Method for characterizing different types of steel scrap and associated method for controlling an electric arc furnace

Abstract

A method for characterizing different types of scrap (si), charged in an Electric Arc Furnace EAF (10) for producing steel, the method comprising: - acquiring operation data that comprise, for each heat (hj) of a series of successive heats achieved with the EAF: o for each type of scrap (si), a measured scrap amount (1) charged in the EAF, o for at least one residual element, a measured residual content (2) of said element in a liquid steel (S) output by the EAF, - determining, for two or more of said types of scrap: data representative of a probability distribution for the residual content of said residual element, in the type of scrap considered, given the operation data (OD) acquired, using a model of operation for the EAF.

Description

Method for characterizing different types of steel scrap and associated method for controlling an electric arc furnace

[0001] The technical field is that of producing steel using an electric arc furnace, in particular that of characterizing scraps charged in an electric arc furnace. Technical background

[0002] More and more steel is produced by melting scrap steel in an electric arc furnace (herein after EAF) as this production route enables for recycling steel efficiently, thus reducing the carbon footprint of the production process.

[0003] To this end, pieces of scrap steel, called scraps in the following, are charged in the EAF, possibly complemented with some additives like lime, dolomite or coal. Iron-based supplementing material, like Hot briquetted Iron (HBI), Direct reduced Iron (DRI) or Pig Iron can also be charged in the EAF, in addition to the scraps. The materials thus charged are melted in the EAF to produce liquid steel, and also slag, which are then output. Each run that comprises loading (charging) the materials, melting, and outputting the products is called a heat.

[0004] The scraps charged in the EAF are mainly composed of iron and also contain small amounts of alloying elements and possibly some impurities (eg: steriles) too.

[0005] These alloying elements may comprise metallic elements, more particularly transition metals such as Nickel Ni, Copper Cu or Molybdenum Mo. Such metallic elements are called residual elements or residuals in the following. Some of these elements, in particular Copper, end up mostly (or even only) in the liquid steel produced. Some other elements, like Manganese Mn, end up distributed between the slag and the liquid steel.

[0006] These alloying elements or impurities may also comprise other elements (which are not transition metals) which end up only or mostly in the slag (in an oxidized form), or which end up distributed between the slag and the liquid steel, such as Silicon Si, Calcium Ca, Magnesium Mg, Sulphur S or Phosphorus P. These elements, also be found in the additives added, are called steriles in the following.

[0007] The residuals contents in the liquid steel produced by the EAF has a major influence over the subsequent stages of steelmaking and over the properties of the steel products finally produced (such as a coil or a beam). High residual contents are usually considered as detrimental. A high Copper content, for instance, may be very detrimental to hot rolling operations, causing cracks and surface damages usually referred to as “hot shortness”.

[0008] The residuals contents in the liquid steel directly depends on the residuals contents in the scraps, which vary a lot from one type of scrap to another, in practice. Indeed, some types of scrap, corresponding for instance to steel making shedding or to stamping shedding, may have very low residuals contents and are thus considered as high-quality scraps, well suitedfor EAF steel making. On the contrary, steel pieces made of a steel previously recycled (possibly several times) may have very high residuals contents and be considered as low- quality scraps.

[0009] Typically, different types of scrap, for instance high quality scraps and low quality scraps as well, are mixed together in the EAF so as to obtain a liquid steel with sufficiently low residuals contents while handling the limited availability of the high quality scraps, and in order to recycle also lower quality scraps.

[0010] In practice, many different types of scrap, (typically more than 4) are charged together in the EAF, to achieve each heat.

[0011] Different classifications of scraps grades exist, to facilitate scraps purchasing, sorting and selection. One example of such a classification is the EU-27 Steel Scrap Specification from the European Ferrous Recovery and Recycling Federation, which defines the eleven different grades E1, E2, E3, E40, E46, E5H, E5M, E6, E8, EHRB, EHRM.

[0012] Knowing the grades of the scraps employed, possibly completed by various information transmitted by a supplier of the scraps, gives a rough estimate of the residual(s) content(s) in these scraps.

[0013] But a more accurate determination of a residual content (or of more than one residuals contents), in the different types of scrap that may be charged in an EAF, is desirable. Indeed, it enables to better anticipate the residual(s) content(s) in a liquid steel to be produced using these types of scrap, and possibly allows for controlling the composition of the liquid steel produced.

[0014] A way to characterize different types of scrap is to do scrap melting tests for the input scraps, and subsequent chemical analysis. But such a procedure is rather complicated, in fact. Indeed, in a pile of scraps, even if the scraps are all of the same type, there are usually some variations of residuals contents from one piece of scrap to another. And so, determining an average residual content, for the type of scrap considered, requires several melting tests and chemical analysis and a complicated averaging procedure. Besides, the different types of scrap to be characterized are usually quite numerous (typically more than 4, or even 8 different types of scrap).

[0015] In this context, there is thus a need for a method enabling to characterize different types of scrap in a way that is both efficient and accurate. Summary

[0016] In this context, a method according to claim 1, for characterizing different types of scrap charged in an Electric Arc Furnace for producing steel, is provided.

[0017] In the instant method, for at least one residual element, the residual content in the liquid steel produced is measured, and, from this measurement, using a kind of back-calculation based on the model of operation of the EAF, residual contents in at least two of the differenttypes of scrap employed are deduced (and possibly in each of different types of scrap employed). More specifically, the residual contents in different types of scrap are each characterized by a probability distribution (from which an estimated residual content can be determined, by computing the mean or selecting the maximum of this probability distribution, for instance).

[0018] In the instant method, different types of scrap are thus characterized somehow a posteriori, after having been employed to produce liquid steel. Though a posteriori, this characterization is very useful. Indeed, knowing more accurately the residual content in the types of scrap employed enables to plan more accurately future heats, in particular regarding the amounts of the different types of scrap to be charged to obtain such or such residual content in the steel produced. Besides, it enables detecting possible drifts or variations of the quality of such or such type of scrap.

[0019] In the instant method, the measurement of the residual content of the element considered, in the liquid steel alone (or, possibly, in the steel and in the slag), allows to determine the residual content of this element in multiple different types of scrap (at least two, and possibly four, or even eight or ten different types of scrap), which is surprising, and not immediate.

[0020] This is made possible by taking into account the data corresponding to multiple successive heats. Indeed, in practice, in a series of heats, the respective proportions of the different types of scrap, mixed together in the EAF, vary from one heat to another (see figure 6). For instance, a given type of scrap may be very abundant in the first heat, and almost absent in the second heat which, by comparing the residual content in the steel produced for these two heats, enable to back-calculate the residual content in this type scrap. In other words, by collecting measurements of the residual content in the liquid steel, and by collecting the respective amounts of the different types of scrap for multiple successive heats, one somehow gathers a set of multiple equations (a system of equations), which, together, enable to determine the values of the multiple variables that are the residual contents of the element considered in the different types of scrap. It is noted that this explanation is a simplified explanation, given solely for the sake of illustrating the usefulness and importance of acquiring operation data for multiple successive heats.

