1
Low Count Anomaly Detection at Large Standoff Distances David M. Pfund, Kenneth D. Jarman, Brian D. Milbrath, Member, IEEE, Scott D. Kiff, Member IEEE, and Daniel E. Sidor Abstract— Searching for hidden illicit sources of gamma radiation in an urban environment is difficult. Background radiation profiles are variable and cluttered with transient acquisitions from naturally occurring radioactive materials and medical isotopes. Potentially threatening sources likely will be nearly hidden in this noise and encountered at high standoff distances and low threat count rates. We discuss an anomaly detection algorithm that characterizes low count sources as threatening or non-threatening and operates well in the presence of high benign source variability. We discuss the algorithm parameters needed to reliably find sources both close to the detector and far away from it. These parameters include the cutoff frequencies of background tracking filters and the integration time of the spectrometer. This work is part of the development of the Standoff Radiation Imaging System (SORIS) as part of DNDO’s Standoff Radiation Detection System Advanced Technology Demonstration (SORDS-ATD) program. Index Terms—anomaly detection, gamma-ray spectroscopy, radiation monitoring.
I. INTRODUCTION
A
mobile radiation detection system capable of finding illicit sources at large standoff distances would be useful in many scenarios including operating along uncontrolled borders, monitoring of cargo in transit and searching for sources from city streets. These applications involve detecting sources at a distance while the source and/or the detector is moving through a background that varies spatially. Benign data may include transient spectra from technologically enhanced, naturally occurring radioactive material (NORM) and from people treated with medical isotopes. The first step in finding an illicit source is the detection of anomalous spectra: that is, those that are probably not background, probably not from NORM, and probably not from medical sources. Once detected, the anomalous source can be Manuscript received May 8, 2009. This work was supported by the U.S. Department of Homeland Security, Domestic Nuclear Detection Office. This is Pacific Northwest National Laboratory (PNNL) report number PNWD-SA8577. D. M. Pfund, to whom correspondence should be sent, is with PNNL, Richland, WA 99352 USA (phone: 509-375-3879; fax: 509-375-3865; e-mail:
[email protected]). K. D. Jarman is with PNNL, Richland, WA 99352 USA (
[email protected]). B. D. Milbrath is with PNNL, Richland, WA 99352 USA (e-mail:
[email protected]). S. D. Kiff is with Sandia National Laboratories, Livermore, CA 94551 USA (
[email protected]). D. E. Sidor is a student at the University of Rochester, Rochester, NY 14627 USA (
[email protected]).
methodically localized and then subjected to secondary screening to identify the source material. In previous work, we discussed a means of distinguishing illicit radiation anomalies from strong background and known nuisances including NORM [1]. The general problem of detecting anomalies is surveyed in [2]. Our specific approach takes as independent variables certain ratios of spectral regions of interest called Spectral Comparison Ratios (SCRs) [3]. The approach is a type of energy windows method [4] based on previous work by others [5], [6]. We will show that this approach can be extended to enable spectra to be distinguished from other nuisance sources including common medical isotopes. Our method requires estimating the mean background and its variability, so that threatening sources can be distinguished from it. For a mobile system looking for moving sources, this means background must be tracked [7]. Even at relatively high count levels, threatening sources at large standoff distances can be mistaken for background because they vary slowly with detector movement. In this work, we tune our method of background tracking so that it always provides a satisfactory estimate of background for use in the SCR method. Because the detector response to threat sources at high standoff does vary slowly, we can improve our detection of such sources by accumulating counts over longer time intervals through a process of rolling summation. We discuss the