基于核主成分分析的多输出模型确认方法

发布时间：2018-01-29 18:28

本文关键词： 模型确认多输出相关性核主成分分析(KPCA) 面积指标　出处：《北京航空航天大学学报》2017年07期 　论文类型：期刊论文

【摘要】：目前对于不确定性环境下多个相关的复杂计算模型进行确认的方法存在计算困难及稳定性较差的问题。针对这类复杂计算模型,提出了一种新的基于核主成分分析(KPCA)的多输出模型确认方法。该方法将核主成分分析与面积法的思想相结合,构造了一个新的易于计算且稳定性高的模型确认指标。所提方法通过核主成分分析将相关的输出变量转化为不相关的核主成分,再对每一核主成分进行模型与实验的对比,从而避免了传统多输出模型确认方法中需要求解多个输出的联合累积分布函数的困难。由于核主成分分析(PCA)方法能够有效提取分析对象的非线性成分,因此基于核主成分分析的多输出模型确认方法较基于主成分分析的模型确认方法更为稳定,这表现在相同的实验样本数据下核主成分分析的方法具有更低的出错率。另外核主成分分析通过核主成分提取,可以实现多输出模型的降维,从而降低多输出模型确认的复杂度。所提方法既可以用于一般的多输出模型的确认,也可以用于多确认点的输出模型的确认。最后通过数值算例和工程算例证明了该方法的正确性与有效性。
[Abstract]:At present, it is difficult to calculate and have poor stability for the methods of confirming many related complex computing models in uncertain environment. In view of this kind of complex computing model. A new multi-output model validation method based on kernel principal component analysis (KPCA) is proposed, which combines the kernel principal component analysis (KPCA) with the area method. A new model is constructed which is easy to calculate and has high stability. The proposed method transforms the relevant output variables into irrelevant kernel principal components by kernel principal component analysis (KPCA). Then the model of each core principal component is compared with the experiment. Therefore, the difficulty of solving the joint cumulative distribution function of multiple outputs in the traditional multi-output model validation method is avoided. Because the kernel principal component analysis (KPCA) method can effectively extract the nonlinear components of the analyzed object. Therefore, the multi-output model validation method based on kernel principal component analysis is more stable than that based on principal component analysis. This shows that the method of kernel principal component analysis has lower error rate under the same experimental sample data. In addition, kernel principal component analysis can reduce the dimension of multi-output model by kernel principal component extraction. Thus, the complexity of multi-output model validation can be reduced. The proposed method can be used for the validation of general multi-output model. It can also be used to confirm the output model of multiple verification points. Finally, the correctness and validity of the method are proved by numerical and engineering examples.
【作者单位】：西北工业大学航空学院;
【基金】：国家自然科学基金(51475370) 中央高校基本科研业务费专项资金(3102015BJ(Ⅱ)CG009)~~
【分类号】：O212.4
【正文快照】： 网络出版地址:www.cnki.net/kcms/detail/11.2625.V.20161114.0912.007.html引用格式:胡嘉蕊,吕震宙.基于核主成分分析的多输出模型确认方法[J].北京航空航天大学学报,2017,43(7):1470-1480.HU J R,LYU Z Z.Model validation method with multivariate output based on kernel

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