[0021] Characterizing at least some of the types of scrap using a probability distribution, instead of a single residual content value, is very useful. Indeed, for heats to come, it allows for determining an expected probability distribution for the residual content in the output liquid steel. This probability distribution allows to better characterize the margin between the expected (predicted) residual content in the liquid steel, and a maximum admissible content not to be exceeded. Indeed, if the expected probability distribution for the residual content in the liquid steel is noticeably spread (like for the distribution ^^([Cu]LS) in figure 2), a highermargin with respect to the maximum admissible content [Cu]maxwill be preferable. While when this probability distribution is narrow (like for the distribution ^^′([Cu]LS) in figure 2), a much lower margin can be used, which in turns allows for using higher amounts of low-quality scraps (thus favorizing recycling of such scraps).

[0022] Besides, determining the probability distribution of the residual content in a type of scrap enables to detect if this type of scrap has high fluctuations of the residual content (or a high uncertainty thereof), and may thus be considered as less reliable than other types of scrap (one then avoiding to use it if possible).

[0023] Remarkably, in the instant method, probability distributions are determined, respectively, for multiple different types of scrap (at least two different types of scrap, and possibly all of them). In other words, an individual probability distribution is determined for each type of scrap (more precisely, for each of the at least two different types of scrap). This is markedly different from determining a global error (eg: a global residual), or a global uncertainty for the estimation of the overall ensemble of residual contents in the different types of scrap. Such a global error is what one would obtain in a back-calculation method based on minimizing cumulated differences between predictions and observations (such as with a least squares base regression). In the instant method, the determination of individual probability distributions, for different types of scrap, is possible thanks to the computation of individual probability distributions conditioned on the measured operation data (and based on the model of operation of the EAF). In other words, it is made possible thanks to the Bayesian inference approach employed.

[0024] Using this approach, in spite of its difficulty of implementation and associated heavy computational burden, allows thus to determine probability distributions for different types of scrap, individually, which is extremely useful.

[0025] The instant method may comprise one or several additional features, defined in claims 2 to 19, considered alone or in combination.

[0026] The instant technology also concerns a computer program comprising instructions (possibly stored in a non-transitory computer-readable media), whose execution on a computer makes the computer to execute the method presented above (said computer being possibly connected to sensors collecting operation data, and possibly to a loading controller of the EAF).

[0027] The instant technology also concerns an electronic characterization device according to claim 21 and a steel making facility according to claim 22. Detailed description

[0028] The instant technology will now be described in more detail and illustrated by examples without introducing limitations, with reference to the appended figures.

[0029] Figure 1 schematically represents a heat achieved using an EAF.

[0030] Figure 2 schematically represents probability distributions for Copper content in a liquid steel produced using an EAF.

[0031] Figure 3 schematically represents a characterization device for characterizing different types of scrap.

[0032] Figure 4 schematically represents steps of a method for characterizing implemented by the characterization device of figure 3.

[0033] Figure 5 schematically represents an expected probability distribution for a residual content, in a liquid steel to be produced using an EAF.

[0034] Figure 6 is a graph representing the respective proportions %i of nine different scrap types si, i=1..9 for a series comprising 25 successive heats.

[0035] Figure 7 is a graph representing a measured Copper content, and a predicted Copper content for the liquid steel produced by the EAF, for several successive heats.

[0036] As above mentioned, the instant technology aims inter alia at characterizing different types of scrap charged in an EAF for producing steel, in terms of residual content and possibly also in terms of metallic (ferrous) yield and / or in terms of sterile content.

[0037] A method for characterizing different types of scrap in this manner is presented first. Different applications of the characteristics of the types of scrap thus determined are presented then. Electric Arc Furnace operation

[0038] Figure 1 schematically represents the operation of an EAF 10. Materials, comprising scraps and possibly additives are charged in the EAF 10 (step E1), where some steel 11, sometimes designated as the “hot heel”, may be already present (remaining from a previous heat). The materials are then melted (step E2), and some liquid steel S is then output by the EAF (step E3). This ensemble of steps is called a heat. The heat hjrepresented in figure 1 is one of a series of successive heats hj, j=1…J achieved with the EAF 10.

[0039] Different types of scrap si, i=1..I can be charged in the EAF.

[0040] Each type of scrap, that is each variety of scrap corresponds to a kind of scrap whose properties, in particular whose copper content and metallic yield, are expected to be constant or to have limited (and possibly smooth) variations over time during the series of heats.

[0041] As mentioned in the technical background section, different normalized classifications exist for steel scraps, each classification defining several grades (several categories) of scrap. The different types of scrap considered in this method may correspond to the different grades of such a classification.

[0042] Still, the scraps may be classified more finely into different types of scrap.

[0043] For instance, scraps of a same grade but provided through different supply routes may be associated to different types of scrap. Such or such supply route may be defined by the supplier providing the scraps (among different suppliers) and / or by the origin (the source) ofthe scrap. It may also be defined by the production source the scraps are coming from, within the plant or within the steelmaking company where the EAF is installed.

[0044] Similarly, scraps of a same grade, provided by a same supplier but at different times (for instance with one week or more, or two weeks or more between the two deliveries considered) may correspond to different types of scrap.

[0045] Besides, different types of scrap can be assigned to the scraps, available at the steel making facility where the EAF is installed, based on features of these scraps observed either manually or automatically. Such features can be observed by an operator, the observed features being then entered by the operator using a human-machine interface. Such features can also be observed automatically using image analysis of one or more images of the scraps. The features of the scraps thus observed, and which may be used so assign a type of scrap to the scraps considered, may comprise one or more of: a density, an homogeneity level, the absence or presence of foreign pieces, the kind of pieces in the scraps (eg: light wheels, pieces resulting from cutting parts initially formed of bent or stamped blanks, …).

[0046] Chemical analysis achieved on samples of scrap, taken on such or such pile of scraps in the steel making facility, may also be taken into account to assign a type of scrap to the pile of scraps considered.

[0047] In practice, the number I of different types of scrap, charged in the EAF during said heats, is typically equal to or higher than 4. More generally, I may be comprised between 4 and 50 and may be equal to or higher than 8, or even equal to or higher than 12.

[0048] In addition to the scraps, different additives can be charged in the EAF, like dolomite, lime, anthracite, coke, slag, refractory fines or aluminium oxide. Different types of additive adl, l=1..L can thus be charged in the EAF during the above-mentioned heats.

[0049] These types of additive adl, l=1..L may correspond directly to the nature of the additive, for instance lime, dolomite, or anthracite. Still, a more detailed classification can be used. For instance, different types of additives can be associated to different kinds of lime employed for the heats, depending on their properties, origin and / or supplier (and the same for the dolomite and coal).

[0050] The number L of different types of additive is may be comprised between 1 and 7 and may be equal to or higher than 3.

