Application of ANN to the design of CFST columns
Introduction
Artificial neural networks (ANN) were developed to model the brain’s neural learning process for computer-based artificial intelligence systems [1]. The ANN has the ability to recognize and learn the relationships between given information (inputs) and desired values (outputs) and to analyse complex datasets that are hard to process with the conventional mathematical methods [2], [3]. An ANN consists of non-linear interconnected processing elements working in unison to produce an output (outputs). The learning process of ANNs can be divided into three types: (i) supervised learning which is based on the direct compare between the target and output values, (ii) unsupervised learning which is only based on the correlation of the inputs, and (iii) reinforcement learning which is a special case of supervised learning [4]. Since the predictions obtained using ANN are based on the experimental data, the predictions could be more realistic than other methods e.g. finite element (FE) analysis [5]. The neural network approach can be used in structural design to replace the structural analysis process with a neural network [6]. ANNs have been successfully used in solving various structural problems such as structural dynamics [7], [8], damage assessment [9], [10], prediction of compressive concrete strength [11], [12], modelling of confined concrete [13], [14], stability problems [5], [15], structural analysis and design [16], [17], vibration of structures [18], [19], modelling of fatigue crack growth [20], [21], fire resistance [22], [23] and reliability assessment of structures [24], [25]. One of the applications of neural networks in structural design is predicting the ultimate strength of concrete-filled steel tubular (CFST) columns. CFST columns are composite members that have been widely used in tall buildings, bridge piers and long-span bridges due to the composite action between the concrete and steel tube, resulting in higher strength, higher energy absorption capacity and better ductility compared to conventional steel and concrete columns [26], [27]. In CFST columns, the steel tube provides confinement to the concrete core, and the concrete core delays the occurrence of the local buckling of the steel tube. Many design codes such as Australian code AS 5100 [28], American code AISC 360-16 [29], European code EC 4 [30], Chinese code DBJ 13-51 [31] and Japanese code AIJ [32] provide provisions to predict the strength of CFST columns. However, each design code shows a different level of accuracy and is only applicable to a certain range of material and geometry properties [33], [34].
The structural behaviour of circular and rectangular CFST columns subjected to pure axial compression and combined axial compression and bending has been investigated by many researchers and their studies provide valuable information, such as the ultimate strength and the load-displacement behaviour of the specimens [35], [36], [37], [38], [39]. The available experimental data can be used to train a neural network to predict the ultimate strength of CFST columns. Although the accuracy of results obtained from ANN models has been validated in the literature [40], studies on using neural network for predicting the ultimate strength of CFST columns are limited. Tran et al. [3] used 300 experimental tests on rectangular CFST columns with the steel tube yield strengths and the concrete compressive cylinder strengths between 228–835 MPa and 16.68–164 MPa, respectively, to train ANN models. They used a graph-based method for deriving empirical equations for predicting the axial compression capacity of CFST columns subjected to pure axial load. A study on the prediction of fire resistance of CFST columns using ANN model was conducted by Al-Khaleefi et al. [41]. In the study, only 35 tests were used to train the neural network and the obtained results from the ANN model were in good agreement with the test results. Tran et al. [42] developed a practical ANN tool for predicting the axial compression capacity of circular CFST columns with ultra-high-strength concrete (UHSC) core under pure axial compression. They modelled circular columns with UHSC in the finite element software ABAQUS [43] and used the obtained FE database for training ANN models. Du et al. [44] used ANN models to predict the axial strength of rectangular CFST columns subjected to pure compression. In addition, they investigated the effects of material strength and section size on the axial strength. An experimental database including 305 tests on axially loaded rectangular CFST columns was used to train the ANN models. The steel tube yield strengths and the concrete compressive cylinder strengths of the tests were between 194–835 MPa and 14.5–164 MPa, respectively. The results showed that the ANN models have good accuracy for estimating the axial strength of rectangular CFST columns. From the mentioned studies, it can be noted that most of the studies focused on predicting the ultimate strength of CFST columns subjected to concentric axial load only. In addition, limited datasets were used to train the networks, which prevents ANNs from learning input-output relationships within different ranges, resulting in less prediction accuracy. Another issue is that most studies just focused on developing ANNs without deriving any empirical equations from the trained networks.
