Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand
Assessing the stiffness of circular foundations is the key to evaluating their deformation; thus, it is important for foundation design. The current determination methods for the stiffness coefficient are either time-consuming or inaccurate. In this paper, a novel stiffness prediction model has been...
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MDPI AG
2023-02-01
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| Online Access: | https://www.mdpi.com/2076-3417/13/4/2653 |
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| author | Chongchong Qi Jiashuai Zheng Chuiqian Meng Mengting Wu |
| author_facet | Chongchong Qi Jiashuai Zheng Chuiqian Meng Mengting Wu |
| author_sort | Chongchong Qi |
| collection | DOAJ |
| description | Assessing the stiffness of circular foundations is the key to evaluating their deformation; thus, it is important for foundation design. The current determination methods for the stiffness coefficient are either time-consuming or inaccurate. In this paper, a novel stiffness prediction model has been proposed, using the decision tree (DT) algorithm optimized by particle size optimization (PSO). The condition of the embedded foundation, the embedded depth (<i>Z<sub>D</sub></i>/2<i>R</i>), the thickness of the clay layer beneath the foundation base (<i>T</i>/2<i>R</i>), and the ratio of shear stiffness between clay and sand (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>G</mi><mrow><mi>s</mi><mi>a</mi><mi>n</mi><mi>d</mi></mrow></msub><mo>/</mo><msub><mi>G</mi><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>y</mi></mrow></msub></mrow></semantics></math></inline-formula>) were used as input variables, while the elastic stiffness coefficients (<i>K</i><sub>c</sub>, <i>K</i><sub>h</sub>, <i>K</i><sub>m</sub>, and <i>K</i><sub>v</sub>) were used as output variables. The optimum DT model has undergone comprehensive validation, and independent model verification using extra simulations. The results illustrate that PSO could promote further increases in the capability of DT modeling in predicting stiffness coefficients. The optimum DT model achieved a good level of performance on stiffness coefficient modeling. (The R for the training set was greater than 0.98 for all of the stiffness coefficients.) The variable importance analysis showed that the <i>T</i>/2<i>R</i> was the most significant variable for all stiffness coefficients, followed by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>G</mi><mrow><mi>s</mi><mi>a</mi><mi>n</mi><mi>d</mi></mrow></msub><mo>/</mo><msub><mi>G</mi><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>y</mi></mrow></msub></mrow></semantics></math></inline-formula>. The optimum DT model achieved good predictive performance upon independent verification, with the R being 0.97, 0.99, 0.99, and 0.95 for <i>K</i><sub>v</sub>, <i>K</i><sub>h</sub>, <i>K</i><sub>m</sub>, and <i>K</i><sub>c</sub>, respectively. The proposed reliable and efficient DT-PSO model for stiffness coefficients in layered soil could further promote the safe and efficient utilization of circular foundations. |
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| spelling | doaj.art-700b6339aab942509fcee743badd2c4b2023-11-16T18:58:51ZengMDPI AGApplied Sciences2076-34172023-02-01134265310.3390/app13042653Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying SandChongchong Qi0Jiashuai Zheng1Chuiqian Meng2Mengting Wu3School of Resources and Safety Engineering, Central South University, Changsha 410083, ChinaSchool of Resources and Safety Engineering, Central South University, Changsha 410083, ChinaFaculty of Civil Engineering and Geosciences, Delft University of Technology, 2628 Delft, The NetherlandsSchool of Resources and Safety Engineering, Central South University, Changsha 410083, ChinaAssessing the stiffness of circular foundations is the key to evaluating their deformation; thus, it is important for foundation design. The current determination methods for the stiffness coefficient are either time-consuming or inaccurate. In this paper, a novel stiffness prediction model has been proposed, using the decision tree (DT) algorithm optimized by particle size optimization (PSO). The condition of the embedded foundation, the embedded depth (<i>Z<sub>D</sub></i>/2<i>R</i>), the thickness of the clay layer beneath the foundation base (<i>T</i>/2<i>R</i>), and the ratio of shear stiffness between clay and sand (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>G</mi><mrow><mi>s</mi><mi>a</mi><mi>n</mi><mi>d</mi></mrow></msub><mo>/</mo><msub><mi>G</mi><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>y</mi></mrow></msub></mrow></semantics></math></inline-formula>) were used as input variables, while the elastic stiffness coefficients (<i>K</i><sub>c</sub>, <i>K</i><sub>h</sub>, <i>K</i><sub>m</sub>, and <i>K</i><sub>v</sub>) were used as output variables. The optimum DT model has undergone comprehensive validation, and independent model verification using extra simulations. The results illustrate that PSO could promote further increases in the capability of DT modeling in predicting stiffness coefficients. The optimum DT model achieved a good level of performance on stiffness coefficient modeling. (The R for the training set was greater than 0.98 for all of the stiffness coefficients.) The variable importance analysis showed that the <i>T</i>/2<i>R</i> was the most significant variable for all stiffness coefficients, followed by <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi>G</mi><mrow><mi>s</mi><mi>a</mi><mi>n</mi><mi>d</mi></mrow></msub><mo>/</mo><msub><mi>G</mi><mrow><mi>c</mi><mi>l</mi><mi>a</mi><mi>y</mi></mrow></msub></mrow></semantics></math></inline-formula>. The optimum DT model achieved good predictive performance upon independent verification, with the R being 0.97, 0.99, 0.99, and 0.95 for <i>K</i><sub>v</sub>, <i>K</i><sub>h</sub>, <i>K</i><sub>m</sub>, and <i>K</i><sub>c</sub>, respectively. The proposed reliable and efficient DT-PSO model for stiffness coefficients in layered soil could further promote the safe and efficient utilization of circular foundations.https://www.mdpi.com/2076-3417/13/4/2653elastic stiffnesscircular footingmachine learningsoil–structure interaction |
| spellingShingle | Chongchong Qi Jiashuai Zheng Chuiqian Meng Mengting Wu Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand Applied Sciences elastic stiffness circular footing machine learning soil–structure interaction |
| title | Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand |
| title_full | Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand |
| title_fullStr | Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand |
| title_full_unstemmed | Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand |
| title_short | Efficient Machine Learning Model for Predicting the Stiffness of Circular Footings on Clay Overlying Sand |
| title_sort | efficient machine learning model for predicting the stiffness of circular footings on clay overlying sand |
| topic | elastic stiffness circular footing machine learning soil–structure interaction |
| url | https://www.mdpi.com/2076-3417/13/4/2653 |
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