The multivariate statistical method such as principal component analysis based on linear dimension reduction and kernel principal component analysis based on nonlinear dimension reduction as the modified principal component analysis method are commonly used. Because of the diversity and correlation of robotic global performance indexes, the two multivariate statistical methods principal component analysis and kernel principal component analysis methods can be used, respectively, to comprehensively evaluate the global performance of PUMA560 robot with different dimensions. When using the kernel principal component analysis method, the kernel function and parameters directly have an effect on the result of comprehensive performance evaluation. Because kernel principal component analysis with polynomial kernel function is time-consuming and inefficient, a new kernel function based on similarity degree is proposed for the big sample data. The new kernel function is proved according to Mercer’s theorem. By comparing different dimension reduction effects of principal component analysis method, the kernel principal component analysis method with polynomial kernel function, and the kernel principal component analysis method with the new kernel function, the kernel principal component analysis method with the new kernel function could deal more effectively with the nonlinear relationship among indexes, and its calculation result is more reasonable for containing more comprehensive information. The simulation shows that the kernel principal component analysis method with the new kernel function has the advantage of low time consuming, good real-time performance, and good ability of generalization.

中文翻译：

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基于修正主成分分析的机器人全局性能综合评价

常用的多变量统计方法，如基于线性降维的主成分分析和基于非线性降维的核主成分分析作为改进的主成分分析方法。由于机器人全局性能指标的多样性和相关性，可以分别采用主成分分析法和核主成分分析法这两种多元统计方法对PUMA560机器人不同维度的全局性能进行综合评价。采用核主成分分析法时，核函数和参数直接影响综合性能评价的结果。由于多项式核函数的核主成分分析耗时且效率低，针对大样本数据提出了一种基于相似度的核函数。根据 Mercer 定理证明了新的核函数。通过比较主成分分析法、多项式核函数的核主成分分析法和新核函数的核主成分分析法的不同降维效果，新核函数的核主成分分析法可以处理更多的问题。有效地利用指标之间的非线性关系，其计算结果更合理，包含更全面的信息。