Method and system for detecting a change in radiological activity

Abstract

The invention relates to a method for processing a detection signal delivered by a radiation detector, comprising: the calculation of reference variation indicators during a phase of detector exposure to radiological background noise alone; the calculation of a current variation indicator ( ) during a phase of potential detector exposure to a change in radiological activity; the comparison (TST) of the current variation indicator ( ) to a threshold function of a statistic ( ) of a distribution of the reference variation indicators; and wherein the calculation of each of the reference variation indicators and the current variation indicator comprises: a smoothing (F1) of a pulse count signal ( ) of pulses contained in the detection signal; the calculation (IC) of a difference ( ) between a simple exponential smoothing and a double exponential smoothing of the smoothed count signal ( ). Figure for the abstract: Figure 2

Description

Title of the invention: Method and system for detecting a change in radiological activity. Technical field

[0001] The field of the invention is that of online detection of changes in radiological activity regime. Previous technique

[0002] Conventional industrial systems dedicated to the detection of radioactive sources rely on triggering a radiological alarm, itself based on the evolution of the nuclear count provided by acquisition and processing electronics downstream of a radiation sensor. More specifically, the alarm is triggered as soon as the online updated value of said count exceeds a triggering threshold, which is determined according to the amplitude of the in-situ radiological background, as well as certain assumptions made regarding the statistical distributions that can model the different signals.

[0003] For the detection system to be sufficiently sensitive to the more or less rapid passage of a radioactive source carrier, depending on whether it is a pedestrian or a vehicle, a primary constraint obviously concerns the implementation of a high-volume radiation sensor at a reasonable cost, typically a gaseous medium or a plastic scintillator. However, optimizing the sensitive volume proves to be an insufficiently effective tactic when the signal-to-noise ratio (classically considered here as the count induced by the mobile radio transmitter divided by the square root of the count attributable to the background radiation) tends towards excessively low levels, typically between one and ten. In order to improve the compromise between detection sensitivity and its specificity with respect to fluctuations in the background radiation, the only technologically viable solution is, therefore, to work on the detection procedure itself.

[0004] A first strategy consists of taking advantage of the characteristic spectral signatures of expected radioisotopes. However, the detection of radio emitters is subject to a significantly more stringent time constraint than their identification: detection must be carried out on the scale of a second, whereas identification only needs to be performed on the scale of a minute. Furthermore, radiological detection is essentially an "all-around" detection, which could be detrimental if it were subordinated to any radioisotopic preconceptions.

[0005] The conventional approach therefore consists of (i) applying to the nuclear count, updated at regular time intervals, a filtering process aimed primarily at reducing high frequency fluctuations, which filtering (ii) makes it possible to detect a change in radiological activity by means of a statistical test that is both reliable and sensitive.

[0006] In the case where the expected value of the counting intensity underlying the measurement is constant, the maximum likelihood estimator of this intensity is simply given by the arithmetic mean of the counts integrated over a given time range. The most widely used counting filter, called a moving average filter, directly uses this estimator to provide, at each measurement update time, a smoothed estimate of the current count.

[0007] Such a filter offers increasingly satisfactory accuracy as its temporal depth increases, while it can only reproduce an abrupt change in radiological activity if it has a temporal extension of the same order of magnitude as that of said change in regime. In practice, this leads to distinguishing two modes of implementing moving average filtering: the first, in which the temporal depth of the smoothing is fixed so as to exclusively satisfy a constraint relating to the system's response time to an abrupt variation in the counting intensity; the second, in which the temporal depth of the smoothing evolves so as to exclusively satisfy a constraint relating to the accuracy of the current estimate.

[0008] Methods based on the optimization of linear or finite impulse response filters encounter, in the presence of sufficiently abrupt changes in activity to be assimilated to steps in counting intensity, the limits of their ability to guarantee an acceptable compromise between response time and accuracy of the estimate.

[0009] These limitations have led to the implementation of nonlinear signal filtering approaches, specifically designed to reproduce, with the best possible compromise between response time and accuracy, a step or steep ramp in the counting intensity. However, the signals produced at the output of such nonlinear filters, no longer being mathematically described by statistical laws that are as well-understood or as repeatable, are less readily amenable (i) to new filtering operations based on Poisson statistics, and (ii) to classical procedures for detecting a change in regime in radiological activity.To address problem (i), namely, designing a second-level filter for the pre-filtered counting signal which still exhibits high-frequency fluctuations, some authors have turned to tools borrowed from economic and financial analysis and adapted to monitoring, or even anticipating, trends underlying highly noisy and continuously updated flows. The most notable of such tools is... Brown's double exponential smoother or filter, whose formulation is based on a linear combination of results from double and single exponential filtering.

[0010] R. Coulon, J. Dumazert, V. Kondrasovs, E. Rohée, S. Normand, “Estimation of nuclear counting by a nonlinear filter based on a hypothesis test and a double exponential smoothing”, IEEE Transactions on Nuclear Science, Vol. 63, Iss. 5, pp. 1-6, 2016, demonstrates the effectiveness of such a second-level filtering on nuclear counting signals previously filtered using the nonlinear smoothing with a centered significance test (CST). This article, however, does not propose any procedure for detecting a change in radiological activity. Description of the invention

[0011] The invention aims to provide a technique for detecting changes in radiological activity regime that is both sensitive to slight changes in radiological activity (for example with a signal-to-noise ratio of the order of four) and rapid changes (for example with a carrier moving at a speed close to 4 km / h in front of a detection portal monitor), and robust against high-frequency fluctuations in the counting signal.

[0012] To this end, the invention proposes a method for processing a detection signal delivered by an ionizing radiation detector, comprising: - the calculation of reference variation indicators during a qualification phase in which the detector is exposed to a single radiological background noise; - the calculation of a current variation indicator during a phase of use during which the detector is likely to be exposed to a change in radiological activity; - the comparison of the current variation indicator to a threshold set according to a statistic of a distribution of reference variation indicators; and - triggering an alarm when the current variation indicator is above the threshold.

