Exploring the stainless-steel beam-to-column connections response: A hybrid explainable machine learning framework for characterization

Abstract

Stainless-steel provides substantial advantages for structural uses, though its upfront cost is notably high. Consequently, it’s vital to establish safe and economically viable design practices that enhance material utilization. Such development relies on a thorough understanding of the mechanical properties of structural components, particularly connections. This research advances the field by investigating the behavior of stainless-steel connections through the use of a four-parameter fitting technique and explainable artificial intelligence methods. Training was conducted on eight different machine learning algorithms, namely, Decision Tree, Random Forest, K-nearest neighbors, Gradient Boosting, Extreme Gradient Boosting, Light Gradient Boosting, Adaptive Boosting, and Categorical Boosting. SHapley Additive Explanations was applied to interpret model predictions, highlighting features like spacing between bolts in tension and end-plate height as highly impactful on the initial rotational stiffness and plastic moment resistance. Results showed that Extreme Gradient Boosting achieved a coefficient of determination score of 0.99 for initial stiffness and plastic moment resistance, while Gradient Boosting model had similar performance with maximum moment resistance and ultimate rotation. A user-friendly graphical user interface (GUI) was also developed, allowing engineers to input parameters and get rapid moment–rotation predictions. This framework offers a data-driven, interpretable alternative to conventional methods, supporting future design recommendations for stainless-steel beam-to-column connections.

Graphical abstract

Keywords

steel connections / stainless-steel / machine learning / explainable models / moment–rotation response

References

[1] Kong Z, Hong S, Vu Q V, Cao X, Kim S E, Yu B. New equations for predicting initial stiffness and ultimate moment of flush end-plate connections. Journal of Constructional Steel Research, 2020, 175: 106336

[2] CiutinaANunesD L. Behavior of end-plate steel connections with 4 bolts per row under large deformations. In: Proceedings of the 9th International Conference on Steel and Aluminum Structures (ICSAS19). Bradford, UK: Independent Publishing Network, 2019

[3] Zandonini R, Bursi O S. Monotonic and hysteretic behavior of bolted endplate beam-to-column joints. Advances in Steel Structures (ICASS'02), 2002, 1: 81–94

[4] Mascolo I, Guarracino F, Sarfarazi S, Della Corte G. A proposal for a simple characterization of stainless steel connections through an equivalent yield strength. Structures, 2024, 68: 107043

[5] Shamass R, Guarracino F. Numerical and theoretical modeling of the web-post buckling of stainless-steel cellular beams. CE/papers, 2021, 4: 1551–1557

[6] Afshan S, Gardner L. The continuous strength method for structural stainless-steel design. Thin-walled Structures, 2013, 68: 42–49

[7] Kim T S, Kuwamura H. Finite element modeling of bolted connections in thin-walled stainless-steel plates under static shear. Thin-walled Structures, 2007, 45(4): 407–421

[8] Bouchaïr A, Averseng J, Abidelah A. Analysis of the behavior of stainless-steel bolted connections. Journal of Constructional Steel Research, 2008, 64(11): 1264–1274

[9] Salih E L, Gardner L, Nethercot D A. Bearing failure in stainless-steel bolted connections. Engineering Structures, 2011, 33(2): 549–562

[10] Yuan H X, Hu S, Du X X, Yang L, Cheng X Y, Theofanous M. Experimental behavior of stainless-steel bolted T-stub connections under monotonic loading. Journal of Constructional Steel Research, 2019, 152: 213–224

[11] Gao J D, Yuan H X, Du X X, Hu X B, Theofanous M. Structural behavior of stainless-steel double extended end-plate beam-to-column joints under monotonic loading. Thin-walled Structures, 2020, 151: 106743

[12] Kong Z, Jin Y, Yang F, Vu Q V, Truong V, Yu B, Kim S E. Numerical simulation for structural behavior of stainless-steel web cleat connections. Journal of Constructional Steel Research, 2021, 183: 106706

[13] Elflah M, Theofanous M, Dirar S, Yuan H X. Behavior of stainless-steel beam-to-column joints—Part 1: Experimental investigation. Journal of Constructional Steel Research, 2019, 152: 183–193

[14] Hasan M J, Al-Deen S, Ashraf M. Behavior of top seat double web angle connection produced from austenitic stainless-steel. Journal of Constructional Steel Research, 2019, 155: 460–479

[15] Eladly M M, Schafer B W. Numerical and analytical study of stainless-steel beam-to-column extended end-plate connections. Engineering Structures, 2021, 240: 112392

