Embed Size (px)
Citation preview
Annals of Nuclear Energy 133 (2019) 483–490
Contents lists available at ScienceDirect
Annals of Nuclear Energy
journal homepage: www.elsevier .com/locate /anucene
Rapid nuclide identification algorithm based on convolutional neuralnetwork
https://doi.org/10.1016/j.anucene.2019.05.0510306-4549/� 2019 Elsevier Ltd. All rights reserved.
⇑ Corresponding author at: Department of Nuclear Science & Engineering,Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China.
E-mail address: [email protected] (X. Tang).
Dajian Liang a, Pin Gong a,b, Xiaobin Tang a,b,⇑, Peng Wang c, Le Gao a, Zeyu Wang a, Rui Zhang a
aDepartment of Nuclear Science & Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, Chinab Jiangsu Key Laboratory of Nuclear Energy Equipment Materials Engineering, Nanjing 210016, Chinac School of Environmental and Biological Engineering, Nanjing University of Science and Technology, Nanjing 210094, China
a r t i c l e i n f o
Article history:Received 11 December 2018Received in revised form 1 April 2019Accepted 27 May 2019
Keywords:Rapid nuclide identificationLow-resolution detectorGamma-ray spectroscopySpace-filling curveConvolutional neural network
a b s t r a c t
Rapid nuclide identification is crucial in improving the performance of radioactivity monitoring. Rapidmeasurement of considerable fluctuation and noise in gamma-ray spectra causes difficulties in nuclideidentification. Current methods require noise removal, background subtraction, feature extraction, andthe information of low-count channels may be lost during these processes. In this study, we developeda rapid nuclide identification method based on convolutional neural network (CNN). A dataset was con-structed using simulation method for CNN training. The algorithm was evaluated with different gamma-ray spectra measured under different times, distances, and mixed radioactive sources. Results showedthat the algorithm has high recognition accuracy for low count rate gamma-ray spectra, and whichcan be used to improve the identification performance of rapid radiation monitoring.
� 2019 Elsevier Ltd. All rights reserved.
Contents
1. Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4832. Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
2.1. Convolutional neural network . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4842.2. Space-filling curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4842.3. Evaluation method to binary classification . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484
3. Methodology. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 485
3.1. Gamma-ray spectra simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4853.2. Network architecture and parameter settings. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4854. Results and discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486
4.1. Evaluation of training results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4864.2. Application to drift spectra . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4884.3. Comparison with different models. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4885. Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490Appendix A. Supplementary data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490
1. Introduction
Nuclide identification is a crucial component of spectrum anal-ysis. The fluctuation of spectra with low count rates causes diffi-culty in rapid radioactive nuclide identification becausecharacteristic peaks are difficult to distinguish. Moreover, peak
484 D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490
matching algorithm has difficulty dealing with complex over-lapped peaks that may possibly appear in low-resolution spectra(Bobin et al., 2016; Tsabaris et al., 2018; Fagan et al., 2012).
Spectra processing is one of the research directions of spectralanalysis. In order to remove poor statistical information in spec-trum caused by low resolution, there are studies to denoise spectrabased on wavelet method (Tsabaris and Prospathopoulos, 2011),and the researchers also develop an automatic analysis software(Tsabaris and Prospathopoulos, 2008; Kalfas et al., 2016). Further-more, some studies have been done using hardware developmentsand configuration for reducing background (Al-Azmi, 2008; Bruchand Wallraff, 2007).
