic) as an indicator of anthropogenic activities over the last three millennia[END_REF]. A rise is also visible in the Colle Gnifetti ice [START_REF] More | Next-generation ice core technology reveals true minimum natural levels of lead (Pb) in the atmosphere: Insights from the Black Death[END_REF], but a 90-year gap starts just at this particular age. [START_REF] Kern | Persistent, multisourced lead contamination in Central Europe since the Bronze Age recorded in the Füramoos peat bog, Germany[END_REF] attribute this Pb signal to a transition to small scale and local mining operations across Europe, although atmospheric Pb-emissions and deposition were generally reduced during this period (e.g. [START_REF] Forel | Historical mining and smelting in the Vosges Mountains (France) recorded in two ombrotrophic peat bogs[END_REF]). Yet, it is striking that neither records from the Southern Alps [START_REF] Segnana | Holocene vegetation history and human impact in the eastern Italian Alps: a multi-proxy study on the Coltrondo peat bog, Comelico Superiore, Italy[END_REF], nor south-west from our site [START_REF] Thevenon | Pre-) historic changes in natural and anthropogenic heavy metals deposition inferred from two contrasting Swiss Alpine lakes[END_REF], nor from locations west and north-west of them (Vosges, Black Forest, Massif de Morvan, Swiss Jura), nor from the Eastern Alps [START_REF] Knierzinger | Anthropogenic and climate signals in late-Holocene peat layers of an ombrotrophic bog in the Styrian Enns valley (Austrian Alps)[END_REF], show increased Pb EF or Pbanth AR at that time [START_REF] Forel | Historical mining and smelting in the Vosges Mountains (France) recorded in two ombrotrophic peat bogs[END_REF][START_REF] Le Roux | Recent atmospheric Pb deposition at a rural site in southern Germany assessed using a peat core and snowpack, and comparison with other archives[END_REF][START_REF] Monna | History and Environmental Impact of Mining Activity in Celtic Aeduan Territory Recorded in a Peat Bog (Morvan, France)[END_REF][START_REF] Shotyk | History of atmospheric lead depostion since 12,37014C yr BP from a Peat bog[END_REF]. Considering that the supra-regional Roman Pb-signal is not very defined in our record, the distinct and synchronous Pb EF and AR signals from 1500 to 1400 cal BP suggest an origin rather close to the Piller Moor. This period was a time of warfare and territorial reorganisation, but the Central Alps were not in the centre of these conflicts [START_REF] Kulikowski | 1 The Western Kingdoms[END_REF]. Late Antiquity silver mining in the Swiss Alps is, however, suggested by [START_REF] Guénette-Beck | New insights into the ancient silver production of the Wallis area, Switzerland[END_REF] and regional Pb and Ag deposits around Imst [START_REF] Gstrein | About prehistoric Mining in Tyrol[END_REF], in the Austrian Vorarlberg region [START_REF] Hofmann | Der historische Bergbau im Montafon[END_REF], and in Tirol [START_REF] Vavtar | Die Erzanreicherungen im Nordtiroler Stubai-, Ötztal-und Silvrettakristallin[END_REF] could have made parts of the Central Alps potential hotspot of Pb-emissions during this particular period.

4.6 Middle Ages to Postmodernity (Period 5 from 1400 cal BP to present)

Land use and climate: In line with a rising MAR in our record, [START_REF] Walde | Die Vegetations-und Siedlungsgeschichte im Oberen Gericht-Pollenanalytische Untersuchungen des Plemun-Weihers (Fließ, Tirol)[END_REF] and [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF] report a general rise of pastoral, cultural and grassland pollen after 1250 cal BP nearby (see Figure 1). A landscape opening is also observed at Serfaus by [START_REF] Wahlmüller | Die Komperdellalm im Wandel der Jahrtausende. Ein Beitrag zur Vegetationsund Besiedlungsgeschichte des Oberen Gerichts[END_REF]. Still elevated mineral input at 900 cal BP coincides with increased charcoal, crops, Plantago spp. and decreased tree pollen in the Piller Moor, while lower land use is indicated at c. 650 and 350 cal BP by both MAR in our record and pollen [START_REF] Hubmann | Palynologische Untersuchunger zweier Sedimentprofile aus dem Oberen Inntal, mit Augenmerk auf die anthropogene Beeinflussung[END_REF].

The gradually declining MAR after 1000 cal BP coincides with glacier advances in the nearby Kauner

Valley [START_REF] Nicolussi | Untersuchungen zur holozänen Gletscherentwicklung von Pasterze und Gepatschferner (Ostalpen)[END_REF]. Consequently, a lower MAR towards the early Modern Period could have resulted from declining mountain farming in the Alps [START_REF] Lichtenberger | Das Bergbauernproblem in den Österreichischen Alpen Perioden und Typen der Entsiedlung (The Problem of Mountain Farming in the Austrian Alps)[END_REF]), which Bender (2010) attributes to a cooler climate. In contrast, the MAR peak after 200 cal BP is associated with a temporary surge of expanding local and regional agriculture and forestry. The forest at Kaunerberg (c.

