Method for determining sets of concentrations of fuel markers

Abstract

Method for determining sets of concentrations of fuel markers A method for determining n sets of i concentrations of fuel markers to be used to mark n fuels

Description

[0001] METHOD FOR DETERMINING SETS OF CONCENTRATIONS OF FUEL MARKERS

[0002] TECHNICAL FIELD

[0003] The present invention is directed at a method for determining n sets of i concentrations of fuel markers to be used to mark n fuels.

[0004] BACKGROUND ART

[0005] An objective of the present invention is the provision of a solution to mark an enlarged number of fuels with a fixed number of fuel markers.

[0006] SUMMARY OF THE INVENTION

[0007] According to a first aspect, a method for determining n sets of i concentrations of fuel markers to be used to mark n fuels is provided, n and i being integers, n>2 and i>3, wherein

[0008] the i concentrations of fuel markers are designated as Mi, M2, ... , Mi,

[0009] the sum of all i concentrations for one fuel marker £, M,- is a constant c,

[0010] the n fuels are made of a first fuel group m and a second fuel group n2 such that n= m + n2, each set of i concentrations is defined as a point in i-dimensional space with coordinates {Mi, M2, ... , M} or as a point in (i-l)-dimensional space with coordinates {Mi, M2, ... , Mu}, wherein the points representing the m sets of i concentrations are designated as first points and the points representing the n2 sets of i concentrations are designated as second points;

[0011] the method comprising:

[0012] determining the first points such that they are coplanar in a first plane or located in a first band around the first plane within a distance c / 5 of the first plane;

[0013] determining the second points such that they are coplanar in a second plane or located in a second band around the second plane within a distance c / 5 of the second plane, the second plane being parallel to the first plane, and such that there are never more than two second points that are aligned, wherein

[0014] there are never two or more second points aligned with one first point.

[0015] According to an embodiment, all first points are

[0016] coplanar in the first plane,

[0017] randomly scattered within the first band,

[0018] coplanar in a plane parallel to the first plane and located within the first band, or provided on a portion of a sphere or spheroid and located within the first band; and / or wherein all second points are

[0019] coplanar in the second plane,

[0020] randomly scattered within the second band,

[0021] coplanar in a plane parallel to the second plane and located within the second band, or provided on a portion of a sphere or spheroid and located within the second band.According to a further embodiment, to ensure there are never more than two second points that are aligned in the second plane, the second points are placed at vertices of a convex polygon or on a circle in the second plane.

[0022] According to a further embodiment,

[0023] the first plane is a surface in which Z;=i

[0024]

[0025] = d , wherein j is an integer, d is a constant integer and d<c; and / or

[0026] the second plane is a surface in which

[0027]

[0028] Mk= e , wherein k is an integer, e is a constant integer, e<c, and optionally wherein d<e.

[0029] According to a further embodiment, the first points are spread, in particular evenly, over a first triangle formed on the first plane and / or the second points are spread, in particular evenly, over a second triangle formed on the second plane.

[0030] According to a further embodiment, the first plane and / or the second plane is located such that none of the values of the i concentrations of fuel markers Mi, M2, ... , Mu drop below respective detection levels thereof.

[0031] According to a second aspect, a method for determining n sets of i concentrations of fuel markers to be used to mark n fuels is provided, n and i being integers, n>2 and i>3, wherein

[0032] the i concentrations of fuel markers are designated as Mi, M2, ... , Mi,

[0033] the sum of all i concentrations for one fuel marker £, M,- is a constant c,

[0034] the n fuels are made of a first fuel group m and a second fuel group n2 such that n= m + n2, each set of i concentrations is defined as a point with coordinates {Mi, M2, ... , Mi} or {Mi, M2, ... , Mu} in a preferably orthonormal reference frame, wherein the points representing the m sets of i concentrations are designated as first points and the points representing the n2 sets of i concentrations are designated as second points;

[0035] the method comprising:

[0036] determining the locations of the first and second points in the reference frame, such that in the reference frame, there is no linear relationship and / or no linear relationship within a margin of c / 25 between:

[0037] more than two second points; or

[0038] between more than one first point and one second point.

[0039] According to an embodiment, the locations of the first and second points in the reference frame are further determined, such that in the reference frame, there is no linear relationship and / or no linear relationship within a margin of c / 25 between:

[0040] more than two first points.According to a further embodiment, the first and second points are all located on a sphere; all first points are all located on a sphere, with the second points being located within the sphere; and / or

[0041] all second points are all located on a sphere, with the first points being located within the sphere.