effect of various rolling summation lengths, or integration times, on source detection performance at different standoff distances. We demonstrate that, after finetuning, the algorithm has much improved performance over a broad range of standoff distances. We begin our discussion with a review of the SCR method and give necessary refinements to it for application in a moving, fieldable instrument. II. ANOMALY ALGORITHM The anomaly detection metric is a covariance-weighted length of a vector of spectral comparison ratios. Each component SCR characterizes the deviation of an acquired gamma-ray spectrum from expected background based on a comparison of counts in two regions of interest or "bins.” We discuss the number of bins and their energy ranges elsewhere in this paper. At time index k, each SCR component is defined by the linear functional, [1] B (1) α1 j k = C1k − 1 C j k B j k where Ci k represents the spectral counts in bin i of acquisition
2 k and B j is the local estimate of mean background counts in bin j. In (1), bin 1 is a common bin in all of the SCRs. The SCRs have the characteristics of being centered on zero and roughly normally distributed over large samples of background spectra. A vector of SCRs based on several such pairs of bins provides a composite measure of the deviation of an acquisition from the estimated mean background. The vector of SCRs is, [8] (2) α k = Tk Ck where Ck is a vector of bin counts from acquisition k and the transformation matrix Tk is, 1 −B B 0 0 1 2 0 1 0 −B1 B3 (3) , Tk = 1 0 0 −B1 Bn k where n is the number of bins or regions of interest. In (3) it has been assumed that the bins have been chosen such that none of the Bi is zero. In that case Tk has a nullity of one. Vectors of bin counts that are in the kernel of the transformation, those that are scalar multiples of the mean background, are most obviously background. Two vectors of bin counts have the same SCR if and only if they differ by a multiple of the mean background count vector. To calculate an SCR, estimates of the mean background counts in each bin are needed. Mean background counts vary with time index k as the detector moves through the complex urban environment. In previous work, we have estimated background with a Kalman filter. [7] In this work, we apply an exponentially weighted moving average (EWMA) to track slow variations in the mean background, rather than the Kalman filter, having found that our detection algorithms perform just as well or better with this simpler method. The estimated mean background is then given by (4) B j k = λB j k + (1− λ )B j k−1 , where the weight, λ, is between zero and one. [9] It should be emphasized that only past background spectra are averaged with EWMA – for the purpose of estimating the transformation matrix Tk. EWMA is not applied to the most recent acquisition, Ck. The simplicity of the EWMA makes it attractive for application to different scenarios because only a single parameter, λ, must be adjusted. We discuss the choice of a value for λ below. The EWMA procedure is a first order digital low pass filter with time constant, τ, and cut-off frequency, fc, given by, 1 1 − λ τ= , fd λ (5)
f c = 1 (2πτ ), where fd is the frequency of acquisition. In this work, the acquisition frequency was 1 Hz. The EWMA parameter, λ, determines the response time of the tracking and the characteristic frequency of changes allowed to pass into the background estimates. As in our previous work, only spectra not flagged as anomalous were passed to the filter and used to update the background estimate. We also needed to estimate the covariance matrix of background bin counts. The
covariance was estimated with
)k (B − B)k + (1− λ )Σ k−1,
(
T
Σk = λ B− B
(6)
where vector Bk denotes the vector of bin counts for acquisition k after deciding they are not anomalous. The magnitude of the vector α of SCRs provides an overall measure of how unlike background and how unlike obvious nuisances and so potentially threatening an acquisition is. We use as an anomaly metric a distance D(α) related to the Mahalanobis distance [10],
{
}k
D 2 (α k ) = α T • S−1 • [(I − P)• α ] ,
(7)
where Sk is the estimated covariance for the SCRs in the background population at time index k, determined from:
(
S k = TΣT T
).