5.5 km south of the mire) lost about 140 ha between 1774 and 1880 CE and losses up to 85 % are documented in the nearby Radurschl, Pitz, Oetz and Paznaun valleys [START_REF] Fromme | Der Waldrückgang im Oberinntal (Tirol) Untersuchungen über das Ausmaß, die Ursachen und Folgeerscheinungen des Wald? rückganges in einem Gebirgslande sowie über die Aussichten der Wiederaufforstung von[END_REF]. Thereafter, documentation from 1850 to 1951 CE can explain the shrinking MAR: Agricultural yields and livestock declined by 50 % and 40 % respectively [START_REF] Fromme | Der Waldrückgang im Oberinntal (Tirol) Untersuchungen über das Ausmaß, die Ursachen und Folgeerscheinungen des Wald? rückganges in einem Gebirgslande sowie über die Aussichten der Wiederaufforstung von[END_REF]. The construction of a tourist infrastructure, high voltage line poles and roads and the subsequent nature conservation measures possibly caused the recent MAR-peak and its decline over the last few decades. Apart from this, the estimated average MAR in this period (3.94 g*a -1 *m -2 ) is higher than in any of the previous periods.

Lower peat accumulation and higher density observed within the top metre (90 to 62cm) of our record could relate to indirect anthropogenic disturbances, similar to observations of [START_REF] Sjögren | The occurrence of an upper decomposed peat layer, or "kultureller Trockenhorizont[END_REF].

The area was listed as a natural resource [START_REF] Von Klebelsberg | Nutzbare Bodenvorkommnisse in Nordtirol[END_REF], leading to industrial peat mining in an adjacent bog between 1949 and 1971 CE. A hydrological link to the exploited site could have promoted disturbance in the Piller Moor's surface layers. Recently introduced conservation measures in the area were likely beneficial for a return to previous peat accumulation rates and current growth rates of over 1 cm*a -1 .

Metallurgy and pollution: All EFs as well as a sharp rise of the Pbanth AR indicate constant metallurgy in the area after 1200 cal BP (750 cal CE), preceding first historical sources on Ag, Pb and Zn extraction in the 12 th century CE [START_REF] Hanneberg | Galmei und schöne Wulfenite: Der Blei-Zink-Bergbau rund um den Fernpass in Tirol[END_REF][START_REF] Wolkersdorfer | Geschichte des Bergbaus im westlichen Mieminger Gebirge/Tirol[END_REF] and the awarding of mining rights in 1352 CE [START_REF] Von Srbik | Überblick des Bergbaues von Tirol und Vorarlberg in Vergangenheit und Gegenwart[END_REF]). An increasing Pb EF is also reported from other sites (e.g. [START_REF] More | Next-generation ice core technology reveals true minimum natural levels of lead (Pb) in the atmosphere: Insights from the Black Death[END_REF][START_REF] Segnana | Holocene vegetation history and human impact in the eastern Italian Alps: a multi-proxy study on the Coltrondo peat bog, Comelico Superiore, Italy[END_REF][START_REF] Thevenon | Pre-) historic changes in natural and anthropogenic heavy metals deposition inferred from two contrasting Swiss Alpine lakes[END_REF], which illustrates that the development was supraregional and more distal sources likely contributed as well.

By 500 cal BP (1450 cal CE), strongly rising EFs (Pb and Sb) are in line with the introduction of a new and more pollutive ore processing technology [START_REF] Breitenlechner | The impact of prehistoric mining activities on the environment: A multidisciplinary study at the fen Schwarzenbergmoos (Brixlegg, Tyrol, Austria)[END_REF][START_REF] Longman | High variability between regional histories of long-term atmospheric Pb pollution[END_REF]. A link to intensifying silver mining around Imst [START_REF] Hanneberg | Galmei und schöne Wulfenite: Der Blei-Zink-Bergbau rund um den Fernpass in Tirol[END_REF] and the Arlberg region [START_REF] Haditsch | Jungalpidische Erzmineralisationen in der Phyllitgneiszone des Arlberggebietes[END_REF], north and west of our record, is also likely. South of Piller in Platzertal (Platzer Valley), Pb was mined and smelted from 1538 CE to 1900 CE [START_REF] Vavtar | Die Erzanreicherungen im Nordtiroler Stubai-, Ötztal-und Silvrettakristallin[END_REF]. A climate induced temporary abandonment of this mining site (1610-1888 CE) is synchronous with a decreasing Pb EF in our record. In addition, regional mining was outcompeted by overseas' ores [START_REF] Wolkersdorfer | Geschichte des Bergbaus im westlichen Mieminger Gebirge/Tirol[END_REF].

