Spectrometry analysis based on approximation coefficients and deep belief networks

Spectrometry analysis based on approximation coefficients and deep belief networks 1 first-author 1 2 corresp Corresponding author. E-mail address: tangxiaobin@nuaa.edu.cn Corresponding author. E-mail address: tangxiaobin@nuaa.edu.cn tangxiaobin@nuaa.edu.cn 1 1 1 1 1 Department of Nuclear Science & Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Department of Nuclear Science & Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China Jiangsu Key Laboratory of Nuclear Energy Equipment Materials Engineering, Nanjing 210016, China Jiangsu Key Laboratory of Nuclear Energy Equipment Materials Engineering, Nanjing 210016, China A method of spectrometry analysis based on approximation coefficients and deep belief networks was developed. Detection rate and accurate radionuclide identification distance were used to evaluate the performance of the proposed method in identifying radionuclides. Experimental results show that identification performance was not affected by detection time, number of radionuclides, or detection distance when the minimum detectable activity of a single radionuclide was satisfied. Moreover, the proposed method could accurately predict isotopic compositions from the spectra of moving radionuclides. Thus, the designed method can be used for radiation monitoring instruments that identify radionuclides. Approximation coefficient Deep belief network Spectrometry analysis Radionuclide identification Detection rate. 1. Introduction 1 Distinguishing useful information from irrelevant information is one of the basic concerns of any spectrometric method. However, extracting the correct information from spectral sections is a very complex task for traditional algorithms that identify radionuclides based on peak search because of the limited resolution of the equipment and the often-overlapped peaks [ 1 1 ]. Thus, deconvolution, expert knowledge, and human participation are needed. An artificial neural network (ANN) is a form of artificial intelligence that attempts to mimic the behavior of the human brain and nervous system [ 2 2 ]. The ANN can extract information using the full spectral range [ 3 3 ]. ANNs have been applied to many aspects of gamma spectral analysis [ 4 4 - 11 11 4-11 ], and feature extraction is the key step in the majority of these studies. To date, algorithms on radionuclide identification are based on feature extraction, and ANNs are a major technique for performing information extraction. For example, Stinnett et al. (2017) proposed a method based on feature extraction and Bayesian classifiers to identify isotopes [ 12 12 ]. Yang et al. (2017) developed an algorithm based on feature extraction and feedforward neural networks (NNs) to discriminate alpha-gamma radiation [ 13 13 ]. However, manually supervised feature extraction requires specialized knowledge, and its parameters need to be determined, which is a complex problem. Deep learning is a class of machine learning algorithm that uses a cascade of many layers of nonlinear processing units for feature extraction (when the number of hidden layers is smaller than the input dimension), or maps the feature to a higher-dimensional space (when the number of hidden layers is larger than the input dimension), which does not require domain knowledge [ 14 14 ]. This algorithm has been applied to automatic speech recognition, image recognition, smart cars, robots, etc. [ 15 15 - 19 19 15-19 ]. In this study, an analytical spectrometry method based on approximation coefficients and deep belief networks (DBNs) is proposed. Experiments with different detection times, different numbers of radionuclides, different detection distances, and moving radionuclides were designed to evaluate the identification performance of the proposed method. 