[0042] According to a further embodiment, i=3 or i=4.

[0043] According to a further embodiment, the steps of determining the locations of the first and second points are performed in a computer-implemented trial and error approach including:

[0044] (51) temporarily placing the first and second points in the orthonormal reference frame, in particular in a random fashion;

[0045] (52) verifying the compliance of the temporarily placed first and second points with the criteria regarding the first and second points; and

[0046] (53) if the criteria regarding the first and second points are satisfied, maintaining the temporarily placed first and second points as final positions of the first and second points, and if the criteria regarding the first and second points are not satisfied, repeating the steps (S1) to (S3).

[0047] According to a third aspect, a method of marking n fuels with n sets of i concentrations of fuel markers determined according to the first aspect, the second aspect, or any embodiment thereof is provided, wherein n and i are integers, n>2 and i>3.

[0048] According to a fourth aspect, a computer-implemented program product stored on a machine-readable medium and comprising machine-readable instructions for executing the method according to the first aspect, the second aspect, or any embodiment thereof.

[0049] According to a fifth aspect, a device for determining n sets of i concentrations of fuel markers to be used to mark n fuels is provided, n and i being integers, n>2 and i>3, the device being configured to perform the method according to the first aspect, the second aspect, or any embodiment thereof.

[0050] The present invention will be described more fully hereinafter with reference to the accompanying figures in which like numerals represent like elements throughout the different figures, and in which prominent aspects and features of the invention are illustrated.

[0051] BRIEF DESCRIPTION OF THE FIGURES

[0052] Fig. 1 - Fig. 4 show a 3D visualization of the solution;

[0053] Fig. 5 - Fig. 14 show a 4D visualization of the solution; and

[0054] Fig. 15 - Fig. 18 show an optimization of the position of the keys.DETAILED DESCRIPTION

[0055] In the example below, we describe a fuel market including a number n of fuels, in which each of these fuels is marked by a mixture of the same i fuel markers, which are provided at different concentrations in each fuel. In the example described herein, i=4, but any other value for i can be chosen (given i>3). For example, if i=3, the problem reduces to 3 dimensions, and if i>5, the problem becomes at 5- or more dimensional problem.

[0056] The fuels are marked such that the identity of the fuel can be determined by analysing the concentration of the (here) 4 fuel markers therein. Further, in case of an illegal mixture of two fuels (adulteration), by analysing the concentration of the 4 fuel markers in the mixture, it can be uniquely determined which two fuels were mixed. The following describes in particular how the concentrations of 4 fuel markers for each of the n fuels are determined

[0057] In the described market, there are 5 big fuel brands (first fuel group m ) that represent -71% of the market share. The remaining -30 smaller fuel brands (second fuel group 02), represent -29% of market share. Big brands may offer several fuel qualities while small brands offer only one fuel quality.

[0058] The expected adulteration cases which can be detected with the solution presented herein are when big brands are adulterated by small brands or other big brands. The detection objective is of 10% or more of small brand fuel mixed into big brand’s fuel.

[0059] Four markers M1 - M4 are available and used together. The naming of the marker is not relevant, but we have chosen to name the marker with the biggest GCMS (gas chromatography-mass spectrometry) detection level M4. The markers M1 to M4 each have a respective GCMS detection level between 0.1 and 0.7 ppm.

[0060] In the present example, the total marking level M1+M2+M3+M4 always sums upto 3 ppm. The value of 3 ppm is chosen as a mere example, and any other total concentration could be chosen, preferably between 1 and 5 ppm.

[0061] Marker distinction can be performed by GCMS in the lab. The detection is performed at a GCMS accuracy of 2% relative error. The system relative error (GCMS + other) is of 5% relative error.

[0062] The goal is to determine whether there is a fraud. The only fraud we are expected to detect is if there is more than 10% of adulteration in that specific, known in advance quality fuel. We want to determine the adulteration level. We further want to determine what fuel was used to adulterate that top brand.We reduce the problem to 3 dimensions to allow for easy visualisation and extend it later to 4 dimensions. In this case, the total marking constraint is reformulated as M1+M2+M3=3 ppm. This corresponds to the equation of the plane M1.x + M2.y + M3.z = 3 ppm, which is represented in Fig.

[0063] 1. Because all compliant marked fuels satisfy the same constraint, every possible measurement lies on this plane.