The recent maximum of Pbanth AR (c. 30 mg*m -2 *a -1 ) and Pb EF (>300) are the result of leaded gasoline emissions [START_REF] Pacyna | An assessment of global and regional emissions of trace metals to the atmosphere from anthropogenic sources worldwide[END_REF]. The sharp drop in the late 1980s is the response to its stepwise reduction and final ban across Europe. Compared to the maximum values in the Alpine Foreland (c. <6 mg*m -2 *a -1 ; [START_REF] Kern | Persistent, multisourced lead contamination in Central Europe since the Bronze Age recorded in the Füramoos peat bog, Germany[END_REF] and to the records summarised in [START_REF] Forel | Historical mining and smelting in the Vosges Mountains (France) recorded in two ombrotrophic peat bogs[END_REF], which are the Black Forest (c. 14 mg*m -2 *a -1 ), Jura (c. 14 mg*m -2 *a -1 ) and Vosges (c. 12 and 39 mg*m -2 *a -1 ), the maximum Pbanth AR in our record is mostly higher. Whilst the Pbanth AR does not return to natural background levels, it is within the upper range of Pb AR around 1 mg*m -2 *a -1 recently observed in Central Europe (e.g. [START_REF] Kempter | Atmospheric Pb and Ti accumulation rates from sphagnum moss: Dependence upon plant productivity[END_REF], yet, lower than values in the black triangle of Eastern Germany, Poland and the Czech Republic (e.g. [START_REF] Zuna | Recent lead deposition trends in the Czech Republic as recorded by peat bogs and tree rings[END_REF]. Our Pb record is in good agreement with the history of pollution in Central Europe. Its steep decline acts just as another time marker, which is confirming our age depth model. Since our peat profile covers a longer time period, the estimated cumulative anthropogenic Pb-deposition of c. 2.7 g*m -2 (Table 2) is slightly higher than in most of the Swiss peat records summarised in [START_REF] Shotyk | A new approach for quantifying cumulative, anthropogenic, atmospheric lead deposition using peat cores from bogs: Pb in eight Swiss peat bog profiles[END_REF].

Conclusions

Mineral and metal accumulation rates (MAR) and enrichment factors (EF), calculated based on geochemical analyses and combined with other palaeoecological proxies, provide continuous evidence of human occupation when archaeological evidence is lacking or isolated. Past episodes of metallurgy and anthropogenic soil disturbances in the Central Alps are revealed in our Piller Moor record.

Methodological evidence shows that pXRF facilitates high-resolution, quantitative data acquisition of certain elements in ombrotrophic peat (Ti, Pb, Zn, Sr, K, Rb, Fe), whereas others (e.g. Cu) cannot be quantified.

Our results suggest mining or metallurgy in the Central Alps between 4500 and 4200 cal BP, predating any archaeological evidence in the area. Around 3400 cal BP, both mineral input and Pbanth AR are elevated synchronously with palynological and archaeological evidence for human activity. A strong mineral input pulse at 2400 cal BP is simultaneous with proximate palynological and archaeological indicators for heavy human landscape disturbance. Despite Roman presence in the Inn valley, their direct impact at higher elevation seems to have remained small. Temporary but distinct increases of Pbanth AR and Pb EF from 1500 to 1400 cal BP strongly indicate post-Roman mining and metallurgy in this part of the Central Alps, encouraging further research to locate potential sources in the area.

However, the anthropogenic impact was very weak in the Early Middle Ages before soil disturbance and metallurgy resumed around 1200 cal BP and did not return to previous levels again. Our data indicate early medieval mining operations, which predate historical documentation by several centuries. While the LIA likely impaired regional agriculture, forestry and mining operations episodically, the comparison of our record to historical documentation highlights the severe influence of expanding forestry and agriculture on regional soil erosion and dust entrainment over the last centuries. Over the last century, nearby peat extraction and construction, but also nature conservation, seem to have influenced mineral and peat accumulation. The abrupt decline of Pb EF and Pbanth AR after the year 1980 CE acts as a time marker. In the form of quantitatively reconstructed atmospheric input, geochemical signals found in our peat record from the Piller Moor mainly reflect the development of local and regional human activities and their impact on the Alpine landscape over the past 4800 years.

  0.7 mg*a -1 *m -2 ), Pbanth AR values are constantly elevated after 1200 cal BP. An extreme peak occurs for bothPbanth and Pb EF between 50 and -50 cal BP (1900-2000 CE), corresponding to 30 mg*a -1 *m -2 and an enrichment over 300. EFs of Zn, Cu and Sb show smaller increases along the profile, but rise strongly in the top layers corresponding to the 20 th century CE. Cu EF shows a continuously declining trend until approx. 1000 cal BP.

  emerged in other areas of the Central Alps.[START_REF] Dietre | Palaeoecological evidence for Mesolithic to Medieval climatic change and anthropogenic impact on the Alpine flora and vegetation of the Silvretta Massif (Switzerland/Austria)[END_REF] report increasing charcoal values and agricultural evidence from 4400 to 4200 cal BP in the Fimba Valley.[START_REF] Bortenschlager | Vegetationsgeschichte im Bereich des Rotmoostales[END_REF] documents tree cover loss and cultural pollen at 4400 cal BP, and[START_REF] Dietre | Neolithic to Bronze Age (4850-3450 cal. BP) fire management of the Alpine Lower Engadine landscape (Switzerland) to establish pastures and cereal fields[END_REF] suggest fire management in the lower Engadine, Switzerland.

Figure 3 :

 3 Figure 3: Cross-plots with regression analysis of ICP-MS and pXRF measurements. Open circles: peat, filled red circles: CRMs in concentration range, blue lines: linear regressions. Error bars depict the standard deviation of the measurements or the CRMs' errors.

Figure 4 :

 4 Figure 4: Piller Moor profiles of elements measured by pXRF (in black) and ICP-MS (in red) and dry bulk density. F 14 C and 14 C-ages (cal BP) given on the right.

