System Engineering and Productivity

System Engineering and Productivity

Predicting the Response of an Engineering System by Developing a Data-Driven Surrogate Model Based on Artificial Neural Networks as an Alternative to Finite Element Analysis

Document Type : Research Paper

Authors
1 M.Sc., Department of Mechanical Engineering, University of Eyvanekey, Eyvanekey, Iran
2 Assistant Professor, Department of Mechanical Engineering, University of Eyvanekey, Eyvanekey, Iran
3 Corresponding author: Assistant Professor, Department of Mechanical Engineering, Imam Hossein University, Tehran, Iran
4 Professor, Faculty of Mechanical Engineering, University of Guilan, Rasht, Iran
Abstract
This study introduces a data‑driven surrogate model based on the Group Method of Data Handling (GMDH) approach, which utilizes artificial neural networks to replace computationally intensive engineering methods such as Finite Element Analysis (FEA), thereby enhancing simulation system efficiency. The approach was developed by focusing on the nonlinear relationships between dimensionless input parameters—including system characteristics (geometry and material properties), operational conditions (impact energy and strain rate)—and the primary output, namely the permanent deformation‑to‑thickness ratio of the sheet. An experimental dataset comprising 65 data points was compiled from actual tests employing hydrodynamic processes to apply loading. The GMDH network, with a 12‑layer architecture and 120 parameters, was trained after data standardization and splitting into training (67%) and test (33%) sets. Its performance was evaluated using metrics such as RMSE (0.884), MAE (0.711), MAPE (6.673%), R² (0.989), and the Willmott index (0.997), which demonstrate high accuracy, absence of overfitting, and a significant reduction in computational time (to seconds versus hours for FEA), thereby improving efficiency in industrial system management. Intrinsic sensitivity analysis, local sensitivity analysis (based on elasticity and partial derivatives), and uncertainty analysis with a confidence band of 0.2167 ranked the importance of input parameters and highlighted the dominant role of operational factors in system optimization. The research innovations include the integration of laboratory data for holistic real‑system modeling, provision of input‑output mapping, and reduction of simulation costs, making the model suitable for industrial applications in manufacturing process optimization and productivity enhancement in automotive industries, and taking a step toward AI‑driven design in systems engineering.

Highlights

  • Data-Driven GMDH Model: Replaces FEA with high accuracy and significant computational time reduction for predicting response of mechanical system.
  • Sensitivity and Uncertainty Analysis: Ranking input parameters (strain rate and impact energy) and confirming model robustness with uncertainty bandwidth of 0.2167, facilitating AI-based design in automotive and aerospace industries.

Keywords
Subjects

Copyright © Masoud Validoust, Tohid Mirzababaie Mostofi, Mohammad Vahab Mousavi, Hashem Babaei

 

License

This article is released under the Creative Commons Attribution (CC BY 4.0) license. Anyone is free to copy, share, translate, and adapt this article for any purpose, whether commercial or non-commercial, as long as proper citation is given to the authors and original publication.

