پیش‌بینی پاسخ یک سیستم مهندسی با توسعه‌ی یک مدل جانشین داده‌محور مبتنی بر شبکه‌ عصبی مصنوعی به‌عنوان جایگزین تحلیل اجزای محدود

ولی‌دوست, مسعود; میرزابابای مستوفی, توحید; موسوی, محمد وهاب; بابایی, هاشم

doi:10.22034/sep.2026.2082317.1452

پیش‌بینی پاسخ یک سیستم مهندسی با توسعه‌ی یک مدل جانشین داده‌محور مبتنی بر شبکه‌ عصبی مصنوعی به‌عنوان جایگزین تحلیل اجزای محدود

مقالات آماده انتشار

نوع مقاله : پژوهشی

نویسندگان

مسعود ولی‌دوست ¹

توحید میرزابابای مستوفی ²

محمد وهاب موسوی ³

هاشم بابایی ⁴

¹ کارشناسی ارشد، گروه مهندسی مکانیک، دانشگاه ایوان‌کی، ایوان‌کی، ایران

² استادیار ، گروه مهندسی مکانیک، دانشگاه ایوان‌کی، ایوان‌‎کی، ایران

³ نویسنده مسئول: استادیار، گروه مهندسی مکانیک، دانشگاه جامع امام حسین(ع)، تهران، ایران

⁴ استاد، دانشکده مهندسی مکانیک، دانشگاه گیلان، رشت، ایران

10.22034/sep.2026.2082317.1452

چکیده

این تحقیق، یک مدل جانشین داده‌محور مبتنی بر روش گروهی پردازش داده‌ها (GMDH) را معرفی می‌کند که از شبکه‌های عصبی مصنوعی برای جایگزینی روش‌های محاسباتی سنگین مهندسی مانند تحلیل اجزای محدود (FEA) بهره می‌برد و بهره‌وری سیستم‌های شبیه‌سازی را افزایش می‌دهد. این رویکرد با تمرکز بر روابط غیرخطی بین پارامترهای ورودی بی‌بعد شامل ویژگی‌های سیستم (هندسه و خواص مواد)، شرایط عملیاتی (انرژی ضربه و نرخ کرنش)، و خروجی اصلی یعنی نسبت تغییرشکل دائمی به ضخامت ورق توسعه یافته است. مجموعه داده‌های تجربی شامل ۶۵ نقطه از آزمایش‌های واقعی تهیه شد که از فرآیندهای هیدرودینامیکی برای اعمال بارگذاری استفاده می‌کند. شبکه GMDH با معماری ۱۲ لایه و ۱۲۰ پارامتر، پس از استانداردسازی داده‌ها و تقسیم به مجموعه‌های آموزش (۶۷%) و آزمون (۳۳%)، آموزش دید و عملکرد آن با معیارهایی مانندRMSE (884/0)۰،MAE (711/0)، MAPE (673/%6)، R² (989/0)، و شاخص ویلموت (997/0) ارزیابی گردید که دقت بالا، عدم بیش‌برازش، و کاهش چشمگیر زمان محاسباتی (تا ثانیه‌ها در مقابل ساعت‌ها برای FEA) را نشان می‌دهد که این امر بهره‌وری در مدیریت سیستم‌های صنعتی را ارتقا می‌بخشد. تحلیل حساسیت ذاتی، محلی (بر اساس الاستیسیته و مشتقات جزئی)، و تحلیل عدم قطعیت با عرض باند 2167/0، اهمیت پارامترهای ورودی را رتبه‌بندی کرد و نقش غالب عوامل عملیاتی در بهینه‌سازی سیستم را برجسته نمود. نوآوری‌های تحقیق شامل ادغام داده‌های آزمایشگاهی برای مدل‌سازی یکپارچه سیستم‌های واقعی، ارائه نگاشت ورودی-خروجی، و کاهش هزینه‌های شبیه‌سازی است که این مدل را برای کاربردهای صنعتی در بهینه‌سازی فرایندهای تولید و افزایش بهره‌وری در صنایع خودروسازی مناسب می‌سازد و گامی به سوی طراحی مبتنی بر هوش مصنوعی در مهندسی سیستم‌ها برمی‌دارد.

تازه های تحقیق

مدل GMDH داده‌محور: جایگزین FEA با دقت بالا و کاهش زمان محاسباتی برای پیش‌بینی پاسخ سیستم مکانیکی.
تحلیل حساسیت و عدم قطعیت: رتبه‌بندی پارامترها (نرخ کرنش و انرژی ضربه) و استحکام مدل با عرض باند عدم قطعیت 0/2167، برای طراحی AI در صنایع خودرو و هوافضا.

کلیدواژه‌ها

مدل جانشین داده‌محور

شبکه‌ عصبی مصنوعی

جایگزینی تحلیل اجزای محدود

پیش‌بینی پاسخ پلاستیک دینامیکی

مدل‌سازی پیش‌بین

موضوعات

مهندسی سیستم‌ها

عنوان مقاله English

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

نویسندگان English

Masoud Validoust ¹

Tohid Mirzababaie Mostofi ²

Mohammad Vahab Mousavi ³

Hashem Babaei ⁴

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

چکیده English

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.

کلیدواژه‌ها English

Data-driven surrogate model

Artificial neural network (ANN)

FEA alternative

Dynamic plastic response prediction

Predictive modeling

Engineering system

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 Engineering, 433, 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 Engineering, 231(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 & Engineering, 9(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 Engineering, 320, 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 Science, 95, 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 Processing, 8(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 mechanics, 117(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 Access, 11, 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 Manufacturing, 36(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/Solids, 100, 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. Heliyon, 10(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. Materials, 18(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 Research, 8(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 Physics, 378, 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 Applications, 233(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 Structures, 131, 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 & Design, 253, 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 Aeronautics, 37(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