Figure 5 :

 5 Figure 5: Mineral accumulation rate (MAR), anthropogenic Pb accumulation rate (Pbanth AR) and metal enrichment factors (Pb EF, Zn EF, Cu EF, Sb EF). Orange lines (Pb AR and Pb E) zoomed in (secondary xaxis). Periods loosely correspond to cultural periods (e.g. Period 1 = Neolithic-Bronze Age transition; Period 2 = Bronze Age; Period 3 = Iron Age; Period 4 = Roman occupation in the Alps; Period 5 = Middle Ages to Postmodernity).

Table 1 :

 1 Radiocarbon sample information on origin, depth, dated material and uncalibrated 14C-ages. Lab codes: GdA=Gliwice, Poz=Poznan. Depths of Poz-101726 and GdA-5493 are corrected to master core A.

	Lab.	Core Depth	Material	14 C-age	Comment
	No.	[cm]		[BP]/F 14 C
	GdA-	Pi17A 43.2	Sphagnum spp.	1.4250 ± 0.0022 F14C
	5492		stems and leaves		Bomb
					pulse
	Poz-	Pi17A 80.3	Sphagnum spp.	725 ± 30	0.5 mgC
	99320		stems and leaves
	GdA-	Pi17A 105.9 Sphagnum spp.	1505 ± 35
	5494		stems and leaves
	Poz-	Pi17A 184.6 Sphagnum spp.	2150 ± 30
	101724		stems and leaves
	GdA-	Pi17A 209.5 Sphagnum spp.	2455 ± 40
	5495		stems and leaves
	GdA-	Pi17A 267.3 Sphagnum spp.	3255 ± 25
	5496		stems and leaves
	Poz-	Pi17B 268.7 Sphagnum spp.	3260 ± 30
	101726		stems and
			leaves, Ericaceae leaf
	GdA-	Pi17B 339.9 Sphagnum spp.	4150 ± 30
	5493		stems and leaves

Table 2 :

 2 Synthesis of model estimates for approximates of average mineral and Pbanth-accumulation rates and for the approximate cumulative deposition of Pbanth within the periods 1 to 5 and in the most recent sample.

	Period Age	Estimated
	[cal	average
	BP]	MAR
		[g*

m -2 *a -1 ] Estimated average Pbanth AR [mg*m -2 *a -1 ] Estimated cumulative Pbanth [g*m -2 ]

	1	4800-	1.01	0.26	0.19
		4000
	2	4000-	1.94	0.33	0.4
		2800
	3	2800-	1.84	0.16	0.12
		2000
	4	2000-	1.41	0.25	0.17
		1300
	5	After	3.94	2.51	1.79
		1300
	Surface c. -65 1.6	1.21	Total: 2.68

Acknowledgements

We would like to thank Marie-Jo Tavella (LEFE) for her assistance in the clean room laboratory, the Service ICP-MS of Observatoire Midi-Pyrénées Toulouse for ICP-MS analyses and Natalia Piotrowska (Gliwice University, POL) for pre-processing the GdA 14 C-samples. Our thanks also go to Chuxian Li for her help in the field, Mathias Bahns for solving technical issues, our friendly local contacts Ernst Partl and his staff at the Naturpark Kaunergrat and the Bezirkshauptmannschaft Landeck for permissions.

We also thank Klaus Oeggl for providing us with detailed pollen information from the Piller Moor study by Hubmann (1994).

Funding

The main funding body was the German Research Foundation (DFG, project no. 39071778) within the GSC 208: "Graduate School for Integrated Studies of Human Development in Landscapes", funding the PhD-position of CvS. Funding for research visits of CvS between the partnering institutions was provided by Université Franco-Allemande (UFA/DFH; code and by the German academic exchange service (DAAD) -"PPP: Frankreich" and by Campus France (PHC procope) 2017, for IU, FDV and CvS (project no. 57316724).

Data availability

Data is provided in the supplementary material and will be made available in the PANGEAE online database.

Author contributions

Declaration of competing interest

We declare that there are no conflicts of interest.


Mônica S Félix

John J Martinez

Christophe Bérenguer

A state-space approach for remaining useful life control

Keywords: Health-aware control, deterioration-aware control, RUL control, deterioration estimation, prognosis, reliability adaptive systems, state-space approach

This paper presents a state-space approach for controlling the Remaining Useful Life (RUL) of deteriorating systems. The proposed approach supposes the availability of a deterioration model that links the deterioration rate with some manipulable control inputs. Such a link can be a non-linear monotonic function between the deterioration-rate and the manipulable control inputs. We propose a method for designing both state observer and state feedback controller for RUL prediction and control. We consider that the manipulable inputs are affected by additive random disturbances and possible multiplicative unknown parameters. In addition, we assume that the control decisions can not be applied instantaneously on the system, which is modeled as a time-delay between control decisions and manipulable inputs of the deterioration dynamics. The proposed methodology is illustrated on a simulated study case which considers an exponential degradation model.