[0013] The calculation of each of the reference variation indicators and the current variation indicator includes: - a smoothing, by means of an averaging filter on a counting history, of a pulse counting signal contained in successive samples of the detection signal; - the calculation of a difference between a first signal resulting from a simple exponential smoothing of the smoothed counting signal and a second signal resulting from a double exponential smoothing of the smoothed counting signal.

[0014] Some preferred but not limiting aspects of this process are the following: - said statistic is a standard deviation of a Gaussian interpolation of the distribution of the reference variation indicators; - each of the simple exponential smoothing and the double exponential smoothing uses a smoother parameter that is set according to the depth of the counting history of the averaging filter; - the averaging filter has a fixed historical depth, for example it is a moving average filter, a weighted moving average filter or an exponential moving average filter; - the averaging filter has adaptive history depth, for example it is a centered significance test filter. Brief description of the drawings

[0015] Other aspects, objectives, advantages and features of the invention will become clearer upon reading the following detailed description of preferred embodiments thereof, given by way of non-limiting example, and made with reference to the accompanying drawings in which:

[0016] - Figure 1 schematically illustrates an online measurement chain for a signal of ionizing radiation according to the invention;

[0017] - [Fig. 2] is a diagram illustrating different stages of a process conforming to the invention.

[0018] DETAILED DESCRIPTION OF SPECIFIC EMBODIMENTS

[0019] The invention provides a method for detecting changes in radiological activity in the environment of an ionizing radiation sensor, for example, consisting of one or more plastic scintillators. The method can be implemented by a processor of a data processing system, for example, associated with a portable radiation detection monitor.

[0020] Figure 1 represents a radiation detection device which includes a detector 1 capable of being exposed to a radioactive radiation signal 2 produced by a radioactive source 3. The detector 1 is coupled to a data processing system 4 to which it provides a detection signal Sd.

[0021] The data processing system 4 comprises: - a first module 5 responsible for acquiring and conditioning the detection signal Sd delivered by detector 1, - a second module 6 responsible for detecting and counting pulses contained in successive samples of the detection signal S^, so as to provide a counting signal and - a third module? responsible for processing the counting signal in order to deliver an AS alarm state.

[0022] The first module 5 may include a preamplifier / impedance matching assembly connected to detector 1 and an analog-to-digital conversion component providing a digitized detection signal to the second module 6.

[0023] The second module 6 is configured to detect and count the pulses contained in successive samples of the detection signal in order to provide the counting signal N. In particular, the second module can estimate a counting rate by means of a two-level Schmitt trigger on the first derivative of the detection signal Sd. The first level is a "high" trigger threshold. When the amplitude of the detection signal reaches this threshold, a gate opens and remains open until this amplitude passes a second level ("low" threshold). The size of the logic gate represents the dead time: any amplitude variation exceeding the first and second thresholds and occurring within this window is ignored. This architecture ensures a certain robustness against noise and prevents the same pulse from being counted multiple times.It should be noted that the closer the threshold values ​​are, the shorter the dead time, which extends the dynamic range of the counting intensity supported by the acquisition chain. However, if the thresholds are too close, the risk of multiple triggers during the same pulse becomes significant, especially in the presence of large fluctuations in the amplitude of the digitized signal. Counters are configured to increment on each rising edge of the gate and are reset, for example, every second. The output of the second module 6 is thus a count rate that can be updated every 100 ms over a sliding one-second window.

[0024] The third module 7 is configured to process the counting signal delivered by the second module in order to detect a change in radiological activity regime in the environment of detector 1.

[0025] As shown in Figure 2, the third module 7 includes a first block Fl for smoothing the counting signal by means of an averaging filter on a counting history. This smoothing, also referred to as first-level filtering in what follows, aims to provide a current estimate * Fm ju counting that is as accurate as possible. as accurately as possible given statistical fluctuations, and as accurately as possible in the presence of significant changes in the counting intensity underlying the measurement. It uses, for this purpose, previous counts N^, . stored in a historical depth m.

[0026] This history can have a fixed depth, the averaging filter being a moving average filter, a weighted moving average filter or an exponential moving average filter.

[0027] Alternatively, this history may have an adaptive depth, the averaging filter being a centered significance test filter.

[0028] A more detailed description of possible realizations of this Fl smoothing is given above.

[0029] The third module 7 includes a second IC block for calculating a MACD current variation indicator of the smoothed counting signal ^F»>. This indicator is based on the convergence-divergence of moving averages, itself dependent on two successive exponential filters.

[0030] More precisely, this MACDi indicator is calculated by taking the difference between a first signal 1 resulting from a simple exponential smoothing of the smoothed counting signal aC» and a second signal A 2 resulting from a double exponential smoothing of the signal ' ii smoothed counting: [coj!] macd^macd^") =p'-îf

[0032] With । = y .> i = .F. + . j_} 1. {)< $ £ (

[0033] And 2 = $F~. i>t [.1 = + ( ].d.) ^2. f)j

[0034] A more detailed description of this IC calculation is given above. It is notably indicated that each of the simple exponential smoothing and the double exponential smoothing uses a smoother parameter which can be fixed as a function of the depth m of the counting history of the first-level averaging filter.

[0035] The third module 7 includes a third TST block configured to compare the current MACD change indicator to a threshold set according to a statistic a(MACD) of a distribution of reference change indicators and to trigger an AS alarm; when the current change indicator is above the threshold.

[0036] This third module more specifically performs a hypothesis test based on comparing the current variation indicator with a statistic of the same indicator previously evaluated in the presence of only the radiological background in the area. In particular,

[0037] this statistic may be a standard deviation of a Gaussian interpolation of the distribution of the reference variation indicators.

[0038] A more detailed description of the operations performed by the third IC block is also given above.

[0039] The method according to the invention for processing the detection signal delivered by the detector comprises, more particularly, the calculation of reference variation indicators during a qualification phase in which the detector is exposed to a single radiological background noise, and the calculation of a current variation indicator during an operational phase in which the detector is likely to be exposed to a change in radiological activity. As previously stated, this method further comprises the TST block comparing the current variation indicator with a threshold set according to a statistical distribution of the reference variation indicators and triggering an alarm when the current variation indicator exceeds the threshold.