2. Theories and methods 1 2.1 Overview of the proposed method 2 The proposed method is composed of DBN training and DBN prediction ( Fig. 1 Fig. 1 ). The DBN is trained according to the flowchart shown in Fig. 1(a) Fig. 1(a) . This technique consists of spectrum simulation, extraction of approximation coefficients of the spectrum, and training. First, the model of the related detector is designed, and simulation spectra of the radionuclides of interest are obtained using the Monte-Carlo N-Particle transport code (MCNP) (a software package for simulating nuclear processes). Second, approximation coefficients of the spectrum are extracted by wavelet decomposition and normalized to eliminate the intensity difference between different spectra. Then, the normalized approximation coefficients are used as the input to the DBN. Finally, the DBN is trained using the samples of the simulation spectra, which are encoded as the input of the DBN and their target output. For DBN prediction, the trained DBN is used to predict the isotopic composition of the spectrum measured in the real environment using the process shown in Fig. 1(b) Fig. 1(b) . This process consists of spectral measurement and background subtraction, extraction of the approximation coefficients of the spectrum, and identification. First, radionuclide and background spectra are detected by the detector and smoothed to reduce noise interference. Then, the subtraction spectrum is obtained by subtracting the portion of the smoothed background spectrum according to the ratio of the radionuclide scan time to the background scan time from the smoothed radionuclide spectrum. Second, the approximation coefficients of the subtraction spectrum are extracted by wavelet decomposition and normalized to remove the effect of the change in spectrum intensity. Then, the normalized approximation coefficients are used as the input for the DBN. Finally, the trained DBN is used to predict the isotopic composition of the spectrum measured in the real environment, and the identification performance of the proposed method is evaluated by comparing the output of the DBN with its target output. 2.2 Approximation coefficients 2 The low-frequency content is the most important part of many signals, because this component gives the signal its identity. The high-frequency content, on the other hand, imparts flavor, or nuance. Approximations and details are often discussed in wavelet analysis. Approximations are high-scale, low-frequency components of the signal, whereas details are low-scale, high-frequency components. The original signal S would be decomposed into approximations and details after the signal underwent a single-level discrete wavelet transform. This process is accomplished by applying two complementary filters to the original signal, which emerges as two signals, as shown in Fig. 2(a) Fig. 2(a) . The decomposition process can be iterated, with successive approximations being decomposed in turn, and the number of iterations is called the decomposition level [ Fig. 2(b) Fig. 2(b) ]. The cA 1 , cA 2 , and cA 3 are the approximations of the original signal S , while cD 1 , cD 2 , and cD 3 are the details at different decomposition levels. Given that the analytical process is iterative, the processes can theoretically be continued indefinitely. In practice, the suitable number of levels is based on the nature of the signal, and a number from 3 to 5 is recommended. Approximation coefficients cA i ( i =1, 2, 3, 4, 5) of the spectrum can be considered as the input to the DBN. The cA i has the same spectral shape as the original spectrum, but it is more smoothed. The original spectrum (dimension: 1024) detected by an ` (Tl) detector is decomposed in this study by 3 levels of discrete wavelet transforms (mother wavelet: Daubechies wavelets) using the MATLAB Wavelet Toolbox [ 20 20 ]. The dimension of the extracted approximation coefficients is 128, which is much lower than the dimension of the original spectrum (dimension: 1024). After normalization, the extracted approximation coefficients are used as the input to the DBN. 2.3 DBN model 2 Deep learning is a machine learning paradigm that focuses on learning deep hierarchical data models. In this algorithm, a hierarchy of intermediate representations is hypothesized to be needed to learn a high-level representation of the data [ 21 21 ]. A DBN is one kind of deep learning. In machine learning, a DBN is a generative graphical model, or alternatively, a type of deep NN composed of multilayers of latent variables (hidden units), with connections between layers but not between units within each layer. A DBN can be viewed as a composition of restricted Boltzmann machines (RBMs), in which the hidden layer of each sub-network serves as the visible layer for the next [ 22 22 , 23 23 ]. Its schematic network structure is shown in Fig. 3 Fig. 3 . The structure comprises one visible layer, three hidden layers ( h 1 , h 2 , h 3 ), and one output layer [ 24 24 ]. The number of RBMs is not constant, and is determined by