INTRODUCTION

Mechanical systems deteriorate during use due to wear and tear, stress, strain, friction, etc. leading to damage, fatigue and eventual equipment failure, affecting the system's reliability. For example, a friction drive system deteriorates as friction stresses and damages the actuator over time. Within this context, adapted control strategies can contribute to ensure the reliability of such degrading systems and guarantee that the controlled system remains functional and keeps operating in the same way throughout its life despite possible failures or changes in its dynamics due to degradation.

According to [START_REF] Rausand | System reliability theory: models, statistical methods, and applications[END_REF], the Remaining Useful Life (RUL) of a system is modeled as a random variable that expresses the time until the system is no longer functional, and its distribution can be used as a reliability metric. If a degradation model is available and if the degradation dynamics can be changed through the control inputs, adaptive control can be used to control the RUL of the system and influence the system reliability, as proposed in Rodriguez [START_REF] Rodriguez Obando | Deterioration estimation for predicting and controlling rul of a friction drive system[END_REF]. This control strategy, referred to as Health-Aware Control (HAC) in [START_REF] Do | State-of-the-art in integrated prognostics and health management control for utility-scale wind turbines[END_REF], proposes to incorporate health state information, such as prognostic and degradation states, into the control loop using available dynamic knowledge about the degradation. In the case where the degradation is influenced by operational decisions and control inputs, the system can be reconfigured to control the potential stress and wear factors that degrade the system. According to [START_REF] Do | Wind turbine lifetime control using structural health monitoring and prognosis[END_REF], this type of control can be used in Prognostic and Health Management (PHM) approaches to integrate maintenance requirements into global control objectives and to trade-off load mitigation and control performance.

Many works address this problem, referred here to as RUL Control, as a multi-objective control problem. With an available degradation model, it is possible to model an optimal control solution to track the desired RUL. For example, [START_REF] Meyer | Controlling the remaining useful lifetime using self-optimization[END_REF] has proposed modeling RUL control to incorporate RUL into the control objectives of a driven system. [START_REF] Gokdere | Lifetime control of electromechanical actuators[END_REF] proposed a model to extend the lifetime of electromechanical actuators. Also, in a more recent work, [START_REF] Sanchez | Health-aware model predictive control of wind turbines using fatigue prognosis[END_REF] proposed a Model Predictive Control (MPC) method to control the RUL of a wind turbine system to meet maintenance requirements while satisfying other control performance requirements. In addition, Rodriguez [START_REF] Rodriguez Obando | An architecture for controlling the remaining useful lifetime of a friction drive system[END_REF] has proposed an architecture to incorporate the RUL requirement into the model to extend the lifetime of a friction drive system.

However, most works propose RUL control methods that model RUL as a deterministic variable. Only some works, such as [START_REF] Langeron | A modeling framework for deteriorating control system and predictive maintenance of actuators[END_REF], [START_REF] Mo | Performancebased maintenance of gas turbines for reliable control of degraded power systems[END_REF] and [START_REF] Pedrosa Alias | Health-aware economic mpc for operational management of flow-based networks using bayesian networks[END_REF], proposed methods that establish a relationship between control and degradation by considering RUL as a random variable and using knowledge of the stochastic dynamics of degradation.

In this paper, we propose to solve the RUL control tracking problem following a state-space control approach. We also consider the stochastic dynamics of the degradation and possible delay in the decision within the relationship between control actions on the system and the degradation rate.

This paper is organized as follows: Section 2 discusses the definition of the problem, then Section 3 describes the deterioration model with the corresponding dynamic states. Next, in Section 4, the stated problem is solved by proposing a state observer to estimate the states of the chosen deterioration process and a state-feedback controller. Finally, a study case which illustrates the proposed approach is presented in Section 5.

PROBLEM STATEMENT

The RUL of a system is defined as the time until it can no longer be used to meet the desired performance, i.e., the remaining time before the system reaches a maximum allowable deterioration, denoted here as D max . Therefore, for a given current time t, the RUL verifies the following equality:

D(t + RU L) = D max
(1) Let us assume that the deterioration dynamics obeys the following differential equation:

dD dt = β 1 D + β 0 (2)
where the parameters β 1 and β 0 dictate the deteriorationrate. If β 1 and β 0 are random (e.g., white noise for β 0 ), the deterioration D is then a stochastic process determined by a Stochastic Differential Equation (SDE) resulting from (2), and particular choices of β 0 and β 1 allow this equation to represent well-known deterioration process dynamics such as Wiener or Gamma processes, often used in reliability and maintenance studies, see for instance [START_REF] Rausand | System reliability theory: models, statistical methods, and applications[END_REF].

Link function definition

Moreover, we assume that the median values of parameters β 1 and β 0 can be governed by a certain number of inputs w that we can control, and the vector of parameters β = [β 0 β 1 ] T can be written as a function of the input w. In particular, we can model the behavior of β as a function of w by using a monotonic nonlinear function f (w) with possible additive perturbations η and uncertain multiplicative parameters γ as follows: 3) models the so-called link function. In particular, the function f (w) is based on the link between controllable process variables w and the degradation rate β. Of course, this relationship depends on the complexity of system dynamics, which may be nonlinear or not straightforward. However, instead of using the full dynamics of the process states to have an explicit link function, we assume that a metamodel is available. The form presented in (3) can therefore be seen as an approximation of the degradation rate dynamics with stochastic behavior. Nevertheless, the unmodeled parts of this dynamic are accounted for by the uncertainty parameters γ and η, which contain the random influence of different operating points and exogenous inputs on the degradation rate.