[0051] Iron-based supplementing materials, such as hot briquetted iron (HBI), direct reduced Iron (DRI) or Pig Iron may also be charged in the EAF. Different types of iron-based supplementing materials smn, n=1..N (with N from 1 to 3, for instance) can thus be charged in the EAF during the above-mentioned heats.

[0052] For each heat hj, a given amount a j s,iof each type of scrap si(which may be zero for some types of scrap) is charged in the EAF. A given amount a j ad,lof each type of additive adl(which may be zero for some types of additive) is charged in the EAF. And a given amount a j sm,nof each type of iron-based supplementing material smn (which may be zero for some types of additive) is charged in the EAF. Here, by amount it is meant the mass (in tons or kg) of the type of scrap or additive considered, that is charged in the EAF. These amounts a j j s,i, aad,land a j sm,nare measured using one or more measuring devices 12, for instance weighting devices like an ensemble of load cells, a crane or plate scale or another industrial weighting device. It may be noted that these measurements may either be direct measurements (like with a crane scale) or non-direct measurements, derived from one or more observations using a model (either a data-based trained model or physics-based model) or a numerical simulation.

[0053] For each heat hj, a chemical composition of the liquid steel S produced during that heat is measured, for instance by taking a sample 14 of liquid steel and characterising it using a characterizing device 15, or by sending the sample 14 to a remote lab or facility for subsequent analysis of its chemical composition (based for instance on a spectroscopic analysis).

[0054] This chemical composition analysis comprises determining, for one or more residual elements rk, k=1..K (in particular for Copper), a measured residual content [r j k]LSin the liquid steel S output by the EAF for the heat hjconsidered. [r j k]LSis the concentration, for instance the mass concentration (expressed for instance in mole per kg of steel or in g per kg of steel) for the residual element rkin the liquid steel S produced during heat hj. The number K of residual elements, whose respective contents are thus measured, may be from 1 to 5, or even from 1 to 8. Still, it is noted that the instant method can be applied as well for K=1, that is when only one residual content (typically Copper content) is measured in the liquid steel, and then determined by back-calculation for the types of scrap charged in the EAF.

[0055] By residual element, it is meant a Metal, or more specifically a transition Metal (in particular one of: Copper Cu, Nickel Ni, Tin Sn, Molybdenum Mo, Chromium Cr) and / or one of: Aluminum Al, Manganese Mn.

[0056] In the embodiment represented in the figures, this chemical composition analysis also comprises determining, for one or more sterile elements tm, m=1..M, a measured sterile content [t ] j in the liquid steeloutput by the EAF for the heat hj. [t ] j mLS m LSis the concentration, for instance the mass concentration (expressed for instance in mole per kg of steel or in g per kg of steel) for the sterile element tmin the liquid steel S produced during heat hj. The number M of sterile elements, whose respective contents are thus measured, may be from 1 to 5 (or may be null).

[0057] By sterile element, it is meant one of the following elements: Calcium Ca, Magnesium Mg, Phosphorous P, Silicon Si, Sulphur S. It is noted that in the additives, these residual elements are mostly present in their oxidized form (SiO2, CaO, MgO,…).

[0058] In the embodiment represented in the figures, for each heat hj, a total liquid steel amount LSj, output by the EAF for said heat, is measured. This measured liquid steel amount LSjis measured by a measuring device 13, for instance a weighting device (like an ensemble of load cells, a crane or plate scale or another industrial weighting device) fitted to the EAF, or fitted to a ladle or converter in which the liquid steel S is poured. This measurement may either be a direct measurement, or non-direct measurement.

[0059] Optionally, a total slag amount, output by the EAF for the heat hj, is measured, or estimated (derived from other measurements and / or process parameters) and a chemical analysis of the slag is also carried out (similarly as the one carried out for the liquid steel), to determine sterile contents in the slag (for the same steriles as the ones measured in the liquid steel), and also possibly to determine some metallic residuals contents in the slag (such as Aluminium or Manganese - in their oxidised form). Operation data acquired

[0060] During the series of heats, operation data OD relative to the characteristics of each heat achieved are acquired by a characterization device 1 (figure 3). These operation data comprise the measured quantities mentioned above. So, in the instant embodiment, the operation data comprise, for each heat hj, j=1…J of the series of heats: - for each type of scrap si, i=1..I, a measured scrap amount a j s,icharged in the EAF, - for each type of additive adl, l=1..L, a measured additive amount a j ad,lcharged in the EAF, - for each type of iron-based supplementing material smn, n=1..N, a measured supplementing material amount a j sm,ncharged in the EAF, - for each residual element r j k, k=1..K, a measured residual content [rk]LSin the liquid steel S output by the EAF, - for each sterile element tm, m=1..M, a measured sterile content [tm] j LSin the liquid steel S output by the EAF, - a total liquid steel amount LSj, output by the EAF for said heat, - and, possibly, a total slag amount output by the EAF for said heat, together with residuals and steriles contents therein.

[0061] Still, in alternative embodiments, the operation data could comprise less data, for instance just the measured scrap amounts and the measured residual content (for one or more residuals) in the liquid steel, possibly completed by the amount of liquid steel produced.

[0062] The number J of heats in the series, for which the operation data are acquired and gather together, is typically equal to or higher than 10, or even 20 or 50, which corresponds typically to one or two days of operation of the EAF. For the reasons outlined in the summary section above (regarding deriving a residual content for multiple input materials, while theresidual content is measured in just one output material – namely in the output liquid steel), the number J of heats in one series may, like here, be equal to or higher than the number I of types of scrap. To take advantage of the variation of the proportions of the different types of scraps from one heat to another (in order to favorize an accurate characterization of the different types of scrap), J may even be equal to or higher than n.I, n being from 2 to 10, or from 3 to 10 for instance. Figure 6 shows the evolution, from one heat to another, of the respective proportions %i (mass proportions, relative to the total mass of scraps charged in the EAF) of nine different types of scrap si, i=1..9 (in the case of figure 6, I=9), for 25 successive heats. As can be seen in this figure, the proportions of the different types of scrap vary substantially during a typical series of heat.

[0063] The operation data OD are collected from the sensors 12, 13, 15 (and possibly from the remote lab) above mentioned. The operation data OD are transmitted, from these devices 12, 13, 15 to the characterization device 1, using wire or wireless communication. The operation data OD may be transmitted through a local network or bus, for instance of the CAN (Controller Area Network), CAN+ or fieldbus type. The operation data OD may also be transmitted to the characterization device 1 through a public network like the internet. The operation data OD may be stored in a storage device or system, for instance within an industrial production database, and then be retrieved by the characterization device 1, by interrogating said database. The operation data OD are acquired by the characterization device 1 using a communication interface.