the nature of the data. RBMs contain a layer of visible units that represent the data, and a layer of hidden units that learn to represent features that capture higher-order correlations in the data. This module is a primitive DBN. An RBM has only a visible layer and a hidden layer, and these layers are connected by a matrix of symmetrically weighted connections W . No connections are found within a layer. Given a vector of activities v for the visible units, the hidden units are all conditionally independent, facilitating the sampling of a vector h from the factorial posterior distribution over hidden vectors p ( h | v , W ). Sampling from p ( v | h , W ) is also easy. A learning signal can be obtained by starting with an observed data vector on the visible units, and alternating several times between sampling from p ( h | v , W ) and p ( v | h , W ). This signal is simply the difference between the pairwise correlations of the visible and hidden units at the beginning and end of the sampling. Several reports have provided more detailed descriptions of RBM [ 25 25 , 26 26 ]. The variables of the final hidden layer represent the desired outputs, which can be encoded to the error backpropagation (BP) NN. The BP algorithm functions much better if the feature detectors (hidden units) in the hidden layers are initialized by learning a DBN that models the structure in the input data. The DBN algorithm was realized in this study using a MATLAB Toolbox named DeepLearnToolbox (https://github.com/rasmusbergpalm/DeepLearnToolbox), and the key parameters of the DBN used during the training process are as follows: the number of hidden layers is 1, and the dimension of the hidden layer is 1024. The dimension of the visible layer is 128 for extracting 128 approximation coefficients as the input to the DBN, the dimension of the output layer is 9 for selecting the spectra of 9 radionuclides (i.e., 57 Co, 75 Se, 60 Co, 133 Ba, 137 Cs, 192 Ir, 241 Am, 152 Eu, and 238 Pu) as training samples, thus the established DBN model is 128×1024×9. Each neuron in the output layer indicated whether the related radionuclide existed or not, and the radionuclide existed in the environment only when the output value of the related output layer neuron was greater than or equal to the threshold (0.85). 3. Experiments and results 1 The selection of training samples for the DBN is an important part of the proposed method. This process determines the predictive ability of the DBN, so detailed information about training samples will be introduced. Experiments using different detection times, numbers of radionuclides, and detection distances were designed, because these parameters can change the shape of the spectrum. The effect of radionuclides in motion on the identification performance of the proposed method was evaluated, because radionuclides may have a certain velocity in the real environment. 3.1 Assessment method 2 A gamma ray spectrometry system, which consists of a 3 in × 3 in NaI (Tl) detector (ORTEC Inc.), a PC-based multichannel analyzer (ORTEC Inc.), and MAESTRO software installed on the PC were used to assess the proposed method, and the MAESTRO 7.01 (ORTEC Inc.) software was used to record the spectra. The energy of this detector ranged from 30 keV to 3,000 keV, and the resolution was approximately 7.7% (at 662 keV). The spectra were recorded by sending a request to MAESTRO 7.01 software using its software development kit. Any spectrum that satisfied the requirements could be detected. Table 1 Table 1 lists the radionuclides utilized in the experiment, and these radionuclides are labeled as Radio-1, Radio-2, and Radio-3. 1 1 Label 1 1 Radio-1 1 1 Radio-2 1 1 Radio-3 1 1 Radionuclide 1 1 238 Pu 1 1 60 Co 1 1 137 Cs 1 1 Activity (µCi) 1 1 8.89 × 10 3 1 1 1.59 1 1 1.42 Given that the DBN can only identify the trained radionuclides, and its predictive ability depends on the number of samples, adding samples of more radionuclides during the training process of the DBN is recommended. However, the majority of radionuclides are not available in the laboratory. Simulation spectra of the radionuclides of interest (i.e., 57 Co, 75 Se, 60 Co, 133 Ba, 137 Cs, 192 Ir, 241 Am, 152 Eu, and 238 Pu) can be obtained by the MCNP, which models the mentioned detector based on its characteristics. All radionuclides except 238 Pu are industrial radionuclides. All simulation spectra are broadened with the response function of the mentioned