For the monitoring of radioactivity in the environment, low-level gamma-ray spectra analysis has been studied (Androulakakiet al., 2016; Caciolli et al., 2011). Several studies have usedmachine learning methods to solve the problem of nuclide identi-fication (Bobin et al., 2016; Hata et al., 2015; Kamuda et al., 2017;Sullivan and Stinnett, 2015), and they have shown that a trainedmachine learning model can automatically identify nuclide. Artifi-cial neural network (ANN) has been used for rapid nuclide identi-fication in low-resolution gamma-ray spectra (Chen and Wei,2009; He et al., 2018; Kamuda et al., 2017). ANNmethod is suitablefor unmanned mobile units due to its automation and stability,which can be applied in radioactivity monitoring and mapping,such as unmanned fixed monitoring site (Tsabaris et al., 2011)and mobile site (Bruin, 2010). However, ANN has difficulty han-dling high-dimensional input data due to the full connectivity ofnodes. Studies have focused on the length reduction of the inputvector by using spectral feature extraction to improve accuracyand efficiency, but the pre-processing methods of feature extrac-tion and background subtraction may lose channels with lowcounts.
Convolutional neural network (CNN) in machine learning hasbeen widely used in computer vision and nature language process-ing (Krizhevsky et al., 2012; Lecun et al., 1998; LeCun et al., 2015).Through convolution operations, spatial correlation features can belearned and dimensions of input are reduced. Compare with a fullconnected network, CNN improves recognition and generalizationperformance. We developed a rapid nuclide identification algo-rithm for full-spectrum input based on CNN in this study. The algo-rithm is different from the mode of ‘‘feature extraction?machinelearning? nuclide identification”. The algorithm can correctlyidentify nuclide with high accuracy for rapid-measurement andcorrect identification of drift spectra.
2. Theory
2.1. Convolutional neural network
CNN is a multi-layer perceptron (MLP) inspired by biologicalthinking and consists of input layer, convolutional layers, pooling
Fig. 1. Illustration of C
layers, fully connected layers and an output layer (Krizhevskyet al., 2012). A full CNN architecture (Fig. 1) is formed by stackingthese layers.
Supposing that we have an input volume X with size of m�m,and the convolutional layer’s parameters consist of a set of learn-able filtersWwith size of n� n� k. The feature mapH can be com-puted as
hkij ¼ f Wk � x
� �ijþ bk
� �ð1Þ
where hkij is the value of k-th feature map matrix H, f() is the activa-
tion function, Wk is the k-th filter matrix and bk is the bias in a con-volution layer. The convolution operation essentially performs dotproducts between the filters and local regions of the input.
Feature map is provided as an input to the pooling layer per-forms a downsampling operation to reduce matrix size. A vectorthat contains all input features extracted by convolution can beobtained after multiple convolution layers and pooling layers.Then, the vector becomes fully connected to the output vector, asseen in regular neural networks.
Unlike the full connection of nodes in ANN, the convolutionoperation enables parameter sharing to control the number ofparameters in the network. Parameter sharing greatly reducesthe amount of computation, which in turn reduces the memoryrequirements of running the network and allows training for largenetworks.
2.2. Space-filling curve
Space-filling curves, such as the Hilbert curve and Z-ordercurve, are usually utilized as a descending dimension algorithmin information retrieval. Faloutsos and Roseman (1989) showedthat the Hilbert curve has ideal data clustering characteristics,but its mapping execution process is complicated. Space-fillingcurves are used in ascending and descending dimensions whilemaintaining a high spatial correlation.
A vector can also be mapped to a 2D space through the transfor-mation of a space-filling curve while preserving the spatial conti-nuity. Based on the characteristics of input and training in CNN,the space-filling curve can reduce the dimension of CNN input dataand enhance the capability of generalization. In Section 3, we com-pared the convergence properties of the vector-transformationmethod.
2.3. Evaluation method to binary classification
Assuming that predicted and actual targets are classified into 0and 1 in the same manner, four possible outcomes are available,namely, true positive (TP), true negative (TN), false positive (FP)and false negative (FN), as shown in Table 1.
NN architecture.
Table 1Four possible outcomes of binary classification.
Reality
1 0
Prediction 1 True Positive (TP) False Positive (FP)0 False Negative (FN) True Negative (TN)
Fig. 2. Examples of the simulated 60Co gamma-ray spectra with different countrates of peaks.