[0064] The characterization device 1 is an electronic device having the structure of a computer (it comprises at least a processor and a memory). It comprises a non-transitory computer- readable media 2 (figure 3), such as a hard drive or a flash memory, which includes a computer program comprising instructions whose execution makes the computer to execute the method for characterizing the types of scrap si, i=1..I described below. Method for characterizing the types of scrap employed

[0065] The characterization device 1 is configured for implementing the following method for characterizing different types of scrap, which comprises: - acquiring the operation data OD, - determining, from the operation data OD and using the model M of operation for the EAF: for two or more of the types of scrap si, i=1..I, here for each type of scrap si, and for at least one of the residual elements rk(typically Copper), possibly for each of the residual elements rk, k=1..K: odata representative of a (conditional) probability distribution ^^ ([rk]s,i|OD) for theresidual content [rk]s,iin the type of scrap si considered, given the operation data OD acquired,o and, optionally, an estimated residual content [rk̂]s,iin the type of scrap siconsidered.

[0066] In the embodiment described here, the method for characterizing also comprises determining, from the operation data OD and using the model M of operation for the EAF: o for each type of scrap si, i=1..I : ▪ data representative of a probability distribution ^^(^^i|OD) for the metallic yield ^^i, given the operation data OD acquired, and an estimated metallic yield ŷi for the type of scrap si, and ▪ an estimated sterile content [t̂m]s,iin the type of scrap si (and possibly also data representative of a probability distribution ^^ ([tm]s,i|OD) for thesterile content [tm]s,i, given the operation data OD acquired), for each of the sterile elements tm, m=1..M, and o for each type of additive adl, l=1..L: an estimated sterile content [t̂m]ad,lin the type of additive adl, for each of the sterile elements tm, m=1..M. model of operation for the EAF

[0067] The model M provides a relationship between: - the amounts and properties of the materials (scraps and additives) charged in the EAF before or during a heat, which are inputs of the model, noted X, to - the amounts and properties of the materials (liquid steel, slag) output by the EAF for that heat, which are outputs of the model, noted Y.

[0068] The model M enables to compute the outputs Y from the inputs X: ^^ ∶ ^^^^^^^^^^^^ ^^ → ^^^^^^^^^^^^^^ ^^

[0069] The model M can be a physics-based model, using for instance material balance (or other conservation law) and modelizing the partition of some elements, typically steriles (and also Aluminum, or Manganese) between the liquid steel and the slag. The partitioning of such an element between steel and slag may be modelized using a constant partition coefficient, or by computing a final amount in the steel and in the slag using a set of chemical equations representing the oxidization and other chemical transformations in which this element is involved.

[0070] The model M can be also be a so-called “black box” data-based model, obtained by regression from past heats data. It can also be a hybrid model based both on physics-law and on data-based empirical relationships; for instance, the model M may be based on the balance of materials while using a data-based model for determining the value of the partition coefficient for such or such element, in the conditions of the heat considered.

[0071] The model may take into account a possible correlation between a preceding heat and a following heat of said series, this correlation being due for instance to the presence of thehot heel 11 remaining in the EAF at the end of the preceding heat; in this case, the hot heel remaining from the preceding heat may be treated as an input material for the following heat.

[0072] In the embodiment considered here in more details, the model M, physics-based, is as follow. The inputs X of the model comprise: - for each type of scrap si i=1..I : the metallic yield yi, the amount as,i charged in the EAF, the residuals contents therein [rk]s,i, k=1..K, the steriles contents therein [tm]s,i, m=1..M, - for each type of additive adl, l=1..L : the amount aad,l charged in the EAF, the steriles contents therein [tm]ad,l, m=1..M, and, optionally the residuals contents therein [rk]ad,l, k=1..K, - for each type of iron-based supplementing material smn, n=1..N : the metallic yield yn, the amount asm,n charged in the EAF, the residuals contents therein [rk]sm,n, k=1..K and the steriles contents therein [tm]sm,n, m=1..M.

[0073] The outputs Y of the model comprise: - an amount of liquid steel LS output by the EAF during said heat, - residuals contents in the liquid steel output by the EAF, [rk]LS, k=1..K, - steriles contents in the liquid steel output by the EAF, [tm]LS, m=1..M.

[0074] According to the model M considered here, the relationships between the outputs Y and the inputs X are:=1.. ^^ (^^^^^^ 3)

[0075] In eqn 3, xmis the ratio between: the amount of the sterile element tmthat ends up in the liquid steel, and the total input amount of that sterile element tm.

[0076] In the following, [rk]ad,lis approximated to 0. Besides, to avoid weighing down the discussion unnecessarily, it is considered in the following that no iron-based supplementingmaterial is charged in the EAF (in other terms, asm,n = 0 ∀ ^^ = 1.. ^^).

[0077] When using the model M above to relate the inputs to the outputs of one heat, the value of the liquid steel amount LS, employed when evaluating or otherwise using eqn 2 and eqn3, may be the measured liquid steel amount LSjfor that heat (rather than the output liquid steelamount estimated through eqn 1). This is beneficial, since it renders the inputs / outputs relationship linear, for said model.

[0078] It is noted that in this exemplary model (and in other models taking material balance into account), the residuals contents for the different residual elements can be treated (analyzed and processed) independently from each other. In other words, eqn 2 for k=1 does not involve residuals contents for elements other than r1 (copper content in the liquid steel does not depend on Nickel content in the scraps, for instance).

[0079] In alternative embodiments, the inputs and outputs of the model of operation of the EAF could be less numerous. For instance, the inputs may comprise of just the input scrap amounts and residual(s) contents in the different types of scrap, possibly completed by the metallic yields of the different types of scrap, the outputs then comprising the residual(s) content(s) in the output steel, possibly completed by the output liquid steel amount.

[0080] Whatever the nature of the model (either physical, empirical, or hybrid), as it enables to determine the outputs Y for any inputs X, it enables to propagate uncertainties regarding the inputs, to the outputs. This is exploited in the instant method, in a kind a reverse manner, in order to derive uncertainties about residual(s) content(s) in the input scraps, from the heats results (i.e.: from the residual(s) content(s) in the liquid steel produced). Characterization of the types of scrap

[0081] In the following, a single residual rk, for instance Copper, is considered first. Possible estimations of other residuals contents, metallic yields and steriles contents are presented later.

[0082] Residual content estimation for one of the residual elements

[0083] For that residual rk, the residual content in each type of scrap si, i=1..I is characterized using a probabilistic approach, by determining (by computing) the probability density

[0084] For each type of scrap si, i=1..I, the probability density ^^ ([rk]s,i|OD) is determinedtaking into account: - a prior probability distribution ^^^^^^^^^^^^([rk]s,i), for the residual content [rk]s,iin the type of scrap si, and -a probability distribution ^^representing a probability to obtain the operationdata OD that have been actually acquired, assuming a residual content [rk]s,iin the type of scrap si; ^^ (OD|[rk]s,i) is calculated using the model M of operation of the EAF (and,possibly, taking into account probability distributions for the residual content for rkin the other types of scrap than si).

[0085] The probability distribution ^^ ([rk]s,i|OD) is determined by Bayesian inference, basedon formula eqnBbelow, or based on a probability estimation method derived thereof such as Monte Carlo Markov Chain probability estimation:

[0086] In eqnB, ^^(OD) is the probability to obtain the operation data OD actually acquired, for the series of heats considered.

