Research on innovative hybrid analysis method for structural seismic response based on neural network restoring force model

Abstract

Quasi-static testing is the primary seismic research method employed. The method proposed in this study utilizes the neural network (NN) algorithm for restoring force identification to extend the hysteretic performance of nonlinear complex components obtained from quasi-static tests shared or performed at a lower cost to the time history analysis of the seismic response of the entire structure. This approach enables accurate analysis of the seismic performance of the structure under real earthquake ground motions at a relatively low experimental costs. At the level of restoring force model recognition, the eight-path hysteresis model recognition theory and the corresponding complete set of input and output variables in the NN algorithm are proposed. The NN restoring force model was established using input and output parameters that characterize hysteresis state features, with a two-hidden-layer NN architecture. The case study results indicate that the prediction results of the NN restoring force model align well with the target values when trained on samples obtained under both seismic and quasi-static loading conditions. At the level of the nonlinear dynamic analysis of structures, the hybrid analysis method of structural seismic response based on NN restoring force model is proposed. In this method, the potentially severe nonlinear and elastic parts of the structure are divided into several NN substructures and principal numerical substructure, respectively. The pseudo-static test data of nonlinear regions were used to train the proposed NN restoring force model to identify the restoring force of NN substructures in the same region under time-history dynamic analysis. The platform was built to complete the data interaction between several NN substructures and principal numerical substructures, and a precise integration method was used to program the dynamic equation solving module, gradually completing dynamic response analysis of the entire structure. A multi-degree-of-freedom nonlinear frame case study indicate that the proposed method has good accuracy and can effectively analyze the structural nonlinear seismic response.

Graphical abstract

Keywords

restoring force model / neural network algorithm / module programming / hybrid analysis method / nonlinear dynamic analysis

References

[1] Liu X, Tian S, Tao F, Yu W. A review of artificial neural networks in the constitutive modeling of composite materials. Composites. Part B: Engineering, 2021, 224: 109152

[2] Huang X, Zhou Z, Xie Q, Guo C, Li C. Seismic analysis of friction-damped self-centering coupled-beams for moment-resisting-frames without floor elongation. Journal of Earthquake and Tsunami, 2018, 12(5): 1850012

[3] Li C, Wu J, Zhang J, Tong C. Elastic displacement spectrum-based design approach for precast concrete frame with replaceable energy-dissipating connectors. Journal of Earthquake Engineering, 2020, 26(5): 2411–2436

[4] WangYLuJWuJ. On-line model updating method for hybrid testings based on the forgetting factor and LMBP neural network. Journal of Vibration and Shock, 2020, 39(9): 42–48,56 (in Chinese)

[5] WangCFanJ S. A general deep learning model MechPerformer for history-dependent response prediction in structural engineering. Journal of Building Structures, 2022, 43(8): 209–219 (in Chinese)

[6] Hakuno M, Shidawara M, Hara T. Dynamic destructive test of a cantilevers beam, controlled by an analog computer. Transactions of the Japan Society of Civil Engineering, 1969, 171: 1–9

[7] Shao X, Griffith C. An overview of hybrid simulation implementations in NEES projects. Engineering Structures, 2013, 56: 1439–1451

[8] NakashimaMTakaiH. Use of Substructure Techniques in Pseudo dynamic Testing. BRI Research Paper No. 111. 1985

[9] Nakashima M. Hybrid simulation: an early history. Earthquake Engineering & Structural Dynamics, 2020, 49(10): 949–962

[10] Kim S J, Holub C J, Elnashai A S. Experimental investigation of the behavior of RC bridge piers subjected to horizontal and vertical earthquake motion. Engineering Structures, 2011, 33(7): 2221–2235

[11] McCrum D P, Broderick B M. Evaluation of a substructured soft-real time hybrid test for performing seismic analysis of complex structural systems. Computers & Structures, 2013, 129: 111–119

[12] Murray J A, Sasani M, Shao X. Hybrid simulation for system-level structural response. Engineering Structures, 2015, 103: 228–238

[13] WangTZhaiX HMengL YWangZ. Hybrid testing method based on an online neural network algorithm. Journal of Vibration and Shock, 2017, 36(14): 1–8 (in Chinese)

[14] ChenZ XZhongW PWangJ W. Model updating method for hybrid simulation based on dynamic time history analysis. China Civil Engineering Journal, 2020, 53(S2): 137–142 (in Chinese)

[15] Azimi M, Eslamlou A D, Pekcan G. Data-driven structural health monitoring and damage detection through deep learning: State-of-the-art review. Sensors, 2020, 20(10): 2778

[16] BaoYLiH. Artificial intelligence for civil engineering. China Civil Engineering Journal, 2019, 52(5): 1–11 (in Chinese)

[17] Wang C, Song L, Yuan Z, Fan J. State-of-the-art AI-based computational analysis in civil engineering. Journal of Industrial Information Integration, 2023, 33: 100470

[18] Dettmer W G, Muttio E J, Alhayki R, Perić D. A framework for neural network based constitutive modelling of inelastic materials. Computer Methods in Applied Mechanics and Engineering, 2024, 420: 116672

[19] Goswami S, Anitescu C, Chakraborty S, Rabczuk T. Transfer learning enhanced physics informed neural network for phase-field modeling of fracture. Theoretical and Applied Fracture Mechanics, 2020, 106: 102447

[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] Gu Y, Lu X, Xu Y. A deep ensemble learning-driven method for the intelligent construction of structural hysteresis models. Computers & Structures, 2023, 286: 107106

