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Novel integrated approaches for predicting the compressibility of clay using cascade forward neural networks optimized by swarm- and evolution-based algorithms

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Abstract

Soft soils are considered as disadvantages in construction, especially in clay layers. It requires many advanced techniques to treat the soft soils before construction, aiming to ensure the safety of the foundation and building structures. In this regard, the clay compressibility behavior is considered an important problem that needs to be processed. To investigate this behavior in clay, 685 tests were conducted under various conditions of void ratio, water content, and plasticity index. Subsequently, the cascade forward neural network (CFNN) was selected to predict the compressibility behavior of clay based on the collected database. Three optimization algorithms were considered to optimize the CFNN model aiming to improve the accuracy of the CFNN model in predicting the compressibility behavior of clay, including grey wolf optimization (GWO), hunger games search (HGS), and genetic algorithm (GA), named as GWO-CFNN, HGS-CFNN, and GA-CFNN model. These hybrid models then were compared with the CFNN and multiple layers perceptron (MLP) neural network to demonstrate the improvement and select the best-generalized model for predicting the compressibility behavior of clay. The results revealed that CFNN and MLP are potential solutions for predicting the compressibility behavior of clay with acceptable accuracies. Moreover, the optimization algorithms are the boosting solution to improve the accuracy of the CFNN. Of those, the findings indicated that the GWO-CFNN model is the best model for predicting the compressibility behavior of clay with a mean absolute error (MAE) of 0.146 and 0.153, root-mean-squared error (RMSE) of 0.187 and 0.199, determination coefficient (R2) of 0.828 and 0.813, and a20-index of 0.643 and 0.612, on the training and testing datasets, respectively. Meanwhile, the HGS-FLNN and GA-FLNN models provided poorer performances on the testing dataset, i.e., MAE = 0.160 and 0.161; RMSE = 0.206 and 0.207; R2 = 0.799 and 0.796; a20-index = 0.607 and 0.606, respectively. Besides, the relative error \(\pm 0.5\%\) was also determined for the GWO-CFNN model, and it is a positive result for using this model in evaluating and predicting the compressibility behavior of clay. In addition, the results of the CFNN (without optimization) and MLP models also showed that the CFNN model is better than the MLP model in predicting compression index CC (i.e., MAECFNN = 0.169, RMSECFNN = 0.218, R2CFNN = 0.796, and a20-indexCFNN = 0.597; MAEMLP = 0.172, RMSEMLP = 0.221, R2MLP = 0.774, and a20-indexMLP = 0.578). In other words, the extra connections and weights between the input and output layers may be the main reason to support this superior. The obtained result of this study is important for geotechnical engineers to make a rational decision or effective solutions for the treatment of soft soils.

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Acknowledgements

This study was supported by National Natural Science Foundation of China (No.41977228). The authors also would like to thank the Center for Mining, Electro-Mechanical Research, Hanoi University of Mining and Geology, Hanoi, Vietnam.

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Authors and Affiliations

  1. Institute of Architecture Engineering, Huanghuai University, ZhumadianHenan, 463000, China

    Ziguang He

  2. Hanoi University of Mining and Geology, 18 Vien str., Duc Thang ward, Bac Tu Liem distr., Hanoi, 100000, Vietnam

    Hoang Nguyen

  3. Innovations for Sustainable and Responsible Mining (ISRM) Group, Hanoi University of Mining and Geology, 18 Vien str., Duc Thang ward, Bac Tu Liem dist., Hanoi, Vietnam

    Hoang Nguyen

  4. Department of Geodesy, National University of Civil Engineering, Hanoi, 100000, Vietnam

    Thai Ha Vu

  5. School of Resources and Safety Engineering, Central South University, Changsha, 410083, China

    Jian Zhou

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

    Panagiotis G. Asteris & Anna Mammou

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  1. Ziguang He
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  3. Thai Ha Vu
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Correspondence to Hoang Nguyen.

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He, Z., Nguyen, H., Vu, T.H. et al. Novel integrated approaches for predicting the compressibility of clay using cascade forward neural networks optimized by swarm- and evolution-based algorithms. Acta Geotech. 17, 1257–1272 (2022). https://doi.org/10.1007/s11440-021-01358-8

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