The objectives of this paper are to develop ANN models to predict the axial strength of circular and rectangular CFST columns subjected to concentric and eccentric loading. In this study, four comprehensive experimental datasets are compiled and used to train the ANN models including (1) 895 rectangular CFST columns subjected to pure compression, (2) 392 rectangular CFST columns under eccentric loading, (3) 1305 circular CFST columns subjected to pure compression and (4) 499 circular CFST columns under eccentric loading. Based on the trained networks, empirical equations are proposed to predict the ultimate strength of circular and rectangular CFST columns subjected to concentric and eccentric loading. The accuracy of the proposed equations in predicting the ultimate strength of CFST columns is compared with that of AISC 360-16, EC 4 and AS 5100. Finally, for the proposed empirical equations, reduction factors are derived in accordance with load standards of America ASCE/SEI 7-16 [45], Europe EC 0 [46] and Australia/New Zealand AS/NZS 1170.1 [47]. The values of the reduction factors are determined by performing reliability analysis using Monte Carlo simulation (MCS) method.
Section snippets
Experimental datasets
To effectively train and generalize the ANN models, a comprehensive database of experimental studies on CFST columns was compiled. A large portion of the database was extracted from Denavit [48] and Goode [49] databases. The collected database only includes specimens subjected to monotonic concentric and eccentric axial compression and without any internal steel reinforcement. The ranges of the test parameters and results are summarized in Table 1, where n, L, B, H, D and t are the number of
Overview of ANN
An ANN is formed from highly parallel and interconnected networks modelling the biological neural network of the human brain [6], [51]. ANNs are capable of modelling systems with unknown characteristics and nonlinearities [52]. There are many types of neural networks in the literature such as Hopfield and NARX. However, one of the widely used ANNs in engineering is the feed-forward network with a back-propagation algorithm (BPA) [42], [53]. The feed-forward BPA involves two phases. In the first
Empirical equations
This section presents empirical equations for predicting the ultimate strength of CFST columns. The equations were derived based on the activation functions used in the proposed networks and the weights and biases obtained from the trained networks. Therefore, the equations provide the same results as those provided by the ANNs. The equations can be used for CFST columns with different section slenderness ratios (compact, non-compact and slender sections) and different length-to-depth ratios
Comparison between test results and empirical equations and code predictions
Three design codes of AISC 360-16, EC 4 and AS 5100 were chosen to compare their prediction accuracy with the proposed empirical equations. For comparison study, all safety factors were taken as unity, and all limitations on material strengths specified by the codes were ignored. Based on AISC 360-16, CFST columns are categorized as compact, non-compact and slender sections. For compact sections, the steel tube can develop its full yield strength and the concrete core can only reach 0.85 for
Conclusions
Four comprehensive experimental datasets were used to develop artificial neural network models to predict the ultimate strength of CFST columns including (1) rectangular columns subjected to pure compression, (2) rectangular columns under eccentric loading, (3) circular columns subjected to pure compression and (4) circular columns under eccentric loading. Based on the trained networks, empirical equations were proposed to predict the ultimate strength of CFST columns. In addition, for the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The research presented in this paper was supported by La Trobe University, School of Engineering and Mathematical Sciences, Australia.
References (80)
- et al.
Review and application of Artificial Neural Networks models in reliability analysis of steel structures
Struct Saf
(2015) - et al.
Artificial neural network prediction of buckling load of thin cylindrical shells under axial compression
Eng Struct
(2017) - et al.
Neurobiological computational models in structural analysis and design
Comput Struct
(1991) - et al.
Artificial neural networks in structural dynamics: a new modular radial basis function approach vs. convolutional and feedforward topologies
Comput Methods Appl Mech Eng
(2020) - et al.
Damage assessment of prestressed concrete beams using artificial neural network (ANN) approach
Comput Struct
(2006) Prediction of concrete strength using artificial neural networks
Eng Struct
(2003)- et al.
Prediction of compressive strength of concrete by neural networks
Cem Concr Res
(2000) - et al.
An Artificial Neural Networks model for the prediction of the compressive strength of FRP-confined concrete circular columns
Eng Struct
(2017) - et al.
Prediction of strength parameters of FRP-confined concrete
Compos B Eng
(2012) - et al.
Neural prediction of buckling loads of cylindrical shells with geometrical imperfections
Int J Non Linear Mech
(2002)