Through the study of scattered gamma beam intensity, material density could be obtained. Most important factor in this densitometry method is determining a relation between recorded intensity by detector and target material density. Such situation needs many experiments over materials with different densities. In this paper, using two different artificial neural networks, intensity of scattered gamma is obtained for whole densities. Mean relative error percentage for test data using best method is 1.27% that shows good agreement between the proposed artificial neural network model and experimental results. 1. Introduction The gamma-ray photons lose their energy in a stopping medium by these processes: photoelectric effect, Compton effect, pair production, and photonuclear effect. With the analysis of these interactions, some information about characteristics of materials can be obtained. Compton scattering is strongly dependent on the materials density. Therefore, this method is very good choice for densitometry of unknown materials [1–6]. El Abd [7] has shown that scattering photons are more sensitive than transmitted photons in order to density meter and void fraction prediction. In [7], the void fraction has been predicted without using artificial neural network (ANN); therefore the error is considerable. In this paper, experimental data have been obtained from a density measurement tomography system [8]. These data were used for training the ANN. Set-up of this tomography system was shown in Figure 1. Figure 1: Schematic of tomography structure system. In investigated tomography system [8], a NaI (Tl) scintillation detector in 3 × 3 inch dimensions has been used. The detector records scattered photons from target sample. The source is 137Cs with 8?mci activation. Distances between the sample from the source collimator and the detector are 5.56?cm and 6?cm, respectively. Investigated samples have dimensions and thickness of 1 × 2?cm2 and 1?cm, respectively. The time durations of measurement are 100 seconds. Relative stochastic error has inverse relation with the number of registered counts in detector. In this study because the scattering method is used and the number of counts in this method is less in comparison with the transmission method, therefore the measurement time should be increased in order to decrease the stochastic error. By taking 100-second time duration, the stochastic errors are in the range of 0.5%–1.5% (5000–20000 counts for different materials). The experimental results are shown in Table 1. Table 1: Number of detected photons
References
[1]
G. Schlieper, “Applying gamma ray densitometry in a PM production plant,” Metal Powder Report, vol. 56, no. 1, pp. 22–27, 2001.
[2]
E. ?bro, V. A. Khoryakov, G. A. Johansen, and L. Kocbach, “Determination of void fraction and flow regime using a neural network trained on simulated data based on gamma-ray densitometry,” Measurement Science and Technology, vol. 10, no. 7, pp. 619–630, 1999.
[3]
S. A. Tjugum, B. T. Hjertake, and G. A. Johansen, “Multiphase flow regime identification by multibeam gamma-ray densitometry,” Measurement Science and Technology, vol. 13, no. 8, pp. 1319–1326, 2002.
[4]
S.-A. Tjugum, J. Frieling, and G. A. Johansen, “A compact low energy multibeam gamma-ray densitometer for pipe-flow measurements,” Nuclear Instruments and Methods in Physics Research B: Beam Interactions with Materials and Atoms, vol. 197, no. 3-4, pp. 301–309, 2002.
[5]
C. M. Salgado, C. M. N. A. Pereira, R. Schirru, and L. E. B. Brand?o, “Flow regime identification and volume fraction prediction in multiphase flows by means of gamma-ray attenuation and artificial neural networks,” Progress in Nuclear Energy, vol. 52, no. 6, pp. 555–562, 2010.
[6]
M. Khorsandi and S. A. H. Feghhi, “Design and construction of a prototype gamma-ray densitometer for petroleum products monitoring applications,” Measurement, vol. 44, no. 9, pp. 1512–1515, 2011.
[7]
A. El Abd, “Intercomparison of gamma ray scattering and transmission techniques for gas volume fraction measurements in two phase pipe flow,” Nuclear Instruments and Methods in Physics Research A: Accelerators, Spectrometers, Detectors and Associated Equipment, vol. 735, pp. 260–266, 2014.
[8]
S. Ashrafi, D. Alizadeh, and O. Jahanbakhsh, “Application of artificial neural networks in densitometry using compton scattering,” in Proceedings of the Iran Physics Conference, 2012.
[9]
G. H. Roshani, S. A. H. Feghhi, A. Mahmoudi-Aznaveh, E. Nazemi, and A. Adineh-Vand, “Precise volume fraction prediction in oil-water-gas multiphase flows by means of gamma-ray attenuation and artificial neural networks using one detector,” Measurement, vol. 51, pp. 34–41, 2014.
[10]
G. H. Roshani, S. A. H. Feghhi, A. Adineh-Vand, and M. Khorsandi, “Application of adaptive neuro-fuzzy inference system in prediction of fluid density for a gamma ray densitometer in petroleum products monitoring,” Measurement, vol. 46, no. 9, pp. 3276–3281, 2013.
[11]
M. Khorsandi, S. A. H. Feghhi, A. Salehizadeh, and G. H. Roshani, “Developing a gamma ray fluid densitometer in petroleum products monitoring applications using Artificial Neural Network,” Radiation Measurements, vol. 59, pp. 183–187, 2013.
[12]
J. G. . Taylor, Neural Networks and Their Applications, John Wiley & Sons, West Sussex, UK, 1996.
[13]
A. R. Gallant and H. White, “On learning the derivatives of an unknown mapping with multilayer feedforward networks,” Neural Networks, vol. 5, no. 1, pp. 129–138, 1992.
[14]
M. T. Hagan and M. B. Menhaj, “Training feedforward networks with the Marquardt algorithm,” IEEE Transactions on Neural Networks, vol. 5, no. 6, pp. 989–993, 1994.
[15]
J. D. Rodriguez, A. Perez, and J. A. Lozano, “Sensitivity analysis of k-fold cross validation in prediction error estimation,” IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 32, no. 3, pp. 569–575, 2010.