[0040] The calculation of each of the reference variation indicators and the current variation indicator is performed by the Fl and IC blocks and thus comprises: - a smoothing, by the Fl block using an averaging filter on a counting history, of the counting signal N, of pulses contained in successive samples of the detection signal; and - the calculation, by the IC block, of a MACD difference between a first signal resulting from a simple exponential smoothing of the smoothed counting signal fiF>« 1i and a second signal resulting from a double exponential smoothing of the smoothed counting signal ^F«'. 'i

[0041] The qualification phase also includes a step of determining the statistic of the distribution of the reference variation indicators. This determination may include calculating a Gaussian interpolation of the distribution of the reference variation indicators and determining a standard deviation of this interpolation.

[0042] The description above gives further details concerning a possible implementation of this qualification phase.

[0043] In one possible embodiment, the third module 7 may include a fourth block F2 configured to implement a so-called "second-level" filtering of the smoothed counting signal based on the two exponential filters used in the calculation of the aforementioned current variation indicator. This second-level filtering provides a filtered signal ^DEMA qUj, expressed, for example, as: ' i

[0044] y / > ^ema = DEMA(= + MACD. (32)

[0045] where the factor kr typically takes its values ​​between 1 and 3. Statistical model of nuclear counting

[0046] A simplified mathematical model of the nuclear counting signal as collected at the output of the second module is presented below. The major physical source of this signal corresponds to the decay of unstable nuclei leading to the emission of gamma radiation. An unstable parent nucleus X is likely, depending on its atomic number Z and its mass number A, to decay according to a given number of decay modes (or processes). For example, beta-minus decay is described by the general equation:

[0048] where 2^- is the time constant associated with the parent nucleus for the decay mode considered, Y denotes the daughter nucleus when it is produced in the ground state and y¥ this same nucleus when it is produced in an excited state. In this latter scenario, the nucleus y* gains its ground state by gamma emission (or internal conversion, or internal pair creation): Y * „ Z* Z'Y+qV (2)

[0049] Depending on the physical nature of the radiation detector, as well as the nuclear signal processing and nuclear information processing implemented within the instrumentation chain, it is therefore charged particles or neutral radiation (in an application to radiation detection portal monitors, gamma radiation accompanying the de-excitation of daughter nuclei) which are, respectively, directly and indirectly, detected and counted.

[0050] In order to model the time distributions associated with the detection and counting of nuclear events, the random variable T is introduced, which represents the waiting time for the decay of an unstable nucleus X. The radioactive decay of unstable nuclei is a homogeneous, rare, and memoryless phenomenon over time. The decay itself is assumed to be instantaneous. The variable T therefore follows an exponential distribution with parameter 2, the decay time constant of the radioisotope. The probability density of the waiting time, denoted t', before the occurrence of the decay of nucleus X is thus given by

[0051] v / >0, fT(t') = (3)

[0052] Starting from an initial instant to = 0, the occurrence of such a decay can be observed at any instant within a population of Nx unstable nuclei. The number of decays in an observation period [Q • / ] is denoted . The probability to observe the decay of a parent nucleus X on [() ; f], denoted PX^Y, is expressed in the form:

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[0066] t Px^O=lfTd)df=l-^< (4) zi. 1 g J Within the population of Nx unstable nuclei, the decays are mutually independent, so that the probability of observing a value n taken by A7(t) is described by a binomial law B(Nx, PX^Y(f)): / Nx \ \ HAS- / For Nx > 30, px^Y < 4 and Nx Px^( ) ( \~PX_*Y (4 ) ) - æ, conditions almost always met in radiological detection applications, Nx^r(t) converges in distribution to a Poisson random variable P( Nx PX^Y ( t ) ). Under the additional condition that 21 > 1, also verified as a general rule, we have: Px^Y(t) = leu ~ Ht (6) A l and therefore the parameter of the Poisson distribution Nx px^Y( t) ~ Nx at t. Ultimately, and subject to the above assumptions, PiN^U) =n) ~ WG) Consequently, the expected value and variance of the number of disintegrations occurring during the observation period [q; are equal to Nx 21. The number of counts 2V(^) recorded during the same observation period and associated with one of the particles emitted during the disintegration of nucleus X can finally be described by weighting the parameter of equation (7) by: - the branching ratio 7 of the particle that triggered the activation; - the extrinsic efficiency s of the detection chain (detector and first two modules) with respect to the emitted particle. The expected counting rate pt y Nx2, thus becomes the Poisson distribution factor that governs the number of counts recorded over the interval [() ; : V neN, ~ p^njnl eA(-p) (8) with p — P t the counting intensity. This mathematical model of nuclear counting is used in a first algorithmic building block of the process, namely the first level filtering (block Fl) of the instantaneous counting Ni. First-level filtering of nuclear counting (Fl block) At each instant h of signal acquisition at the output of the head electronics, defined such that 1() = 0) V i > 1, tM = t{+ At ( 9 ), the raw estimate of the counting intensity, denoted 'p., is given by: Vi>l, 3=^ (10)

[0067] where Nh denotes the number of pulses processed by the first two modules, is assumed to take its values ​​in the distribution described by equation (8).

[0068] The primary challenge of digital processing applied to instantaneous nuclear counting N is to return a continuously smoothed estimate of the counting rate that is both: the most accurate possible, that is to say, exhibiting the lowest possible variance V( / xj) for a given instantaneous counting intensity; and - the most accurate possible, that is to say, presenting the smallest deviation with the instantaneous counting intensity.

[0069] However, finding an acceptable compromise between precision and accuracy can prove difficult in the presence of abrupt variations in the counting intensity underlying the measurement, particularly in applications for monitoring radiological activity using RPM. Therefore, the invention proposes using an averaging filter on a counting history, various embodiments of which are mentioned below.