[0087] Prior probability distribution

[0088] For the residual rk, the prior probability distribution ^^^^^^^^^^^^([rk]s,i) may be determined based on a residual content range, specified for a scrap category to which said type of scrap si belongs. The residual content range for said scrap category is specified for instance in a normalized scrap specification, such as the EU-27 Steel Scrap Specification above mentioned. The residual content range may also be specified by a supplier providing the type of scrap si. In these cases, the residual content range usually takes the form of a zero-to-maximum content range. The prior probability distribution ^^^^^^^^^^^^([rk]s,i) is for instance determined, for such a range, as a uniform (a constant) probability distribution spreading over the entire residual content range. It could also be a gaussian probability distribution, or another peak-like probability distribution, having a mean value equal to the mean value of said residual content range and having a standard deviation equal to, or proportional to the standard deviation corresponding to the residual content range in question. The prior probability distribution^^^^^^^^^^^^(x) could also be a beta distribution, of the form ^^^^^^^^^^^^^^^^. ^^ ^^−1. (^^^^ − ^^)^^−1(with ^ and β positive), which has the advantage of having a finite support (which is the interval [0, xo], xobeing chosen as equal to the maximum content range mentioned above, for instance), and of leading possibly to explicit (closed-form) expressions for the posterior probability that^^ ([rk]s,i|OD) is.

[0089] Alternatively, the prior probability distribution ^^^^^^^^^^^^([rk]s,i) may be a probably distribution of the residual content in said type of scrap, determined previously for a series a heats preceding the current series of heats (for instance for the series of heats achieved immediately before the current series of heats), this previous determination being achieved, for instance, using the instant method for characterizing. This allows to take advantage of a knowledge regarding the types of scrap, previously acquired during the preceding series of heats.

[0090] In alternative embodiments, the prior probability distribution ^^^^^^^^^^^^([rk]s,i) may be derived, or adjusted based on observations made for the type of scrap considered (for instancetaking into account chemical analysis results obtained for a sample of the type of scrap considered).

[0091] Anyhow, these different possible choices regarding the prior distribution ^^^^^^^^^^^^([rk]s,i) illustrate one of the benefits of the Bayesian inference post-characterization method employed here, which is to integrate (to take into account) prior information (prior knowledge) regarding the residual content in the different types of scrap considered.

[0092] Example procedure 1: Monte Carlo Markov Chain estimation

[0093] In this first procedure, the probability distribution ^^ ([rk]s,i|OD) is determined bysampling the distribution thanks to multiple successive draws of the quantity [rk]s,i, that are drawn according to a Monte Carlo Markov Chain (herein after MCMC) estimation method. According to this method, a chain of samples is constructed sample by sample, each new sample being drawn randomly (but depending on the preceding sample in the chain), based on specific rules. In this section, the quantity [rk]s,iis denoted x for the sake of conciseness. The MCMC estimation method is implemented here using the Metropolis-Hastings technique.

[0094] According to this technique, a probability distribution q(xn|xc) is employed to draw a candidate new sample xn, given the current sample xc. The so-called proposal distribution q is chosen so as to explore efficiently the possible values of x (with steps, between successive samples, that are not too big, nor too small, for instance). It may be a gaussian (normal) probability distribution whose argument is the distance between xnand xc.

[0095] Each new sample of the chain is determined by: - drawing randomly a candidate new sample xn, according to the proposal distribution q(xn|xc), - accepting xnas the next sample in the chain, with a probability ^^, and, if not accepted, setting the next sample as being (again) xc, with ^^ = ^^^^^^ {1,

[0096] Except for a number of first samples at the beginning of the chain (which are discarded, in a so-called burn-in procedure), the samples generated successively, in this way are distributed according to the probability distribution ^^(x|OD)(i.e.: with a density which, as a function of x, is ^^(x|OD) ), which enables to determine ^^(x|OD). ^^(x|OD) may be determined from these samples as a histogram (or, in other words, a probability mass function), by binning, or as a continuous probability density function (by fitting such an histogram, for instance).

[0097] In equation eqn M-H, the quantity ^^(^^^^|^^^^) ^^(^^^^|^^^^) is equal to 1 when the proposal distribution q employed is symmetric (which is the case for the normal-law example given above) and isanyhow straightforward to compute. Regarding the values of ^^^^^^^^^^^^(^^^^) and ^^^^^^^^^^^^(^^^^), they are also readily calculated.

[0098] The computation of the value of ^^(OD|^^^^)and ^^(OD|^^^^), however, is less direct. It is achieved based on the model M of operation of the EAF and may, like here, takes into account probability distributions for the residual content for rk in the other types of scrap than si.

[0099] For instance, to determine ^^(OD|^^^^), the value of [rk]s,iif fixed (as equal to ^^^^), and then the probability to obtain such or such operation data (such or such residual content in the liquid steel produced) is computed, based on the prior distributions for [rk]s,i'≠iin the other types of scrap si’, i’=1..I, i’^i. The probability to obtain such or such operation data, in view of the uncertainties (in view of the prior distributions) for [rk]s,i'≠i, is computed by propagating these uncertainties from the inputs to the outputs of model M. This can be achieved for instance by Monte Carlo sampling (not necessarily MCMC; it could be a simple, with no correlation between samples, Monte Carlo sampling), by drawing multiples samples for each input residual content [rk]s,i'≠i(according to the corresponding prior distributions), computing the output quantity [rk]LSobtained for each of these input samples (using model M), and then mapping the density of [rk]LS. In practice, this operation of deriving the probability distribution^^ (OD|[rk]s,i) can be achieved for all the different types of scrap si, i=1..I in lockstep (by MCsampling, based on the priors for [rk]s,i, i=1..I), rather than independently and sequentially for the different types of scrap. This avoids redundantly computing identical quantities. This determination in lockstep is achieved by evolving, in the same way described before, a joint probability distribution encompassing the different residual contents (i;e.: the residual contents, in the different types of scrap, for the residual considered). Such a joint-determination procedure may be necessary if the different types of scrap are not independent from each other (in terms of residual content).

[0100] It is noted that the operation data OD gather the data for the different successive heats hj, j=1…J of the series of heats considered. If successive heats are, according to model M, independent from each other (like for the model defined by eqn 1 to 3 above), then, the probability ^^(OD|^^^^) can be computed as a product of individual (independent) probabilities each associated to one of the heats, which facilitates the computation of ^^(OD|^^^^); forinstance, if considering just the quantity [r ] : ^^(OD|^^ ) = ([r ] jk LS ^^k LS = [rk]LS | [rk]s,i = ^^^^)(where it is recalled that [rk] j LSis an observed, measured quantity).

[0101] In alternative embodiments, the MCMC estimation method could be implemented using another technique than the Metropolis-Hastings one, for instance using Gibbs sampling, or the so-called No U-Turn sampling (NUTS).