(8)
k
The SCR vector may contain contributions resulting from linear combinations of known nuisance spectra. We reject such contributions before estimating the magnitude, D, by applying a projection operator (I-P) with P given by [1], −1 (9) Pk = Α • Α T • S−1 • Α • Α T • S−1 , k where the (n-1) x m matrix A of nuisance templates has as column vectors the SCRs from m nuisances. The projection was designed to make the anomaly metric invariant to any linear combinations of the nuisances. We have shown elsewhere that the rejection procedure can screen out false detections from concentrations of common nuisances such as rock salt [8]. The square of the metric D is distributed roughly chi-square over a large sample of benign spectra, with degrees of freedom (n-m-1). Plotted in Fig. 1 are normalized frequencies versus D2 developed from a sample of 28,184 benign spectra. The spectra were down-binned into n=8 bins, and m=4 nuisance signatures were projected out. The sample of benign spectra, the bins, and the nuisances (this choice of which are compromises) are discussed below. Plotted as a dashed line in the figure is the chi-square probability density for 3 degrees of freedom. The approximate agreement of the experimental distribution with the chi-square density is a consequence of the individual SCRs being roughly normally distributed over the population of benign spectra, as we observed in our previous work [1]. The nuisance rejection procedure is intended to reduce the frequency of very long-tail outliers, particularly those resulting from infrequent and technologically enhanced sources. When trying to achieve false alarm rates of only a few per day, such long-tail outliers tend to increase the detection threshold value needed so their presence is detrimental to detection probabilities. The nuisance rejection procedure in (9) used to eliminate them does not come without cost. Potential threat spectra generally have SCR components that fall at least partially in the nuisance subspace. However, if the set of templates is kept small and is restricted to only those nuisances that appear with high frequency, the rejection procedure can reduce the detection threshold to an extent that outweighs the associated cost. Our algorithm issues a detection alarm when metric D for an
(
)
3 acquisition exceeds a threshold. The threshold is set high enough to limit the nuisance and false alarm probability (N/FAP) to a desired target fraction of acquisitions. In other words,
{
[(
) ]}
12
α T • S -1 • I − P • α D(α k ) k > 1 ⇒ alarm, (10) = DN/FAP DN/FAP where DN/FAP is the threshold. The N/FAP value the threshold is based on is the allowed fraction of false positive alarms in a large sample of benign spectra. Because D2 are distributed roughly chi-square for benign spectra, squared thresholds are roughly equal to the value needed to enclose a 1-N/FAP fraction of the chi-square distribution with (n-m-1) degrees of freedom. In this work, we use empirical thresholds. These values tend to be slightly larger than the theoretical estimates from the chi-square distribution, as will be illustrated below.
Fig. 1. Example distribution of squared distances in benign Seattle data. For observations in scenarios where both source and detector are stationary, longer integration times translate into higher signal-to-noise ratio and better detection performance. When the source of interest is moving relative to the detector, integration times may be driven by operational constraints and/or estimates of typical time of observation of objects of interest, such as suspect vehicles passing the detector at an average speed. Additionally, point sources in the presence of distributed background sources can be “averaged” out by a moving detector with integration times that are too long. In this work, we tested the effect of integration time on the relative magnitude of the anomaly metric, and so on the detection rate of threats, at various standoff distances. We performed rolling summations of varying lengths on downbinned spectra according to, k′−1 (11) C′k = ∑ C k−l , l=0 where k′ is the variable integration time under test. The rolling-summed count vectors, C′k , were passed to the background tracking and anomaly detection routines at the original acquisition rate of fd = 1 Hz. Spectra were thus accumulated before further processing without regard as to whether or not they might be anomalous.