β = γf (w) + η (3) Equation (
In this paper, we make the simplifying assumption that w can be directly controlled, and we propose to act on β by making decisions on the value of w, denoted by w d . Of course, in practice, the considered deterioration would take place in a controlled system, and it has to be noted that w may be different from the control inputs to this deteriorating system, usually expressed by u, whose purpose is to make the system work according to a reference or set point. For example, w could be a state variable of the deteriorating system, that could be controlled by u. We also consider that the decisions w d are not perfectly executed at a given time t and may contain delays t d . Thus, the behavior of β is described by the following time-delay relationship:

β(t + t d ) = γf (w d (t)) + η (4)

RUL control definition

Now, the RUL control problem can be stated as follows: at every time instant t, for a given desired median value of the RUL, denoted RU L ref (t), decide the values of w d to modify the predicted RUL, denoted RU L(t), in such a way that the deterioration D, starting at D(t), achieves its maximal and admissible value D max at time t + RU L ref , respecting both the deterioration dynamics ( 2) and the deterioration-rate parameter dynamics (4).

Remark that the desired RU L ref (t) can be chosen according to maintenance constraints or operational requirements for the given deteriorating system.

In order to control the RUL, we also assume that β and D can be estimated by using an available dynamical model of deterioration and the available data coming from noisy deterioration measurements or imperfect estimates. Thus, we propose a state observer that can estimate both β and D, which allows us to continuously compute RUL control decisions w d . The final proposed control architecture is depicted in Fig. 1.

In the following sections, we propose to solve the control and observer design problems using a state space approach. We will show that, based on a given link function model and a chosen degradation model, we can control degradation by making decisions on w d to impose properties on the lifetime distribution, such as, e.g., its median value.

DETERIORATION MODELS

According to the nature of the deterioration behavior and to model the item-to-item variability and heterogeneity of deterioration paths, the parameters β can be considered as random variables that follow a particular a priori probability distribution, see [START_REF] Gebraeel | Residual-life distributions from component degradation signals: A bayesian approach[END_REF]. Here we will focus on deterioration models for which the parameter β follows a normal distribution, i.e., β ∼ N (µ, σ 2 ), as described in [START_REF] Rausand | System reliability theory: models, statistical methods, and applications[END_REF].

In doing so, we consider the evolution of deterioration as a stochastic process with random effects. For the control design, it is more interesting to model it as an SDE-like equation ( 2) and to consider a "median" solution of Equation ( 2) described by: D(t) = D(0)e µ1t + µ 0 t (5) where µ 1 and µ 0 are the median values of β 0 and β 1 , as previously defined as β, and with an initial deterioration state D(0). Equation ( 5) can also be expressed in terms of RUL:

D(t + RU L(t)) = D(t)e β1RU L(t) + β 0 RU L(t) (6
) where RU L(t) is the interval time between the time instant t and the time when the degradation first reaches a maximum degradation D(t + RU L(t)) = D max .

Finally, based on (6), for a given D max , the value of RU L(t) can be determined as a function of β and D, variables that can be estimated. However, the solution would require a numerical procedure. Therefore, we will proceed with the linear and exponential deterioration models, each separately, to continue the investigation with an analytical solution.

Linear model

Used to model mechanisms of wear from surface contact [START_REF] Archard | Contact and rubbing of flat surfaces[END_REF], the wear rate Ḋ is a constant β 0 proportional to dynamical variables such as the load N and the speed of sliding of contact ṽ: Ḋ = β 0 (N, ṽ) (7) This model represents a linear behavior of the deterioration process that obeys approximately:

D(t) = D(0) + β 0 • t (8)
with an initial deterioration state D(0) and a random parameter β 0 . Based on (8), we then consider a constant value for β 0 to predict when the deterioration at a given time t will reach its maximum D max in D(t + RU L(t)), as follows:

D max = D(t) + β 0 • RU L(t) (9
) And therefore, RU L(t) at the given time t can be written as a function of the chosen value of β 0 for the prediction and the current state of deterioration D(t) as follows:

RU L(t) = 1 β 0 (D max -D(t)) (10)

Exponential model

Let us now consider degradation with exponential behavior, which is common in processes where degradation occurs in a cumulative manner (e.g., wear, fatigue), especially in bearing applications: Ḋ = β 1 D (11) It will approximately follow an exponential trend:

D(t) = D(0)e β1•t
(12) with a random degradation-rate β 1 . If we consider now a constant value of degradation-rate for β 1 to predict when the degradation reaches D max , then we can write RU L(t) at time t as:

RU L(t) = 1 β 1 ln D max D(t) (13)
Note that if we consider that β obeys a given probability distribution function f (•), then the predicted RUL(t) will obey its inverse one. Now we are ready to introduce the state-space approach to observe the states of the deterioration dynamics (β and D(t)) as the system deteriorates and then control the RUL. The following section presents the design of a stateobserver and a state-feedback controller to be implemented within the proposed RUL control architecture. For the sake of simplicity, we will focus on the exponential deterioration model and a given link function.

