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

Aug 5, 2026

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The development of reinforced polymer composite materials motivates reliable shielding against high-energy photons, especially X-rays and gamma rays. Linear attenuation coefficient (LAC) is a key factor for assessing gamma-ray attenuation in concrete-like systems, where theoretical calculations can be time- and resource-intensive. A dataset was built using magnetite and seventeen mineral powder combinations across densities and water/cement ratios, with photon energies from 1 to 1006 keV. XCOM (NIST cross-section database) generated LAC targets for comparison with machine-learning regression models. Results show the proposed hierarchical extreme machine learning (HELM) achieves the strongest agreement with XCOM and delivers the best accuracy, lowest MAE and RMSE, and highest R² among tested methods.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages19

Reading Time48 min

AccessFree to download

Introduction

High-energy photon applications and safety concerns

Concrete shielding parameters and LAC significance

Aim of data-driven ML forecasting

entropy Article A Novel Hierarchical Extreme Machine-Learning-Based Approach for Linear Attenuation Coefﬁcient Forecasting Giuseppe Varone 1,*, Cosimo Ieracitano 2, Aybike Özyüksel Çiftçio ˘glu 3, Tassadaq Hussain 4, Mandar Gogate 4, Kia Dashtipour 4, Bassam Naji Al-Tamimi 5, Hani Almoamari 6, Iskender Akkurt 7 and Amir Hussain 4 Citation: Varone, G.; Ieracitano, C.;Çiftçio ˘glu, A.Ö.; Hussain, T.; Gogate, M.; Dashtipour, K.; Al-Tamimi, B.N.; Almoamari, H.; Akkurt, I.; Hussain, A. A Novel Hierarchical Extreme Machine-Learning-Based Approach for Linear Attenuation Coefﬁcient Forecasting. Entropy 2023, 25, 253 . [https://doi.org/10.3390/e25020253](https://doi.org/10.3390/e25020253) Academic Editor: Gholamreza Anbarjafari Received: 25 November 2022 Revised: 17 January 2023 Accepted: 28 January 2023 Published: 30 January 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license ([https://](https://)[ ](https://)[creativecommons.org/licenses/by/](creativecommons.org/licenses/by/)[ ](creativecommons.org/licenses/by/)[4.0/](4.0/)) . 1 Department of Neuroscience and Imaging, University of Chieti Pescara, 66100 Chieti, Italy 2 DICEAM, University Mediterranea of Reggio Calabria, Via Graziella, Feo di Vito, 89060 Reggio Calabria, Italy 3 Department of Civil Engineering, Manisa Celal Bayar University, 45140 Manisa, Turkey 4 School of Computing, Merchiston Campus, Edinburgh Napier University, Edinburgh EH10 5DT, UK 5 School of Computing and Digital Technology, Birmingham City University, Birmingham B4 7XG, UK 6 Faculty of Computer and Information Systems, Islamic University of Madinah, Medina 42351, Saudi Arabia 7 Physics Department, Suleyman Demirel University, 32260 Isparta, Turkey * Correspondence: [giuseppevaronech@gmail.com](giuseppevaronech@gmail.com) Abstract: The development of reinforced polymer composite materials has had a signiﬁcant inﬂuenceon the challenging problem of shielding against high-energy photons, particularly X-rays and g-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 g-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 g-ray shielding characteristics (LAC) . The XCOMcalculated 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 an

FAQs

What is the main goal of the proposed work?

To forecast linear attenuation coefficient (LAC) values using a data-driven hierarchical extreme machine learning approach, replicating XCOM-simulated results.

How were the LAC reference values generated?

LAC targets were computed with XCOM, using the NIST photon cross-section database and its software methodology.

Which machine learning models were compared, and what was the outcome?

The study evaluated SVM, 1D-CNN, MLP, linear regressor, decision tree, HELM, extreme learning machine (ELM), and random forest; HELM outperformed the others with the highest R² and lowest MAE and RMSE.

Aug 5, 2026

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