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A Novel Hierarchical Extreme Machine-Learning-Based Approach for Linear Attenuation Coefficient Forecasting

Varone, Giuseppe; Ieracitano, Cosimo; Çiftçioğlu, Aybike Özyüksel; Hussain, Tassadaq; Gogate, Mandar; Dashtipour, Kia; Al-Tamimi, Bassam Naji; Almoamari, Hani; Akkurt, Iskender; Hussain, Amir


Giuseppe Varone

Cosimo Ieracitano

Aybike Özyüksel Çiftçioğlu

Bassam Naji Al-Tamimi

Hani Almoamari

Iskender Akkurt


The development of reinforced polymer composite materials has had a significant influence on the challenging problem of shielding against high-energy photons, particularly X-rays and γ-rays in industrial and healthcare facilities. Heavy materials’ shielding characteristics hold a lot of potential for bolstering concrete chunks. The mass attenuation coefficient is the main physical factor that is utilized to measure the narrow beam γ-ray attenuation of various combinations of magnetite and mineral powders with concrete. Data-driven machine learning approaches can be investigated to assess the gamma-ray shielding behavior of composites as an alternative to theoretical calculations, which are often time- and resource-intensive during workbench testing. We developed a dataset using magnetite and seventeen mineral powder combinations at different densities and water/cement ratios, exposed to photon energy ranging from 1 to 1006 kiloelectronvolt (KeV). The National Institute of Standards and Technology (NIST) photon cross-section database and software methodology (XCOM) was used to compute the concrete’s γ-ray shielding characteristics (LAC). The XCOM-calculated LACs and seventeen mineral powders were exploited using a range of machine learning (ML) regressors. The goal was to investigate whether the available dataset and XCOM-simulated LAC can be replicated using ML techniques in a data-driven approach. The minimum absolute error (MAE), root mean square error (RMSE), and R2score were employed to assess the performance of our proposed ML models, specifically a support vector machine (SVM), 1d-convolutional neural network (CNN), multi-Layer perceptrons (MLP), linear regressor, decision tree, hierarchical extreme machine learning (HELM), extreme learning machine (ELM), and random forest networks. Comparative results showed that our proposed HELM architecture outperformed state-of-the-art SVM, decision tree, polynomial regressor, random forest, MLP, CNN, and conventional ELM models. Stepwise regression and correlation analysis were further used to evaluate the forecasting capability of ML techniques compared to the benchmark XCOM approach. According to the statistical analysis, the HELM model showed strong consistency between XCOM and predicted LAC values. Additionally, the HELM model performed better in terms of accuracy than the other models used in this study, yielding the highest R2score and the lowest MAE and RMSE.

Journal Article Type Article
Acceptance Date Jan 28, 2023
Online Publication Date Jan 30, 2023
Publication Date 2023
Deposit Date Feb 8, 2023
Publicly Available Date Feb 8, 2023
Journal Entropy
Electronic ISSN 1099-4300
Publisher MDPI
Peer Reviewed Peer Reviewed
Volume 25
Issue 2
Article Number 253
Keywords hierarchical extreme machine learning, linear attenuation coefficient, XCOM


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