III. URBAN BENIGN SPECTRA For this work, we collected a new sample of urban benign spectra with a broad calibrated energy range for use in algorithm testing. A representative sample of benign spectra was needed for estimating the covariance appearing in the equation for the anomaly metric (10). The sample of 28,184 benign spectra was taken in Seattle, Washington in late April of 2008. The large sample was intended to capture urban variability and included data taken downtown on granite paved streets and sidewalks and in a neighborhood with several hospitals. To collect the data, a detection system was loaded inside a van and driven around the city for nearly 8 hours. The distance driven was approximately 120 miles. Points of interest such as hospitals and granite structures with elevated background radiation were chosen in advance, and thorough measurements were made near these landmarks. In addition to the preselected landmarks, the detector was driven through areas of commerce, industry, and residence; it was also driven over Lake Washington on two bridges to sample a reduced background environment resulting from attenuated terrestrial background due to the water. We consider the number and variety of spectra to be typical of what might be collected during one shift of operation of a deployed mobile search instrument. The detector used for obtaining the benign spectra had a 10×10×41 cm3 NaI(TI) scintillator crystal. The detector’s photomultiplier tube was connected to a Bridgeport Instruments TwinBase high-voltage supply and read out by a Bridgeport Instruments eMorpho digital multichannel analyzer. These equipment were mounted on an aluminum frame and installed in a shipping crate. Energy spectra with 512 channels and binned in sequential 1-s intervals were stored on a PC/104-based Via Pentium 3 processor board from Diamond Systems. Though the temperature inside the van was relatively well controlled, the NaI(Tl) detector was surrounded with foam insulation to further minimize temperature gradients. The foam also served to firmly hold the detector inside its crate. An accurate calibration was required of this system, from below 100 keV up to nearly 3000 keV. An additional requirement of the calibration procedure was that it be performed frequently in recognition of the known drift of NaI(Tl) light output [11] and photomultiplier tube amplitudes [12] in uncontrolled environments. Each calibration used the prominent natural background lines from 40K (1461 keV) and 208 Tl (2614 keV) as well as μCi-level sealed 241Am (60 keV) and 137Cs (662 keV) sources. This set of four calibration points has sufficient accuracy over the entire range of interest: compared to a thorough nine-point calibration study representing the best-case laboratory calibration, a three-point calibration using only the lines from 241Am, 40K, and 208Tl was shown to have a maximum deviation of approximately 10 keV [8]. At the beginning of the measurement campaign, calibrations were performed hourly; as time progressed, this interval was relaxed to two hours based upon observations of stable operation. The mean of the benign Seattle spectra is plotted as the black curve in Fig. 2. Grey curves indicate one standard
4 deviation from the mean and exhibit the expected features from varying background potassium and thorium. The upper curve has a feature at approximately 500 keV from possible medical sources (discussed below). The mean total count rate (at energies greater than 75keV) was approximately 710 counts per second (cps), with a standard deviation of about 230 cps. The urban benign spectra were highly variable, as expected.
Fig. 2. The mean background in Seattle. The benign spectra appeared to contain spectra from medical sources. The data taken near the hospitals included a roughly 30-second-long series of high-count spectra with an obvious feature at 511 keV. The average of these spectra appears as the upper, solid curve in Fig. 3. These spectra may have been from a person treated with 18F. These data also included three brief but distinct series of spectra with counts that were predominantly at low energy (below about 150keV). An example of one of these appears as the heavy dashed curve in Fig. 3. We hypothesize that these were also of medical origin, perhaps 99mTc. Both of the illustrated spectra were profoundly dissimilar to mean background (plotted as a grey line in the figure). These spectra tend to trigger false alarms when using only NORM-based nuisance templates in the rejection procedure. To eliminate false alarms from the benign Seattle spectra that appeared to be 99mTc, we used one of them (the one plotted in Fig. 3 with a heavy dashed line) to develop a template for nuisance rejection in (9). Other medical sources were either too infrequent or too weak in the Seattle data to generate false alarms.
compared to average background. Templates for rejection of NORM nuisances were developed from spectra intended to represent what would be measured from the surface of uniformly enhanced soil or concrete. Such sources would be characteristic of construction materials and may also be similar to NORM-enhanced cargo or potential masking agents. Three such spectra were acquired with a 10×10×41 cm3 NaI(Tl) detector placed on top of three different concrete pads used for calibrating small radiation detectors and located at the Hanford site outside of Richland, Washington. The concrete pads were 1.1 m in diameter, 0.6 m thick, and had a density of 1.9 g/cm3. Each pad was dominated in composition either by 232Th, 226Ra (a daughter of U) or 40K. In particular, the pad compositions were, in units of pCi/g [13]: Pad 1– 51.64 40K, 0.58 226Ra, 0.01 232Th; Pad 2¬ 14.45 40K, 6.68 226Ra, 30.8 232Th; Pad 3– 15.97 40K, 96.67 226Ra, 0.59 232Th. The Seattle spectra