Fig. 3. Four transformation methods from vector mapping to a matrix.
D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490 485
Receiver operating characteristic (ROC) curve and precision-recall (P-R) curve are used to evaluate the classification problemin machine learning (Bradley, 1997; Davis and Goadrich, 2006;Ozenne et al., 2015). The ROC curve is defined by true positive rate(TPR) and false positive rate (FPR):
TPR ¼ TP=ðTP þ FNÞ ð2Þ
FPR ¼ FP=ðFP þ TNÞ ð3ÞThe P-R curve is defined by precision and recall:
precision ¼ TP=ðTP þ FPÞ ð4Þ
precision ¼ TPR ¼ TP=ðTP þ FNÞ ð5ÞTherefore, ROC and the P-R curves can be illustrated by chang-
ing threshold t for the test data (Davis and Goadrich, 2006). Thearea under the curve (AUC) is computed as
AUC ¼Z 1
�1TPR tð ÞFPR0
tð Þdt ð6Þ
where t is the classifier threshold. AUC is used to evaluate the per-formance of the classifier by using value size. The larger AUC is, thebetter the classification performance is. The specific evaluationresults need to be combined with the above data for description.
3. Methodology
3.1. Gamma-ray spectra simulation
The algorithm proposed in this study is based on a large trainingdataset used for learning to fit CNN parameters. The spectra simu-lated with Monte Carlo N-Particle transport (MCNP) by using a NaI(Tl) detector model are used as the training dataset. The radioac-tive sources we tested include 60Co, 137Cs, 238Pu, and 131I.
To ensure that the characteristic peak and Compton scatteringcontribution can be observed of the simulated spectrum, the parti-cle number was set to 108. We measured background spectra atintervals of 1 s in 1–20 s. These background spectra were randomlyadded to the simulated spectra to produce diverse training sam-ples. Fig. 2 shows 60Co gamma-ray spectra with different countrates of peaks.
In accordance with the simulation method, a total of 8000 spec-tra were simulated and used as a dataset. The dataset containedvarious spectra with different activities, different types of nuclideand different background signals. The total number of sampleswas randomly divided into training set and validation set, whichhad 7000 and 1000 samples, respectively.
3.2. Network architecture and parameter settings
The CNN architecture in this study contains two convolutionallayers, two pooling layers and one fully connected layer. TheCNN input is a 32 � 32 matrix and output layer is a target vectorcontaining the probability of each existence nuclide. In addition,rectified linear unit (ReLU) is the activation function for convolu-tional layer.
f ðxÞ ¼ maxð0; xÞ ð7Þ
Fig. 4. Convergence curves for each transformation method.
Fig. 5. Example of the transformed 60Co gamma-ray spectrum using Hilbert curve.
Table 2Radionuclides for the experiments con-ducted in this study.
Radionuclides Radioactivity (Ci)
60Co 1.34 � 10�6
137Cs 1.39 � 10�6
238Pu 8.80 � 10�3
131I 9.2 � 10�7
486 D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490
ReLU is an activation function widely used in deep learning(Lecun et al., 1998). The function, which outputs maximum value,is greatly reduced the amount of calculation from judging whetherthe input is greater than 0, and the convergence is much faster thansigmoid and tanh function (Krizhevsky et al., 2012).
It can effectively solve the vanishing gradient problem andspeed up data training. Furthermore, hyperparameters remarkablyinfluence the CNN output, which must be optimized to preventCNN from falling into the local optimum and over fitting.
To test the feasibility of the space-filling curve in CNN training,we projected the spectrum onto a 2D plane using the Hilbert and Z-order curves and vertical and horizontal scanning and input into
Fig. 6. ROC curve for the predicted res
CNN for training. Figs. 3 and 4 show the illustrations of each2nd-order curve and the convergence curves for each transforma-tion method, respectively. The results showed that the loss func-tion curve of the space-filling curve transformation methodconverged to a small value, that is, the prediction accuracy usingthe space-filling curve transformation method was high underthe same training conditions. Compared with the Z-order curve,the Hilbert curve converged faster and smoother. The Hilbert curvewas used as a matrix transformation method for gamma-ray spec-trum in this study. Fig. 5 shows an example of the transformed60Co gamma-ray spectrum using Hilbert curve.