detector. Detection rate was used to assess the identification performance of the proposed algorithm. This rate is the ratio of the correctly identified data to the total amount of data, as shown in Eq. (1) [ 27 27 ], as follows: <math display="block" id="M1"><mrow><mi>D</mi><mi>e</mi><mi>t</mi><mi>e</mi><mi>c</mi><mi>t</mi><mi>i</mi><mi>o</mi><mi>n</mi><mtext> </mtext><mi>r</mi><mi>a</mi><mi>t</mi><mi>e</mi><mo stretchy="false">(</mo><mi>%</mi><mo stretchy="false">)</mo><mo>=</mo><mfrac><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi></mrow><mrow><mi>T</mi><mi>P</mi><mo>+</mo><mi>T</mi><mi>N</mi><mo>+</mo><mi>F</mi><mi>P</mi><mo>+</mo><mi>F</mi><mi>N</mi></mrow></mfrac><mo>×</mo><mn>100</mn></mrow></math> where TP indicates true positive, TN indicates true negative, FP indicates false positive, and FN indicates false negative. The accurate radionuclide identification distance (ARID) of each radionuclide was calculated from the detection rate results with respect to the distance from the source to the detector. The ARID is the maximum distance at which detection rates are reliably ascertained to be above the required level [ 28 28 ]. The detection rate of the acceptance level in this study is 98.3%, as recommended by the ANSI N42.35 standard [ 29 29 ]. 3.2 DBN training 2 Training samples were selected. Simulation spectra of radionuclides of interest (i.e., 57 Co, 75 Se, 60 Co, 133 Ba, 137 Cs, 192 Ir, 241 Am, 152 Eu, and 238 Pu) were simulated by the MCNP, and the normalized simulation spectra generated 511 (2 9 –1=511) spectra according to the theory of combinations, which were all used as training samples for the DBN. The conditions with 1 radionuclide corresponded to 9 combinations (i.e., 57 Co, 75 Se, 60Co, 133 Ba, 137 Cs, 192 Ir, 241 Am, 152 Eu, and 238 Pu), the conditions with 2 radionuclides corresponded to 36 combinations (i.e., 57 Co+ 75 Se, 57 Co+ 60 Co,…, 152 Eu+ 238 Pu), and the number of combinations for the conditions with 3, 4, 5, 6, 7, 8, and 9 radionuclides can be acquired according to the theory of combinations, which is how we obtained the 511 spectra. The 511 normalized spectra are encoded as the input to the DBN and their target output before DBN training, and the target output was composed of 9 figures ranging from 0 to 1. For example, the target output of the 57 Co spectrum would be [1 0 0 0 0 0 0 0 0] if we sequenced the radionuclides as 57 Co, 75 Se, 60 Co, 133 Ba, 137 Cs, 192 Ir, 241 Am, 152 Eu, and 238 Pu. So, the target output of the 75 Se spectrum was [0 1 0 0 0 0 0 0 0], the target output of the 57 Co+ 75 Se spectrum was [1 1 0 0 0 0 0 0 0], and so on. Whether the trained DBN has learned the training samples properly should be verified. If not, the related parameters (section: DBN model) of the DBN should be adjusted until the mean square error of the DBN on the training set reaches an acceptable value. Table 2 Table 2 lists the results of the DBN training. The trained DBN learned the high-level features of the training set completely. Theoretically, this DBN could predict the isotopic compositions of the spectrum measured in the real environment for all radionuclides (i.e., 57 Co, 75 Se, 60 Co, 133 Ba, 137 Cs, 192 Ir, 241 Am, 152 Eu, and 238 Pu) with a detection rate of 100%. 1 1 Radionuclide 1 1 57 Co 1 1 75 Se 1 1 60 Co 1 1 133 Ba 1 1 137 Cs 1 1 192 Ir 1 1 241 Am 1 1 152 Eu 1 1 238 Pu 1 1 Detection rate 1 1 100% 1 1 100% 1 1 100% 1 1 100% 1 1 100% 1 1 100% 1 1 100% 1 1 100% 1 1 100% 3.3 Effect of detection time on the proposed method 2 Experiments using different detection times were conducted, because detection time can lead to a change in spectral intensity. The detector was installed at a fixed location, and the radionuclides were placed in front of the detector at point A ( Fig. 4 Fig. 4 ). The background spectrum without any source was recorded for 300 s to generate the background template. The spectra of Radio-1, Radio-2, and Radio-3 placed at point A ( Fig. 4 Fig. 4 ) were recorded to evaluate the detection time effect on the identification performance of the proposed method. The measurement was repeated 10 times for each condition, and detection times were 1, 2, 3, 4, and 5 s. For example, the measurement for Radio-1 with monitoring point at A ( Fig. 4 Fig. 4 ) and a detection time of 1 s would be repeated 10 times. The same rules apply to other detection times and radionuclides. A total of 150 spectra were recorded, which were all used as verifying samples. 