served as a basis for estimating false alarm rates from the algorithm. Approximate detection rates of threat sources were estimated by adding intensity-scaled spectra from likely threat sources to the sample of Seattle data. We have discussed using this injection study procedure elsewhere [7] for sources that are either very close to the detector or moving very rapidly. In this work, we considered sources that are either very far from the detector or are moving very slowly relative to it. The model sources were considered to be points moving normal to the line of sight at closest approach. The detector size was neglected. Total counts per second from background-subtracted threat sources were varied with time according to [14], 1 (12) I k = I ki ; fo = vx y , 2 2 1+ f o (k − k i ) and added to the Seattle time series. In (12), vx is the speed of the source relative to the detector and normal to the line of sight, y is the source distance at closest approach, and Iki is the count rate at closest approach. At each time, k, the value of Iki was chosen from a Poisson distribution with mean and variance, I, equal to a fixed mean count rate for the threat of interest. The set {k1, k2,…} represents the locations within the Seattle time series where the model threat sources were inserted. Because at high standoff distances fo was small, the injected sources were very broad in time. We spaced the ki very far apart to avoid overlap and injected only eight or nine sources per run through the Seattle data. The injection locations were shifted and the run repeated to generate more realizations. We refer to this procedure of injecting sources with a wide temporal profile as “hump injection” below. IV. ALGORITHM PARAMETERS
Fig. 3. Two possible medical sources in the Seattle data,
A. Regions of Interest (bins) As mentioned in the Introduction, our method is designed to detect spectral anomalies and not to identify particular isotopes. However, we do use spectra from likely threat sources in choosing the broad energy regions that will be tested for count rate anomalies. Spectral regions of interest for
5 use in calculating the SCRs were determined for three classes of special nuclear materials. Our particular partitioning of threats into three classes is a common sense one based on their gross spectral characteristics. DU-like sources: Have characteristic features near 766 and 1001 keV from 234mPa, the first daughter of 238U. The DU- like spectra differ from that of natural uranium in that features from isotopes further down the decay chain are absent in depleted uranium. HEU-like sources: Exhibit the strong emission near 186 keV from 235U in highly enriched uranium. Pu-like sources: Have a broad spectrum from about 100 to 500 keV from 239Pu, with no distinct features. We developed the bins using from three to six spectra from example threats for each class, spectra differing in the origin or shielding of the material. The shielding of the examples ranged from relatively light to relatively heavy. No bare sources were used to develop the bins. During operation of the algorithm we performed the alarm test (10) three times with each acquisition, Dα Pu Dα HEU Dα DU k k k > 1 or > 1 ⇒ alarm, (13) > 1 or D DU D HEU D Pu N/FAP
N/FAP
N/FAP
where the distances, SCRs, and thresholds were unique for each class. We down-binned spectra from the original 512 energy channels output from the spectrometer to eight bins for each class of threats. The energy boundaries of each bin were set using the procedure discussed in [1] that attempts to maximize the squared anomaly metric for prototype threat sources of fixed intensity. The bin boundaries for each threat class maximized a Figure of Merit (FOM), T (14) FOM = trace Ατ • S−1 • (I − P)• Ατ , where matrix Aτ has as column vectors the SCRs for the prototype threats in the threat class, each evaluated at 1000 cps. For this work, we specified that the bins be constrained between 75 and 2904 keV. In (14) the covariance matrix, S, and projection, P, were evaluated using the aggregate of the Seattle data and so had no time or location dependence. The maximization of the FOM arrived at bins that increased the separation between the SCRs of the benign and those of a threat plus benign populations, under the assumption that the two had the same covariance matrix. It also tended to choose bins that reduce the projection of the prototype threats into the nuisance subspace, PAτ. Down binning the spectra significantly reduces the volume of SCR space, and so the alarm threshold, needed to contain a large fraction of the population of benign spectra. This reduction in threshold comes at the expense of the loss of the ability to resolve features that characterize threats. Using a simplified analysis that considers benign and threat populations of SCRs to be normally distributed, we concluded there was little benefit, in terms of reducing minimum detectable threat counts at a specified false alarm rate, in using more than six to eight bins for each class of threat. In the simplified analysis, the approximate minimum detectable
[
]