[0070] Moving average filter on m counts

[0071] The task assigned to a smoothing algorithm is to improve the estimation of the count rate, the raw version of which is represented by equation (10) above. The simplest and most commonly applied first-level filter is the moving average, denoted MA(N − m), over a historical depth denoted m. The accuracy of the count rate estimate can, in fact, be increased by using count values ​​acquired previously at the current time h: ... under the assumption that the counting intensity P, underlying the measurement, is constant, the maximum likelihood estimator being, in this case, simply the average of the data recorded and stored in memory in the history: [00721 ​​V i>mt p^MAiN, = (11)

[0073] where m therefore represents the temporal depth of the filter. The variance yl * Fm j associated with the estimated s Fm is then given by the equality Z y 100741 V v(pF-)=^ 100751 V i>mt + (12)

[0076] Where Cov denotes the covariance.

[0077] And is, in fact, inversely proportional to the size of the historical m.

[0078] Weighted moving average filter and exponential moving average filter on m counts

[0079] The counting intensity p(t) is likely to vary over time. An estimate of the acquisition time that effectively corresponds to the smoothed estimate of the counting rate 'p' is given by

[0080] w « îFm tm A , / i \ i>m-ï, tL at t ( 13 )

[0081] the counting values ​​(Nj used in equation (11) being identically weighted. It thus appears, within the framework of a moving average filtering, that minimizing variance y F™ j via increasing the size of the smoothing window m directly leads to an increase in the gap between h and ?Fm, a gap which, since the intensity is not constant, translates into a h degradation of the detector's response time.

[0082] To limit the influence of such a bias, the conventional approach consists of implementing fixed-variance filtering or finite impulse response (FIR) filtering, in which the older the counts Nj are weighted less heavily in the calculation of p. Among these, it is possible to use: - the weighted moving average (WMA^N? m), over a historical period m. For example, the weighted moving average used in technical analysis of financial data can be considered, where the weights decrease arithmetically according to the age index of the sample used. lWi (14)

[0085] The variance yf associated with the estimated ^F»< is then calculated in the same way r \Fi / i than in equation (12):

[0086] vv(^) = _±_ [E^ / Ay+2£^^^^^ (15) - the exponential moving average (EMA^Np m), over a historical depth m. Theoretically, this is a first-order infinite impulse response filter involving weights of exponentially decreasing amplitudes as a function of the age index of the sample used, and an approximation with a finite number of terms m is described as follows:

[0087] vp^'^EMAiN;, m^alNt+Aa) NiA+ ... + ( l-«) m2 N,-^+ ( 1-a) 100881 VHm-l p^EMA(Nt «n)=alLwl(la)^ Nj (16)

[0089] where the smoothing constant governs the index decay rate of the weights applied to the counts and is fixed such that m samples weigh / 7% in the calculated average

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[0091] a=l-(M)À (17) The variance associated with this last estimated / T® is following the same principles that are in equations (12) and (15)

[0092] V i>,nL (18)

[0093] Weighted and exponential moving averages are among the most widespread of the first level filters implemented in radiological detection chains, but can fail in the presence of an abrupt variation in the counting intensity ^), which can be likened to a step.

[0094] CST filter with a size history

[0095] A different approach consists of updating, after each new acquisition of a count value Ni, the denoted depth of the history implemented in the calculation of a moving average of the type described by equation (11) above (the size of the memory register for the counts being denoted m as in the preceding paragraphs). The recursive updating of Ni, which leads to the construction of a non-linear filter, is based on the result of a hypothesis test aimed at detecting any change in the counting intensity underlying the measurement. The null hypothesis Ho and the alternative hypothesis H can be defined as follows:

[0096] Ho: V (j,k) gj[im;+l; i]2, p(tj) = p(tk) = p ----- (19) H. - q ----p(t^=p^p^

[0097] A first definition of such a filtering method was introduced in the form of a sequential probability ratio test (SPRT). The performance of this method was evaluated under the assumption that the value of is known a priori. The approach was then generalized to the case where intensity is an unknown, via the formulation of a generalized likelihood ratio test (GLRT). An algorithmic approach, inspired by the two aforementioned references, proposes a nonlinear filter based on a hypothesis test, called a centered significance test (CST).

[0098] The aforementioned digital filtering is thus based on updating the integration window mi of a moving average filter at each measurement refresh time h, based on the result of a hypothesis test. More specifically, the test quantifies, over a sweep of integration sub-windows of sizes 1 < ε < ε, the deviation of a residual representing the stability of the estimate, under the conditions

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[0112] acceptance of a central distribution hypothesis (representative of a constant average activity). At the acquisition time h, the estimate of the current counting rate *Fm by The moving average is given by: p"' = MA(N„ml)=^ X, (20) A vector of estimates is then formed, whose components are ' ' !<£<»!, calculated as follows: V ^=MA(Nt k) U, ,,. x, (21) The vector (Apk) of residuals between these estimates and the reference estimate of Equation (20) is then constructed, the components of which are expressed in the form: ^pk=\p'nf-ptk\ (22) The components of ( will then be centered on 0 under the assumption 'r' \ <k<m; Ho and on a strictly positive value under the hypothesis H, as defined by equation (19). The significance of the values ​​of must, moreover, be assessed with regard to the variances y ZA ) 9^ are respectively associated with these: \ ' i / y ke J t , V( A p*) = V() + V(p'1)-2 Cov() V [E>„i+1A'7 + 2^^^^ + [^7=,-71+1^7 + 2 (Nj, ^= / -+,+^ / =+6+ / ^(^ / .^ / ) Am! A k / A t \ P* P' V pk) + 2 [A Np + $ .¾) ] (23) The detection threshold for a change in counting intensity P on the size k estimator at time h is, in fact, expressed in the form: V ke [ 1; nii J, SD* - ka ^2 v(Apk) (24) where ka is the broadening factor associated with a risk of false detection (0 < a < 1). The calibration function a = f(ka) can be constructed empirically. Subject to certain assumptions (sufficient counting statistic: pm' > 15', negligible stacking...), a normal approximation of the Poisson distribution allows us to identify L with a quantile of the centered normal distribution N^0 c( A pk^ ) • In an implementation presented below, ka = 1.63. The The number of significant deviations from a standard normal distribution detected in the vector (An*) is thus given by: [°113] L^Card^e [1;^-]] / Ap^SD^) (25)

[0114] The updating of the filter window, which is the basis of the nonlinear smoothing method, is then described by the following algorithm: Algorithm 1#:

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[0116] VZ > 1

[0117] If L{ = 0, then the hypothesis Ho is accepted. Assuming the counting intensity is constant, the size of the history is incremented to improve precision (Ç(pj) decreases) and without affecting the accuracy of the estimate: + 1;

[0118] If > 0, then the hypothesis Hf is accepted. It is then considered that the counting intensity has varied over the entire history, so that the size of the history must be reduced in order to improve the accuracy of the estimate (y) increases): mj+l = mt - Lj.