10 spectra could be recorded at each detection time for each radionuclide, resulting in 50 spectra for each radionuclide. Each spectrum has a sample number, the value of which was determined by the measurement sequence. For example, 10 Radio-1 spectra with a detection time of 1 s would have sample numbers 1 to 10, 10 Radio-1 spectra with a detection time of 2 s would have sample numbers 11 to 20, etc. The same rules apply to Radio-2 and Radio-3. We were focused only on the output neurons of the DBN for 238 Pu, 60 Co, and 137 Cs to select three radionuclides ( 38 Pu, 60 Co, and 137 Cs) to evaluate the identification performance of the proposed method in the real environment, and all the results related to verifying samples in this study were computed by analyzing the output value of the above three output neurons. Fig. 5 Fig. 5 shows the results for samples with different detection times when only 238 Pu exists in the environment. The output value of the DBN for 238 Pu is greater than the threshold (0.85) at different times when only 238 Pu exists in the environment. The output value for 60 Co or 137 Cs is less than the threshold, indicating the presence of 238 Pu in the environment, but the absence of 60 Co and 137 Cs. The results are consistent with the actual situation because of the normalization of approximation coefficients, which can eliminate the effect of the change in spectral intensity. Therefore, the identification performance of the proposed method is not affected by the detection time if the minimum net count of the spectrum of related radionuclides is satisfied. Figures 6 Figures 6 and 7 7 illustrate similar results. The net count of the spectrum of each radionuclide measured at point A ( Fig. 4 Fig. 4 ) with a detection time of 5 s, and the count of background spectrum with a detection time of 5 s are listed in Table 3 Table 3 . The dose rate of the background without a shielding apparatus was measured in the laboratory (approximately 0.1 μSv/h). 1 1 Radionuclide 1 1 238 Pu 1 1 60 Co 1 1 137 Cs 1 1 Net count 1 1 3049 1 1 8161 1 1 3585 1 1 Background 1 1 2614 1 1 2614 1 1 2614 3.4 Effect of the number of radionuclides on the proposed method 2 Experiments with different numbers of radionuclides were performed, because this parameter can change the spectral shape. The detector was installed at a fixed location, and the radionuclides were placed in front of the detector at point A ( Fig. 4 Fig. 4 ). The spectra of the cases with different numbers of radionuclides (i.e., Radio-1, Radio-2, Radio-3, Radio-1+Radio-2, Radio-1+Radio-3, Radio-2+Radio-3, and Radio-1+Radio-2+Radio-3) placed at point A ( Fig. 4 Fig. 4 ) were recorded to evaluate the effect of the number of radionuclides on the identification performance of the proposed method. The measurement was repeated 10 times for each condition, and the detection time was 5 s. For example, the measurement for Radio-1 with monitoring point at A ( Fig. 4 Fig. 4 ) and a detection time of 5 s would be repeated 10 times. The same rules apply to other combinations. Hence, 70 spectra were recorded, which were all used as verifying samples. Three combinations (i.e., Radio-1, Radio-2, and Radio-3) correspond to the condition with 1 radionuclide. Three combinations (i.e., Radio-1+Radio-2, Radio-1+Radio-3, and Radio-2+Radio-3) correspond to the condition with two radionuclides. One combination (i.e., Radio-1+ Radio-2+ Radio-3) corresponds to the condition with three radionuclides. Table 4 Table 4 lists the results of samples with different numbers of radionuclides. All radionuclides (i.e., 238 Pu, 60 Co, and 137 Cs) have a detection rate of 100%, which demonstrates that the proposed algorithm can predict the isotopic compositions of the spectra of multiple radionuclides. This phenomenon is due to the fact that the DBN was trained using samples with mixed spectra of multiple radionuclides. However, the training samples are composed of simulation spectra which differ from the spectra measured in the real environment, especially in the low-energy region, although their shapes are similar. This phenomenon may reflect the fact that the DBN has strong tolerance, indicating promising machine learning for spectrometry analysis. 