【摘要】：敏感性分析方法廣泛應(yīng)用于模型驗(yàn)證、模型優(yōu)化和模型診斷,是我們研究數(shù)學(xué)模型非常重要的工具。然而,自敏感性分析的幾大算法尤其是Sobol方法提出數(shù)十年來,使用Sobol系數(shù)進(jìn)行敏感性分析主要關(guān)注用于參數(shù)優(yōu)先的一階Sobol系數(shù)和用于參數(shù)固定的總階Sobol系數(shù)。只有一階系數(shù)和總階系數(shù)大量用于建模分析,而二階系數(shù)的應(yīng)用相當(dāng)少。二階系數(shù)能夠定量描述相互作用的優(yōu)勢(shì)完全被忽視,其使用僅限于定性比較相互作用大小。使用二階Sobol系數(shù)定量分析相互作用的潛在使用價(jià)值并沒有被充分地研究。網(wǎng)絡(luò)聚類分析同樣廣泛應(yīng)用于各系統(tǒng)網(wǎng)絡(luò)模型中,用于社團(tuán)發(fā)現(xiàn),使我們更加深入地理解各系統(tǒng)模型的結(jié)構(gòu)。而二階Sobol系數(shù)反映了參數(shù)間的相互作用強(qiáng)度,這是模型的固有特性。這種相互作用也可以看成一種相似性度量指標(biāo),從而我們可以通過二階系數(shù)建立模型參數(shù)間的相互作用網(wǎng)絡(luò),再進(jìn)行網(wǎng)絡(luò)聚類分析發(fā)現(xiàn)參數(shù)間的分組關(guān)系。因此二階Sobol系數(shù)能夠用于參數(shù)聚類分組,它顯示了模型參數(shù)間的相互作用網(wǎng)絡(luò)。根據(jù)這一特性,我們提出一種新的基于二階敏感性系數(shù)的模型參數(shù)分組方法。該方法結(jié)合了敏感性分析二階Sobol系數(shù)和網(wǎng)絡(luò)聚類分析。我們的方法能夠在沒有建模先驗(yàn)知識(shí)的前提下對(duì)參數(shù)進(jìn)行"盲"分組。該方法的意義在于能夠根據(jù)模型固有的相互作用特性進(jìn)行分組,而不需要建模者的主觀知識(shí)。這樣能夠避免先驗(yàn)知識(shí)的不確定性影響參數(shù)分組以及之后的分組分析。
[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.
【學(xué)位授予單位】：中國科學(xué)院大學(xué)(中國科學(xué)院武漢物理與數(shù)學(xué)研究所)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O157.5

【參考文獻(xiàn)】

相關(guān)期刊論文 前1條

1 周海強(qiáng);張琦兵;顧康慧;;基于軌跡靈敏度的動(dòng)態(tài)等值模型參數(shù)分類優(yōu)化方法[J];電力建設(shè);2015年08期

相關(guān)碩士學(xué)位論文 前1條

1 李慧馳;基于三度信息的雙重層次聚類算法[D];武漢理工大學(xué);2013年

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本文編號(hào)：2247389