[0119] Using the CST filter, we thus have a formed couple at each instant acquisition h, by the estimated * F«> of the counting rate and the variance associated with the latter: [01201 V 1. (26) 101211 V i>L v(^-j (27)

[0122] where the value of mi, bounded on the left by mg = 1 and bounded on the right by the maximum depth m of the history, is updated at each iteration according to algorithm 1.

[0123] Variation indicator and trigger test (IC and TST blocks)

[0124] Following one of the smoothing operations described above, at each measurement refresh time t, a pre-filtered current count ^F«> is available. The trigger function of the process according to the invention, signaling a change in radiological activity, uses a trend indicator denoted MACD^ by analogy with the Moving Average Convergence Divergence (MACD) indicator. The latter, derived from the technical analysis of financial markets, is specifically designed to highlight the trend in price movements subject to high-frequency statistical fluctuations. The first step of this new processing implements two exponential filters.

[0125] MACD variation indicator (IC block)

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[0140] Exponential smoothing, an empirical tool for smoothing and, therefore, predicting chronologically ordered data affected by fluctuations, plays the role of a low-pass filter eliminating high frequencies from the input signal. The first exponential smoothing implemented in the process is a simple exponential smoothing applied to the smoothed count signal. It is described by: = V <>! = p^, 0<5,^l (28) where the smoother parameter represents the relative weight of the present. This weight logically decreases with the value of m (or mî in the case where the first level filter is the CST filter), and its amplitude depends on an adjustable intensity parameter W; 1-ew^ siF^e EMA^m)} vi> 1, 5;= ( (29) 1-e-^ siFm = CST In an implementation shown below, W = 0.07. The second exponential smoothing implemented in the process is a double exponential smoothing applied to the smoothed count signal ^F«'. It is described by: * i p(=P'--, V i > 1, % = 5,^+(1-5,) P^, o < s, g 1 (so) where ôi has the same value as that given by equation (29) and used in equation (28). Note that each of the simple exponential smoothing and double exponential smoothing methods uses a smoother parameter 5, which is fixed according to the depth (m or mi, depending on the filter type) of the filter's counting history. averager. The MACD trend reversal indicator is calculated using the two estimates calculated above: V i > 1, MACD{ = MACD ( p^ ) = / l1 -p^ (31) It is the temporal distribution of this indicator that is used to construct the trigger function of a change in radiological activity described in the following paragraph. Trigger test (TST block) According to the preceding paragraph, there is a distribution of MACD values ​​for each selected first-level filter. To construct the test for detecting a change in radiological activity, during the qualification phase, the counts acquired in the presence of only background radiation are filtered, before evaluating the MACD trend indicator based on the pre-filtered counts thus obtained. The series of MACD observations, which acts as a continuous numerical variable, is then fitted by a Gaussian distribution, for example using the Henry's line method. Provided that the coefficient of determination (or, equivalently, the reduced chi-square) of the fit is sufficiently close to unity, the standard deviation αMACD of the Gaussian distribution is used to parameterize the hypothesis test that governs the triggering of a radiological alarm according to Algorithm 2 below. The notation MACDj denotes the current trend indicator of the counting signal, and αAS represents the alarm state delivered by the TST block, which can, for example, take the values ​​0 (count intensity identical to that of the background noise) and 1 (increase in counting intensity, which may signal the presence of a radio transmitter to be detected). > k aÇMACDY al°rs a significant increase in the regime Algorithm 2#:

[0141] AS^O

[0142] V z > 1 [DUS] &iMACD. radiological activity is detected and AS, = 1;

[0144] Otherwise, no significant increase in the radiological activity regime is detected and AS) - 0.

[0145] The expansion factor kp is fixed such that, for the distribution adjusting the MACD of the radiological background, itself dependent on the first level filter selected, the false alarm rate noted FAR (for false alarm rate in English) is zero over a period of twenty-four hours, or kp — 5.7 in the implementation presented below.

[0146] Second-level filtering of the nuclear count (block F2)

[0147] The two successive exponential smoothings of the current pre-filtered count can also serve, as disclosed in the aforementioned article, to develop a second-level filtering of the counting signal, called double exponential filtering and abbreviated DEMA (for double exponential moving average in English), according to the equation:

[0148] = (32)

[0149] where fi 1 and MACDj are defined by equations (28) to (31), and where the factor kr takes ' i typically its values ​​are between 1 and 3 (kr = 2 in the implementation shown below).

[0150] The variance y / A DEMA \ associated with the final estimate of the current count is evaluated in several stages. We obtain, firstly and from equations (28) and (30), the variances

[0151] yi> 1 =(52 V^) + (1-¾)2 v(p^)+25i (1-¾) (33)

[0152] V i> I, v(p^) = ôj V^'”) + ( 1 -¾)2 V(pf) +2 Si ( I-Ô;) Cov^”, pj) (34)

[0153] The variance associated with the MACD estimation is then calculated as follows

[0154] v V(MACDi) v( / z)+V(p.2)-2^ pf} (35)

[0155] from which we can deduce:

[0156] vr > 1, p”EMA = V (p.1) + kj V (MACD;) + 2 kr Cov (p', MACD{) (3ô)

[0157] the details of the above calculations depending both on the method of generating current estimates and on the first level filter Fm implemented upstream of the double exponential smoothing.