Azarhoosh, Z., & Ghazaan, M. I. (2025). A review of recent advances in surrogate models for uncertainty quantification of high-dimensional engineering applications. Computer Methods in Applied Mechanics and Engineering433, 117508. https://doi.org/10.1016/j.cma.2024.117508
Babaei, H., & Mirzababaie Mostofi, T. (2020a). Modeling and prediction of fatigue life in composite materials by using singular value decomposition method. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 234(2), 246-254. https://doi.org/10.1177/1464420716660875
Babaei, H., & Mirzababaie Mostofi, T. (2020b). New dimensionless numbers for deformation of circular mild steel plates with large strains as a result of localized and uniform impulsive loading. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 234(2), 231-245. https://doi.org/10.1177/1464420716654195
Babaei, H., Mirzababaie Mostofi, T., & Alitavoli, M. (2017a). Experimental and theoretical study of large deformation of rectangular plates subjected to water hammer shock loading. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering231(3), 490-496. https://doi.org/10.1177/0954408915611055
Babaei, H., Mirzababaie Mostofi, T., & Armoudli, E. (2017b). On dimensionless numbers for the dynamic plastic response of quadrangular mild steel plates subjected to localized and uniform impulsive loading. Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering, 231(5), 939-950. https://doi.org/10.1177/0954408916650713
Babaei, H., Mostofi, T. M., & Alitavoli, M. (2015a). Study on the response of circular thin plate under low velocity impact. Geomechanics & Engineering9(2), 207-218. https://doi.org/10.12989/gae.2015.9.2.207
Babaei, H., Mostofi, T. M., Alitavoli, M., & Namdari, M. (2015b). Experimental investigation and a model presentation for predicting the behavior of metal and alumina powder compaction under impact loading. Journal of Modares Mechanical Engineering, 15(5), 357-366. https://dor.isc.ac/dor/20.1001.1.10275940.1394.15.5.36.0
Belytschko, T., Liu, W. K., Moran, B., & Elkhodary, K. (2014). Nonlinear finite elements for continua and structures. John wiley & sons.
Bessa, M. A., Bostanabad, R., Liu, Z., Hu, A., Apley, D. W., Brinson, C., ... & Liu, W. K. (2017). A framework for data-driven analysis of materials under uncertainty: Countering the curse of dimensionality. Computer Methods in Applied Mechanics and Engineering320, 633-667. https://doi.org/10.1016/j.cma.2017.03.037
Bostanabad, R., Zhang, Y., Li, X., Kearney, T., Brinson, L. C., Apley, D. W., ... & Chen, W. (2018). Computational microstructure characterization and reconstruction: Review of the state-of-the-art techniques. Progress in Materials Science95, 1-41. https://doi.org/10.1016/j.pmatsci.2018.01.005
Cheng, L., Guo, H., Sun, L., Yang, C., Sun, F., & Li, J. (2024). Real-time simulation of tube hydroforming by integrating finite-element method and machine learning. Journal of Manufacturing and Materials Processing8(4), 175. https://doi.org/10.3390/jmmp8040175
Fakhrusy, M., & Rosalia, C. A. (2025). Data-driven machine learning techniques for crashworthiness analysis of thin-walled structures: A review. In E3S Web of Conferences (Vol. 664, p. 01014). EDP Sciences. https://doi.org/10.1051/e3sconf/202566401014
Ghaboussi, J., Garrett Jr, J. H., & Wu, X. (1991). Knowledge-based modeling of material behavior with neural networks. Journal of engineering mechanics117(1), 132-153. https://doi.org/10.1061/(ASCE)0733-9399(1991)117:1(132)
Haghgoo, M., Babaei, H., & Mostofi, T. M. (2022). 3D numerical investigation of the detonation wave propagation influence on the triangular plate deformation using finite rate chemistry model of LS-DYNA CESE method. International Journal of Impact Engineering, 161, 104108. https://doi.org/10.1016/j.ijimpeng.2021.104108
Hashemi, A., Jang, J., & Beheshti, J. (2023). A machine learning-based surrogate finite element model for estimating dynamic response of mechanical systems. IEEE Access11, 54509-54525. https://doi.org/10.1109/ACCESS.2023.3282453
Jamali, A., Babaei, H., Nariman-Zadeh, N., Ashraf Talesh, S. H., & Mirzababaie Mostofi, T. (2020). Multi-objective optimum design of ANFIS for modelling and prediction of deformation of thin plates subjected to hydrodynamic impact loading. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, 234(3), 368-378. https://doi.org/10.1177/1464420716660332
Lechner, P., Scandola, L., Maier, D., Hartmann, C., Rizaiev, Y., & Lieb, M. (2025). A physically-informed machine learning model for freeform bending. Journal of Intelligent Manufacturing36(6), 4351-4363. https://doi.org/10.1007/s10845-024-02452-w
