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A TLBO-optimized artificial neural network for modeling axial capacity of pile foundations

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Abstract

Due to a considerable level of uncertainty describing the pile–soil behavior, many pile capacity prediction methods have focused on correlation with in situ tests. In recent years, artificial neural networks (ANNs) have been applied successfully in many problems in geotechnical engineering, especially, axial pile capacity estimation for driven and drilled shaft piles. Training neural networks is a crucial task that needs effective optimization algorithms. The most popular algorithm is a back-propagation method (BP), which is based on a gradient descent that can trap in local minima. The paper proposes a new artificial neural network (ANN) in which the learning is performed using a recent teaching–learning-based optimization algorithm (TLBO), improving axial capacity predictions. The model is trained and validated on 479 data sets for a wide range of uncemented soils and pile configurations, obtained from the literature. Results show that the considered TLBO-ANN model outperforms other state-of-the-art models in the prediction accuracy and the generalization capability. For instance, we obtained a coefficient of determination \(R^2=0.941\) and a variance accounted for \({\text{VAF}} = 94.09\%\) for TLBO-ANN while \(R^2=0.871\) and \({\text{VAF}} = 87.31\%\) for the classical BP-ANN. In addition, error investigation with log-normal approaches demonstrates that the probability that predictions fall within a \(\pm \,25\%\) accuracy level for TLBO-ANN model is 0.93 and that for BP-ANN model is 0.75. The proposed TLBO-ANN model predicts pile capacity with more accuracy, less scatter, and higher reliability.

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Author information

Authors and Affiliations

  1. Department of Civil Engineering, University of Djilali Bounaama, Khemis Miliana, Algeria

    Amel Benali & Aouda Bounif

  2. Laboratory of Pure and Applied Mathematics, University of M’Sila, M’Sila, Algeria

    Mohammed Hachama

  3. Faculty of Civil Engineering, University of Science and Technology, Beb Ezzouar, Algiers, Algeria

    Ammar Nechnech

  4. Department of Civil Engineering, University of Sherbrooke, Sherbrooke, Canada

    Amel Benali & Mourad Karray

Authors
  1. Amel Benali
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  2. Mohammed Hachama
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  3. Aouda Bounif
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  4. Ammar Nechnech
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  5. Mourad Karray
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Correspondence to Mohammed Hachama.

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Weights and biases of the developed TLBO-ANN model

Weights and biases of the developed TLBO-ANN model

$$\begin{aligned} W_{1,1}= & {} \begin{bmatrix} -\,0.916097142&3.233093526&4.999995932&-\,3.410657184&1.705901358&-\,0.353471811&-\,1.134692603&1.424020204&-\,0.798977706 \\ 3.833845865&-\,1.550185312&-\,1.995298526&-\,3.171750562&-\,1.026155515&-\,0.914674308&1.235564886&-\,0.846186269&0.610652682 \\ 0.434729196&2.007720495&1.595550235&1.149538121&-\,0.861395011&4.999998664&-\,4.594423533&-\,0.922594389&0.690247806 \\ -\,1.804443544&0.02125135&4.999987105&-\,4.999560407&1.514593622&4.99999991&-\,0.917238335&-\,3.126790594&0.666309617 \\ 4.728029613&-\,0.295634338&1.575292152&-\,2.284665291&-\,1.0214764&-\,1.59564312&0.807132696&4.999999999&0.322308619 \\ 0.978652405&0.372546365&-\,1.34138682&-\,3.083465908&2.329963325&2.515508663&4.607963613&4.999999039&-\,0.319794243 \\ -\,2.163205602&3.947826123&1.443402665&-\,3.763317535&4.999999122&1.814411564&0.570368615&-\,1.258445944&0.511208251 \\ -\,2.596461235&-\,1.930616448&0.343200321&-\,4.65663045&1.004188733&-\,2.742914364&2.393936336&0.380112959&-\,0.511441673 \\ -\,1.329387049&3.758175771&1.112905587&-\,2.531075254&-\,4.999996507&-\,0.081859643&2.177900554&0.071164907&1.677386263 \\ 0.14533895&-\,2.2183597&2.60182057&4.999996299&1.234342306&2.084157367&2.185431415&2.725954881&-\,0.566754717 \end{bmatrix} \\ W_{2,1}= & {} \begin{bmatrix} -\,4.99211974&4.78517808&4.96900424&-\,4.99929697&4.99615628&-\,4.09317538&-\,3.20679187&5 \end{bmatrix} \\ b_1= & {} \begin{bmatrix} 0.99950584 \\ 2.02640275 \\ 4.99996893 \\ 5 \\ -\,4.9964599 \\ -\,4.5583188 \\ -\,3.0332818 \\ -\,4.9984299 \\ -\,4.9999978 \\ 4.65363322 \end{bmatrix}, \quad b_2 = [-\,4.9992929]. \end{aligned}$$

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Benali, A., Hachama, M., Bounif, A. et al. A TLBO-optimized artificial neural network for modeling axial capacity of pile foundations. Engineering with Computers 37, 675–684 (2021). https://doi.org/10.1007/s00366-019-00847-5

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