For multi-classification problems, the output layer generallyuses the softmax function. However, obtaining multiple correctidentification results is difficult for multi-nuclide spectra. Multi-nuclide identification can be classified into multiple binary-classification problems, which are generally implemented usingthe sigmoid function
f xð Þ ¼ 1=ð1þ e�xÞ: ð8ÞThe sigmoid function maps real numbers to [0, 1], the outputs
of sigmoid are considered to be probabilities. Instead of outputthe proportion of probability for each nuclide from softmax func-tion, we can divide the values of output into a positive class whenthe output satisfies a certain probability condition.
Through Hilbert-curve transform and convolution operation,the information around the characteristic peaks in spectrum canbe well extracted. The amount of weights in CNN is greatly reducedcompared with a fully-connected network, i.e., the data storagerequired is reduced, which helps with applications on sensorsand chips.
4. Results and discussion
4.1. Evaluation of training results
To evaluate the proposed method, a trained CNN was used topredict nuclide in the measured spectrum. The radioactive sourceinformation used is shown in Table 2. The spectra were measuredusing a 200 � 200 NaI (ORTEC Inc.) detector whose measuring energyranged from 30 keV to 3000 keV and with a resolution of approxi-mately 7.7% at 662 keV. We measured 750 spectra for CNN predic-tion, in which spectra were measured at different detection times,different distances, and different mixed radioactive sources.
ults; (b) shows the details of (a).
Fig. 7. P-R curve for the predicted results; (b) shows the details of (a).
D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490 487
All spectra were transformed into 32 � 32 matrices as inputs byusing the Hilbert curve. Figs. 6 and 7 show the ROC and P-R curvesfor the predicted results of 60Co, 137Cs, 238Pu, and 131I. Both curvesare very close to the ideal point ((0,1) in the ROC curve and (1,1) inthe P-R curve), indicating that the trained CNN was reliable in theclassification of nuclide identification. Table 3 shows the AUC val-ues of the identified nuclide in ROC and P-R curves. These valuesprove that the trained CNN can judge the species of the nuclidewith high accuracy for test spectra.
Different influencing factors affect the accuracy of CNN identifi-cation results. Fig. 8 shows the 60Co gamma-ray spectra with dif-ferent gross counts, which were measured at 20 s and 4 s, and
Fig. 8. 60Co spectra of different gross counts. (a) 9
Table 3AUC values of respectively identified nuclide in ROC and P-R curves.
Radionuclides AUCROC AUCP-R
60Co 0.9953 0.9776137Cs 0.9925 0.9772238Pu 0.9921 0.9760131I 0.9953 0.9787
labeled as SPE-1 and SPE-2, respectively. As shown in Table 4,the CNN output value of SPE-2 was similar to that of SPE-1, butthe fluctuation of SPE-2 was large. The output value can be denotedthat probability of 60Co existence was greater than 99%. Mean-while, the output of other nuclide was less than 0.5, which canbe considered non-existent.
Fig. 9(a) shows the gamma-ray spectrum mixed with 137Cs and60Co. Fig. 9(b) shows the spectrum mixed with 238Pu, 137Cs and60Co. Fig. 9(a) and (b) are labeled SPE-3 and SPE-4, respectively.The output values of each nuclide in SPE-3 and SPE-4 wereobtained using CNN through the sigmoid function in the output
648 gross counts and (b) 1884 gross counts.
Table 4Output values of CNN for 60Co gamma-ray spectra with different gross counts.
Radionuclides Output
SPE-1 SPE-2
60Co 0.9998 0.9991137Cs 0.2308 0.0099238Pu 0.0013 0.0003131I 0.1218 0.2711
Table 5Output values of CNN for different mixed gamma-ray spectra.
