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ROLE OF NUCLEAR FORENSICS DEFINED AS DIGITAL PROBLEM WITH
NEUROFUZZY APPROACH IN VARIOUS APPLICATIONS
Dr. Miltiadis Alamaniotis, University of Utah, Salt Lake City, UT
Dr. Hermilo Hernandez, University of Utah, Salt Lake City, UT
Dr. Tatjana Jevremovic, University of Utah, Salt Lake City, UT
Abstract
Nuclear Forensics identifies matching of unknown sample nuclear fingerprints with those that
are already known as one of its major issues requiring development of powerful methods to be highly
fast and accurate. Therefore, computer based approaches offer the capability for developing automated
methods applicable to nuclear forensics. To develop such methods the role of nuclear forensics and the
respective challenges should be clearly defined in the “digital computer-based world”. In this paper
we discuss nuclear forensics as a digital problem and we introduce a neuro-fuzzy methodology
applicable to nuclear forensics. The methodology is specialized for matching unknown gamma ray
signals to signals already known, but can also generalized for other type of signals and/or fingerprints.
The presented methodology is tested on a set of known signals.
Introduction
With this paper we introduce the importance of a highly needed discipline in the country, the
nuclear forensics. It applies to all fields of interest to nuclear science and engineering, chemical
engineering and chemistry, and all other associated fields and disciplines [1]. Nuclear forensics is a
science highly relying on interdisciplinary knowledge culminating in precise analysis of samples of
any origin by identifying their “true home”, in other words in finding where there were taken from,
how they and if they were smuggled to a given location by identfiying pathways [2]. Such analysis
applies to many fields of interest to nuclear fuel cycle [3,4] and chemistry. The analysis consists of a
digital data-based search process (recently found to be of high value) to find the origin of the sample
based on its nuclear signature. Such a signature includes measuring of specific samples properties
using a predetermined method, for example gamma spectroscopy, and subsequent matching of such
measurements to a set of known (digital) values [5].
Recently, all steps in the nuclear fuel cycle have acquired important relevance in the country
in finding the best way for the fuel management in the future. Thus, elevated importance of an
increasing volume of nuclear data as pertaining to nuclear fuel cycle/nuclear forensics being generated
to be organized and accurately managed and analyzed. Therefore, there is an emerging demand for
developing new, fast and accurate ad-hoc methods in defining the nuclear signatures of real-time data
analyses [6]. Towards that end there are ongoing research efforts on developing digital libraries and
databases populated by the existing nuclear data, while at the same time to allow easy updates. A
nuclear library that is still under development is presented and described in [5], while a coincidence
signature library with associated algorithms aiming at radionuclide analysis is presented in [7].
In this paper we present how the artificial intelligence technologies [8] could be applied in
nuclear fuel cycle data analysis in generating a novel algorithm to collect and organize data pertaining
to nuclear forensics. The algorithm should be based on developed and yet to be developed digital data
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libraries [9]. In adopting a synergism of fuzzy logic and neural networks methods [10], we show how
to analyze as an example a complex gamma spectroscopic data, and therefore attribute the nuclear fuel
cycle needs. This neurofuzzy model [11] is comprised of two modules:
- in (1) the model utilizes fuzzy logic to represent values of specific extracted material properties
taking into account inherent uncertainties, and
- in (2) the fuzzified values are fed into a neural network which provides in its output a number
to be used to designate origin of nuclear material.
Before that, the neural network, which plays the role of digital library, is trained on a set of known data
that uniquely characterize the sources of interest [12]. This methodology allows for automated and fast
analysis of incoming data, while eases the process of inference and decision-making. This method has
been already tested on a set of various gamma spectra where the efficiency of the neurofuzzy model
was well demonstrated.
Background
Fuzzy Logic Elements
The theory of fuzzy logic was based on the human way of thinking [10]. More particularly,
fuzzy logic models to a degree the way that humans think and make inferences. For instance, let’s
consider the way humans are characterized depending on their height. The linguistic terms used in that
case are: short, medium and tall. The questions raised in that case is whether there are distinct limits
among those terms or not; is there a numerical threshold for discriminating tall people from medium
height people. The answer is no. However, by a visual inspection of a person, we are able to
characterize him by giving him one or two of those terms. In the latter case, we are certain that the
person does not belong to one group (e.g. tall) but rather it belongs to two groups with some degree for
each one; a person is looks tall but he is more of a medium height person. Thus, there is uncertainty
in our linguistic based classification [10].