[16] Song Y, Li D, Uy B, Wang J. Ultimate behavior and rotation capacity of stainless-steel end-plate connections. Steel and Composite Structures, 2022, 42(4): 569–590

[17] Żur K K, Firouzi N, Rabczuk T, Zhuang X. Large deformation of hyperelastic modified Timoshenko–Ehrenfest beams under different types of loads. Computer Methods in Applied Mechanics and Engineering, 2023, 416: 116368

[18] Firouzi N, Alzaidi A S M, Nezaminia H, Dalalchi D. Numerical investigation on the effect of different parameters on nonlinear vibration response of fully geometrically exact Timoshenko beams. Applied Physics. A, Materials Science & Processing, 2024, 130(9): 618

[19] Firouzi N, Alzaidi A S M. Non-linear elastic beam deformations with four-parameter Timoshenko beam element considering through-the-thickness stretch parameter and reduced integration. Symmetry, 2024, 16(8): 984

[20] Samaniego E, Anitescu C, Goswami S, Nguyen-Thanh V M, Guo H, Hamdia K, Zhuang X, Rabczuk T. An energy approach to the solution of partial differential equations in computational mechanics via machine learning: Concepts, implementation and applications. Computer Methods in Applied Mechanics and Engineering, 2020, 362: 112790

[21] Anitescu C, Atroshchenko E, Alajlan N, Rabczuk T. Artificial neural network methods for the solution of second-order boundary value problems. Computers, Materials & Continua, 2019, 59(1): 345–359

[22] Liu B, Vu-Bac N, Rabczuk T. A stochastic multiscale method for the prediction of the thermal conductivity of polymer nanocomposites through hybrid machine learning algorithms. Composite Structures, 2021, 273: 114269

[23] Liu B, Lu W, Olofsson T, Zhuang X, Rabczuk T. Stochastic interpretable machine learning based multiscale modeling in thermal conductivity of polymeric graphene-enhanced composites. Composite Structures, 2024, 327: 117601

[24] Liu B, Vu-Bac N, Zhuang X, Fu X, Rabczuk T. Stochastic full-range multiscale modeling of thermal conductivity of polymeric carbon nanotubes composites: A machine learning approach. Composite Structures, 2022, 289: 115393

[25] Liu B, Lu W. Surrogate models in machine learning for computational stochastic multi-scale modelling in composite materials design. International Journal of Hydromechatronics, 2022, 5(4): 336–365

[26] Xia Y, Zhang C, Wang C, Liu H, Sang X, Liu R, Zhao P, An G, Fang H, Shi M, Li B, Yuan Y, Liu B. Prediction of bending strength of glass fiber reinforced methacrylate-based pipeline UV-CIPP rehabilitation materials based on machine learning. Tunnelling and Underground Space Technology, 2023, 140: 105319

[27] Liu B, Vu-Bac N, Zhuang X, Fu X, Rabczuk T. Stochastic integrated machine learning based multiscale approach for the prediction of the thermal conductivity in carbon nanotube reinforced polymeric composites. Composites Science and Technology, 2022, 224: 109425

[28] Liu B, Vu-Bac N, Zhuang X, Lu W, Fu X, Rabczuk T. Al-DeMat: A web-based expert system platform for computationally expensive models in materials design. Advances in Engineering Software, 2023, 176: 103398

[29] Gao X, Lin C. Prediction model of the failure mode of beam-column joints using machine learning methods. Engineering Failure Analysis, 2021, 120: 105072

[30] Mangalathu S, Jeon J. Classification of failure mode and prediction of shear strength for reinforced concrete beam−column joints using machine learning techniques. Engineering Structures, 2018, 160: 85–94

[31] Alwanas A A H, Al-Musawi A A, Salih S Q, Tao H, Ali M, Yaseen Z M. Load-carrying capacity and mode failure simulation of beam-column joint connection: Application of self-tuning machine learning model. Engineering Structures, 2019, 194: 220–229

[32] Park S H, Yoon D, Kim S, Geem Z W. Deep neural network applied to joint shear strength for exterior RC beam−column joints affected by cyclic loadings. Structures, 2021, 33: 1819–1832

[33] Kotsovou G M, Cotsovos D M, Lagaros N D. Assessment of RC exterior beam-column joints based on artificial neural networks and other methods. Engineering Structures, 2017, 144: 1–18

[34] Haido J H. Prediction of the shear strength of RC beam−column joints using new ANN formulations. Structures, 2022, 38: 1191–1209

