The solution of the unconstrained optimization problem of AGRS with several data files taken with a 3" NaI detector and logged by a1024 MC
(Peter 2018) using stochastic quasi-Newton techniques in neural network is described in this section. This data set is listing the counts logged channel by channel in a1028 MC to determine the attenuation coefficients. A lead absorber with different thickness took between the source and detector place to attenuate the energy of this gamma ray. The used source was Cs137, which gives off a gamma at energy 662 KeV. This data allows us to determine values of the attenuation coefficients of the gamma ray. All data were taken with the same source-detector geometry. The counts of these experiments were collected in 120 seconds. The experimental data for 662 KeV gamma ray with lead absorber can be summarized as follow:
1) The “no absorber” data set contains spectra data for the Cs137 source with no absorber. Collection time was two minutes.
2) The file “absorber C” contains spectra data for the Cs137 source with a lead absorber of thickness 2.651 g/cm2. Collection time was two minutes.
3) The file “absorber D” contains spectra data for the Cs137 source with a lead absorber of thickness 4.451 g/cm2. Collection time was two minutes.
4) The file “absorber E” contains spectra data for the Cs137 source with a lead absorber of thickness 7.194 g/cm2. Collection time was two minutes.
5) The file “absorber C and E” contains spectra data for the Cs137 source with a lead absorber of thickness 9.845 g/cm2. Collection time was two minutes.
The 662 KeV photopeaks in all cases were seen at around channel 390.
The parameters of all examined training methods were set or tuned to achieve best validation, these parameters lead the algorithm to minimize the search direction. In our experiments, training stops when any of the following conditions occurs:
1) The maximum number of epochs (repetitions) is reached.
2) The maximum time limit is exceeded.
3) Performance is minimized to the goal.
4) The performance gradient falls below the stopping criterion MSE.
5) Validation performance has increased more than maximum fail times since the last time when it decreased (when using validation).
The energy levels of MC were considered as input units of the neural network to compute a series of transformations between counted gamma ray photons and their related AGRS altitudes for various gamma sources. Fig \ref{931769}-3 present the statistical data for the normalized MSE, validation and convergence speed of the quasi-Newton techniques compared with the proposed ERAS training algorithm, which were tested on ANN for the AGRS. All the quasi-Newton methods training algorithms met the stopping criterions, at different training times, in all training trials, and none of them failed to converge. The proposed ERAS algorithm requires less computation in each iteration and more storage than LMBP \cite{Sapna_2012} , S-CGBP \cite{Nayak_2017} , RBP \cite{Saputra_2017} , BFGS \cite{Silaban_2017} , CGBP-PR \cite{Ghani_2017} , CGBP-FR \cite{Wanto_2017} , CGBP-HS \cite{Gazi_Sharee_2014} , CGBP-DY \cite{Dai_2013} methods, although it generally converges in fewer iterations.