基于敏感性分析二阶系数的模型参数分组研究
发布时间：2018-09-18 08:48
【摘要】：敏感性分析方法广泛应用于模型验证、模型优化和模型诊断,是我们研究数学模型非常重要的工具。然而,自敏感性分析的几大算法尤其是Sobol方法提出数十年来,使用Sobol系数进行敏感性分析主要关注用于参数优先的一阶Sobol系数和用于参数固定的总阶Sobol系数。只有一阶系数和总阶系数大量用于建模分析,而二阶系数的应用相当少。二阶系数能够定量描述相互作用的优势完全被忽视,其使用仅限于定性比较相互作用大小。使用二阶Sobol系数定量分析相互作用的潜在使用价值并没有被充分地研究。网络聚类分析同样广泛应用于各系统网络模型中,用于社团发现,使我们更加深入地理解各系统模型的结构。而二阶Sobol系数反映了参数间的相互作用强度,这是模型的固有特性。这种相互作用也可以看成一种相似性度量指标,从而我们可以通过二阶系数建立模型参数间的相互作用网络,再进行网络聚类分析发现参数间的分组关系。因此二阶Sobol系数能够用于参数聚类分组,它显示了模型参数间的相互作用网络。根据这一特性,我们提出一种新的基于二阶敏感性系数的模型参数分组方法。该方法结合了敏感性分析二阶Sobol系数和网络聚类分析。我们的方法能够在没有建模先验知识的前提下对参数进行"盲"分组。该方法的意义在于能够根据模型固有的相互作用特性进行分组,而不需要建模者的主观知识。这样能够避免先验知识的不确定性影响参数分组以及之后的分组分析。
[Abstract]:Sensitivity analysis is widely used in model validation, model optimization and model diagnosis, which is a very important tool for us to study mathematical models. However, since several algorithms of self-sensitivity analysis, especially Sobol method, have been proposed for decades, sensitivity analysis using Sobol coefficients has focused on the first-order Sobol coefficients for parameter priority and the total Sobol coefficients for fixed parameters. Only the first order coefficient and the total order coefficient are used for modeling and analysis, but the second order coefficient is seldom used. The advantage that second-order coefficients can describe interaction quantitatively is completely ignored, and its use is limited to qualitative comparison of interaction size. The potential value of using the second order Sobol coefficient in quantitative analysis of interactions has not been fully studied. Network clustering analysis is also widely used in network models for community discovery, which makes us understand the structure of system models more deeply. The second order Sobol coefficient reflects the strength of the interaction between the parameters, which is the inherent characteristic of the model. This kind of interaction can also be regarded as a measure of similarity, so we can establish the interaction network between model parameters through second-order coefficients, and then cluster analysis to find the grouping relationship between parameters. Therefore, the second-order Sobol coefficients can be used for parameter clustering and grouping, which shows the interaction network between the parameters of the model. According to this characteristic, we propose a new model parameter grouping method based on second order sensitivity coefficient. The method combines sensitivity analysis with second order Sobol coefficients and network clustering analysis. Our method can group parameters "blind" without modeling prior knowledge. The significance of this method is that it can be grouped according to the inherent interaction characteristics of the model without the subjective knowledge of the modeler. In this way, the uncertainty of prior knowledge can avoid the influence of parameter grouping and subsequent grouping analysis.
【学位授予单位】：中国科学院大学(中国科学院武汉物理与数学研究所)
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
本文编号：2247389
[Abstract]:Sensitivity analysis is widely used in model validation, model optimization and model diagnosis, which is a very important tool for us to study mathematical models. However, since several algorithms of self-sensitivity analysis, especially Sobol method, have been proposed for decades, sensitivity analysis using Sobol coefficients has focused on the first-order Sobol coefficients for parameter priority and the total Sobol coefficients for fixed parameters. Only the first order coefficient and the total order coefficient are used for modeling and analysis, but the second order coefficient is seldom used. The advantage that second-order coefficients can describe interaction quantitatively is completely ignored, and its use is limited to qualitative comparison of interaction size. The potential value of using the second order Sobol coefficient in quantitative analysis of interactions has not been fully studied. Network clustering analysis is also widely used in network models for community discovery, which makes us understand the structure of system models more deeply. The second order Sobol coefficient reflects the strength of the interaction between the parameters, which is the inherent characteristic of the model. This kind of interaction can also be regarded as a measure of similarity, so we can establish the interaction network between model parameters through second-order coefficients, and then cluster analysis to find the grouping relationship between parameters. Therefore, the second-order Sobol coefficients can be used for parameter clustering and grouping, which shows the interaction network between the parameters of the model. According to this characteristic, we propose a new model parameter grouping method based on second order sensitivity coefficient. The method combines sensitivity analysis with second order Sobol coefficients and network clustering analysis. Our method can group parameters "blind" without modeling prior knowledge. The significance of this method is that it can be grouped according to the inherent interaction characteristics of the model without the subjective knowledge of the modeler. In this way, the uncertainty of prior knowledge can avoid the influence of parameter grouping and subsequent grouping analysis.
【学位授予单位】：中国科学院大学(中国科学院武汉物理与数学研究所)
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O157.5
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相关硕士学位论文 前1条
1 李慧驰;基于三度信息的双重层次聚类算法[D];武汉理工大学;2013年
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