[35] Alagundi S, Palanisamy T. Neural network prediction of joint shear strength of exterior beam-column joint. Structures, 2022, 37: 1002–1018

[36] Naderpour H, Nagai K. Shear strength estimation of reinforced concrete beam–column sub-assemblages using multiple soft computing techniques. Structural Design of Tall and Special Buildings, 2020, 29(9): e1730

[37] Shah S N R, Ramli Sulong N H, El-Shafie A. New approach for developing soft computational prediction models for moment and rotation of boltless steel connections. Thin-walled Structures, 2018, 133: 206–215

[38] Cao Y, Wakil K, Alyousef R, Jermsittiparsert K, Si Ho L, Alabduljabbar H, Alaskar A, Alrshoudi F, Mustafa Mohamed A. Application of extreme learning machine in behavior of beam to column connections. Structures, 2020, 25: 861–867

[39] Abdalla K M, Stavroulakis G E. A backpropagation neural network model for semi-rigid steel connections. Computer-Aided Civil and Infrastructure Engineering, 1995, 10(2): 77–87

[40] Faridmehr I, Nikoo M, Pucinotti R, Bedon C. Application of component-based mechanical models and artificial intelligence to bolted beam-to-column connections. Applied Sciences, 2021, 11(5): 2297

[41] Kueh C Y. Artificial neural network and regressed beam−column connection explicit mathematical moment–rotation expressions. Journal of Building Engineering, 2021, 43: 103195

[42] Zakir Sarothi S, Sakil Ahmed K, Imtiaz Khan N, Ahmed A, Nehdi M L. Predicting bearing capacity of double shear bolted connections using machine learning. Engineering Structures, 2022, 251: 113497

[43] Anderson D, Hines E L, Arthur S J, Eiap E L. Application of artificial neural networks to the prediction of minor axis steel connections. Computers & Structures, 1997, 63(4): 685–692

[44] Tran V L, Kim J K. Revealing the nonlinear behavior of steel flush endplate connections using ANN-based hybrid models. Journal of Building Engineering, 2022, 57: 104878

[45] de Lima L R O, Vellasco P C G D S, de Andrade S A L, da Silva J G S, Vellasco M M B R. Neural networks assessment of beam-to-column joints. Journal of the Brazilian Society of Mechanical Sciences and Engineering, 2005, 27(3): 314–324

[46] BritishStainless-Steel Association. BSSA stainless-steel sections directory. 2nd ed. UK: British Stainless-Steel Association, 2006

[47] ABAQUS Incorporated. ABAQUS analysis user’s manual for version 6.12, 2012

[48] Sarfarazi S, Shamass R, Della Corte G, Guarracino F. Assessment of design approaches for stainless-steel joints through an equivalent FE modelling technique. ce/papers, 2022, 5(4): 271–281

[49] EN1993-1-4: 2006. Eurocode 3: Design of Steel Structures—Part 1–4: General Rules–Supplementary Rules for Stainless Steels. Brussels: European Committee for Standardization, 2006

[50] Sarfarazi S, Shamass R, Mascolo I, Della Corte G, Guarracino F. Some considerations on the behavior of bolted stainless-steel beam-to-column connections: A simplified analytical approach. Metals, 2023, 13(4): 753

[51] Rasmussen K J. Full range stress-strain curves for stainless-steel alloys. Journal of Constructional Steel Research, 2003, 59(1): 47–61

[52] Breda A, Coppieters S, Kuwabara T, Debruyne D. The effect of plastic anisotropy on the calibration of an equivalent model for clinched connections. Thin-walled Structures, 2019, 145: 106360

[53] Sarfarazi S, Saffari H, Fakhraddini A. Shear behavior of panel zone considering axial force for flanged cruciform columns. Civil Engineering Infrastructures Journal, 2020, 53(2): 359–377

[54] Saffari H, Sarfarazi S, Fakhraddini A. A mathematical steel panel zone model for flanged cruciform columns. Steel and Composite Structures, 2016, 20(4): 851–867

[55] Sarfarazi S, Fakhraddini A, Modaresahmadi K. Evaluation of panel zone shear strength in cruciform columns, box-columns and double-web columns. International Journal of Structural and Civil Engineering Research, 2016, 5(1): 52–56

[56] Shi Y, Shi G, Wang Y. Experimental and theoretical analysis of the moment–rotation behavior of stiffened extended end-plate connections. Journal of Constructional Steel Research, 2007, 63(9): 1279–1293