count rate for a particular threat is inversely proportional to the square root of its contribution to the FOM for a particular combination of bins. Using more bins can lead to a larger FOM and so a smaller minimum detectable count rate. However, a factor in the constant of proportionality is the noncentrality parameter of the non-central chi-square distribution. That parameter grows larger with an increasing number of degrees of freedom, n-m-1. The use of too many bins increases the parameter and can lead to a larger minimum detectable count rate. In this work we uniformly adopted eight bins for each threat class. B. Background Tracking As discussed above, the background tracking algorithm is a low-pass filter that allows low-frequency changes in spectra (provided they have not been recognized as anomalous) to be incorporated into the estimate of mean background. The danger is that counts from sources at high standoff distance change so slowly that they can pass through the filter and can be mistaken for changes in the background. Sources fitting the above hump model (12) have approximately 86% of their signal energy at frequencies between +/- fo. The EWMA tuning parameter, λ, must be set at a value that balances the need to track slow background variation with not allowing significant counts from the slowly varying injections of high-standoff threat sources to enter into the background estimates. First addressing the latter concern, we studied the impact of the EWMA parameter on the response to high-standoff threats from the anomaly algorithm. Plotted in Fig. 4 are normalized (divided by an alarm threshold) anomaly metrics from (10) versus time for three values of the parameter. The source was a bare 137Cs source moving at 10m/s perpendicular to the line of sight and located 100m away from the detector at closest approach. Source counts were injected into the Seattle background spectra with closest approach at time index 5000. At that time the injection rate was 1000 cps. The integration time in (11) was k′ =1 second. The time series of anomaly metrics obtained with the largest value of the parameter shown here (λ=0.008, plotted with the light grey line in the figure) had a very small hump at the injection location. The metrics with the smallest EWMA parameter value shown here (λ=0.002, plotted with the heavy black line in the figure) showed a large peak at the injection point of the high-standoff threat. Additionally, using a sequence of nine injected source spectra, we found that only 5.8% of the signal energy of the train of the injections (with y=100m, vx=10m/s) was able to pass into the background estimate when using λ=0.002. Driving this parameter to even lower values might result in larger responses to distant threats; however, smaller parameter values also degrade the ability to track large-scale variations in background. We studied the impact of varying λ on overall performance for short standoff distances as well and found that performance begins to degrade for values of λ less than about 0.002 to 0.004. We deemed the competing priorities to be best met with an EWMA parameter value of λ=0.002.
6
Fig. 4. Example anomaly metric values from (10) for hump injection of a 137Cs source. C. Detection Thresholds DU HEU , D Pu Detection thresholds DN/FAP for source , DN/FAP N/FAP injection studies were set for each threat class to give a total false alarm rate for all three tests of 1 in all 28,184 Seattle spectra when not injecting any threat counts. The single false alarm was the large hypothesized 18F source, and it was a false alarm common to all three alarm tests in (13). The resulting threshold values are listed in Table I. They can be compared to the theoretical value of 4.824 obtained assuming chi-square distributed values over benign populations of D2 at the same false alarm rate and three degrees of freedom. TABLE I
Integration time k’ 1 5 10 15 20 25 30
Alarm Thresholds DN/FAP (allowing 1 false alarm per 28,184 benign Seattle spectra, injecting zero threat counts) Pu-like threats DU-like threats HEU-like threats 6.219 5.558 6.044 5.553 5.221 4.832 4.991
5.687 5.568 5.110 4.910 4.935 5.171 5.145
6.181 6.745 7.010 7.071 7.010 7.271 6.964
D. Integration Times As mentioned in Section II and as is readily evident, integration time has an impact on the signal-to-noise ratio (SNR). The following theoretical argument, which examines the influence of total background and source counts, suggests why increasing the integration time, k′ , may be beneficial. The Seattle measurements indicate that background variance, even when adjusted for low-frequency variations using the EWMA, is greater than that predicted by Poisson-distributed counts. However, here we use the Poisson assumption first to derive an analytical result and then use an empirical study to determine how well the approximation holds up. Consider a SNR that is proportional to the ratio of mean signal counts, S, to the standard deviation of background counts, σB, and that the mean background, B , is constant. If integrated background counts are Poisson-distributed, then σB2 = B . Considering only time intervals of width k′ around the instant of closest