Li, X., Li, Z., Chen, Y., & Zhang, C. (2023). An enhanced data-driven constitutive model for predicting strain-rate and temperature dependent mechanical response of elastoplastic materials. European Journal of Mechanics-A/Solids100, 104996. https://doi.org/10.1016/j.euromechsol.2023.104996
Liang, R., Tang, X., Huang, J., Bastien, C., Zhang, C., & Tuo, W. (2024). A machine learning-based crashworthiness optimization for a novel pine cone-inspired multi-cell tubes under bending. Heliyon10(18),  e37828. https://doi.org/10.1016/j.heliyon.2024.e37828
Marković, E., Marohnić, T., & Basan, R. (2025). A Surrogate Artificial Neural Network Model for Estimating the Fatigue Life of Steel Components Based on Finite Element Simulations. Materials18(12), 2756. https://doi.org/10.3390/ma18122756
Mirzababaie Mostofi, T., & Babaei, H. (2019a). Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part II: Analytical and empirical modelling. Journal of Solid and Fluid Mechanics, 9(2), 15-29. https://doi.org/10.22044/jsfm.2019.7816.2778
Mirzababaie Mostofi, T., & Babaei, H. (2019b). Plastic deformation of polymeric-coated aluminum plates subjected to gas mixture detonation loading: Part I: Experimental studies. Journal of Solid and Fluid Mechanics 9(1), 71-83. https://doi.org/10.22044/jsfm.2019.7815.2777
Mirzababaie Mostofi, T., Sayah Badkhor, M., & Ghasemi, E. (2019c). Experimental investigation and optimal analysis of the high-velocity forming process of bilayer plates. Journal of Solid and Fluid Mechanics, 9(3), 65-80. https://doi.org/10.22044/jsfm.2019.8586.2953
Mostofi, T. M., Babaei, H., & Alitavoli, M. (2017). The influence of gas mixture detonation loads on large plastic deformation of thin quadrangular plates: Experimental investigation and empirical modelling. Thin-Walled Structures, 118, 1-11. https://doi.org/10.1016/j.tws.2017.04.031
Mousavi, M. V., & Khoramishad, H. (2019). The effect of hybridization on high-velocity impact response of carbon fiber-reinforced polymer composites using finite element modeling, Taguchi method and artificial neural network. Aerospace Science and Technology, 94, 105393. https://doi.org/10.1016/j.ast.2019.105393
Pei, Y., Han, B., Kumar, D., Adams, S., Khoo, S. Y., Norton, M., & Kouzani, A. Z. (2025). Machine Learning as a Surrogate for FEM: Predicting Mechanical Properties of Tyres. Advanced Industrial and Engineering Polymer Research8(4), 499-515.  https://doi.org/10.1016/j.aiepr.2025.08.003
Raissi, M., Perdikaris, P., & Karniadakis, G. E. (2019). Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations. Journal of Computational Physics378, 686-707.  https://doi.org/10.1016/j.jcp.2018.10.045
Rezasefat, M., Mirzababaie Mostofi, T., Babaei, H., Ziya-Shamami, M., & Alitavoli, M. (2019). Dynamic plastic response of double-layered circular metallic plates due to localized impulsive loading. Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications233(7), 1449-1471. https://doi.org/10.1177/1464420718760640
Rokhy, H., & Mostofi, T. M. (2023). Tracking the explosion characteristics of the hydrogen-air mixture near a concrete barrier wall using CESE IBM FSI solver in LS-DYNA incorporating the reduced chemical kinetic model. International Journal of Impact Engineering, 172, 104401. https://doi.org/10.1016/j.ijimpeng.2022.104401
Stoffel, M., Bamer, F., & Markert, B. (2018). Artificial neural networks and intelligent finite elements in non-linear structural mechanics. Thin-Walled Structures131, 102-106. https://doi.org/10.1016/j.tws.2018.06.035
Tasdemir, B., Pellegrino, A., Su, X., & Tagarielli, V. L. (2025). Learning the non-proportional multiaxial elastic–plastic response of an aluminium alloy with neural networks. Materials & Design253, 113956. https://doi.org/10.1016/j.matdes.2025.113956
Yong, P. A. N. G., Zhang, S., Liang, P., Muchen, W. A. N. G., Zhuangzhuang, G. O. N. G., Xueguan, S. O. N. G., & Ziyun, K. A. N. (2024). Surrogate model uncertainty quantification for active learning reliability analysis. Chinese Journal of Aeronautics37(12), 55-70. https://doi.org/10.1016/j.cja.2024.08.055
Zamani, J., Mousavi, M. V., & Khalili, S. M. R. (2015). Numerical investigation of formation of Mach reflection in explosive free forming of confined cylindrical shells. Modares Mechanical Engineering, 14(13), 131-142. https://dor.isc.ac/dor/20.1001.1.10275940.1393.14.13.36.9

Articles in Press, Accepted Manuscript
Available Online from 08 February 2026

  • Receive Date 20 December 2025
  • Revise Date 29 January 2026
  • Accept Date 08 February 2026
  • First Publish Date 08 February 2026
  • Publish Date 08 February 2026