[0102] Example procedure 2: Analytical derivation

[0103] A closed-form expression for ^^ ([rk] can be derived (analytically) in some case,depending on the model and prior distributions. For instance, when the prior distributions are independent normal distributions and when the model of operation is linear (like for the one ofeqn 1 to 3 above), it can be shown that ^^ ([rk]s,i|OD) is a normal distribution whose meandepends (in a closed-from manner) on the means of the prior distributions and on the operation data OD, and whose variance depends (also in a closed-form manner) on the variances of the prior distributions and on the operation data OD. More particularly, in such a case, the meanof ^^ ([rk]s,i|OD) is a weighted average between:- a value obtained by applying the linear model of operation to the respective means of the prior distributions, and - a value corresponding to an (explicit) least-square estimation of the parameters [rk]s,i,i=1..I of the linear regression problem of estimating these parameters from the operation data, the weighting coefficients depending on the respective variances associated to these two values.

[0104] More generally, it is noted that when using the model M defined by equations eqn 1 – 3 above, determining the probability distributions for the residual content for element rk, in the different types of scrap si, i=1..I, is a problem of probabilistic estimation of the parameters of a linear input-output model (the parameters to be estimated being [rk]s,i,i=1..I), since eqn 2 is linearly relating the input material amounts to the output residual content in the liquid steel. So, any method designed for Bayesian linear regression could be employed to determine

[0105] From a computational point of view, other procedures than procedure 1 or 2 abovecould be employed to determine the probability distribution ^^ ([rk]s,i|OD). For instance,parameters characterizing the probability distribution (like the mean and variance of the distribution, assumed to be a normal distribution) could be determined using a numerical optimization (like a gradient descent, or a metaheuristics-based optimization) of the likelihood of the parameters [rk]s,i,i=1..I given the operation data OD, the likelihood being evaluated through direct Monte-Carlo sampling (i.e.: simple Mont Carlo sampling, with no correlations between successive sample draws).

[0106] In the instant method, an estimated residual content [^̂^k]s,iin each type of scrap isdetermined from the probability distribution ^^ ([rk] for each type of scrap, for instanceby computing the mean (the average) of this probability distribution, or by computing its maximum (maximum a-posteriori). This enables to characterize each type of scrap in a conciseway and facilitate detecting possible drifts of the residual content in this type of scrap. Aquantity representative of a width of the probability distribution ^^ ([rk]s,i|OD), like its standarddeviation ^k,i, may also be computed for each type of scrap.

[0107] Content estimation for other elements, and metallic yield estimation

[0108] For another residual element rk’, for instance for Nickel instead of Copper, theprobability distributions ^^ ([rk']s,i|OD) for that residual, in the different types of scrap si, i=1..I,can be determined using the same procedure as the one presented above for element rk, and the same applies for the sterile elements tm, m=1..M.

[0109] In this regard, it is noted that in the model M defined by eqn 1 – 3 above, the input- output relationships for the different residual and sterile elements are independent from one another (as this model is based on material balance), and so, the scraps and additive characterizations can be achieved independently for the different elements. In other words, the computations for Nickel content characterization can be achieved independently from the ones for Copper content characterization, and from the ones for Chromium content characterization and so on.

[0110] Regarding the metallic yields (ferrous yields) of the different types of scrap, their probability distributions ^^(yi|OD), i=1..I can be determined using the same procedure as the one presented above for [rk]s,i,1..I (except that, in practice, it is eqn 1 of model M, instead of eqn 2 that will be employed). Exemplary results for Copper content

[0111] Figure 7 represents, for 225 successive heats, the measured Copper content [Cu]LS in the liquid steel S output by the EAF, in mass fraction (mass %). Figure 7 represents also an predicted Copper content [Cu]LS,pfor the liquid steel, based on the scrap characterization above described. The predicted Copper content [Cu]LS,p, for a given heat, is calculated based on the different amounts of scrap charged in the EAF for this heat, and based on the probability distributionsi=1..I determined for the scrap types (determined prior to said heat). In this example, the number I of scrap types is equal to 16 (and no Iron-based supplementing material are charged, while there are two types of additive, namely Lime and Dolomite). The number J of heats in each series is equal to 35 (number of heats taken into account to back-calculate the set of probability distributions for the Copper content in the different types of scrap), and the prior distributions for the Copper content are Gaussian distributions. As illustrated by figure 7, the probability distributions for the Copper content in the different types of scrap, determined are explained above, enable indeed to predict the Copper content in the liquid steel produced. And they provide in addition an estimation of the Copper content variability, in the scraps, and in the produced steel.Uses of the characteristics of the different types of scrap

[0112] For each type of scrap si, i=1..I, the characteristics of the type of scrap considered, determined according to the method for characterizing above, comprise at least the probabilitydistribution ^^ ([rk]. It may also, like here, comprise the estimated residual content [^̂^k]s,iand associated standard deviation ^k,i. The ensemble gathering these characteristics, for the different types of scrap si, i=1..I is denoted CR in the following (figure 4). Different uses of the characteristics of the types of scrap CR are presented below.

[0113] Application 1: scrap monitoring.

[0114] According to a first application, at least some of the characteristics CR (for instance [^̂^k]s,iand ^k,i, i=1..I) are output, via a Human Machine Interface 3 of the characterization device 1, such as a screen. For an operator controlling the EAF operation, and possibly controlling the scraps ordering, it allows for checking that the residual(s) content(s) in the scraps does not drift (drift of [^̂^k]s,i), or does not become hardly predictable (increase of ^k,i).

[0115] Alternatively, or as a completement, the characteristics of the types of scrap CR may be output (using a communication interface of the characterization device), to be stored in an industrial production database 20 (figure 3).

[0116] Application 2: automatic scrap drift detection.

[0117] According to a second application, an alert signal is emitted automatically by the characterization device 1 (for instance via the Human Machine Interface 3) when it detects thata width (for instance ^k,i) of the probability distribution ^^ ([rk]s,i|OD) becomes higher than agiven threshold, or when it detects that an increase (for instance a weekly increase) of this width is above a given, increase threshold.

[0118] Application 3: determining scraps amounts for a next heat, based on a target residual content or based on a maximum admissible residual content.

[0119] The characteristics of the types of scrap CR, more particularly the probabilitydistribution ^^ ([rk]s,i|OD), i=1..I, can be used to determine an expected probability distribution^^^^^^^^^^_ℎ^^^^^^([rk])for the residual content [rk] in the liquid steel, for a heat to come, depending on candidate scrap amounts a's,i, i=1..I for the different types of scrap.

[0120] ^^^^^^^^^^_ℎ^^^^^^([rk]) may in particular be determined using the same model M as for the scrap characterization. In such a case, ^^^^^^^^^^_ℎ^^^^^^([rk]) is determined by propagating the uncertainties regarding the residual content for the different types of scrap (uncertaintiescharacterised by the probability distributions ^^ ([rk] , from the inputs of the EAF to theoutputs, using model M (for instance by monte Carlo sampling).