[22] Wang C, Xu L, Fan J. A general deep learning framework for history-dependent response prediction based on UA-Seq2Seq model. Computer Methods in Applied Mechanics and Engineering, 2020, 372: 113357

[23] Huang C, Li Y, Gu Q, Liu J. Machine learning-based hysteretic lateral force-displacement models of reinforced concrete columns. Journal of Structural Engineering, 2022, 148(3): 04021291

[24] Zhou Y, Meng S, Lou Y, Kong Q. Physics-informed deep learning-based real-time structural response prediction method. Engineering, 2024, 35: 140–157

[25] Huang P, Chen Z. Deep learning for nonlinear seismic responses prediction of subway station. Engineering Structures, 2021, 244: 112735

[26] Liu Y, Liao S, Yang Y, Zhang B. Data-driven and physics-informed neural network for predicting tunnelling-induced ground deformation with sparse data of field measurement. Tunnelling and Underground Space Technology, 2024, 152: 105951

[27] Grillanda N, Milani G, Ghosh S, Halani B, Varma M. SHM of a severely cracked masonry arch bridge in India: Experimental campaign and adaptive NURBS limit analysis numerical investigation. Construction & Building Materials, 2021, 280: 122490

[28] Han C, Wang S, Madan A, Zhao C, Mohanty L, Fu Y, Shen W, Liang R, Huang E S, Zheng T. . Intelligent detection of loose fasteners in railway tracks using distributed acoustic sensing and machine learning. Engineering Applications of Artificial Intelligence, 2024, 134: 108684

[29] Xu Y, Fei Y, Huang Y, Tian Y, Lu X. Advanced corrective training strategy for surrogating complex hysteretic behavior. Structures, 2022, 41: 1792–1803

[30] Kim T, Kwon O S, Song J. Response prediction of nonlinear hysteretic systems by deep neural networks. Neural Networks, 2019, 111: 1–10

[31] Teranishi M. Neural network constitutive model for uniaxial cyclic plasticity based on return mapping algorithm. Mechanics Research Communications, 2022, 119: 103815

[32] Liu X, Tao F, Yu W. A neural network enhanced system for learning nonlinear constitutive law and failure initiation criterion of composites using indirectly measurable data. Composite Structures, 2020, 252: 112658

[33] Hashash Y M A, Marulanda C, Ghaboussi J, Jung S. Systematic update of a deep excavation model using field performance data. Computers and Geotechnics, 2003, 30(6): 477–488

[34] Shin H S, Pande G N. On self-learning finite element codes based on monitored response of structures. Computers and Geotechnics, 2000, 27(3): 161–178

[35] Jung S, Ghaboussi J. Neural network constitutive model for rate-dependent materials. Computers & Structures, 2006, 84(15–16): 955–963

[36] Kim J, Ghaboussi J, Elnashai A S. Mechanical and informational modeling of steel beam-to-column connections. Engineering Structures, 2010, 32(2): 449–458

[37] Kim J H, Ghaboussi J, Elnashai A S. Hysteretic mechanical–informational modeling of bolted steel frame connections. Engineering Structures, 2012, 45: 1–11

[38] Yun G J, Ghaboussi J, Elnashai A S. Self-learning simulation method for inverse nonlinear modeling of cyclic behavior of connections. Computer Methods in Applied Mechanics and Engineering, 2008, 197(33–40): 2836–2857

[39] Wang C, Song L, Fan J. End-to-End Structural analysis in civil engineering based on deep learning. Automation in Construction, 2022, 138: 104255

[40] Horton T A, Hajirasouliha I, Davison B, Ozdemir Z. Accurate prediction of cyclic hysteresis behaviour of RBS connections using deep learning neural networks. Engineering Structures, 2021, 247: 113156

[41] Xu Y, Lu X, Fei Y, Huang Y. Hysteretic behavior simulation based on pyramid neural network: Principle, network architecture, case study and explanation. Advances in Structural Engineering, 2023, 26(13): 2359–2374

[42] Yun G J, Ghaboussi J, Elnashai A S. A new neural network-based model for hysteretic behavior of materials. International Journal for Numerical Methods in Engineering, 2008, 73(4): 447–469

[43] Rumelhart D E, Hinton G E, Williams R J. Learning representations by back-propagating errors. Nature, 1986, 323(6088): 533–536

[44] FEMA-P695. Quantification of Building Seismic Performance Factors. Washington, D.C.: Federal Emergency Management Agency, 2009

[45] ACICommittee 374.2 R-13. Guide for Testing Reinforced Concrete Structural Elements under Slowly Applied Simulated Seismic Loads. Farmington Hills, MI: American Concrete Institute, 2013

[46] Zhong W X, Williams F W. A precise time step integration method. Proceedings of the Institution of Mechanical Engineers. Part C, Journal of Mechanical Engineering Science, 1994, 208(6): 427–430

[47] Zhong W X. On precise integration method. Journal of Computational and Applied Mathematics, 2004, 163(1): 59–78

[48] GuG Y. Research on refined integration method and its pseudo-dynamic testing algorithm. Thesis for the Master’s Degree. Changsha: Central South University, 2014 (in Chinese)

[49] Wang M, Au F T K. Assessment and improvement of precise time step integration method. Computers & Structures, 2006, 84(12): 779–786

[50] Fung T C. Stability and accuracy of differential quadrature method in solving dynamic problems. Computer Methods in Applied Mechanics and Engineering, 2002, 191(13–14): 1311–1331

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