Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm
Uniaxial compressive strength (UCS) is a critical parameter in the disaster prevention of engineering projects, requiring a large budget and a long time to estimate in different rocks or the early stage of a project. If predicted accurately, the UCS of rocks significantly affects geotechnical applic...
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| Format: | Article |
| Language: | English |
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MDPI AG
2022-09-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/19/3490 |
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| author | Junbo Qiu Xin Yin Yucong Pan Xinyu Wang Min Zhang |
| author_facet | Junbo Qiu Xin Yin Yucong Pan Xinyu Wang Min Zhang |
| author_sort | Junbo Qiu |
| collection | DOAJ |
| description | Uniaxial compressive strength (UCS) is a critical parameter in the disaster prevention of engineering projects, requiring a large budget and a long time to estimate in different rocks or the early stage of a project. If predicted accurately, the UCS of rocks significantly affects geotechnical applications. This paper develops a dataset of 734 samples from previous studies on different countries’ magmatic, sedimentary, and metamorphic rocks. Within the study context, three main factors, point load index, P-wave velocity, and Schmidt hammer rebound number, are utilized to estimate UCS. Moreover, it applies extreme learning machines (ELM) to map the nonlinear relationship between the UCS and the influential factors. Five metaheuristic algorithms, particle swarm optimization (PSO), grey wolf optimization (GWO), whale optimization algorithm (WOA), butterfly optimization algorithm (BOA), and sparrow search algorithm (SSA), are used to optimize the bias and weight of ELM and thus enhance its predictability. Indeed, several performance parameters are utilized to verify the proposed models’ generalization capability and predictive performance. The minimum, maximum, and average relative errors of ELM achieved by the whale optimization algorithm (WOA-ELM) are smaller than the other models, with values of 0.22%, 72.05%, and 11.48%, respectively. In contrast, the minimum and mean residual error produced by WOA-ELM are less than the other models, with values of 0.02 and 2.64 MPa, respectively. The results show that the UCS values derived from WOA-ELM are superior to those from other models. The performance indices (coefficient of determination (<i>R</i><sup>2</sup>): 0.861, mean squared error (MSE): 17.61, root mean squared error (RMSE): 4.20, and value account for (VAF): 91% obtained using the WOA-ELM model indicates high accuracy and reliability, which means that it has broad application potential for estimating UCS of different rocks. |
| first_indexed | 2024-03-09T21:29:03Z |
| format | Article |
| id | doaj.art-ecee1bf91a9744cfbc1c34e0abd28f56 |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T21:29:03Z |
| publishDate | 2022-09-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ecee1bf91a9744cfbc1c34e0abd28f562023-11-23T21:02:24ZengMDPI AGMathematics2227-73902022-09-011019349010.3390/math10193490Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic AlgorithmJunbo Qiu0Xin Yin1Yucong Pan2Xinyu Wang3Min Zhang4School of Civil Engineering, Wuhan University, Wuhan 430072, ChinaSchool of Civil Engineering, Wuhan University, Wuhan 430072, ChinaSchool of Civil Engineering, Wuhan University, Wuhan 430072, ChinaYellow River Engineering Consulting Co., Ltd., Zhengzhou 450003, ChinaBeijing Aidi Geological Engineering Technology Co., Ltd., Beijing 100144, ChinaUniaxial compressive strength (UCS) is a critical parameter in the disaster prevention of engineering projects, requiring a large budget and a long time to estimate in different rocks or the early stage of a project. If predicted accurately, the UCS of rocks significantly affects geotechnical applications. This paper develops a dataset of 734 samples from previous studies on different countries’ magmatic, sedimentary, and metamorphic rocks. Within the study context, three main factors, point load index, P-wave velocity, and Schmidt hammer rebound number, are utilized to estimate UCS. Moreover, it applies extreme learning machines (ELM) to map the nonlinear relationship between the UCS and the influential factors. Five metaheuristic algorithms, particle swarm optimization (PSO), grey wolf optimization (GWO), whale optimization algorithm (WOA), butterfly optimization algorithm (BOA), and sparrow search algorithm (SSA), are used to optimize the bias and weight of ELM and thus enhance its predictability. Indeed, several performance parameters are utilized to verify the proposed models’ generalization capability and predictive performance. The minimum, maximum, and average relative errors of ELM achieved by the whale optimization algorithm (WOA-ELM) are smaller than the other models, with values of 0.22%, 72.05%, and 11.48%, respectively. In contrast, the minimum and mean residual error produced by WOA-ELM are less than the other models, with values of 0.02 and 2.64 MPa, respectively. The results show that the UCS values derived from WOA-ELM are superior to those from other models. The performance indices (coefficient of determination (<i>R</i><sup>2</sup>): 0.861, mean squared error (MSE): 17.61, root mean squared error (RMSE): 4.20, and value account for (VAF): 91% obtained using the WOA-ELM model indicates high accuracy and reliability, which means that it has broad application potential for estimating UCS of different rocks.https://www.mdpi.com/2227-7390/10/19/3490uniaxial compressive strengthprediction modelextreme learning machinemetaheuristic algorithm |
| spellingShingle | Junbo Qiu Xin Yin Yucong Pan Xinyu Wang Min Zhang Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm Mathematics uniaxial compressive strength prediction model extreme learning machine metaheuristic algorithm |
| title | Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm |
| title_full | Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm |
| title_fullStr | Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm |
| title_full_unstemmed | Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm |
| title_short | Prediction of Uniaxial Compressive Strength in Rocks Based on Extreme Learning Machine Improved with Metaheuristic Algorithm |
| title_sort | prediction of uniaxial compressive strength in rocks based on extreme learning machine improved with metaheuristic algorithm |
| topic | uniaxial compressive strength prediction model extreme learning machine metaheuristic algorithm |
| url | https://www.mdpi.com/2227-7390/10/19/3490 |
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