approach, the signal is proportional to the integrated source counts: k′ 2 1 arctan f o . dt = S(k′) ∝ ∫ −kk′ ′22 (15) 2 2 2 fo 1+ f o t Under the above assumptions, the SNR in this interval then depends on integration time, k′ , according to the ratio S(k′) k′ . This ratio achieves a maximum when k′ dS dk′ − S = 0 , which requires that the optimum integration time, k′ max, satisfy: k′ f o k′max = arctan f o max . (16) 2 2 k′max 1+ f o 2 Numerical solution of (16) yields for an optimum integration time with Poisson-distributed background spectra: k′max ≈ 2.8 f o [15], [16]. These results suggest that the integration time that maximizes sensitivity to hidden sources will depend primarily on the source characteristic frequency fo. If the mode of instrument operation is to detect sources that are relatively far away, relatively long integration times will improve SNR. For example, assuming the target sources are at a characteristic standoff distance of y=100m and move at a relative speed of vx=10m/s, the optimal integration time is approximately k′max ≈ 28 seconds. The theoretical model above is clearly too restricted in its assumptions to apply directly to our data, as it assumes Poisson counts and constant mean background. It does, however, suggest how integration time may impact performance. We compare the theoretical result to empirical results. We tested the effect of various integration times on detection probabilities for bare 137Cs and weapons-grade plutonium (WGPu) sources at varying standoff distances using the injection study method. Anomaly metrics as in (10) were calculated for each of the three classes of threat. We injected 137 Cs and bare WGPu sources at mean count rates of 60 cps and 170 cps (at energies greater than 75keV), respectively, as would be measured at the detector at closest approach. These levels were chosen to give a high number of alarms for some integration time, but never to alarm at all of the injection points. The sources were modeled as moving at speed vx=10m/s and closest approach distance, y, of either 50m or 100m. This gives theoretical optimal integration times of approximately 14 s and 28 s, respectively. Detection thresholds for the various integration times were set as in Table I. Listed in Table II are the numbers of true alarms (totaled over all three threat classes) obtained with different integration times in 503 injections. The sample size of 503 injections was small and so the results may vary slightly with repetition. The injection studies demonstrated that an integration time of k′ =15 seconds yielded a high number of alarms for sources at high standoff distances and so that value is a good choice when searching for such sources.
7
Integration time k’ 1 5 10 15 20 25 30
TABLE II Number of true alarms in 503 injections 60 cps 170 cps bare 60 cps 137Cs 170 cps bare 137 Cs at WGPu at 50m WGPu at 100m at 100m 50m 30 42 63 62 75 96 325 260 214 304 373 374 273 428 354 417 223 430 299 429 137 375 176 383 84 328 137 342
As expected, an integration time of k′ =1 second yielded the best results for close-up and or fast-moving sources. We injected 137Cs and bare WGPu sources at mean count rates of 175 cps and 300 cps, respectively, and set speeds to vx=13m/s and distances, y, to 3m. This gives a theoretical optimal integration time of approximately 0.65 s. Listed in Table III are the numbers of true alarms (totaled over all three threat classes) obtained with different integration times in 503 injections. Alarm rates dropped significantly for k′ >1 for the close-up sources. To maximize the algorithm’s performance for both near and far sources during practical operation, one could run parallel analyses using different integration times. TABLE III Number of true alarms in 503 injections Integration time k’ 1 5 10 15 20
175 cps 137Cs at 3m
300 cps bare WGPu at 3m
381 17 25 45 53
411 10 25 30 40
As we have previously reported [1], our algorithm is significantly more sensitive than an alarm metric based on simple gross counts. To achieve a false alarm rate of 1 in 28,184 Seattle spectra would have required a detection threshold of at least 2534 cps (assuming an integration time k′ =1 s) for a criterion based on gross counts. The highlighted values in Table IV are an order of magnitude lower than a total-count-based detection threshold. We have estimated the quantities of threat materials that deliver MDC-levels of counts at a 10×10×41 cm3 NaI detector. Listed in Table V are the source activity levels in air corresponding to the highlighted MDC values of Table IV. To convert the MDC values to source activities, we used a measured Pu source of known activity and distance and scaled accordingly, while we calculated the 137Cs activities assuming a peak detector efficiency of 50% at 662 keV [11] and a 662 keV branching ratio of 0.852 [17]. Thus, our values for Pu include self-shielding while our values for Cs do not. For air attenuation, we used a density of air as 0.0012929 g/cm3 and mass attenuation coefficients of 0.0825 cm2/g (for the 137Cs662 keV gamma) and 0.12 cm2/g (for the Pu gammas, which averaged approximately 220 keV for the energy range used) [18]. The near milliCurie detection level for cesium at the 100m distance illustrates the practicality of high-standoff passive detection for this bare source. TABLE V Source and standoff Integration time Approx. source activity at MDC and distance k’ specified standoff 137 Cs, 3m 1 0.82 µCi Bare WGPu, 3m 1 1.0 Ci 137