RUL CONTROL DESIGN

State-observer problem

The contribution of this paper is to present a method for synthesizing a RUL controller to impose some desired characteristics to the RUL distribution law (e.g. its median value) by modifying w d . In the proposed framework (see Figure ( 1)), the RUL controller finds the optimal corrections w d based on the current estimated degradation and observations of the degradation rate.

Let us consider a deteriorating system that follows an exponential behavior (11). The problem of the stateobserver is then to estimate the parameters β and D(t).

Note that β is considered as a random variable influenced by w with a relation described in (3). Nevertheless, the model ( 3) cannot be used to design the observer here, since this model is treated as uncertain and may have a complex form inherent to each application. Therefore, we propose a more general equation: β = -cβ + ϵ (14) based on the Langevin equation to estimate the deterioration rate parameter β, with a model parameter c and a noise term ϵ. Although the Equation ( 14) dynamics is not determined by w, it allows us to represent the fluctuating behavior of β while suffering from state-observer corrections.

Finally, D can be measured or calculated from health condition indicators. In this case, the model can consider (11) and ( 14), leading to the following observer:

ẋ = 0 D 0 -c x + K(y -ŷ) (15)
where x := [D β] T and the outputs are simply y = D +ε m .

Here, ε m denotes a possible measurement error or noise. Then, the observer gain K can be obtained as a solution of an Extended Kalman Filter problem, for instance.

Control problem

For the control problem, we assume that the parameter β follows a monotonic uncertain behavior wrt w, which allows us to write β as the following link function: β = γw + η (16) with an uncertain parameter γ > 0, a normal noise η, and one-step delay on decisions, defined as w d .

Thus, by writing the model dynamics in a discrete-time representation, we have:

w k+1 = w d k (17) β k = γ • w k + η k (18)
Hence, the problem of tracking a desired median value for RUL , RU L ref , can be rewritten into the problem of guaranteeing that β tracks a desired reference value β ref that can be obtained from the following reference generator:

β ref k = 1 RU L ref k ln D max Dk (19)
which is based on ( 13), where β is written in terms of RU L and D is substituted by its estimate D.

Remark that RU L ref k can be calculated, at each iteration k, given a desired End of Life (EoL), EoL ref , since

RU L ref k = EoL ref -k.
(20) In order to the minimize the tracking errors on β, the control design should include an integral action, that can be implemented as follows:

z k+1 = z k + ( βk -β ref k ) ( 21
)
where βk is the estimated value of β k , which is used instead of the real one, because we assume that this value can not be measured directly from the process.

Then, the control design considers the models in ( 17) and ( 21) written in terms of a state vector defined as x := [w z] T . That is, find a state feedback control w d k which stabilises the following state-space model:

w k+1 z k+1 = 0 0 γ 1 w k z k + 1 0 w d k + 0 -1 β ref k (22) for 0 < γ min ≤ γ ≤ γ max .
Therefore, the state feedback control law will be given by:

w d k = -K p • w k -K i • z k (23)
where the control gain parameters can be obtained by using robust control design techniques, for instance. Remark that in practice the value of w k can be obtained by using (17), and then, the control law becomes:

w d k = -K p • w d k-1 -K i • z k (
24) Thus, the RUL controller can be implemented by using ( 19), ( 21) and ( 24), as it is depicted in Fig. 2. Remark that the same approach can be applied for controlling a linear degradation dynamics. In that case, we only need to generate the references on β 0 from (10). In all cases, estimations of D and parameters β are necessary for implementing the proposed RUL control law in (24). These estimations come from an observer stated previously.

Finally, the values of K p and K i in ( 24) can be found with any optimal controller, such as H ∞ , Robust Control, Linear-Quadratic Regulator (LQR), etc. In this paper, we solve the study case controller design using a LQR.

STUDY CASE

In this section, the proposed approach is illustrated using an exponential deterioration model.

Description of the system

For this study case, we consider an exponential deterioration model, as described in (11), and we assume that this deterioration is measured. That is, where η noise is a white noise of 10 -1 amplitude.

y k = D k + η noise (25)
Thus, the state-space representation of the deterioration dynamics can be written as follows: ẋ = H(x)x (26) y = Cx + η noise (27) where

H(x) = 0 D 0 0 , (28)
C = [1 0] and x := [D β] T .
Now, by considering a sampling time t s to be exactly equal to the actuator time-delay, the exponential model of deterioration (11) has a discrete-time representation:

D k+1 = D k + t s β k D k (29)
where we will consider D 0 = 1 because D starts with a minimum deterioration which has to be an strictly positive measure.

Discrete-time observer -

Here the chosen observer will estimate the states x = [ D β] using an Extended Kalman Filter, as proposed in Rodriguez [START_REF] Rodriguez Obando | Deterioration estimation for predicting and controlling rul of a friction drive system[END_REF]. We consider a initialization of the estimates as follows:

x0 = D0 0.1 T (30)
with the initial estimate of deterioration D0 = 1.

The EKF also requires a choice of the covariance matrices. Then, we consider: R = 0.01 (31) which assumes that the sensor noise variances are known and equal to 0.01. The matrix Q has been selected to consider innovations of the system with the following variance:

Q = 0.01 0 0 2.5 • 10 -5 (32)
Finally, an initial matrix P 0|0 was chosen as follows:

P 0|0 = 100 0 0 2.5 • 10 -3 (33)
Study case degradation parameters -The chosen link function for this example is described in ( 16). Without control intervention, β should vary randomly depending on probability distribution of random parameters η and γ.