1 1 Number 1 1 238 Pu 1 1 60 Co 1 1 137 Cs 1 1 1 1 1 100 1 1 100 1 1 100 1 1 2 1 1 100 1 1 100 1 1 100 1 1 3 1 1 100 1 1 100 1 1 100 3.5 Effect of detection distance on the proposed method 2 Experiments with different detection distances were conducted, because this parameter can also lead to a change in the spectral shape. The detector was installed at a fixed location, and the radionuclides were placed in front of the detector at points A, B,…, O (15 points) at 10 cm intervals ( Fig. 8 Fig. 8 ). The spectra of the radionuclides were recorded to evaluate the effect of detection distance on the identification performance of the proposed method. The measurement was repeated 10 times for each condition, and the detection time was 10 s. For example, the measurement for Radio-1 with monitoring point at A ( Fig. 8 Fig. 8 ) and a detection time of 10 s would be repeated 10 times. The same rules apply to other monitoring points or radionuclides. Thus, 450 spectra were recorded, which were all used as verifying samples. Fig. 9 Fig. 9 shows the results of samples with different detection distances. The ARIDs of Radio-1 ( 238 Pu with an activity of 8.89×10 3 μCi and a detection time of 10 s), Radio-2 ( 60 Co with an activity of 1.59 μCi and a detection time of 10 s), and Radio-3 ( 137 Cs with an activity of 1.42 μCi and a detection time of 10 s) are greater than or equal to 60, 70, and 60 cm, respectively. The corresponding minimum detectable activities (MDAs) of Radio-1( 238 Pu with a detection distance of 60 cm and a detection time of 10 s), Radio-2 ( 60 Co with a detection distance of 70 cm and a detection time of 10 s), and Radio-3 ( 60 Cs with a detection distance of 60 cm and a detection time of 10 s) are less than or equal to 8.89 × 10 3 , 1.59, and 1.42 µCi, respectively [ 30 30 , 31 31 ]. Thus, the identification performance of the proposed method is not affected by the detection distance under certain conditions, because the effect of detection distance on the proposed method can be eliminated by the normalization of approximation coefficients. The detection rate of radionuclides (i.e., 238 Pu, 60 Co, and 137 Cs) is over 60% when the detection distance is greater than the ARID of the related radionuclide [ Fig. 9(a)–(c) Fig. 9(a)–(c) ]. This result is due to the fact that the detection rate is a statistic, and the numerator TN of Eq. (1) remains almost constant, although the numerator TP in Eq. (1) decreases with an increase in distance. This phenomenon is due to the low percentage of error in identification, which indicates the proposed method is a robust method. The spectra of radionuclides ( 238 Pu, 60 Co, and 137 Cs) placed in front of the detector according to their ARIDs are plotted to further visualize the identification performance of the proposed method ( Fig. 10 Fig. 10 ). The signal-to-noise ratio (SNR) is extremely low in this condition, and the corresponding characteristic peaks of radionuclides are not obvious (fewer counts in the photopeak region). However, the proposed method can recognize these radionuclides with a detection rate of 100%. Therefore, the proposed method is suitable for fast radionuclide identification, because it requires a lower spectrum count. 3.6 Effect of radionuclides in motion on the proposed method 2 Radionuclides may be carried by people or transported by car in the real environment. Thus, these molecules have a certain velocity. The effect of radionuclides in motion on the identification performance of the proposed method should be evaluated. The detector was installed at a fixed location, and the radionuclides were placed in front of the detector at points A, B,…, O at 10 cm intervals ( Fig. 8 Fig. 8 ). An experiment was designed to assess the effect of radionuclides in motion on the identification performance of the proposed method. A person with Radio-1, Radio-2, and Radio-3 approached point A from the starting point O along the line segment OA at a speed of approximately 0.375 m/s. The whole process took approximately 4 s, and 33 spectra were recorded at intervals of approximately 0.1 s. All spectra were used as verifying samples. Fig. 11 Fig. 11 shows the results of the samples of the moving radionuclides. The output value of the DBN for 137 Cs is greater than the threshold (0.85) at time 2.5 s, indicating the identification of 137 Cs. The corresponding value for 238 Pu is also greater than the threshold (0.85) at time 2.76 s, indicating the identification of 238 Pu. The corresponding value for 60 Co is greater than the threshold (0.85) at time 3.0 s, indicating the identification of 60 Co. Thus, the output value of the DBN for related radionuclides