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Designing new hybrid artificial intelligence model for CFST beam flexural performance prediction

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Abstract

A substantial number of experimental studies have reported on the flexural performance of concrete-filled steel tube (CFST) beams. Due to the problem complexity, theoretically modeling of the flexural bending capacity (Mu) and the flexural stiffness at the initial and serviceability limits (\(K_{{\text{i}}}\) and \(K_{{\text{s}}}\)) of CFST beams remains challenging mission in the structural engineering field. Hence, this research proposes new numerical models for modeling the flexural capacities (Mu, \(K_{{\text{i}}}\), and \(K_{{\text{s}}}\)) of CFST beams under static bending load. For this purpose, numerous existing experimental and numerical results of CFST beams are collected for developing a new numerical model called as hybridized artificial neural network (ANN) model with particle swarm optimization (PSO) algorithm. The results of the proposed model validated against the existing results of CFST beams tested over the literature. In addition, PSO–ANN model verified with those obtained by the existing standards and approaches (EC4, BS5400, AISC, AIJ, and others) for the same corresponding beams. The proposed PSO–ANN model confirmed its capability to be used as an alternative theoretical approach to predict the flexural strength and stiffness capacities of CFST beams. The PSO–ANN model achieved mean values of about 0.933–0.989 with a coefficient of variation ranged from 4.98 to 9.53% compared to the existing results that obtained by others.

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Abbreviations

A c :

Area of concrete core cross-section, mm2

A s :

Area of steel tube cross-section, mm2

AR:

The ratio of concrete core cross-section area, estimated from Ac/(As + Ac)

B :

Width of rectangular steel tube, mm

COV:

Coefficient of variation

C 1 :

The learning parameters associated with individual particles

C 2 :

The learning parameters associated with other particles

D :

Diameter of circular steel tube/depth of rectangular steel tube, mm

E c :

Modulus of elasticity for concrete, GPa

E s :

Modulus of elasticity for steel, GPa

f :

Compression stress of concrete at relevant strain (ε) value, MPa

f cu :

Concrete cube compressive strength at 28 days, MPa

f co :

Unconfined concrete cylinder compressive strength at 28 days, MPa

f cc :

Confined concrete strength, MPa

f comp :

Nominal composite stress, MPa

f ck :

Characteristic concrete strength (0.67fcu), MPa

f cr :

Stress of concrete at cracking failure, MPa

f scy :

Yield strength of the composite section, MPa

f t :

Tensile stress of concrete at relevant strain (εt) value, MPa

f u :

Ultimate strength of steel, MPa

f y :

Yield strength of steel, MPa

G best :

The optimal duty cycle D value for all particles

I c :

Moment of inertia for concrete tube cross-section, mm4

I s :

Moment of inertia for steel tube cross-section, mm4

K i :

Initial flexural stiffness of composite section, kN m2

K s :

Serviceability-level flexural stiffness of composite section, kN m2

K i-P :

Predicted initial flexural stiffness of composite section, kN m2

K s-P :

Predicted serviceability-level flexural stiffness of composite section, kN m2

L e :

Effective length of specimen, mm or m

M :

Bending moment, kN m

M u :

Ultimate bending moment (flexural strength capacity), kN m

MR:

The ratio of concrete modulus of elasticity, estimated from Ec/(Es + Ec)

M u-p :

Predicted ultimate bending moment capacity, kN m

MV:

Mean value

N :

The number of times each particle moves.

n :

Is the number of the training pattern

ns:

Is the number of test data points

O i :

Is the output of the network

Rand1(·):

A value between 0 and 1 generated by the first random number generator

Rand2(·):

A value between 0 and 1 generated by the second random number generator

P :

The number of points tracked at different initial duty cycle D values.

PAi and PEi :

Are the actual value and estimated value of the flexural capacity and stiffness values, respectively

\(P_{i}^{j}\) :

The duty cycle D value for the ith particle during the jth iteration

\(P_{{{\text{best}},i}}\) :

The optimal duty cycle D value for the ith particle

r :

Internal radius of concrete, mm

t :

Wall thickness of steel tube, mm

\(t_{i}\) :

Is the output of the target

\(V_{i}^{j}\) :

The movement speed of the ith particle during the jth iteration

W :

The correlation with the most recent particle movement distance

W scm :

Section modulus for the circular/rectangular tube sections, m3

Z ccmp :

Section modulus for the circular/rectangular composite sections, m3

γ m :

Flexural strength index

β :

Flexural index (in the current study)

ε :

Strain at relevant concrete compression stress (f) value

ε t :

Strain at relevant concrete tension stress (ft) value

ε co :

Strain at unconfined concrete compressive strength (fco), 0.003 (current study)

ε cc :

Strain at confined concrete compressive strength (fcc)

ε cu :

Ultimate strain limit of confined concrete, = 11 εcc (current study)

ε cr :

Strain of concrete at ultimate cracking failure (fcr)

ε y :

Yield strain of steel

ε u :

Ultimate strain of steel

ξ :

Steel confinement factor (As·fy)/(Ac·fck)

λ i :

Reduction factor for Ki of composite section

λ s :

Reduction factor for Ks of composite section

φ i :

Curvature value relevant to the initial-level flexural stiffness (Ki), 1/m

φ s :

Curvature value relevant to the serviceability-level flexural stiffness (Ks), 1/m

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Acknowledgements

The authors gratefully acknowledge the financial support for the research provided by the University of Baghdad and the Universiti Kebangsaan Malaysia (UKM) with project Grant GGPM-2020-001 (Pusat Pengurusan Penyelidikan dan Instrumentasi).

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Authors and Affiliations

  1. Department of Reconstruction and Projects, University of Baghdad, Baghdad, Iraq

    Ammar N. Hanoon

  2. Department of Civil Engineering, Universiti Kebangsaan Malaysia, Bangi, Selangor, Malaysia

    Ahmed W. Al Zand

  3. Institute of Research and Development, Duy Tan University, Da Nang, 550000, Vietnam

    Zaher Mundher Yaseen

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Hanoon, A.N., Al Zand, A.W. & Yaseen, Z.M. Designing new hybrid artificial intelligence model for CFST beam flexural performance prediction. Engineering with Computers 38, 3109–3135 (2022). https://doi.org/10.1007/s00366-021-01325-7

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