[0158] Study of the execution time of an implementation of the third module

[0159] In order to study the execution time of a computer program implementing the functionalities of the third module, a dataset produced in the following manner was injected as input to it: - the counting intensity associated with the radiological background noise recorded by the detector is noted Pq and assumed constant over a number of samples ze II; 1000]; - a counting intensity step, occurring at i = 500 and with an amplitude A / ?, was superimposed on the intensity Pq. The counting intensity, underlying the simulated measurement, is thus given by Pi = π / ¾ for i < 500 and pi = ph + Ap for i ≥ 500. We set pb = 200 cs⁻¹ and Ap = 28.5 cs⁻¹. The signal-to-noise ratio, denoted RSN, is given by: [016°] RSB=^ (37) H

[0161] which, for a measurement update time At = 1 s, gives RSB = 2; - a random draw was performed in the Poisson distribution with parameter (JaF) a^n generate a frame of simulated counts 'l <i<1000 ( there-''1000 at the program's entry.

[0162] The execution time associated with processing the ith count is denoted ri and expressed in ps. Executing the program when the centered significance test filter acts as the first-level filter potentially provides access to the richest information, since the size of the history used is updated with each new count value.

[0163] It has been observed that the execution time ri follows an evolution analogous to the evolution, expected by construction, of the depth mi of the history used by the centered significance test filter. In order to verify the existence of a systematic evolution of the execution time Tt as a function of the size mi of the history used by the first-level filter, the size of the memory usable by the filtering algorithm was increased to m = 400. Such a systematic evolution has was confirmed, adjustable with a coefficient of determination -0.9998 By a quadratic function of mi: T; = 0.0432 ml + 1.3953 mi + 167.33 ( 38 )

[0164] Two conclusions can be drawn from this study. First, the program execution time is almost exclusively governed by the depth of the counting history used by the first-level filter, regardless of the filter's nature (since the arithmetic operations implemented by the different filters are identical). Second, the quadratic interpolation of r — / M allows us to fix the memory size m, usable by each of the first-level filters presented in the following paragraph, so that the program execution time remains negligible compared to the time step of updating the measure Ar, i.e., Vi, T. At. In practice, it is possible to impose the condition: y ≤ 21 < i%, which, given the value of At - 100 ms indicated in the paragraph dedicated to the data processing system architecture, amounts to imposing that: Vft, < 1 ms.The interpolation above shows that it suffices to limit the size of the memory used by a first-level filter to m = 100 to satisfy this condition.

[0165] Based on the preceding observations, it was decided to study the performance, with respect to the detection of an abrupt change in radiological activity regime, of coupling the following first-level Fm filters with a convergence and divergence of moving averages: - linear moving average filters on m counts MA(N^m), with me {2; 10; 20; 30; 40; 50; 100}; - linear filters with weighted moving average on m counts WMA(Ni? m) , with me {2; 1Q 20,30,40,50, 100}; - linear filters with exponential moving average on m counts EMAÇN^ m) with me IQ 20; 30; 40,50, 100} and « = 1 - ( 1-0.99) * ; - nonlinear filter with centered significance test CST ( N / ) , with a memory size m = 100.

[0166] Test bench dedicated to the experimental study of the detection procedure

[0167] In order to evaluate the performance of the change detection method To simulate the radiological activity regime of the invention, a test bench has been designed that, to a first approximation, simulates the passage of a pedestrian carrying a radioactive source in front of a radiation detection portal monitor. The portal monitor consists of plastic scintillators with a sensitive capacitance of 40 µL and eight photomultiplier tubes. To ensure the movement of radioactive sources at a controlled linear speed v, a motor with a rotational speed Q — [0; 200] rpm is used. is used, the motor disk having a radius R = 10 cm, as well as a cable of length L = 17 m from which said sources can be suspended. The relationship existing between the linear speed of the cable wound around the motor disk and the rotational speed of the latter

[0168] r = (39)

[0169] allows, by fixing O = 115 rpm, obtaining a passing speed v — 1.2 m.8'1 - 4.3 km.h1 in front of the monitor-gantry, both stable and representative of a pedestrian's speed. The setup allows for an arbitrary number of passes at regular intervals, fixed at N = 100 for practical reasons.

[0170] In order to induce abrupt changes in the radiological activity recorded at the monitor-portal, a Cs-137 source is used, the activity of which A = 483 kBq is given with an uncertainty expanded to three standard deviations ≥ 99.7% (≥ ) = 72 kBq. The greatest approach distance of the radioactive source to the nearest face of the monitor-portal is given by d ± U₀₁� ... Simulation study

[0171] The behavior of the detection system was first studied by simulation. To this end, the average count rate attributable to the radiological background and recorded by the detection and recording chain described above was evaluated over a period representative of the time range over which a negligible false alarm rate must be guaranteed, i.e., twenty-four hours. The expected count rate obtained is equal to 2915 CS'1, to which is attached, under the assumption of a limiting normal distribution of the Poisson distribution for a count intensity over 1 s much greater than 10, an expanded uncertainty y ^)-3 — J 57 es-1' Une A synthetic time frame associated with the updated radiological background count Ni, with a time step A / = 1 s, is then obtained by sampling equation (8) with p = Pb = 2915 C.S'1. The counts thus generated digitally are, in fact, homogeneous with an instantaneous counting rate expressed in counts per second. Such a configuration corresponds to a signal-to-noise ratio RSN = (4.1 ± 0.2) according to equation (37) above, which is very low (on the order of unity).

[0172] The second step of the simulation scheme consists of applying (i) to the raw counts of the time frame associated with the radiological background each of the filters of first level Fm listed above, then (ii) to the counts thus filtered ^F«> the calculation of the MACD variation estimator^ and finally (iii) to evaluate the second level filtered estimate ^DEMA associated with the current count.

[0173] The detection of a change in radiological activity regime is based on the Gaussian interpolation of the MACD indicator; associated with each of the filtered counting frames ^Fm, always in the presence of the only simulated radiological background.

[0174] The standard deviations associated with the fit of the different simulated MACD distributions, denoted a(MACD), are reported in the table below, along with the values ​​of the coefficient of determination R^ associated with them. It is these standard deviation values ​​which, in accordance with algorithm 2 above, are used to parameterize the test for detecting a change in radiological activity with respect to the radiological background thus characterized.