Cs, 100m Bare WGPu, 100m
15 15
1.6 mCi 3300 Ci
V. DETECTION PERFORMANCE WITH SOURCES AT HIGH AND LOW STANDOFF DISTANCES
VI. CONCLUSION
We often express algorithm performance in terms of the 95% minimum detectable counts (MDC) value – the mean counts per second value at closest approach needed at the detector to trigger alarms in 95% of the injections. Listed in Table IV are approximate (based on only 503 injections per case) 95% MDC values for sources at 100m (with vx=10m/s) and 3m (with vx=13m/s), assuming integration times of either k′ =1 or k′ =15 seconds. The detection thresholds were again set to yield 1 false alarm per 28,184 benign spectra. The best results at each standoff distance are highlighted in Table IV. The highlighted values are less than the mean background count rate of 710 cps. Using the appropriate integration time (high for far-away sources, low for close-up sources) greatly lowers the minimum detectable count rate of threat sources. TABLE IV
In this work, we fine-tuned our SCR-based anomaly detection algorithm for urban searches of high-standoff sources. Important parameters in the algorithm included the choice of nuisance spectra to be rejected, the number and placement of energy bins for special nuclear materials, a parameter (related to the cut-off frequency) in the background tracking filter, and the integration time of incoming spectra. Urban spectra taken in Seattle, Washington contained several instances of what appeared to be medical nuisances. One of these spectra was selected and added to the basis set of nuisances that also contained spectra from NORM. Bin energy boundaries were determined from spectra in three classes of special nuclear material. Both the changes to the nuisance basis and to the bin structure were expected to improve the probabilities of source detections at both low and high standoff distances. A particular goal of this work was to improve performance at high source standoff distances. The signal from distant or slow moving sources can be mistaken for background shifts if the filter cut-off is too high, and the signal-to-noise ratio can be degraded if the integration time is too short. Improving the performance of the algorithm for highstandoff sources required tuning the background tracking filter
Approximate 95% MDC value, cps above background Source and standoff distance 137 Cs, 3m Bare WGPu, 3m 137
Cs, 100m Bare WGPu, 100m
Integration time k’=1
Integration time k’=15
210 345
350 1700
200 385
70 225
8 and increasing the width of time integrations applied to the incoming spectra. Estimates of mean background were made with a first order EWMA filter. A very small filter parameter of 0.002 was needed to make sure that counts from distant sources were not mistaken for background. The resulting slight loss of fidelity in tracking real shifts in urban background spectra had no adverse impact on threat detection performance. Signal-to-noise, and consequently detection performance, was improved for sources 50 to 100m distant by increasing the integration time from 1 to 15 seconds. This result was demonstrated by injection studies using the Seattle spectra as prototypical urban background. As expected however, such an increase in integration time was detrimental when trying to detect sources close to the sensor. After finetuning, the algorithm was found to be able to detect relatively small quantities of threat sources at high standoff distances. Achieving the desired high performance for both close and distant sources will likely require doing parallel computations with two ( k′ =1s and k′ =15s, for example) integration times. If, as in this study, the false alarm sets for both integration times are the same, there will be no increase in false alarm rates when performing such multiple tests for alarms. In addition to maintaining sensitivity to close-up sources, the shorter integration time will help maintain performance in urban environments where the line of sight from the detector to the source is often blocked by buildings. In this work, we have illustrated how integration time, source standoff distance, and velocity affect the detectable (at specified N/FAP and PD) source strength values in our anomaly detection method. We have not discussed how these variables influence the time-to-detection – the point in the source temporal profile when an alarm is issued. The time-todetection problem will be the subject of future investigation. ACKNOWLEDGMENT Pacific Northwest National Laboratory is operated for the U.S. Department of Energy by Battelle under Contract DE-AC0576RL01830. REFERENCES [1]
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