[0064] For example, in Fig. 1, 'x' represents the point (x,y,z)=(0.8, 0.8, 1.4) and 'o' the point (x,y,z)=(2, 1, 0).

[0065] Furthermore, if two different compliant brands are marked, which is the only case we consider, the total marker concentration of the mix will also total 3 ppm and therefore will lie on the same surface.

[0066] Let's formally define the following naming convention: the big players keys are named B, with individual big player keys being named Bi (0<i<n2, where n2 is the number of big player keys), and the small players keys are named A, with individual small player keys being named Ai (0<i<ni , where ni is the number of small player keys).

[0067] We can check that visually in Fig. 2. Let's set the marking one big brand (B) to (0.8, 0.8, 1.4), shown as 'x' in Fig. 2. Now let's define one small player adulterant (A) as (2, 1, 0). We can choose an adulteration level of 30% (alpha = 0.3) and see where the resulting mix is located on the plot below. We name that mix M (for Mix).

[0068] We can make the following observations:

[0069] • As expected, the mix is located on the same plane surface as A and B, and

[0070] • A, B and M are aligned.

[0071] With the prior knowledge of B and the measurement M, we can find what the adulterant A could be by drawing a line that goes through B and M. By extending it, that line must pass through A (in reality, due to noise, close to A). And therefore if point A is indeed on the line (or very close), it is the adulterant. We can compute the amount of adulteration by measuring the distances between A B and M.

[0072] On the field, we have different small brands that may be potential adulterants. Let's denote them A1 A2 ... Ani. However, with the previous approach, to be able to determine which adulterant is used, no more than one Ai must be collinear with B and M. Fig. 3 and Fig. 4 show an example where we purposedly select collinear adulterants.

[0073] In this situation, B, M A1 and A2 are collinear. Thus, from B and M only, it's impossible to know whether M is the result of a mix between B and A1 or between B and A2. Indeed, M could be theresult of a 50 / 50 adulteration of B with A2, or a 30 / 70 adulteration of B with A1. Both mixes would result to the same exact M. We say that the two cases are "confounded".

[0074] This limitation imposes a strong requirement on the relative location of B and A: when deciding where to place keys for B and for A on the locus of the keys (the blue plane above), among all the segment formed by B1 and all the A, none of them must be collinear. Same for B2: among all the segment formed by B1 and all the A, none must be collinear. An so forth for all Bi.

[0075] For completeness it is indicated that if the Bi were not expected to be mixed together, it can be convenient to distribute the Ai uniformly on the largest circle that can be fit in the locus. All the Bi could be located inside the circle, close to its centre. In this way, we maximize the angle between the Bi and the Ai and reduce collinearities of the adulterants. But, the assumption that allows us to reject the case of Bi adulterating other Bi is usually not valid.

[0076] One geometric solution that enforces the absence of collinearity is to put all keys, regardless if they are Ai or Bi on a circle or sphere. That way, no pairs of point are ever aligned with another point of the polygon. The conclusion is that it severely reduces the amount of available keyspace, unless there is no need to detect small quantities of adulteration.

[0077] In this regard, the fourth dimension (4D) can be considered. It is still possible to think in 3D. However, for the 4D case, the requirement for the locus of all the possible key is no longer M1 + M2 + M3 = 3ppm, but M1 + M2 + M3 <= 3ppm. This represents a volume, as shown in Fig. 5.

[0078] Indeed, any point within that volume will have a total marker concentration contained within 0 and 3. We can always add another marker (M4) to complete the sum of all markers to 3ppm. In fact, every plane that is parallel to blue plane of Fig. 1 is the locus of all the keys with a given, fixed amount of M4. As shown in Fig. 6, the locus where M4 = 0 is the blue plane, the locus where M4 = 1 is the green plane, the locus where M4 = 1 is the pink plane, and the locus where M4 = 3 degenerates to the origin point.

[0079] If we recap what we know so far:

[0080] • The fuel from the small players are not adulterated withing each other. This translate that we don't care about the collinearity of the points A among themselves.

[0081] • The Bi can be adulterated by other Bi or Ai, therefore we must ensure the non-collinearity between all the BA and BB vectors.

[0082] One suggested geometry that solves that issues could be:

[0083] • All A are located on a plane. With no constraint on alignments, this is not an issue because adulteration between an A and another A is not a use case.• All B are in another parallel plane. We know that a B must never be aligned any pair of A. Thus, If we put the B in a different plane than the A, that constraint is fulfilled wherever we put the Bi or the Ai as long as they stay on their respective plane.