Fuzzy logic provides the mathematical foundation for modeling the uncertainty of human way
of thinking. More particularly, it introduces the use of fuzzy sets which consist of a generalized version
of crisp sets [10]. Fuzzy sets are represented by special functions called membership functions. A
membership function assigns a value MS(x) to an input value x. M(x) expresses the degree with which
the value x belongs to the fuzzy set S. A value x may belong to more than one fuzzy set with a different
degree to each one:
 M A ( x)  d1

x: 
(1)
....
M ( x)  d
 Z
Z
Where d# expresses the numberical value of degrees of membership in fuzzy set the respective fuzzy
set (in that case on of A,…,Z).
Artificial Neural Networks
The foundation for development of artificial neural networks is the human brain structure [10].
The human brain is comprised of billions of biological neurons. Each biological neuron consists of
synapses, dendrites, soma and axon. In an analogy to a biological neuron, an artificial neuron is
comprised of weights, sum of weights, activation function and the output path as shown in figure 1. An
artificial neural network is consisted of many artificial neurons; neurons are grouped according to i)
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their position in the network and ii) their connection to other neurons. Therefore we have three groups
(or layers) of neurons: the input layer, the hidden layer and the output layer as presented in figure 2.
Figure 1. Schematic diagram of an artificial neuron
Figure 2. Schematic diagram of an artificial neuron
Neurons of each layer are connected to neurons of the next layer; in some special cases neurons
of the same layer are also connected to each other. The number of layers, neurons and connections
depend on modeler’s needs and on the specific application [10]. The weight evaluation is performed
through a process called training. The training process makes use of pairs of known outputs and inputs
in order to evaluate the network weights via specialized algorithms such as the error backpropagation
algorithm [10].
Nuclear Forensics: Digital Approach
Nowadays computer play a significant role in our daily routine. Actions that have being done
manually in the past currently are performed by computers. More particularly, computers exhibit a
performance that did not a decade ago. This computer performance is the result of developments in
software engineering, databases, artificial intelligence, pattern recognition, and machine vision.
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Nuclear forensics is a recently developed area that adopts parts of many other areas. The main
goal in nuclear forensics is to match measured data to known ones and subsequently make inferences
about the origin of the measurement. In such a framework, computers can play a significant role as it is
identified by Sutton et al. in [5]. On other words, nuclear forensics can be framed as a computer based
problem (or digital problem) and therefore use modern techniques from artificial intelligence and
pattern recognition [13,14].
The challenges in nuclear forensics defined as a digital problem include database development,
knowledge representation, measurement uncertainty handling, pattern matching accuracy, and speed of
matching. The architecture of a digital nuclear forensics system is presented in figure 3.
Figure 3. Architecture of digital nuclear forensics system
Though computers automate the processing of input signals, they are not necessarily fast.
Crucial to computer system performance is the amount of computational load to be processed. The
computational load depends on various factors (based on figure 3): the volume of stored data, volume
of extracted features, the speed of matching algorithm and speed of inference mechanism. Hence,
challenges in defining the role of nuclear forensics as a digital problem overlap with the above factors.
Research should focus on developing efficient ways for nuclear data representation. The term
knowledge representation is the significant key for efficient nuclear forensics systems development. To
elaborate on that, the existing knowledge should be encoded by selecting suitable features. Selection of
features should be done in such a way that the matching uncertainty is reduced and subsequently the
pattern recognition algorithm identifies the true patterns giving zero error (zero rates of false
identifications and misses).
Overall, integration of nuclear and radiochemistry with digital computers and the challenges
that should be addressed define a new research horizon with a lot of potential applications in nuclear
forensics.
Neuro-fuzzy Approach for Digital Nuclear Forensics
The block diagram of the neuro-fuzzy methodology is shown in figure 4. Initially we assume
that the fingerprint of a sample is obtained. In computer parlance the fingerprint is comprised of a set
of values that express the numerical values of the selected features, i.e. the features that have been
selected for knowledge representation.
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The fingerprint is forwarded to the neuro-fuzzy approach, where it is being processed. The first
step of the proposed approach includes the fuzzification of the fingerprint. More particularly, the
features go under fuzzification using a set of fuzzy sets for each one. The fuzzy sets are formulated in
such a way that each one expresses the expected value and the associated uncertainty. An example of
fuzzy sets regarding isotope abundance from various origins is depicted in figure 5, where we observe
that the fuzzy sets overlap. Set overlapping implicitly expresses the uncertainty about a feature value
by assigning to the feature value a non-zero degree of membership to two sets. Overall, fuzzification is
performed for all features and the fuzzy values are forwarded to the next step.
