Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering
Slope deformation poses significant risks to infrastructure, ecosystems, and human safety, making early and accurate predictions essential for mitigating slope failures and landslides. In this study, we propose a novel approach that integrates a fractional-order grey model (FOGM) with particle swarm...
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2025-03-01
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| author | Zhenzhu Meng Yating Hu Shunqiang Jiang Sen Zheng Jinxin Zhang Zhenxia Yuan Shaofeng Yao |
| author_facet | Zhenzhu Meng Yating Hu Shunqiang Jiang Sen Zheng Jinxin Zhang Zhenxia Yuan Shaofeng Yao |
| author_sort | Zhenzhu Meng |
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| description | Slope deformation poses significant risks to infrastructure, ecosystems, and human safety, making early and accurate predictions essential for mitigating slope failures and landslides. In this study, we propose a novel approach that integrates a fractional-order grey model (FOGM) with particle swarm optimization (PSO) to determine the optimal fractional order, thereby enhancing the model’s accuracy, even with limited and fluctuating data. Additionally, we employ a <i>k</i>-means clustering technique to account for both temporal and spatial variations in multi-point monitoring data, which improves the model’s ability to capture the relationships between monitoring points and increases prediction relevance. The model was validated using displacement data collected from 12 monitoring points on a slope located in Qinghai Province near the Yellow River, China. The results demonstrate that the proposed model outperforms the traditional statistical model and artificial neural networks, achieving a significantly higher coefficient of determination <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> up to 0.9998 for some monitoring points. Our findings highlight that the model maintains robust performance even when confronted with data of varying quality—a notable advantage over conventional approaches that typically struggle under such conditions. Overall, the proposed model offers a robust and data-efficient solution for slope deformation prediction, providing substantial potential for early warning systems and risk management. |
| format | Article |
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| institution | OA Journals |
| issn | 2504-3110 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
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| series | Fractal and Fractional |
| spelling | doaj-art-df26d0f6f7384a4a98cbf2bb7a602d842025-08-20T02:28:28ZengMDPI AGFractal and Fractional2504-31102025-03-019421010.3390/fractalfract9040210Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means ClusteringZhenzhu Meng0Yating Hu1Shunqiang Jiang2Sen Zheng3Jinxin Zhang4Zhenxia Yuan5Shaofeng Yao6School of Hydraulic Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, ChinaSchool of Infrastructure Construction, Nanchang University, Nanchang 330031, ChinaHangzhou Fuyang State Owned Resources Development Group Co., Ltd., Hangzhou 311400, ChinaCollege of Water Conservancy and Hydropower Engineering, Hohai University, Nanjing 210098, ChinaSchool of Hydraulic Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, ChinaSchool of Architecture and Civil Engineering, Zhongyuan University of Technology, Zhengzhou 450007, ChinaSchool of Hydraulic Engineering, Zhejiang University of Water Resources and Electric Power, Hangzhou 310018, ChinaSlope deformation poses significant risks to infrastructure, ecosystems, and human safety, making early and accurate predictions essential for mitigating slope failures and landslides. In this study, we propose a novel approach that integrates a fractional-order grey model (FOGM) with particle swarm optimization (PSO) to determine the optimal fractional order, thereby enhancing the model’s accuracy, even with limited and fluctuating data. Additionally, we employ a <i>k</i>-means clustering technique to account for both temporal and spatial variations in multi-point monitoring data, which improves the model’s ability to capture the relationships between monitoring points and increases prediction relevance. The model was validated using displacement data collected from 12 monitoring points on a slope located in Qinghai Province near the Yellow River, China. The results demonstrate that the proposed model outperforms the traditional statistical model and artificial neural networks, achieving a significantly higher coefficient of determination <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mi>R</mi><mn>2</mn></msup></semantics></math></inline-formula> up to 0.9998 for some monitoring points. Our findings highlight that the model maintains robust performance even when confronted with data of varying quality—a notable advantage over conventional approaches that typically struggle under such conditions. Overall, the proposed model offers a robust and data-efficient solution for slope deformation prediction, providing substantial potential for early warning systems and risk management.https://www.mdpi.com/2504-3110/9/4/210deformationdisplacement predictionfractional-order grey modelk-means clusteringparticle swarm optimizationmonitoring data |
| spellingShingle | Zhenzhu Meng Yating Hu Shunqiang Jiang Sen Zheng Jinxin Zhang Zhenxia Yuan Shaofeng Yao Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering Fractal and Fractional deformation displacement prediction fractional-order grey model k-means clustering particle swarm optimization monitoring data |
| title | Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering |
| title_full | Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering |
| title_fullStr | Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering |
| title_full_unstemmed | Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering |
| title_short | Slope Deformation Prediction Combining Particle Swarm Optimization-Based Fractional-Order Grey Model and <i>K</i>-Means Clustering |
| title_sort | slope deformation prediction combining particle swarm optimization based fractional order grey model and i k i means clustering |
| topic | deformation displacement prediction fractional-order grey model k-means clustering particle swarm optimization monitoring data |
| url | https://www.mdpi.com/2504-3110/9/4/210 |
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