Radionuclides Output
Fig. 9. (a) Mixed spectrum of 137Cs and 60Co and (b) mixed spectrum of 238Pu, 137Cs, and 60Co.
488 D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490
layer, as indicated in Table 5. The output values of the mixednuclides in the spectra were close to 1, whereas the values ofnon-existing nuclide are small. In addition, a high-count false peakappeared in the low energy region of SPE-3, which caused a high-value output of 238Pu in SPE-3, although the value was still lessthan 0.5. This result indicates that CNN has the potential to elimi-nate possible false positive peaks.
SPE-3 SPE-4
60Co 0.9977 1.0000137Cs 0.9999 0.9996238Pu 0.3335 0.9659131I 0.0101 0.0762
4.2. Application to drift spectra
High temperatures may cause spectrum drift. The 60Co driftspectrum was simulated by changing the photomultiplier tubevoltage to estimate the identification performance of CNN withdrift spectra, as shown in Fig. 10. Table 6 shows the CNN outputvalues of the original spectrum and drift spectrum. 60Co was accu-rately identified from the original spectrum and 10-channel driftspectrum, whereas an identification error occurred in the 20-channel drift spectrum.
Compared with other machine learning methods, CNN was ableto omit explicit feature extraction by implicitly learning from thetraining set in the network. CNN has the advantages of identifyinggraphics with displacement, scaling and other forms of distortioninvariance. In this work, CNN was able to identify the drift spec-trum within a certain range.
Fig. 10. Illustration of drift gamma-ray spectra and original spectrum.
Table 6Output values of CNN for different drift gamma-ray spectra.
Radionuclides Output
Origin 10 Channels Drift 20 Channels Drift60Co 1.0000 1.0000 0.1337137Cs 0.0189 0.0234 0.2651238Pu 0.0361 0.0381 0.0230131I 0.0297 0.0353 0.0368
4.3. Comparison with different models
A full connected back propagation neural network (BPNN) isused to compare the identification performance with CNN. The testspectra were measured in a short time. To reduce network compu-tation, 128 feature vectors were extracted as the BPNN input viawavelet transform. The number of neurons in hidden layer was100. To prevent overfitting, we added dropout to BPNN and set itto 0.5. Furthermore, 3 machine learning method of k-NearestNeighbor (kNN), support vector machine (SVM) and decision treeare also used to compare with ANN method, which are often usedfor classification task.
The dataset used for this test consisted of 137Cs gamma-rayspectra obtained by short-time, long-distance measurement. Thespectra were measured at 32, 40, 45, 60, 70 cm, and the count rateswere 3, 5, 10, 15 and 20 cps, respectively. All spectra were mea-sured in 2–12 s at each position. Fig. 11 shows the maximumand minimum gross count spectra.
The output threshold was set to 0.5. If one output value isgreater than 0.5, then the nuclide will be considered existent.The results showed in Fig. 12. The accuracy of different models
Fig. 12. Accuracy of nuclide ident
Fig. 13. Examples spectra w
Fig. 11. Measured 137Cs gamma-ray spectra for evaluation.
D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490 489
indicates that ANN method has good identification ability forspectra with large noise and insignificant features, and the accu-racy of BPNN and CNN are greater than 80% in each position. Inaddition, the accuracy of CNN was above 90% for the spectradetected at 5 positions, which show that CNN method is morestable than BPNN.
Fig. 13 shows some spectra with a low count rate that aredifficult to artificially identify in the above test set. The algo-rithm eliminated spectra preprocessing, such as backgroundsubtraction and spectrum smoothing, indicating that the back-ground noise was also inputted into the networks and thatlow-count channels may have been recognized as a noise signal.As shown in Table 7, the output values of 137Cs did not meetthe requirements but were greater than the other output val-ues. The output values of BPNN were able to converge to asmall value, but the CNN output of 137Cs was highly differentfrom the other values. Changing the threshold may result inenhanced recognition accuracy.
ification for different models.
ith a low-count rate.