[0175] This table also shows the standard deviations associated with the fit of different MACD distributions from the measure presented below, denoted a(MACD) expj, as well as the values ​​of the coefficient of determination Rjxp associated with them. The last column of this table contains the associated relative deviations a (MACD) . sim »2 ^sim o(MACD)exp Ap S%^(MACD) MA(., 10) 2.1512 0.9996 2.2112 0.9998 + 2.79 % MAC 20) 2.0677 0.9996 2.1722 0.9999 + 5.05 % MAC3Q) 1.8169 0.9988 1.9878 0.9999 + 9.41 % MAC 40) 1.6667 0.9992 1.7887 0.9996 + 7.32 % MAC50) 1.6145 0.9980 1.6583 0.9993 + 2.71 % MAC 100) 1.2724 0.9989 1.2569 0.9962 - 1.22 % WM AC 10) 2.8615 0.9999 2.9272 0.9998 + 2.30 % WMAC 20) 2.7767 0.9998 2.9232 0.9997 + 5.28 % WMAC 30) 2.4843 0.9989 2.6683 0.9993 + 7.41 % WM AC A0) 2.2743 0.9992 2.4349 0.9995 + 7.06 % WMAC 50) 2.1671 0.9994 2.2483 0.9996 + 3.75 % WMAC 100) 1.5399 0.9956 1.7282 0.9988 + 12.23 % EMA(„ 10) 5.1145 0.9996 5.1766 0.9998 + 1.21 % EM AC 20) 4.7710 0.9998 4.9791 0.9998 + 4.36 % EMA(, 30) 4.1964 0.9997 4.4390 0.9997 + 5.78 % 3.7988 0.9991 4.0120 0.9996 + 5.61 % EMA^ 50) 3.4261 0.9996 3.6886 0.9996 + 7.66 % EMA^ 100) 2.5163 0.9982 2.7958 0.9989 + 11.11 % CST 1.2025 0.9874 1.3200 0.9689 + 9.77 % The final step in the simulation study consists of adding to the expected count Pq induced by the radiological background the expected count generated by the

[0176]

[0177]

[0178]

[0179]

[0180]

[0181]

[0182] periodic approaches of the radioactive source, including interaction with the detector was simulated using the particle transport code. In the presence of radio- mobile transmitter, the value of the instantaneous counting rate hoped for at a pace The measurement refresh rate is a function of the wearer's position. itself dependent on time, a function described in equation (40) below under the simplifying assumptions (i) that the source and the sensor can be reduced to their respective centers of mass and (ii) that the radius of the disk R < d, the disk-RPM distance: VL p. = p + p -4—; =p+p(40) 1 tb ' sd 'h ' $ d\iv Atp ' A synthetic time frame of counts associated with successive passes of the radio transmitter is obtained by sampling equation (8) with a count intensity described by equation (40). As before, the raw counts undergo first-level filtering Fm, then the MACDt variation estimator is applied to the filtered counts and a filtered second-level estimate i A DEM A associated with current metering. A merit factor is the true detection rate (TDR) of the radio transmitter passing in front of the monitor-portal. Denoting Altv as the number of detections per Al passes of the radio transmitter to be detected, the TDR, along with the associated repeatability standard deviation (Pd), is calculated as follows: TDR ~ (41) ex (TDR) = ^T tdr ^ - TDR) (42) First, an increase in the TDR accessible by the MA filter is observed, up to a maximum of (95 ± 2)%, reached at a useful depth m = 30, followed by a decrease to (1 ± 1)% for a memory size m = 100. The same phenomenon appears for the WMA and EMA filters, with an increase in TDRs up to maxima of 100%, reached at their respective useful depths. and, followed by a slower decay than before, down to (36 ± 5)% and (92 ± 3)% respectively for m = 100. Three partial conclusions can be drawn. First, the fact that a TDR of 100% is achievable by coupling the MACD calculation with the WMA and EMA first-level filters, for an ESB as low as four, corroborates the detection power offered by the invention. Second, the superiority of the EMA filter over the WMA filter, and that of the latter over the MA filter, with regard to the trade-off between sensitivity to a change in radioactivity and the specificity of the procedure with respect to fluctuations in the radiological background, seems to be confirmed. Finally, the fact that, for the same time frame, detection is maximal for different filtering depths depending on the nature of the smoothing implemented, illustrates the difficulty associated with adjusting the procedure solely on the basis of the radiological background recording.This is when the comparative merit of the CST first-level filter becomes clear: indeed, starting from the single specified memory size m = 100 and without any prior adjustment of the optimal smoothing depth, it gives access to the maximum TDR of 100%.

[0183] This numerical study thus points towards the success of the two main objectives assigned to the embodiment of the invention combining a CST filter and a MACD test: namely, to provide access to a high TDR, against a very low FAR, and in the presence of rapid and subtle variations in radiological activity, without requiring an optimal setting that is excessively sensitive a priori with respect to the usable historical depth. In order to corroborate this result as well as to study the performance of the method with regard to the second of these objectives, these simulation data will now be compared with the results of the study on their experimental counterparts.

[0184] Filtered time frames and variation indicator in the presence of radiological background noise only

[0185] The evolution of the counts attributable to the radiological background was first recorded over a twenty-four-hour period, which should lead to a negligible number of false alarms. For the reasons indicated above, the counts are homogeneous to an instantaneous counting rate expressed in counts per second. Each of the first-level filters Fm listed above is then applied to the raw counts Nt of the experimental time frame of the radiological background, and then (ii) the calculation of the MACDb variation indicator is performed on the counts thus filtered. Finally, H (iii) the second-level filtered estimate ^DEMA associated with the current count is 1i evaluated.

[0186] Statistical study of background noise and parameterization of the hypothesis test on the convergence and divergence of moving averages

[0187] The background noise in the laboratory's radiological environment, representative of that of an area vulnerable to the introduction of a radio transmitter, was the subject of a statistical study. The recorded probability density function, as well as its interpolation by a normal distribution and by a normal distribution representing the limit of a Poisson distribution, were determined. It was found that the experimental distribution produced estimates of the mean θ = 2914.5; of the variance θ = 3028; of the normalized skewness θ = 0.045; of the normalized kurtosis θ = 0.056. There is thus a deviation of the order of 5% from the normal form parameters of the normal distribution, and a relative deviation of the order of +4% between θ and θ (the equality of which would have been characteristic of a normal distribution that is the limit of a Poisson distribution). Such discrepancies can, obviously, be considered negligible with regard to their consequences on the detection of an abrupt change in radiological activity..