[57] Pedregosa F, Varoquaux G, Gramfort A, Michel V, Thirion B, Grisel O, Blondel M, Prettenhofer P, Weiss R, Dubourg V. . Scikit-learn: Machine learning in Python. Journal of Machine Learning Research, 2011, 12: 2825–2830

[58] Thai H T. Machine learning for structural engineering: A state-of-the-art review. Structures, 2022, 38: 448–491

[59] Breiman L. Random forests. Machine Learning, 2001, 45(1): 5–32

[60] Peterson L E. K-nearest neighbor. Scholarpedia, 2009, 4(2): 1883

[61] Le Q H, Nguyen D H, Sang-To T, Khatir S, Le-Minh H, Gandomi A H, Cuong-Le T. Machine learning-based models for predicting compressive strength of geopolymer concrete. Frontiers of Structural and Civil Engineering, 2024, 18(7): 1028–1049

[62] Friedman J H. Greedy function approximation: A gradient boosting machine. Annals of Statistics, 2001, 29(5): 1189–1232

[63] ChenTGuestrinC. XGBoost: A scalable tree boosting system. In: Proceedings of the 22nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. New York: Association for Computing Machinery, 2016, 785–794

[64] Chen S, Chen C, Li S, Guo J, Guo Q, Li C. Predicting torsional capacity of reinforced concrete members by data-driven machine learning models. Frontiers of Structural and Civil Engineering, 2024, 18(4): 444–460

[65] KeGMengQFinleyTWangTChenWMaWYeQLiuT Y. LightGBM: A highly efficient gradient boosting decision tree. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. New York: Curran Associates Incorporated, 2017, 3149–3157

[66] Qiong T, Jha I, Bahrami A, Isleem H F, Kumar R, Samui P. Proposed numerical and machine learning models for fiber-reinforced polymer concrete-steel hollow and solid elliptical columns. Frontiers of Structural and Civil Engineering, 2024, 18(7): 1169–1194

[67] Freund Y, Schapire R E. A decision-theoretic generalization of on-line learning and an application to boosting. Journal of Computer and System Sciences, 1997, 55(1): 119–139

[68] FreundYSchapireR E. Experiments with a new boosting algorithm. In: Proceedings of the 13th International Conference on Machine Learning. San Francisco: Morgan Kaufmann Publishers Incorporated, 1996, 148–156

[69] FerreiraA JFigueiredoM A T. Boosting Algorithms: A Review of Methods, Theory, and Applications. In: Ensemble Machine Learning: Methods and Applications. New York: Springer, 2012, 35–85

[70] Abarkan I, Rabi M, Ferreira F P V, Shamass R, Limbachiya V, Jweihan Y S, Pinho Santos L F. Machine learning for optimal design of circular hollow section stainless-steel stub columns: A comparative analysis with Eurocode 3 predictions. Engineering Applications of Artificial Intelligence, 2024, 132: 107952

[71] LundbergS MLeeS I. A unified approach to interpreting model predictions. In: Proceedings of the 31st International Conference on Neural Information Processing Systems. New York: Curran Associates Incorporated, 2017, 4768–4777

[72] Lai D, Demartino C, Xiao Y. Interpretable machine-learning models for maximum displacements of RC beams under impact loading predictions. Engineering Structures, 2023, 281: 115723

[73] Karathanasopoulos N, Singh A, Hadjidoukas P. Machine learning-based modelling, feature importance and Shapley additive explanations analysis of variable-stiffness composite beam structures. Structures, 2024, 62: 106206

[74] Wang S, Liu J, Wang Q, Dai R, Chen K. Prediction of non-uniform shrinkage of steel-concrete composite slabs based on explainable ensemble machine learning model. Journal of Building Engineering, 2024, 88: 109002

[75] Liu T, Cakiroglu C, Islam K, Wang Z, Nehdi M L. Explainable machine learning model for predicting punching shear strength of FRC flat slabs. Engineering Structures, 2024, 301: 117276

[76] IDEA StatiCa. IDEA StatiCa: User Guide, 2018

[77] LundhF. An Introduction to Tkinter. 1999 (Available at the website of Pythonware)

[78] SarfaraziS. Stainless-steel Flush End-plate Beam-to-Column Connections Response GUI. 2024 (available at the website of GitHub)

[79] Liu B, Wang Y, Rabczuk T, Olofsson T, Lu W. Multi-scale modeling in thermal conductivity of polyurethane incorporated with phase change materials using physics-informed neural networks. Renewable Energy, 2024, 220: 119565

Conflict of Interests

The authors declare that they have no conflicts of interest.

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