[0084] • All B must never be aligned with two other B. If we put them at the vertices of a convex polygon, that constraint is fulfilled.

[0085] We also have to consider that the concentration of the markers must not drop below their respective minimum detection levels. Let's update our plots to take this into account, and we get Fig. 7. The blue volume in Fig. 7 is the locus of all the key with the constraint that M1, M2, and M3 are within their detection level. M4 is not. M4 has a substantial detection level and this will reduce the surface of the blue plane. We will see later that this is not an issue for the detection.

[0086] The A keys should be spread across the blue triangle with a maximum coverage. A simple triangular tessellation of the space is the optimal approach.

[0087] The problem is simplified if we choose the number of A key to be a part of: the series

[0088]

[0089] : 3, 6, 10, 15, 21, 28, 36, .... Let's chose 28 here (n=7). This gives the location of the A keys as shown in Fig. 8. Some keys are too far away from the centre of the triangle and are expected to be the most challenging ones. Removing the keys at the tips, we obtain Fig. 9.

[0090] Concerning the location of the B keys, as explained earlier, if we put the B keys on a convex polygon, they won't align with each other.

[0091] We have more freedom to choose the amount of B keys, but the lower the better. Let's choose 6 B keys, as shown in Fig. 10.

[0092] Now we have to choose the location of the green plane that will contain all the B keys. There is a trade-off to make here. The more we space the blue and the green plane apart, the more robust to noise the system is when considering B fuels adulterated with A fuels. But, the more we space the blue and the green plane apart, the smaller the green place becomes. Therefore the performances and robustness of the system decreases when considering B fuels adulterated with other B fuels.

[0093] Fig. 11 shows a superposition of Fig. 9 and 10 and can be used to visualize adulterations of a B with an A. We assume that B is chosen as shown in Fig. 12. The mixture M point is located above the green plane, as shown in Fig. 13.

[0094] If we draw a line through B and M it must pass through the A that was used to adulterate the B (see Fig. 14). We see that the A that was used in the mix is the one that is on that line.One optimal way of locating the keys in a place where they are in the largest. This is the definition of a circle. In this case, the optimal centre is located where we can create the circle with the largest radius to cover most of the surface. All the B must be located inside the circle, as far as possible to the A. This means that all the B are close to the centre of the circle, slightly apart, just enough that we can classify them correctly when not adulterated.

[0095] If these constraints are met, all the goals are covered:

[0096] • We can detect a fraud. All non-adulterated sample has a different key. If we don't measure the correct key, there is a fraud.

[0097] • We are able to return the adulterant identity. By finding which A is aligned with the expected B and the M, we return the A used in the mix.

[0098] • We are able to return the adulteration level. Knowing the location of A, B, and M, we can measure an adulteration level Alpha.

[0099] To test the performances, we must take into account the errors, otherwise the system will always return a 100% accuracy. In order to do so, we must interpret the error values given to feed the model accurately. The systematic error of the marking and the measurement instrument is expected to be 0 due to calibration. The added noise is gaussian with some standard deviation. Two error sources are included in the model:

[0100] • The marking error

[0101] • The detection error

[0102] The key location can be further optimized. We have guessed the distance we moved the B keys on the edge of the triangle. Let's numerically optimize that distance by simulating various distances and keep the best one. This is shown in Fig. 15. We observe that at a distance of 0.1 , we are at the best choice. Let's fix the distance to that value.

[0103] The location of the green plane was also guessed. Let's simulate various location for it (Fig. 16) and keep the best. Fig. 16 shows all the simulated location for the green plane and Fig. 17 displays the performances vs the location of that plane. The blue line represent the accuracy to identify the correct adulterant when a B fuels was adulterated with another B fuel. The red line represents the accuracy to identify the correct adulterant when a B fuels was adulterated with an A fuel. The amount of M4 we put on the B keys that has not been moved in the previous section is set as 1.2 based on Fig. 17.

[0104] Now that everything is fixed, we can recompute the exact location of all the keys using the chosen parameters, as shown in Fig. 18. This allows us to correctly identify the adulteration of a B key with an A key with an accuracy of 92.7%.The above disclosed subject-matter is to be considered illustrative, and not restrictive, and serves to provide a better understanding of the invention defined by the independent claims.