[0121] Predicting the expected probability distribution ^^^^^^^^^^_ℎ^^^^^^([rk]), for the heat to come, is very useful. Indeed, it allows for adjusting the candidate scrap amounts a's,i, i=1..I so that ^^^^^^^^^^_ℎ^^^^^^([rk])satisfies a target criteria relative to the final residual content in the liquid steel.

[0122] This target criteria may specify a positioning of the expected probability distribution ^^^^^^^^^^_ℎ^^^^^^([rk])relative to a target residual content [rk]target for the liquid steel, or relative to the maximum admissible residual content in the liquid steel [rk]max (for instance [Cu]max).

[0123] This target criteria may concern a mean value m (or a most probable value m) and a width ^ (eg standard deviation) of ^^^^^^^^^^_ℎ^^^^^^([rk]). For instance, this target criteria may specify that:where ‘thershold’ is a constant value (which depends on the desired margin between m and [rk]max), for instance equal to or higher than 2.

[0124] Alternatively, the target criteria (for ^^^^^^^^^^_ℎ^^^^^^([rk])) may be that the interval [m - ^, m + ^] is within a target interval [[rk]min,target, [rk]max,target].

[0125] According to another alternative, the target criteria for ^^^^^^^^^^_ℎ^^^^^^([rk])may be that: a probability Pexd, that [rk] exceeds [rk]max in the liquid steel produced, is below a maximum admissible probability (risk) Po, for instance below 5%, or even below 2% or 1%. Pexd is a cumulated probability that is determined from ^^^^^^^^^^_ℎ^^^^^^([rk]) and [rk]max (see figure 5).

[0126] The candidate scrap amounts a's,i, i=1..I may be adjusted until manufacturing- suitable scrap amounts a"s,i, i=1..I are obtained, the manufacturing-suitable scrap amounts being such that ^^^^^^^^^^_ℎ^^^^^^([rk])satisfies the above target criteria. The manufacturing-suitable scrap amounts a"s,i, i=1..I, may be determined using a trial-and-error method, or using a sampling method, or using another optimisation (for instant gradient based optimisation) aiming at approaching said criteria. In the process of determining the manufacturing-suitable scrap amounts a"s,i, i=1..I, some constraints may be taken into account, like using at least a minimum amount of such or such low quality scrap, or like limiting the amount of the scrap types that have widespread probability distributions. The constraints taken into account may also be related to the availability levels of the different types of scrap to be employed. Indeed, some types of scrap, typically high-quality scraps, are available only in small amounts, or at high prices, and it is thus important in practice to optimize the global usage of the scraps taking into account different availability levels for the different types of scraps.

[0127] Application 4: controlling

[0128] According to a fourth application, manufacturing instructions are transmitted (by the characterization device 1) to a loading controller 17 of the EAF, to control loading devices of the EAF (like an electrically actuated overhead crane bucket or scoop, or a scrap claw orelectromagnet) so that the manufacturing-suitable amounts of scrap, determined according to application 3 above, are charged in the EAF to achieve a heat.

[0129] Characterization and control device

[0130] In the embodiment corresponding to the figures, the characterization device 1 presented above is configured to implement the applications 1 to 4 above, in addition to the characterization method previously described (and it is thus both a characterization device, and a control device for the EAF).

[0131] More particularly, the non-transitory computer-readable media 2 or another such media of the characterization device 1, comprise additional computer programs or program modules for executing respectively the methods according to application1, 2, 3 and 4 above.

[0132] In this embodiment, these four applications are all implemented by the characterization device 1. Still, in alternative embodiments, they could be implemented by a distributed computer system comprising for instance two or more computers operatively connected to each other (for instance, one for the characterisation of the types of scrap, and another one for determining the amounts to be charged for next heat and for controlling the EAF and loading devices), and possibly comprising remote (and possibly distributed) computing resources such a cloud computing resources.

[0133] The characterization device 1 may more particularly be configured for executing the method represented in figure 4. This method comprises steps s1 to s7.

[0134] Step s1 is a step of acquiring the operation data OD. Step s2 is a step of determining the characteristics of the different types of scrap CR, using the method for characterizing above described.

[0135] Step s3 is a step of outputting all or some of the characteristics CR thanks to the Human Machine Interface 3.

[0136] Step s4 is a step of testing if the width (for instance ^k,i) of the probability distribution^^ ([rk]s,i|OD) becomes higher than a given threshold, or if it has an increase that becomeshigher than a given increase threshold, in which case an alarm signal is automatically emitted by the characterization device.

[0137] Step s5 is a step of determining the manufacturing-suitable scrap amounts a"s,i, i=1..I, using the model M, using the characteristics of the different types of scrap CR, and based on the maximum admissible residual content [rk]max(which is acquired by the characterizing device 1, and may change from one heat to another).

[0138] Step s6 (optional) is a step of transmitting the set of manufacturing-suitable scrap amounts to the Human-Machine Interface (HMI) of the characterizing device, and controlling the HMI for executing a step of validation or adjustment of this set of scrap amounts by an operator.

[0139] Step s7 is a step of transmitting manufacturing instructions to the loading controller 17 of the EAF, to control the loading devices of the EAF so that the manufacturing-suitable amounts of scrap a"s,i, i=1..I are charged in the EAF to achieve a heat.

[0140] From a temporal point of view, steps s1 and s2 may be repeated regularly, or even continuously, for instance once every day (the series of heats, analyzed each time the method for characterizing is executed, being then a one-day long series of heats). It enables to monitor the types of scrap employed, and to detect possible drifts or evolutions. Steps s5 to s7 may be executed each time a new heat is planned and then achieved. Steps s5 to s7 may also be executed less often, that is just for some of the heats achieved with the EAF.

[0141] The instant technology concerns also a steel making facility that comprises: the EAF 10, the sensors 12, 13, the characterizing device 1, and possibly the loading controller 17.

Claims

CLAIMS 1. A method for characterizing different types of scrap (si), charged in an Electric Arc Furnace (10) for producing steel, the Electric Arc Furnace being designated hereinafter as the EAF, the method comprising: - (s1) acquiring operation data (OD) that comprise, for each heat (hj) of a series of successive heats (hj) achieved with the EAF: j o for each type of scrap (si), a measured scrap amount (as,i) charged in the EAF, j o for at least one residual element (rk), a measured residual content ([rk]LS) of said element in a liquid steel (S) output by the EAF (10), for said heat (hj), - (s2) determining, for two or more of said types of scrap: data representative of a probability distribution (^^ ([rk]s,i|OD)) for the residual content of said residualelement (rk), in the type of scrap (si) considered, given the operation data (OD) acquired, the data representative of said probability distributions being determined from the operation data (OD) acquired and using a model of operation (M) for the EAF, inputs of the model of operation (M) comprising at least, for each type of scrap (si): o an input scrap amount (as,i) charged in the EAF, and o an input residual content ([rk]s,i) for said residual element in said type of scrap (si), and wherein outputs of the model of operation, determined from said inputs, comprise at least: for said residual element, an output residual content ([rk]LS) for said residual element in an output liquid steel produced by the EAF.