Table 7Output value of CNN for spectra with a low count rate from Fig. 13.
Radionuclides SPE-5 SPE-6 SPE-7
CNN BPNN CNN BPNN CNN BPNN
60Co 0.0046 0 0.0047 0 0.0041 0137Cs 0.1946 0.0338 0.1219 0.0559 0.2745 0.0153238Pu 0.1290 0.0001 0.0912 0.0001 0.0341 0.0001131I 0.0171 0 0.0684 0 0.0062 0
490 D. Liang et al. / Annals of Nuclear Energy 133 (2019) 483–490
5. Conclusions
A rapid nuclide identification method based on CNN was devel-oped for low-resolution spectra. By training simulated spectra, thetrained CNN can effectively extract energy peaks and informationaround channels. Comparing the predictions of short-term mea-sured spectra by various models, the proposed method has higheraccuracy. The evaluation results proved that the algorithm can beapplied for rapid nuclide identification, also applied for mappingand site characterization as well as for integrating sensors inunmanned vehicles for mapping applications. Future work willanalyze the impact of background and overlapping peaks onunmanned monitoring site.
Acknowledgments
This work was supported by the National Natural Science Foun-dation of China (Grant No. 11675078), the Primary Research andDevelopment Plan of Jiangsu Province, China (Grant No.BE2017729), and the Foundation of Graduate Innovation Centerin NUAA, China (Grant No. kfjj20180601).
Appendix A. Supplementary data
Supplementary data to this article can be found online athttps://doi.org/10.1016/j.anucene.2019.05.051.
References
Al-Azmi, D., 2008. Simplified slow anti-coincidence circuit for Compton suppressionsystems. Appl. Radiat. Isot. Incl. Data Instrum. Methods Use Agric. Ind. Med. 66,1108–1116.
Androulakaki, E.G., Kokkoris, M., Tsabaris, C., Eleftheriou, G., Patiris, D.L., 2016. Insitu c -ray spectrometry in the marine environment using full spectrumanalysis for natural radionuclides. Appl. Radiat. Isot. 114, 76–86. https://doi.org/10.1016/j.apradiso.2016.05.008.
Bobin, C., Bichler, O., Lourenço, V., Thiam, C., Thévenin, M., 2016. Real-timeradionuclide identification in c-emitter mixtures based on spiking neuralnetwork. Appl. Radiat. Isot. 109, 405–409. https://doi.org/10.1016/j.apradiso.2015.12.029.
Bradley, A.P., 1997. The use of the area under the ROC curve in the evaluation ofmachine learning algorithms. Pattern Recognit. 30, 1145–1159. https://doi.org/10.1016/S0031-3203(96)00142-2.
Bruch, T., Wallraff, W., 2007. The Anti-Coincidence Counter shield of the AMStracker. Nucl. Inst Methods Phys. Res. A 572, 505–507.
Bruin, S. De, 2010. Optimization of mobile radioactivity monitoring networks. Int. J.Geogr. Inf. Sci. 24, 365–382.
Tsabaris, C., Prospathopoulos, A., 2011. Appl. Radiat. Isot. 69, 1546–1553.C. Tsabaris, A. Prospathopoulos, 2008. An information system for radioactivity level
in aquatic environments.Tsabaris, C., Androulakaki, E.G., Alexakis, S., Patiris, D.L., 2018. An in-situ gamma-ray
spectrometer for the deep ocean. Appl. Radiat. Isot. 142, 120–127. https://doi.org/10.1016/j.apradiso.2018.08.024.
Tsabaris, C., Patiris, D.L., Lykousis, 2011. KATERINA: an in situ spectrometer forcontinuous monitoring of radon daughters in aquatic environment. Nucl.Instruments Methods Phys. Res. 626, S142–S144.