is always beyond the threshold after the corresponding radionuclide is recognized. The proposed method exhibits enhanced identification performance for the spectra of moving radionuclides and requires only a short time to identify all radionuclides in the environment. This characteristic is recommended for fast radionuclide identification. Fig. 12 Fig. 12 demonstrates the spectra in radionuclide identification. The spectrum has a low SNR at each time of identification of the related radionuclide, and its corresponding characteristic peak cannot be observed. The proposed method is not based on peak detection, but on information from the full spectrum. The proposed algorithm makes a judgment using information from the full spectrum, contrary to the method based on peak detection. Specialized knowledge, deconvolution, and other parameters previously used were not needed after the DBN was trained. The identification results of the spectra contained within Fig. 12(a) Fig. 12(a) , Fig. 12(b) Fig. 12(b) , and Fig. 12(c) Fig. 12(c) using MAESTRO 7.01 software (a software for gamma-ray spectrometry analysis) were all "No peaks found," as shown in Fig. 13 Fig. 13 . This is primarily because there were lower counts of radionuclide spectrum in the photopeak region, so the MAESTRO 7.01 software couldn’t find a peak that satisfied its default requirement. Experimental results demonstrate once again that the proposed method is not based on peak detection, but on information from the full spectrum. 4. Conclusion 1 A method of spectrometry analysis based on approximation coefficients and a DBN was proposed in this study. This method consisted of DBN training and DBN prediction. Approximation coefficients of the spectrum were extracted by wavelet decomposition. The DBN was trained using samples of simulation spectra of radionuclides of interest, and was used to predict the isotopic compositions of the spectrum measured in the real environment. Experimental results show that the identification performance of the proposed method was not affected by the detection time, number of radionuclides, or detection distance when the MDA of a single radionuclide was satisfied. The radionuclides used in this study were 238 Pu (8.89×10 3 μCi), 60 Co (1.59 μCi), and 137 Cs (1.42 μCi). The dose rate of the background without a shielding apparatus was measured in the laboratory (approximately 0.1 μSv/h). The proposed method showed better performance for predicting the isotopic compositions of the spectrum of moving radionuclides. The proposed method identified the isotopic compositions in the spectrum using information from the full spectrum, contrary to the method based on peak detection. The proposed method may exhibit enhanced identification performance for the spectrum of radionuclides with higher energy, because the DBN is trained using samples of the simulation spectra of radionuclides of interest, and the difference between the spectrum simulated by the MCNP and that measured in the real environment in the low energy (< 100 keV) region is larger. In summary, a novel method for spectrometry analysis was developed which overcomes the difficulties caused by the insufficient availability of the majority of radionuclides in the laboratory. Further work, such as using different detectors (e.g., lanthanum bromide scintillation detector, cadmium zinc telluride detector, high-purity germanium detector), and the addition of gamma-ray shielding will be performed to verify the identification performance of the proposed method. In addition, complex methods combined with the latest advanced algorithms, such as optimization algorithms (e.g., genetic algorithms, particle swarm algorithms), feature extraction algorithms (Karhunen-Loeve transform, singular-value decomposition), and fuzzy logic algorithms, will be studied to develop more intelligent methods for spectrometry analysis. The proposed method can be executed in a mobile or an embedded system because of the simplicity of the trained DBN. In this study, the algorithm was executed on a Windows-based mini-PC. The proposed method may potentially be suitable for radionuclide identification of radiation monitoring instruments because of its high stability and low execution time. 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(Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0402-4 http://dx.doi.org/10.1007/s41365-018-0402-4 . 2018 Nuclear Science and Techniques 05 29