# A Deep Learning-Based Approach for the Identification of a Multi-Parameter BWBN Model
###### Abstract  
A restoring-force model is a versatile mathematical model that can describe the relationship between the restoring force and the deformation obtained from a large number of experiments. Over the past few decades, a large body of work on the development of restoring-force models has been reported in the literature. Under high intensity cyclic loadings or seismic excitations, reinforced concrete (RC) structures undergo a wide range of hysteretic deteriorations such as strength, stiffness and pinching degradations. These characteristic behaviors can be described by the multi-parameter Bouc-Wen-Baber-Noori (BWBN) model, which offers a wide range of applicability. This model has been applied for the response prediction and modeling restoring-force behavior in structural and mechanical engineering systems, by adjusting the distribution range of this model's parameters. However, a major difficulty in utilizing the multi-parameter BWBN model is the parameters' identification. In this paper, a deep neural network model is used to estimate the hysteresis parameters of the BWBN model. This model is one of the most versatile and widely used general hysteresis models that can describe the hysteretic behavior of RC columns. The experimental data of the RC columns used in this paper are collected from the database of the Pacific Earthquake Engineering Research Center (PEER). Firstly, the hysteretic loop obtained from a physical experiment is described by the BWBN model, and the parameters of the BWBN model are identified via a genetic optimization algorithm. Then a neural network is established by a backpropagation (BP) algorithm for associating the identified BWBN model parameters with physical parameters of the RC column. Finally, the regression analysis of the identified parameters is carried out to obtain the regression characteristics of the RC columns. The trained neural network model can directly identify the parameters of BWBN model based on the physical parameters of RC columns, and is effective and computationally efficient for multi-parameter BWBN model identification. The proposed approach overcomes the difficult problem of identifying the parameters of BWBN model and provides a promising approach for a wider application of this multi-parameter hysteresis model. BWBN model; hysteresis loop; parameter identification; artificial neural networks; deep learning; RC columns +
Footnote †: journal: Applied Sciences  
impact of earthquakes, extensive research has been conducted and reported in the literature on the dynamic response of structures under earthquake action, and in particular the nonlinear dynamic analysis of concrete structures under strong earthquake action [6; 7; 8; 9; 10; 11; 12; 13; 14]. When concrete structures experience nonlinear deformation under high intensity dynamic loads, such as earthquake loadings, their strength and stiffness deteriorate through a hysteretic behavior. Quasi-static load tests are important experiments that help to understand the nature of this deterioration, especially in seismic research. A large number of quasi-static experiments have shown that the hysteresis loops of concrete members under different failure modes are significantly different. For example, the hysteresis loops of reinforced concrete (RC) columns can be divided into flexural failure (FF), flexural shear failure (FS) and shear failure (SF) modes. As part of the analysis required to study, understand and describe the characteristics of these various failure modes and the corresponding hysteresis loops, multi-parameter restoring-force models are needed. If a versatile hysteresis model can be used, by adjusting the parameter values of the model, it can accurately predict the nonlinear yield behavior of RC structures under different failure modes. The existing models for predicting the hysteretic restoring force of concrete structures are generally divided into polygonal hysteresis models (PHM) and smooth hysteresis models (SHM) [15; 16; 17; 18].