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Prediction of axial load capacity of rectangular concrete-filled steel tube columns using machine learning techniques

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Abstract

This work aims to develop a novel and practical equation for predicting the axial load of rectangular concrete-filled steel tubular (CFST) columns based on soft computing techniques. More precisely, a dataset containing 880 experimental tests was first collected from the available literature for the development of an artificial neural network (ANN) model. An optimization strategy was conducted to obtain a final set of ANN’s architecture as well as its weight and bias parameters. The performance of the developed ANN was then compared to current codes (AS, EN, AIJ, ACI, AISC, LRFD, and DBJ) and existing empirical equations. The accuracy of the present model was found superior to the results obtained by others when predicting the axial load of rectangular CFST columns. For practical application, an explicit equation and an Excel-based Graphical User Interface were derived based on the ANN model. The graphical user interface is provided freely for all interested users, to support the design, teaching, and interpretation of the axial behavior of CFST columns.

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Data availability

The raw/processed data required to reproduce these findings will be made available on request.

Abbreviations

ANN(s):

Artificial neural network(s)

A c :

Area of concrete core section

A s :

Area of steel tube section

A sc :

Area of composite section

B :

Width of tubes section

BPNN:

Back propagation neural network

CFST:

Concrete filled steel tube

Co:

Competitive transfer function

E c :

Concrete modulus of elasticity

E s :

Steel modulus of elasticity

\(f_{{\text{c}}}^{\prime }\) :

Concrete compressive strength

f y :

Steel yield limit

f u :

Steel ultimate strength

GP:

Genetic programming

GUI:

Graphical user interface

H :

Height of tubes section

HTS:

Hyperbolic tangent sigmoid transfer function

I s :

Moment of inertia of steel tube section

I c :

Moment of inertia of concete core section

L :

Length of column

L e :

Effective length of column

Li:

Linear transfer function

LS:

Log-sigmoid transfer function

MAPE:

Mean absolute percentage error

MSE:

Mean square error

N :

Axial load capacity

N b :

Buckling capacity of column

N cr :

Elastic critical bucking load

N pl :

Squash load

NRB:

Normalized radial basis transfer function

PLi:

Positive linear transfer function

R :

Pearson correlation coefficient

RB:

Radial basis transfer function

SM:

Soft max transfer function

SSE:

Sum square error

SP:

Superplasticizer

SSL:

Symmetric saturating linear transfer function

t :

Wall thickness of steel tubes

TB:

Triangular basis transfer function

\(\xi\) :

Confinement factor

\(\rho\) :

Concrete density

\(N_{{\text{u}}}^{{{\text{predicted}}}}\) :

Prediction of axial load of CFST columns

[I w]:

Weight matrix of the hidden layer

[b i]:

Bias matrix of the hidden layer

[L W]:

Weight matrix of the output layer

[b o]:

Bias matrix of the output layer

B min, B max :

Min and max values of width of tubes sections

H min, H max :

Min and max values of height of tubes sections

t min, t max :

Min and max values of thickness of tubes sections

L emin, L emax :

Min and max values of effective length of column

f ymin, f ymax :

Min and max values of steel yield limit

\(f_{0}^{\prime }\), \(f_{{{\text{c}}\max }}^{\prime }\) :

Min and max values of concrete compressive strength

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Authors and Affiliations

  1. Faculty of Mechanical Engineering and Mechatronics, PHENIKAA University, Yen Nghia, Ha Dong, Hanoi, 12116, Viet Nam

    Tien-Thinh Le

  2. PHENIKAA Research and Technology Institute (PRATI), A&A Green Phoenix Group JSC, No. 167 Hoang Ngan, Trung Hoa, Cau Giay, Hanoi, 11313, Viet Nam

    Tien-Thinh Le

  3. Computational Mechanics Laboratory, School of Pedagogical and Technological Education, Heraklion, 14121, Athens, Greece

    Panagiotis G. Asteris & Minas E. Lemonis

Authors
  1. Tien-Thinh Le
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  2. Panagiotis G. Asteris
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  3. Minas E. Lemonis
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Correspondence to Panagiotis G. Asteris.

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366_2021_1461_MOESM1_ESM.xlsx

Supplementary file1The Excel-based Graphical User Interface for prediction of axial compressive load of CFST columns, based on the optimal machine learning model is appended to this paper (XLSX 438 kb)

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Le, TT., Asteris, P.G. & Lemonis, M.E. Prediction of axial load capacity of rectangular concrete-filled steel tube columns using machine learning techniques. Engineering with Computers 38 (Suppl 4), 3283–3316 (2022). https://doi.org/10.1007/s00366-021-01461-0

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  • DOI: https://doi.org/10.1007/s00366-021-01461-0

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