Claims

CLAIMS1. A method for determining n sets of i concentrations of fuel markers to be used to mark n fuels, n and i being integers, n>2 and i>3, whereinthe i concentrations of fuel markers are designated as Mi, M2, ... , Mi,the sum of all i concentrations for one fuel marker £, M,. is a constant c,the n fuels are made of a first fuel group m and a second fuel group n2 such that n= m + n2, each set of i concentrations is defined as a point in i-dimensional space with coordinates {Mi, M2, ... , Mi} or as a point in (i-l)-dimensional space with coordinates {Mi, M2, ... , Mn}, wherein the points representing the m sets of i concentrations are designated as first points and the points representing the n2 sets of i concentrations are designated as second points;the method comprising:determining the first points such that they are coplanar in a first plane or located in a first band around the first plane within a distance c / 5 of the first plane;determining the second points such that they are coplanar in a second plane or located in a second band around the second plane within a distance c / 5 of the second plane, the second plane being parallel to the first plane, and such that there are never more than two second points that are aligned, whereinthere are never two or more second points aligned with one first point.

2. The method according to claim 1, wherein all first points arecoplanar in the first plane,randomly scattered within the first band,coplanar in a plane parallel to the first plane and located within the first band, or provided on a portion of a sphere or spheroid and located within the first band; and / or wherein all second points arecoplanar in the second plane,randomly scattered within the second band,coplanar in a plane parallel to the second plane and located within the second band, or provided on a portion of a sphere or spheroid and located within the second band.

3. The method according to claim 1 or 2, wherein to ensure there are never more than two second points that are aligned in the second plane, the second points are placed at vertices of a convex polygon or on a circle in the second plane.

4. The method according to any one of claims 1 to 3, whereinthe first plane is a surface in whichMj = d , wherein j is an integer, d is a constant integer and d<c; and / orwherein the second plane is a surface in whichMk =e, wherein k is an integer, e is a constant integer, e<c, and optionally wherein d<e.

5. The method according to any one of claims 1 to 4, wherein the first points are spread, in particular evenly, over a first triangle formed on the first plane and / or the second points are spread, in particular evenly, over a second triangle formed on the second plane.

6. The method according to any one of claims 1 to 5, wherein the first plane and / or the second plane is located such that none of the values of the i concentrations of fuel markers Mi, M2, ... , MM drop below respective detection levels thereof.

7. A method for determining n sets of i concentrations of fuel markers to be used to mark n fuels, n and i being integers, n>2 and i>3, whereinthe i concentrations of fuel markers are designated as Mi, M2, ... , Mi,the sum of all i concentrations for one fuel marker £, M,- is a constant c,the n fuels are made of a first fuel group m and a second fuel group n2 such that n= m + n2, each set of i concentrations is defined as a point with coordinates {Mi, M2, ... , Mi} or {Mi, M2, ... , Mu} in a preferably orthonormal reference frame, wherein the points representing the m sets of i concentrations are designated as first points and the points representing the n2 sets of i concentrations are designated as second points;the method comprising:determining the locations of the first and second points in the reference frame, such that in the reference frame, there is no linear relationship and / or no linear relationship within a margin of c / 25 between:more than two second points; orbetween more than one first point and one second point.

8. The method of claim 7, wherein the locations of the first and second points in the reference frame are further determined, such that in the reference frame, there is no linear relationship and / or no linear relationship within a margin of c / 25 between:more than two first points.

9. The method of claim 7 or 8, whereinthe first and second points are all located on a sphere;all first points are all located on a sphere, with the second points being located within the sphere; and / orall second points are all located on a sphere, with the first points being located within the sphere.

10. The method according to any one of claims 1 to 9, wherein i=3 or i=4.

11. The method according to any one of claims 1 to 10, wherein the steps of determining the locations of the first and second points are performed in a computer-implemented trial and error approach including:(51) temporarily placing the first and second points in the orthonormal reference frame, in particular in a random fashion;(52) verifying the compliance of the temporarily placed first and second points with the criteria regarding the first and second points; and(53) if the criteria regarding the first and second points are satisfied, maintaining the temporarily placed first and second points as final positions of the first and second points, and if the criteria regarding the first and second points are not satisfied, repeating the steps (S1) to (S3).

12. A method of marking n fuels with n sets of i concentrations of fuel markers determined according to any one of claims 1 to 11 , wherein n and i are integers, n>2 and i>3.

13. A computer-implemented program product stored on a machine-readable medium and comprising machine-readable instructions for executing the method according to any one of claims 1 to 12.

14. A device for determining n sets of i concentrations of fuel markers to be used to mark n fuels, n and i being integers, n>2 and i>3, the device being configured to perform the method of any one of claims 1 to 11.

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