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      Design deep neural network architecture using a genetic algorithm for estimation of pile bearing capacity

      research-article
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      PLoS ONE
      Public Library of Science

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          Abstract

          Determination of pile bearing capacity is essential in pile foundation design. This study focused on the use of evolutionary algorithms to optimize Deep Learning Neural Network (DLNN) algorithm to predict the bearing capacity of driven pile. For this purpose, a Genetic Algorithm (GA) was developed to select the most significant features in the raw dataset. After that, a GA-DLNN hybrid model was developed to select optimal parameters for the DLNN model, including: network algorithm, activation function for hidden neurons, number of hidden layers, and the number of neurons in each hidden layer. A database containing 472 driven pile static load test reports was used. The dataset was divided into three parts, namely the training set (60%), validation (20%) and testing set (20%) for the construction, validation and testing phases of the proposed model, respectively. Various quality assessment criteria, namely the coefficient of determination (R 2), Index of Agreement (IA), mean absolute error (MAE) and root mean squared error (RMSE), were used to evaluate the performance of the machine learning (ML) algorithms. The GA-DLNN hybrid model was shown to exhibit the ability to find the most optimal set of parameters for the prediction process.The results showed that the performance of the hybrid model using only the most critical features gave the highest accuracy, compared with those obtained by the hybrid model using all input variables.

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          Root mean square error (RMSE) or mean absolute error (MAE)? – Arguments against avoiding RMSE in the literature

          Both the root mean square error (RMSE) and the mean absolute error (MAE) are regularly employed in model evaluation studies. Willmott and Matsuura (2005) have suggested that the RMSE is not a good indicator of average model performance and might be a misleading indicator of average error, and thus the MAE would be a better metric for that purpose. While some concerns over using RMSE raised by Willmott and Matsuura (2005) and Willmott et al. (2009) are valid, the proposed avoidance of RMSE in favor of MAE is not the solution. Citing the aforementioned papers, many researchers chose MAE over RMSE to present their model evaluation statistics when presenting or adding the RMSE measures could be more beneficial. In this technical note, we demonstrate that the RMSE is not ambiguous in its meaning, contrary to what was claimed by Willmott et al. (2009). The RMSE is more appropriate to represent model performance than the MAE when the error distribution is expected to be Gaussian. In addition, we show that the RMSE satisfies the triangle inequality requirement for a distance metric, whereas Willmott et al. (2009) indicated that the sums-of-squares-based statistics do not satisfy this rule. In the end, we discussed some circumstances where using the RMSE will be more beneficial. However, we do not contend that the RMSE is superior over the MAE. Instead, a combination of metrics, including but certainly not limited to RMSEs and MAEs, are often required to assess model performance.
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            ON THE VALIDATION OF MODELS

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              Back-propagation neural networks for modeling complex systems

              A.T.C. Goh (1995)
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                Author and article information

                Contributors
                Role: ConceptualizationRole: Formal analysisRole: InvestigationRole: ValidationRole: Writing – original draftRole: Writing – review & editing
                Role: Writing – original draftRole: Writing – review & editing
                Role: Writing – original draft
                Role: Writing – review & editing
                Role: Editor
                Journal
                PLoS One
                PLoS One
                plos
                plosone
                PLoS ONE
                Public Library of Science (San Francisco, CA USA )
                1932-6203
                17 December 2020
                2020
                : 15
                : 12
                : e0243030
                Affiliations
                [001]University of Transport Technology, Hanoi, Vietnam
                Vietnam National University, VIET NAM
                Author notes

                Competing Interests: The authors have declared that no competing interests exist.

                Author information
                https://orcid.org/0000-0002-4157-7717
                Article
                PONE-D-20-26359
                10.1371/journal.pone.0243030
                7746167
                33332377
                40335812-a5ac-4441-af5c-56886be142a8
                © 2020 Pham et al

                This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

                History
                : 22 August 2020
                : 16 November 2020
                Page count
                Figures: 11, Tables: 13, Pages: 25
                Funding
                The authors received no specific funding for this work.
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