| 冯翔宇,石茂林,马跃,宋学官,孙伟,田腾.基于支持向量回归的定性-定量因子混合建模方法[J].,2020,60(6):599-609 |
| 基于支持向量回归的定性-定量因子混合建模方法 |
| A qualitative-quantitative factors mixed data modeling method based on support vector regression |
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| DOI：10.7511/dllgxb202006007 |
| 中文关键词: 混合数据 核函数 支持向量回归 计算机实验 |
| 英文关键词: mixed data kernel function support vector regression (SVR) computer experiment |
| 基金项目:国家重点研发计划资助项目(2018YFB1702500). |
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| 摘要点击次数: 377 |
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| 中文摘要: |
| 在科学研究及工程实践中，输入参数经常同时包含定性因子与定量因子，为实现此类数据的有效建模，提出基于支持向量回归(SVR)的定性-定量因子建模方法，以用于工程实验及数值仿真的定性定量因子分析．引入超球面分解量化定性因子相关关系，构建了一种新型核函数描述定性因子与定量因子关联关系，提出了定性-定量因子支持向量回归算法实现定性定量数据的混合建模与预测．通过数值算例和经典工程算例，发现所提算法能提供相比于普通的支持向量回归算法及基于高斯过程回归的定性-定量因子算法更优的预测结果．以种植体骨应力分析为例，其中种植体材料类型为定性因子、结构参数为定量因子，实验结果表明所提算法能够显著提升骨应力预测精度，可为种植体的设计优化提供模型基础，揭示了所提算法的工程可用性． |
| 英文摘要: |
| In the process of scientific research and engineering practice, it is very common to conduct engineering experiments and numerical simulation in which the input parameters have both qualitative and quantitative factors. To achieve effective modeling of such kind of data, a method for modeling qualitative and quantitative factors based on support vector regression (SVR) is proposed for qualitative-quantitative factors analysis in engineering experiments and numerical simulation. It quantizes the correlation between qualitative factors by using the hypersphere decomposition, and describes the correlation between qualitative factors and quantitative factors by constructing a special kernel function. A support vector regression algorithm for qualitative-quantitative factors is constructed for mixed data modeling and prediction of qualitative and quantitative data. Numerical experiments and classical engineering problems show that the proposed algorithm can provide better prediction results compared with ordinary support vector regression algorithm and qualitative-quantitative factor algorithms based on Gaussian process regression. Taking bone stress analysis of implant as an example, the type of implant material is considered as qualitative factors and the structural parameters as quantitative factors. Experimental results show that the proposed algorithm can significantly improve the accuracy of bone stress prediction and provide a model basis for implant design optimization, which verifies the engineering rationality of the proposed algorithm. |
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