2. A method according to claim 1, further comprising, for said two or more types of scrap: determining an estimated residual content ([rk̂]s,i) in the type of scrap considered, and, optionally, determining a quantity (^k,i) representative of a width of the probability distribution for the residual content of said residual element in the type of scrap considered.

3. A method according to any one of the preceding claims wherein, for the two or more types of scrap, the data representative of the probability distribution ^^ ([rk]for the residualcontent in the type of scrap considered is determined:- based on a prior probability distribution ( ^^^^^^^^^^^^([rk]s,i) ) for the residual content in the type of scrap considered, - and by computing, for different possible values of the residual content ([rk]s,i) in the type of scrap (si) considered, and using the model of operation (M) of the EAF: a probabilitiy ( ^^ (OD|[rk]s,i) ) to obtain the operation data (OD) acquired, given thevalue considered for said residual content.

4. A method according to claim 3 wherein, for the two or more types of scrap, said prior probability distribution ( ^^^^^^^^^^^^([rk]s,i) ) is determined at least from a residual content range, specified for a scrap category to which said type of scrap belongs, the residual content range for said scrap category being specified in a normalized scrap specification.

5. A method according to claim 3 or 4 wherein, for the two or more types of scrap, said prior probability distribution is determined at least from residual content specifications provided by a supplier of said type of scrap.

6. A method according to anyone of claims 3 to 5 wherein, for the two or more types of scrap, said prior probability distribution ( ^^^^^^^^^^^^([rk]s,i) ) is determined at least from a previous probably distribution of the residual content in said type of scrap, the previous probably distribution having been determined from heats achieved before said series of heats.

7. A method according to anyone of the preceding claims wherein a total amount of scraps charged in the EAF comprises of respective proportions of the different types of scrap, and wherein the ensemble of said respective proportions varies from one of the heats to another, for at least some of said heats (hj).

8. A method according to claim 7 wherein the number (J) of heats (hj) in said series of heats is higher than or equal to the number (I) of types of scrap (si).

9. A method according to anyone of the preceding claims, wherein data representative of the probability distribution ( ^^ ([rk]s,i|OD) ) for the residual content of said residual element, inone of the types of scrap (si), given the operation data (OD) acquired, are determined for each of the types of scrap (si), and wherein the number (I) of types of scrap is equal to or above four.

10. A method according to anyone of the preceding claims, wherein the operation data (OD) comprise also, for each heat of the series of successive heats, a measured liquid steel amount (LSj) output by the EAF for said heat (hj).

11. A method according to the preceding claim, further comprising determining, for the two or more types of scrap: a probability distribution ( ^^(yi|OD) ) for a metallic yield (yi) of the type of scrap (si) considered given the operation data (OD) acquired, and optionally determining an estimated metallic yield (ŷi) for said type of scrap, the probability for the metallic yield being determined from the operation data acquired and using the model (M) of operation for the EAF, the inputs of the model of operation further comprising an input metallic yield for each type of scrap and the outputs of the model of operation further comprising an output liquid steel amount (LS).

12. A method according to anyone of the preceding claims, wherein the at least one residual element (rk) is one of: Copper Cu, Nickel Ni, Tin Sn, Molybdenum Mo, Chromium Cr, Aluminum Al, Manganese Mn.

13. A method according to anyone of the preceding claims: - wherein the operation data (OD) comprise also, for one or more sterile elements (tm), a measured sterile content ([tm] j LS) in the liquid steel (S) output by the EAF (10) for each heat (hj) of the series of successive heat, - the method further comprising determining, from the operation data acquired and using the model of operation for the EAF, for each type of scrap and for at least one of the sterile elements: odata representative of a probability distribution (^^ ([tm]s,i|OD) ) for the sterilecontent in the type of scrap considered, given the operation data acquired, and o optionally, an estimated sterile content ([t̂m]s,i) in the type of scrap considered.

14. A method according to the preceding claim: - wherein the operation data (OD) comprise also, for each heat (hj) of the series of successive heat and for one or more types of additive (adl, l=1..L): a measured additive amount (a j ad,l) charged in the EAF,- the method further comprising determining an estimated sterile content ([t̂m]ad,l) in each type of additive, for each of the one or more sterile elements, from the operation data acquired and using the model of operation for the EAF.

15. A method according to claim 13 or 14, wherein at least one of the sterile elements is one of: Calcium Ca, Magnesium Mg, Phosphorous P, Silicon Si, Sulphur S.

16. A method according to anyone of the preceding claims, further comprising controlling a Human Machine Interface (3) so that the Human Machine Interface outputs data representative of, or derived from the probability distribution (^^ ([rk]) for the residualcontent in each of said two or more types of scrap.

17. A method according to anyone of the preceding claims, further comprising: -testing if a width (^k,i) of the probability distribution (^^ ([rk]s,i|OD) ) for the residualcontent of said residual element in at least one of said two or more types of scrap, becomes higher than a given threshold, or if it has an increase that becomes higher than a given increase threshold, - if the result of said testing is positive, outputting an alarm signal automatically.

18. A method for determining manufacturing-suitable scrap amounts (a"s,i) of the different types of scrap (si, i=1..I), for a heat to come, the manufacturing-suitable scrap amounts being determined so that an expected probability distribution (^^^^^^^^^^_ℎ^^^^^^([rk])) for the residual content of said residual element in the liquid steel fulfils a target criteria which specifies a positioning of the expected probability distribution (^^^^^^^^^^_ℎ^^^^^^([rk])) relative to a target residual content in the liquid steel, or relative to a maximum admissible residual content in the liquid steel ([rk]max), the expected probability distribution being determined: - using said model of operation (M) of the EAF, and -based on the probability distributions (^^ ([rk]s,i|OD)) for the residual content of saidresidual element, for said two or more types of scrap, said probability distributions being determined by executing the method according to anyone of the preceding claims.

19. A method according to the preceding claim, further comprising transmitting manufacturing instructions to a loading controller (17) of the EAF, to control loading devices of the EAFso that the manufacturing-suitable amounts of scrap (a"s,i), determined according to the method of the preceding claim, are charged in the EAF.

20. Computer program comprising instructions whose execution on a computer (1) makes the computer to execute the method according to anyone of the preceding claims.

21. Electronic characterization device (1) comprising at least a processor and a memory (2), configured for executing the method according to anyone of claims 1 to 19.

22. Steel making facility comprising - an Electric Arc Furnace (10), - measuring devices (12, 13) for measuring amounts of different types of scrap charged in the Electric Arc Furnace (10) and for measuring an amount of liquid steel (S) output by the Electric Arc Furnace (10), - a chemical analyzer (15) for measuring, for at least one residual element, a measured residual content of said element in the liquid steel (S) output by the Electric Arc Furnace (10), - the characterizing device (1) according to claim 21, operatively connected to the measuring devices (12, 13) and chemical analyzer (15), - and, optionally, a loading controller 17 operatively connected to the characterizing device (1), for controlling loading devices.

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