[0188] The experimental histogram obtained in response to the periodic passage of the Cs-137 source described above reveals, conversely, a second mode of the nuclear counting distribution, centered on the expectation P^ — 3135 Cs4. It follows from this result that the experimental expectation of the counting rate attributable to the radio transmitter p = 221 Cs*1 E [ps + Uggj % (ps) ], with the notation of the preceding paragraph. The measurement is thus in agreement with the Monte Carlo simulations described above.

[0189] The standard deviations associated with the Gaussian fit of the different distributions of the MACD from the measurement, denoted (j(MACD) exp, are reported in the table presented above, as well as the values ​​of the coefficient of determination l£xp which are associated respectively with said fits.

[0190] The Rexp values ​​obtained, of the order of 97% after the first level filter CST, and greater than 99.5% for all the parameters of the MA and EMA filters, legitimize the Gaussian formalism on which the detection test is based.

[0191] The aforementioned table also presents, for each of the reported first-level filters, the relative difference s^.macd) between the standard deviation of the experimental distribution and that of the simulated distribution (taken as a reference because the formalism of the detection procedure is based on it), expressed as a percentage:

[0192] a(MACD)exp-o(MACDCn ^(ÀMACD}- GtMACD\.m V43)

[0193] is, on average, equal to (5.77 ± 3.47)%. It is therefore concluded, once again, that the simulation scheme described in the preceding paragraph is reliable. Consequently, the MAC standard deviation values ​​(D)exp are used, in accordance with Algorithm 2 presented previously, to parameterize the test for detecting a change in radiological activity relative to the characterized radiological background.

[0194] As in the paragraph dedicated to the simulation study, the TDR detection rate of the radio transmitter's passages in front of the RPM is used to quantify the performance of the procedure.

[0195] It is noted, firstly and in accordance with the observations of the numerical study, that the distributions associated with the non-adaptive first-level filters MA, WMA, and EMA each exhibit a local maximum, respectively equal to (12 ± 3)%, (35 ± 5)%, and (36 ± 5)% for useful history depths m ∈ [20; 30], m = 30, and m = 40, respectively. The decay exhibited by these experimental distributions as a function of m is, however, much faster than the decay observed by the ideal distributions in the cited paragraph, particularly after the WMA and EMA filters. This observation indicates that the implementation of the detection procedure based on the MACD estimator is, in practice, even more dependent on a specific preset for each of the non-adaptive first-level filters than expected by simulation, which supports the point highlighted in the numerical study.Finally, it must be emphasized that the maximums achievable in practice, for a signal-to-noise ratio as low as four, are clearly degraded due to the experimental deviations mentioned; none of the implementations of the detection procedure introduced herein, after one of the first non-adaptive filters considered, even leads to a TDR of 50% under the operational constraint of a false alarm every twenty-four hours.

[0196] By contrast, the TDR achieved when the detection procedure is backed by the CST first-level filter, whose implementation, we recall, is based solely on the specified memory size m = 100 and requires no prior adjustment of an optimal smoothing depth, amounts to (85 + 4)%. Two conclusions immediately follow from this. First, the detection procedure proves to be significantly more resilient when transitioning from Poisson modeling to experimentation when backed by an adaptive first-level filter, such as the CST filter; the TDR achieved is, in fact, nearly two point five times higher after the latter than after the non-adaptive WMA and EMA filters. The aforementioned value of 85%, in the presence of an ESB which we recall is only on the order of magnitude of unity, proves to be quite high in absolute terms, which corroborates the detection power offered by the approach described above.The experimental study described in this paragraph thus tends to consolidate the perspective of a compromise between sensitivity (high TDR) and selectivity (FAR compatible with an operational constraint) maximized by a coupling between (i) an adaptive first-level filtering of the signal and (ii) a fast and reliable detection test based on a variation indicator derived from the convergence-divergence of moving averages.

[0197] The invention is not limited to the method previously described but also extends to a data processing system comprising a processor configured to implement such a method and to a computer program product comprising instructions which, when executed by a computer, cause the computer to implement such a method.

Claims

Demands

1. A method for processing a detection signal (¾) delivered by an ionizing radiation detector, comprising: - the calculation of reference variation indicators during a qualification phase in which the detector is exposed to a single radiological background; - the calculation of a current variation indicator (MACDj) during a usage phase in which the detector is likely to be exposed to a change in radiological activity; - the comparison (TST) of the current variation indicator (MACDj) to a threshold set according to a statistic (a(MACD)) of a distribution of the reference variation indicators; and - the triggering of an alarm (AS^) when the current variation indicator is greater than the threshold;in which the calculation of each of the reference variation indicators and the current variation indicator includes: - a smoothing (Fl), by means of an averaging filter on a counting history, of a counting signal (M) of pulses contained in successive samples of the detection signal; - the calculation (IC) of a difference (MACD^ between a first signal resulting from a simple exponential smoothing of the smoothed counting signal ( *F«<) and a second signal resulting from a double exponential smoothing of the smoothed counting signal ( A Fm\ n )*;

2. A method according to claim 1, wherein said statistic is a standard deviation of a Gaussian interpolation of the distribution of the reference variation indicators.

3. A method according to any one of claims 1 and 2, wherein each of the simple exponential smoothing and the double exponential smoothing exploits a smoother parameter that is fixed as a function of the depth of the counting history of the averaging filter.

4.

5.

6.

7.

8.

9. A method according to any one of claims 1 to 3, wherein the averaging filter has a fixed historical depth. A method according to claim 4, wherein the averaging filter is a sliding average filter, a weighted sliding average filter or an exponential sliding average filter. A method according to any one of claims 1 to 3, wherein the averaging filter has adaptive history depth. Method according to claim 6, wherein the averaging filter is a centered significance test filter. Data processing system comprising a processor configured to implement the method according to any one of claims 1 to 7. Product computer program comprising instructions which, when executed by a computer, cause the computer to carry out the process according to any one of claims 1 to 7.

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