In order to achieve maximum deterioration at around a EoL equal to k = 100 (in units of time), the distribution of random parameters follows η ∼ N (0, 0.01), and γ ∼ U(0.7, 1.3).

RUL controller parameters -For this example, we establish an admissible maximum deterioration D max = 100 where it should be reached at EoL ref = 100 (units of time). Thus, by considering (20), a value for β ref is calculated from (19). Finally, the control gain parameters are calculated using the LQR-based control synthesis, which leads to K p = 0.088, K i = 0.955.

(34) According to (24), we calculated the initial value for the integral action as:

z 0 = w d 0 + K p w d 0 -K i . ( 35
)
where we will choose the initial decision parameter to be w d 0 = 1. This value concerns the nominal one, and then we suppose that ideally w 0 has to remain around this value for achieving the desired EoL ref .

Stochastic results for 10 4 realisations

This case study aims to show that the proposed statespace feedback controller can control deterioration so that it reaches its maximum at the desired lifetime. Two applications are proposed: the first one, concerning one possible realisation of the link function, which depends on an additive noise η and a multiplicative unknown but fixed parameter γ, and the second one, intended for illustrating the case where γ may vary randomly from one realization to another.

The results for 10 4 realizations are shown in Fig. 3. In the first application, it is chosen a fixed γ = 1.2, which physically represents 20% more load than the nominal one. The results shows that the control actions dislocated the distribution of EoL, which it was around 86th cycle, towards the desired one, 100th cycle. In the second case, the system has a random γ, which physically represents random loads uniformly distributed around the the nominal one. In this case, the realizations without RUL control exhibit an EoL distribution with higher variance and a non-normal distribution. In contrast, when adding the RUL control actions, the EoL of these realisations remains closer around the desired one. Table 1 resumes the obtained distributions of EoL resulted from both cases: constant γ = 1.2 and random γ ∼ U(0.7, 1.3).

RUL-control evaluation for 1 realisation

Now we are interesting in the evaluation of the response of the control system for one realisation. For this purpose, Figs. 4 and5 show the results for the realisation i = 42.

The results in Fig. 4a show the assessment of RUL, represented by RU L and estimated using (13), comparing We remark also, from Fig. 5a, that β follows the trend β ref calculated as in (19). Finally, the deterioration, shown in 5b, obeys an exponential model. With the control proposed, we ensures that it reaches D max at the desired EoL.

CONCLUSION

In this paper, we have presented a state-space approach for controlling the Remaining Useful Life (RUL) of systems subject to degradation. The proposed method is based on the fact that the degradation-rate can be modeled in a state-space representation. Even if the systems, for observation and control, are linear-time varying, LPV or uncertain linear systems, this paper shows that the control design can be performed using well-known robust control techniques. This paper illustrates the approach on exponential degradation model but other degradation-rate model can be considered if they can be written under a state-space form. In cases where the degradation trends are linear or exponential, RUL predictions can be easily obtained by using explicit equations that are functions of both the current deterioration-rate and the current deterioration level. In addition, such relationships allow us to explicitly write the desired RUL in terms of the desired deterioration-rate. As it is illustrated in the presented study case, the RUL control problem can be efficiently solved by keeping state-space models expressed on the deterioration-rate space. This aspect allows us to solve the problem as a deterioration-rate tracking control problem.

The solution was validated using a given link function expressing the system dynamics. Future work includes testing the presented framework for practical cases with a given physical system that can be expressed as a special case of the link function.

Fig. 1 .

 1 Fig. 1. Proposed RUL control architecture.

Fig. 2 .

 2 Fig. 2. Complete proposed RUL controller algorithm.

Fig. 3 .

 3 Fig. 3. Distribution of obtained EoL (when D(t) = D max ) for a (a) open-loop and (b) closed-loop with a constant γ = 1.2, and for a (c) open-loop and (d) closed-loop with a unknown random γ ∼ U(0.7, 1.3) to the desired one RU L ref . RUL resulted tracks the reference one thanks to the regulation of β, shown in Fig. 5a. The decisions in Fig. 4b are computed to control β(k) based on proposed control and estimated states ( D and β) shown in Fig. 5. In the first 40 iterations, the decision resulted is lower than the nominal value (black dashed line), which leads to a RUL greater than the desired one. After, we remark an important change on decisions to compensate and minimizing the tracking error e(k) = RU L(k) -RU L ref , which results in a greater degradation-rate in Fig (5a).

Fig. 4 .

 4 Fig. 4. Response of estimated RUL (a) in function of calculated decisions w d (b).

Fig. 5 .

 5 Fig. 5. Estimated and measured system states deterioration-rate β (a) resulting a deterioration D (b).

Table 1 .

 1 Control effect on the distribution of EoL for different cases of γ.

		EoL for γ = 1.2 EoL for γ ∼ U (0.7, 1.3)
	System in	median	std	median	std
	Open-loop	86	1.66	103	18.60
	Closed-loop	100	0.63	100	0.79