Abstract
This paper uses the recently proposed grasshopper optimization algorithm (GOA) to develop a new hybrid, stochastic training algorithm for the feed-forward neural networks (FFNN). The state-of-the-art hybrid model is then applied to study observing pattern of scour depth which is a challenging problem in hydraulic engineering. In order to verify and control the accuracy, stability, and efficiency of the proposed model and its computational process, the model results are compared to networks trained by three different training algorithms. To achieve this, backpropagation, backpropagation with momentum, and Levenberg–Marquardt learning algorithms, which are widely used for various hydraulic problems, are chosen. The results of the model indicated that the proposed model has high stability and performance in solving regression problems. The comparison of prediction accuracy and convergence curves represented that the model could predict the maximum scour depth with the higher convergence speed. Applying the proposed model improves the correlation coefficient (R), root mean square error (RMSE), and mean absolute error (MAE) values by approximately 6%, 30%, and 18%, respectively.
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Funding
This research was partly funded by Fulbright US-ASIAN Visiting Scholar Program (G-1–00005) for Duong Tran Anh at University of South Florida, USA (N0031836361).
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K.K. and D.T.A designed the study, processed, and analyzed the data, developed the models, interpreted the results, and wrote the paper. D.N.N and Q.B.P check the methodology and proofreading and finalize the manuscript.
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The authors declare no competing interests.
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Responsible Editor: Zeynal Abiddin Erguler
Highlights
• A novel hybrid stochastic training algorithm was developed for FFNN;
• New computational strategies and numerical algorithms in neural networks;
• The accuracy, stability, and efficiency of the model was controlled and proven;
• The proposed model shows efficient and accurate compared to other existing models.
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Kaveh, K., Mai, D.N., Pham, Q.B. et al. A hybrid feed-forward neural network with grasshopper optimization for observing pattern of scour depth around bridge piers. Arab J Geosci 14, 2352 (2021). https://doi.org/10.1007/s12517-021-08617-8
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DOI: https://doi.org/10.1007/s12517-021-08617-8