Figure 4. Block diagram of the Neuro-fuzzy approach
Figure 5. Example of fuzzy sets regarding isotope abundance from various origins
The second step includes the use of the neural network for sample matching. The neural
network gets as an input the set of fuzzified values from the previous step, and outputs the
identification result. It should be noted that the neural network goes under training, where known
fingerprints are presented to its input and the respective known origin are presented to its output.
Therefore, the weight values of the neural networks are evaluated. The purpose of the training process
is to evaluate the weights in such way that the neural network remembers the patterns and their origin.
In other words the neural network plays the role of the database (or library). By adopting a neural
network the proposed methodology manages to reduce the computational load, since knowledge is
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represented in the form of weights. At the same time, the neural network implements both the pattern
recognition algorithm and inference mechanism. Therefore, the use of a neural net reduces the
processing parts of a digital nuclear forensics system since it implements in a single unit the database,
information extraction mechanism, pattern matching algorithm and inference mechanism steps as
shown in figure 3. Once the neural network is trained, it is used for classifying unknown inputs. The
output of the neural network that is also the final output of the neurofuzzy approach is a number
determining the origin the sample. Needless to say that the output of the proposed approach may
include be more than one number; as it was mentioned earlier the neural network architecture depends
on the modeler and the specific application.
Overall, the proposed neuro-fuzzy methodology offers a powerful framework for nuclear
forensics in finding the origin of unknown samples. The advantage of the approach is that it allows
modeling of uncertainties via fuzzy sets, and “computational inexpensive” information
representation and processing via the neural network.
Test Results on a Simple Case
A set of samples of experimental measured sources are obtained with a NaI detector as
available in the Utah Nuclear Engineering Facility (UNEF). The samples include measurements taken
from two sources: i) a 60Co and ii) a 137Cs source. The measurement times are 40 sec and 60 sec
respectively. Therefore we have four measurements: i) 40sec 60Co, ii)60sec 60Co, iii) 40sec 137Cs, and
iv)60sec 137Cs. The goal is to use the neurofuzzy approach to classify unknown measurements as one
of the above four measurements.
Initially, a set of features that makes discrimination of the above measurement possible was
identified. Thus, we select the following features: i) number of characteristic peaks (1 for 137Cs, 2 for
60
Co), ii) peak energy (662keV for 137Cs, 1.17 and 1.33 for 60Co), iii) number of peak counts (useful to
discriminate between 40sec and 60 sec measurements). Therefore, we define respective fuzzy sets for
each one of the aforementioned features. The fuzzy sets are triangular with peak at expected value and
support set equal to its expected standard deviation [10].
The neural network is comprised of three layers: the input layer (three neurons), the hidden
layer (four neurons) and the output layer (one neuron). The feature values of the four measurements are
fed into the neural network during its training phase. Once the neural network is trained, it is
appropriate for measurement matching.
In order to test the presented approach we create a set of unknown 40 samples adopting the
following procedure. For each of the four measurements, Poisson fluctuation is added. By doing ten
times, we get for each measurement ten new signals that are not identical, i.e. overall 40 samples. Then
we forward the 40 samples to the presented system. Results are depicted in Table 1.
We observe in Table 1 that the proposed system identified correctly 38/40 of the samples which
means that the correct rate is 95% and the false rate is 5%. The false rate is very low and it resulted as
the false identification of 60Co: the two samples were identified as 60Co but not their respective correct
measurement time. It should be mentioned that the case under study is a simple case but it is very
indicative of the potentiality of the neurofuzzy approach.
Lastly, it should be mentioned that the average per sample execution time of the presented
approach is 1.2 sec. However, it is expected the execution time to be higher for more complicated cases
but it will still remain low.
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Table 1. Test Case Results in 40 Samples
Sample Description
Correct Identification
False Identification
40sec 137Cs
10/10
0/10
60sec 137Cs
10/10
0/10
40sec 60Co
9/10
1/10
60sec 60Co
9/10
1/10
Average Processing
Time
1.2 sec
Conclusion
We have discussed the role of nuclear forensics as a digital problem and presented a
neuro-fuzzy approach for sample classification. Our focus was to identify the samples in a fast and
accurate manner by keeping the computational cost low. The approach was based on a synergy of two
different artificial intelligence tools, namely, fuzzy logic and neural networks. The approach is
developed with the idea to be extended to be a generic and robust method capable of identifying
various signals and be applicable to nuclear forensics. In addition the neuro-fuzzy approach was tested
on a simple case by using samples coming from four different measurements. Results exhibit high
accuracy and fast processing. Our future work will include testing on integration of more different
features, i.e. more complicated fingerprints, and testing on more challenging cases.
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