Bayesian regularization of multilayer perceptron neural network for estimation of mass attenuation coefficient of gamma radiation in comparison with different supervised model-free methods

Multilayer perceptron (MLP) neural networks have been used extensively for estimation/regression of parameters. Moreover, recent studies have shown that learning algorithms of MLP which are based on Gaussian function are more accurate. In this paper, the mass attenuation coefficient (MAC) of gamma radiation for light-weight materials (e.g. O-8), mid-weight materials (e.g. Al-13), and heavy-weight materials (e.g. Pb-82) is modelled using Gaussian function based regularization of MLP (i.e. Bayesian regularization (BR)) and by a modular estimator. The results are compared with the Reference results. To show better performance of the utilized algorithm, the results of the different supervised methods including support vector machine (SVM) with different kernel functions, decision tree (DT), and radial basis network (RBN) are given. Average mean relative error (AMRE) and cumulative distribution function (CDF) of errors of MACs estimation are calculated. Comparison of the results indicates that MLP-BR gives more accurate results (e.g. ${\text{AMRE}}_{O-8}=0.0014$, ${\text{CDF}}_{O-8}\left(0.0069\right)=0.99$, ${\text{AMRE}}_{Al-13}=0.0015$, ${\text{CDF}}_{Al-13}\left(0.0048\right)=0.99$, ${\text{AMRE}}_{Pb-82}=0.0117$, ${\text{CDF}}_{Pb-82}\left(0.0523\right)=0.99$).