Caciolli, A., Baldoncini, M., Bezzon, G.P., Broggini, C., Buso, G.P., Callegari, I., Colonna,T., Fiorentini, G., Guastaldi, E., Mantovani, F., 2011. A new FSA approach forin situ $\gamma$-ray spectroscopy. Eprint Arxiv 414, 639–645.
Chen, L., Wei, Y.-X., 2009. Nuclide identification algorithm based on K-L transformand neural networks. Nucl. Instruments Methods Phys. Res. Sect. A Accel.Spectrometers. Detect. Assoc. Equip. 598, 450–453.
Davis, J., Goadrich, M., 2006. The Relationship Between Precision-Recall and ROCCurves. In: Proceedings of the 23rd International Conference on MachineLearning. ACM. https://doi.org/10.1145/1143844.1143874.
Fagan, D.K., Robinson, S.M., Runkle, R.C., 2012. Statistical methods applied togamma-ray spectroscopy algorithms in nuclear security missions. Appl. Radiat.Isot. 70, 2428–2439. https://doi.org/10.1016/j.apradiso.2012.06.016.
Faloutsos, C., Roseman, S., 1989. Fractals for secondary key retrieval, in: Proceedingsof the Eighth ACM SIGACT-SIGMOD-SIGART Symposium on Principles ofDatabase Systems. ACM, pp. 247–252.
Hata, H., Yokoyama, K., Ishimori, Y., Ohara, Y., Tanaka, Y., Sugitsue, N., 2015.Application of support vector machine to rapid classification of uranium wastedrums using low-resolution c-ray spectra. Appl. Radiat. Isot. 104, 143–146.https://doi.org/10.1016/j.apradiso.2015.06.030.
He, J.-P., Tang, X.-B., Gong, P., Wang, P., Han, Z.-Y., Yan, W., Gao, L., 2018a.Spectrometry analysis based on approximation coefficients and deep beliefnetworks. Nucl. Sci. Tech. 29, 69. https://doi.org/10.1007/s41365-018-0402-4.
He, J., Tang, X., Gong, P., Wang, P., Wen, L., Huang, X., Han, Z., Yan, W., Gao, L., 2018b.Rapid radionuclide identification algorithm based on the discrete cosinetransform and BP neural network. Ann. Nucl. Energy 112, 1–8. https://doi.org/10.1016/j.anucene.2017.09.032.
Kalfas, C.A., Axiotis, M., Tsabaris, C., 2016. SPECTRW: A software package for nuclearand atomic spectroscopy. Nucl. Instruments Methods Phys. Res. 830, 265–274.
Kamuda, M., Stinnett, J., Sullivan, C.J., 2017. Automated isotope identificationalgorithm using artificial neural networks. IEEE Trans. Nucl. Sci. 64, 1858–1864.https://doi.org/10.1109/TNS.2017.2693152.
Krizhevsky, A., Sutskever, I., Hinton, G.E., 2012. Imagenet classification with deepconvolutional neural networks. Adv. Neural Inf. Process. Syst., 1097–1105
LeCun, Y., Bengio, Y., Hinton, G., 2015. Deep learning. Nature 521, 436.Lecun, Y., Bottou, L., Orr, G., Müller, K.-R., 1998. Efficient BackProp, Neural
Networks: Tricks of the Trade.Ozenne, B., Subtil, F., Maucort-Boulch, D., 2015. The precision–recall curve
overcame the optimism of the receiver operating characteristic curve in rarediseases. J. Clin. Epidemiol. 68, 855–859. https://doi.org/10.1016/j.jclinepi.2015.02.010.
Sullivan, C.J., Stinnett, J., 2015. Validation of a Bayesian-based isotope identificationalgorithm. Nucl. Instruments Methods Phys. Res. Sect. A Accel. Spectrometers,Detect. Assoc. Equip. 784, 298–305. https://doi.org/10.1016/j.nima.2014.11.113.
